Subgroups — C₂×#23777127 #35196611

Order 20224.

8006 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777127	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099277	C₂	1	2	yes	maximal, complemented
3	C₂×#19099258	C₂	1	2	yes	maximal, complemented
4	C₂×#19099256	C₂	1	2	yes	maximal, complemented
5	C₂×#19099241	C₂	1	2	yes	maximal, complemented
6	C₂×#19099236	C₂	1	2	yes	maximal, complemented
7	C₂×#19099211	C₂	1	2	yes	maximal, complemented
8	C₂×#19099210	C₂	1	2	yes	maximal, complemented
9	C₂×#19099202	C₂	1	2	yes	maximal, complemented
10	C₂×#19099193	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#19099184	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#19099180	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#19099166	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#19099126	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#19099111	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#19099110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#19099098	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#19099095	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#19099073	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#121×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#19099042	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#19099035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#117×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#540×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11929624	C₂²	1	2	yes	complemented
26	C₂²×#11929623	C₂²	1	1	yes	characteristic
27	C₂²×#11929623	C₂²	1	2	yes	complemented
28	C₂²×D₄×D₇₉	C₂²	1	1	yes	characteristic
29	C₂²×D₄×D₇₉	C₂²	1	2	yes	—
30	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic
31	#19099277	C₂²	1	32	yes	complemented
32	#19099258	C₂²	1	32	yes	complemented
33	#19099256	C₂²	1	32	yes	complemented
34	#19099241	C₂²	1	32	yes	complemented
35	#19099236	C₂²	1	32	yes	complemented
36	#19099211	C₂²	1	32	yes	complemented
37	#19099210	C₂²	1	32	yes	complemented
38	#19099202	C₂²	1	32	yes	complemented
39	#19099193	C₂²	1	16	yes	complemented
40	#19099184	C₂²	1	16	yes	complemented
41	#19099180	C₂²	1	16	yes	complemented
42	#19099166	C₂²	1	16	yes	complemented
43	#19099126	C₂²	1	16	yes	complemented
44	#19099111	C₂²	1	16	yes	complemented
45	#19099110	C₂²	1	16	yes	complemented
46	C₂×#14579161	C₂²	1	1	yes	characteristic, complemented
47	C₂×#14579160	C₂²	1	1	yes	characteristic, complemented
48	C₂×#14579160	C₂²	1	2	yes	complemented
49	C₂×#14579157	C₂²	1	1	yes	characteristic, complemented
50	#19099098	C₂²	1	16	yes	complemented
51	#19099095	C₂²	1	16	yes	complemented
52	C₂×#14579156	C₂²	1	2	yes	complemented
53	C₂×#14579156	C₂²	1	2	yes	complemented
54	C₂×#14579154	C₂²	1	2	yes	complemented
55	C₂×#14579154	C₂²	1	2	yes	complemented
56	C₂×#14579152	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14579151	C₂²	1	2	yes	complemented
58	C₂×#14579149	C₂²	1	1	yes	characteristic, complemented
59	C₂×#14579148	C₂²	1	2	yes	complemented
60	C₂×#14579148	C₂²	1	1	yes	characteristic, complemented
61	C₂×#14579148	C₂²	1	2	yes	complemented
62	C₂×#14579147	C₂²	1	2	yes	complemented
63	C₂×#14579147	C₂²	1	2	yes	complemented
64	#19099073	C₂²	1	16	yes	complemented
65	C₂×#14579146	C₂²	1	2	yes	complemented
66	C₂×#14579145	C₂²	1	2	yes	complemented
67	C₂×#14579143	C₂²	1	2	yes	—
68	C₂×#14579143	C₂²	1	2	yes	complemented
69	C₂×#14579143	C₂²	1	2	yes	complemented
70	C₂×#14579143	C₂²	1	2	yes	complemented
71	C₂×#14579142	C₂²	1	2	yes	complemented
72	C₂×#14579141	C₂²	1	2	yes	—
73	C₂×#14579141	C₂²	1	1	yes	characteristic, complemented
74	C₂×#14579140	C₂²	1	1	yes	characteristic, complemented
75	C₂×#14579139	C₂²	1	2	yes	—
76	C₂×#14579139	C₂²	1	2	yes	complemented
77	C₂×#14579138	C₂²	1	2	yes	complemented
78	C₂×#14579136	C₂²	1	1	yes	characteristic
79	C₂×#14579135	C₂²	1	1	yes	characteristic
80	C₂×#14579134	C₂²	1	2	yes	—
81	C₂×#14579134	C₂²	1	2	yes	complemented
82	C₂×#14579133	C₂²	1	2	yes	—
83	C₂×#14579133	C₂²	1	2	yes	complemented
84	C₂×#14579133	C₂²	1	2	yes	complemented
85	C₂×#14579133	C₂²	1	2	yes	complemented
86	C₂×#14579132	C₂²	1	1	yes	characteristic
87	C₂×#14579132	C₂²	1	2	yes	complemented
88	C₂×#14579132	C₂²	1	2	yes	complemented
89	C₂×#14579132	C₂²	1	1	yes	characteristic, complemented
90	#121×D₇₉	C₂²	1	16	yes	complemented
91	C₂×#14579129	C₂²	1	2	yes	—
92	C₂×#14579129	C₂²	1	2	yes	—
93	C₂×#14579129	C₂²	1	2	yes	—
94	#19099042	C₂²	1	16	yes	complemented
95	#19099035	C₂²	1	16	yes	complemented
96	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
97	C₂×#14579126	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
99	C₂×D₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
100	C₂×D₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
101	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
102	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
103	C₂×#14579123	C₂²	1	1	yes	characteristic, complemented
104	C₂×#14579123	C₂²	1	2	yes	complemented
105	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	—
106	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
107	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
108	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
109	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	—
110	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
111	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
112	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
113	C₂×#14579120	C₂²	1	2	yes	complemented
114	C₂×#14579119	C₂²	1	1	yes	characteristic
115	C₂×#14579119	C₂²	1	1	yes	characteristic
116	C₂×#14579119	C₂²	1	1	yes	characteristic
117	C₂×#14579119	C₂²	1	2	yes	complemented
118	C₂×#14579118	C₂²	1	1	yes	characteristic
119	C₂×#14579118	C₂²	1	1	yes	characteristic
120	C₂×#14579117	C₂²	1	1	yes	characteristic, complemented
121	C₂×#14579117	C₂²	1	1	yes	characteristic, complemented
122	C₂×#14579117	C₂²	1	2	yes	complemented
123	#117×D₇₉	C₂²	1	16	yes	complemented
124	C₂²×Dic₇₉⋊C₄	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
128	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
129	C₂×C₂²⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
132	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
133	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
135	#540×C₇₉	C₂²	1	16	yes	complemented
136	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
137	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
138	C₂×#123×C₇₉	C₂²	1	2	yes	complemented
139	C₂×#123×C₇₉	C₂²	1	2	yes	complemented
140	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
141	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
142	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
143	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
144	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
146	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
148	C₂⁴×D₇₉	C₂³	1	2	yes	—
149	C₂×#11929624	—	4	8	no	—
150	C₂×#11929624	C₂³	1	16	yes	complemented
151	C₂×#11929623	—	2	8	no	—
152	C₂×#11929623	—	4	8	no	—
153	C₂×#11929623	C₂³	1	8	yes	—
154	C₂×#11929623	C₂³	1	16	yes	complemented
155	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
156	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
157	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
158	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
159	C₂²×D₃₁₆	C₂³	1	2	yes	—
160	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
161	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
162	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
163	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
164	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
165	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
166	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
167	C₂×D₄×D₇₉	—	2	8	no	—
168	C₂×D₄×D₇₉	—	4	8	no	—
169	C₂×D₄×D₇₉	C₂³	1	8	yes	—
170	C₂×D₄×D₇₉	C₂³	1	16	yes	—
171	C₂³×Dic₇₉	C₂³	1	2	yes	—
172	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
173	C₂³×Dic₇₉	C₂³	1	2	yes	—
174	C₂³×Dic₇₉	C₂³	1	2	yes	—
175	C₂²×C₄×D₇₉	—	2	8	no	—
176	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
178	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
179	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
180	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
182	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
183	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
184	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
185	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
186	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
187	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
188	#14579161	C₂³	1	8	yes	complemented
189	#14579160	C₂³	1	8	yes	complemented
190	#14579160	C₂³	1	16	yes	complemented
191	#14579157	C₂³	1	8	yes	complemented
192	#14579156	C₂³	1	16	yes	complemented
193	#14579156	C₂³	1	16	yes	complemented
194	#14579154	C₂³	1	16	yes	complemented
195	#14579154	C₂³	1	16	yes	complemented
196	#14579152	C₂³	1	8	yes	complemented
197	#14579151	C₂³	1	16	yes	complemented
198	#14579149	C₂³	1	8	yes	complemented
199	#14579148	C₂³	1	16	yes	complemented
200	#14579148	C₂³	1	8	yes	complemented
201	#14579148	C₂³	1	16	yes	complemented
202	#14579147	C₂³	1	16	yes	complemented
203	#14579147	C₂³	1	16	yes	complemented
204	#14579146	C₂³	1	16	yes	complemented
205	#14579145	C₂³	1	16	yes	complemented
206	#14579143	C₂³	1	16	yes	—
207	#14579143	C₂³	1	16	yes	complemented
208	#14579143	C₂³	1	16	yes	complemented
209	#14579143	C₂³	1	16	yes	complemented
210	#14579142	C₂³	1	16	yes	complemented
211	#14579141	C₂³	1	16	yes	—
212	#14579141	C₂³	1	8	yes	complemented
213	#14579140	C₂³	1	8	yes	complemented
214	#14579139	C₂³	1	16	yes	—
215	#14579139	C₂³	1	16	yes	complemented
216	#14579138	C₂³	1	16	yes	complemented
217	#14579136	C₂³	1	8	yes	—
218	#14579135	C₂³	1	8	yes	—
219	#14579134	C₂³	1	16	yes	—
220	#14579134	C₂³	1	16	yes	complemented
221	#14579133	C₂³	1	16	yes	—
222	#14579133	C₂³	1	16	yes	complemented
223	#14579133	C₂³	1	16	yes	complemented
224	#14579133	C₂³	1	16	yes	complemented
225	#14579132	C₂³	1	8	yes	—
226	#14579132	C₂³	1	16	yes	complemented
227	#14579132	C₂³	1	16	yes	complemented
228	#14579132	C₂³	1	8	yes	complemented
229	#14579129	C₂³	1	16	yes	—
230	#14579129	C₂³	1	16	yes	—
231	#14579129	C₂³	1	16	yes	—
232	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
233	#14579126	C₂³	1	8	yes	complemented
234	C₄×D₃₁₆	C₂³	1	8	yes	complemented
235	D₄×Dic₇₉	C₂³	1	8	yes	complemented
236	D₄×Dic₇₉	C₂³	1	8	yes	complemented
237	D₄×Dic₇₉	C₂³	1	16	yes	complemented
238	D₄×Dic₇₉	C₂³	1	16	yes	complemented
239	#14579123	C₂³	1	8	yes	complemented
240	#14579123	C₂³	1	16	yes	complemented
241	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
242	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
243	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
244	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
245	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	—
246	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
247	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
248	#14579120	C₂³	1	8	yes	complemented
249	#14579120	C₂³	1	16	yes	complemented
250	#14579119	C₂³	1	8	yes	—
251	#14579119	C₂³	1	8	yes	—
252	#14579119	C₂³	1	8	yes	—
253	#14579119	C₂³	1	16	yes	complemented
254	#14579118	C₂³	1	8	yes	—
255	#14579118	C₂³	1	8	yes	—
256	#14579117	C₂³	1	8	yes	complemented
257	#14579117	C₂³	1	16	yes	complemented
258	#14579117	C₂³	1	8	yes	complemented
259	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
264	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
265	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
266	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
267	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
272	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
273	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
274	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
275	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
276	C₂×Dic₇₉⋊C₄	C₂³	1	16	yes	complemented
277	C₄⋊C₄×D₇₉	C₂³	1	8	yes	—
278	C₄⋊C₄×D₇₉	C₂³	1	8	yes	complemented
279	C₄⋊C₄×D₇₉	C₂³	1	8	yes	complemented
280	C₂×C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
283	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
284	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
285	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
286	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
287	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
288	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
289	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
290	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
293	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
296	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
297	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
298	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
299	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
300	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
301	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
302	C₂²⋊C₄×D₇₉	C₂³	1	8	yes	—
303	C₂²⋊C₄×D₇₉	C₂³	1	8	yes	—
304	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
305	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
306	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
313	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
314	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
315	C₄²×D₇₉	C₂³	1	8	yes	complemented
316	C₄²×D₇₉	C₂³	1	8	yes	complemented
317	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
318	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
319	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
320	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
321	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
322	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
323	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
324	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
325	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
326	#127×C₇₉	C₂³	1	8	yes	complemented
327	#125×C₇₉	C₂³	1	8	yes	complemented
328	#123×C₇₉	C₂³	1	16	yes	complemented
329	#123×C₇₉	C₂³	1	16	yes	complemented
330	#121×C₇₉	C₂³	1	8	yes	—
331	#121×C₇₉	C₂³	1	8	yes	complemented
332	#121×C₇₉	C₂³	1	16	yes	complemented
333	#121×C₇₉	C₂³	1	16	yes	complemented
334	C₄×D₄×C₇₉	C₂³	1	8	yes	complemented
335	C₄×D₄×C₇₉	C₂³	1	8	yes	complemented
336	#117×C₇₉	C₂³	1	8	yes	complemented
337	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
342	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
343	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
346	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
347	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
348	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
349	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
351	C₂³×D₇₉	—	2	4	no	—
352	C₂³×D₇₉	—	2	4	no	—
353	C₂³×D₇₉	—	2	8	no	—
354	C₂³×D₇₉	—	4	2	no	—
355	C₂³×D₇₉	—	4	4	no	—
356	C₂³×D₇₉	—	4	4	no	—
357	C₂³×D₇₉	C₂⁴	1	2	yes	—
358	C₂³×D₇₉	C₂⁴	1	4	yes	—
359	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
360	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
361	C₂³×D₇₉	C₂⁴	1	8	yes	—
362	#11929624	—	4	32	no	—
363	#11929623	—	2	32	no	—
364	#11929623	—	4	32	no	—
365	C₂×Dic₁₅₈	—	2	4	no	—
366	C₂×Dic₁₅₈	—	4	4	no	—
367	C₂×Dic₁₅₈	—	4	4	no	—
368	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
369	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
370	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
371	C₂×D₃₁₆	—	2	8	no	—
372	C₂×D₃₁₆	—	2	4	no	—
373	C₂×D₃₁₆	C₂⁴	1	8	yes	—
374	C₂×D₃₁₆	C₂⁴	1	4	yes	—
375	C₂×C₂²⋊D₇₉	—	2	8	no	—
376	C₂×C₂²⋊D₇₉	—	2	8	no	—
377	C₂×C₂²⋊D₇₉	—	2	8	no	—
378	C₂×C₂²⋊D₇₉	—	2	8	no	—
379	C₂×C₂²⋊D₇₉	—	4	4	no	—
380	C₂×C₂²⋊D₇₉	—	4	4	no	—
381	C₂×C₂²⋊D₇₉	—	4	4	no	—
382	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
383	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
384	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
385	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
386	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
387	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
388	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
389	D₄×D₇₉	—	2	32	no	—
390	D₄×D₇₉	—	4	32	no	—
391	C₂²×Dic₇₉	—	2	8	no	—
392	C₂²×Dic₇₉	—	2	4	no	—
393	C₂²×Dic₇₉	—	4	4	no	—
394	C₂²×Dic₇₉	—	4	4	no	—
395	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
397	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
398	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
399	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
400	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
405	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
406	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
407	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×D₇₉	—	2	4	no	—
409	C₂×C₄×D₇₉	—	2	32	no	—
410	C₂×C₄×D₇₉	—	2	4	no	—
411	C₂×C₄×D₇₉	—	2	4	no	—
412	C₂×C₄×D₇₉	—	2	4	no	—
413	C₂×C₄×D₇₉	—	2	4	no	—
414	C₂×C₄×D₇₉	—	4	4	no	—
415	C₂×C₄×D₇₉	—	4	2	no	—
416	C₂×C₄×D₇₉	—	4	4	no	—
417	C₂×C₄×D₇₉	—	4	2	no	—
418	C₂×C₄×D₇₉	—	4	4	no	—
419	C₂×C₄×D₇₉	#41	1	8	yes	complemented
420	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
421	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
422	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
423	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
424	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
425	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
426	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
427	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
428	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
429	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
430	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
431	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
432	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
433	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
434	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
435	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
436	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
437	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
438	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
439	Dic₇₉⋊C₄	C₂⁴	1	4	yes	—
440	Dic₇₉⋊C₄	C₂⁴	1	4	yes	—
441	Dic₇₉⋊C₄	C₂⁴	1	4	yes	—
442	Dic₇₉⋊C₄	C₂⁴	1	4	yes	—
443	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
444	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
445	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
446	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
447	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
448	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
449	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
450	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
451	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
452	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
453	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
454	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
455	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
456	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
457	(C₂×D₇₉)⋊C₄	C₂⁴	1	4	yes	—
458	(C₂×D₇₉)⋊C₄	C₂⁴	1	4	yes	—
459	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
460	(C₂×D₇₉)⋊C₄	C₂⁴	1	4	yes	—
461	(C₂×D₇₉)⋊C₄	C₂⁴	1	4	yes	—
462	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
463	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
464	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
465	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
466	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
467	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
468	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
469	C₄×Dic₇₉	C₂⁴	1	4	yes	—
470	C₄×Dic₇₉	C₂⁴	1	4	yes	—
471	C₄×Dic₇₉	C₂⁴	1	4	yes	—
472	C₄×Dic₇₉	C₂⁴	1	4	yes	—
473	C₄×Dic₇₉	C₂⁴	1	4	yes	—
474	C₄×Dic₇₉	C₂⁴	1	4	yes	—
475	C₄×Dic₇₉	C₂⁴	1	8	yes	—
476	C₄×Dic₇₉	C₂⁴	1	8	yes	—
477	C₄×Dic₇₉	C₂⁴	1	8	yes	—
478	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
479	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
480	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
481	C₂×D₄×C₇₉	—	2	4	no	—
482	C₂×D₄×C₇₉	—	2	4	no	—
483	C₂×D₄×C₇₉	—	4	4	no	—
484	C₂×D₄×C₇₉	—	4	4	no	—
485	C₂×D₄×C₇₉	—	4	4	no	—
486	C₂×D₄×C₇₉	—	4	4	no	—
487	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
488	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
489	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
490	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
491	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
492	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
493	C₂²×C₄×C₇₉	—	2	4	no	—
494	C₂²×C₄×C₇₉	—	4	4	no	—
495	C₂²×C₄×C₇₉	—	4	4	no	—
496	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
498	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
503	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
504	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
505	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
506	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
507	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
508	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
509	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
510	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
511	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
512	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
513	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
514	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
515	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
516	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
517	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
518	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
519	C₄²×C₇₉	C₂⁴	1	4	yes	—
520	C₄²×C₇₉	C₂⁴	1	4	yes	—
521	C₂³×C₇₉	—	2	4	no	—
522	C₂³×C₇₉	—	2	2	no	—
523	C₂³×C₇₉	—	2	4	no	—
524	C₂³×C₇₉	—	2	4	no	—
525	C₂³×C₇₉	—	2	4	no	—
526	C₂³×C₇₉	—	2	2	no	—
527	C₂³×C₇₉	—	2	4	no	—
528	C₂³×C₇₉	—	2	4	no	—
529	C₂³×C₇₉	—	2	2	no	—
530	C₂³×C₇₉	C₂⁵	1	4	yes	—
531	C₂³×C₇₉	C₂⁵	1	2	yes	—
532	C₂³×C₇₉	C₂⁵	1	4	yes	—
533	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
534	C₂²×D₇₉	—	2	2	no	—
535	C₂²×D₇₉	—	2	2	no	—
536	C₂²×D₇₉	—	2	2	no	—
537	C₂²×D₇₉	—	2	2	no	—
538	C₂²×D₇₉	—	2	4	no	—
539	C₂²×D₇₉	—	2	4	no	—
540	C₂²×D₇₉	—	2	4	no	—
541	C₂²×D₇₉	—	2	8	no	—
542	C₂²×D₇₉	—	2	8	no	—
543	C₂²×D₇₉	—	2	16	no	—
544	C₂²×D₇₉	—	4	4	no	—
545	C₂²×D₇₉	—	4	16	no	—
546	C₂²×D₇₉	—	4	8	no	—
547	C₂²×D₇₉	—	4	8	no	—
548	C₂²×D₇₉	—	8	16	no	—
549	C₂²×D₇₉	C₂×#41	1	4	yes	—
550	C₂²×D₇₉	H(5,𝔽₂)	1	4	yes	—
551	C₂²×D₇₉	C₂⁵	1	4	yes	—
552	C₂²×D₇₉	C₂⁵	1	2	yes	—
553	C₂²×D₇₉	C₂⁵	1	2	yes	—
554	D₄×C₇₉	—	2	8	no	—
555	D₄×C₇₉	—	2	8	no	—
556	D₄×C₇₉	—	4	8	no	—
557	D₄×C₇₉	—	4	8	no	—
558	D₄×C₇₉	—	4	8	no	—
559	D₄×C₇₉	—	4	8	no	—
560	C₂×C₄×C₇₉	—	2	2	no	—
561	C₂×C₄×C₇₉	—	2	2	no	—
562	C₂×C₄×C₇₉	—	2	2	no	—
563	C₂×C₄×C₇₉	—	2	4	no	—
564	C₂×C₄×C₇₉	—	2	2	no	—
565	C₂×C₄×C₇₉	—	2	4	no	—
566	C₂×C₄×C₇₉	—	2	2	no	—
567	C₂×C₄×C₇₉	—	2	8	no	—
568	C₂×C₄×C₇₉	—	4	8	no	—
569	C₂×C₄×C₇₉	—	4	8	no	—
570	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
571	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
572	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
573	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
574	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
575	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
576	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
577	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
578	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
579	C₂²⋊D₇₉	—	2	16	no	—
580	C₂²⋊D₇₉	—	2	16	no	—
581	C₂²⋊D₇₉	—	2	16	no	—
582	C₂²⋊D₇₉	—	2	16	no	—
583	C₂²⋊D₇₉	—	4	8	no	—
584	C₂²⋊D₇₉	—	4	8	no	—
585	C₂²⋊D₇₉	—	4	8	no	—
586	C₂×Dic₇₉	—	2	2	no	—
587	C₂×Dic₇₉	—	2	4	no	—
588	C₂×Dic₇₉	—	2	2	no	—
589	C₂×Dic₇₉	—	2	2	no	—
590	C₂×Dic₇₉	—	2	4	no	—
591	C₂×Dic₇₉	—	2	4	no	—
592	C₂×Dic₇₉	—	2	2	no	—
593	C₂×Dic₇₉	—	2	2	no	—
594	C₂×Dic₇₉	—	2	8	no	—
595	C₂×Dic₇₉	—	2	16	no	—
596	C₂×Dic₇₉	—	4	8	no	—
597	C₂×Dic₇₉	—	4	8	no	—
598	C₂×Dic₇₉	C₂×#41	1	4	yes	—
599	C₂×Dic₇₉	C₂⁵	1	2	yes	—
600	C₂×Dic₇₉	C₂⁵	1	2	yes	—
601	C₂×Dic₇₉	C₂⁵	1	4	yes	—
602	C₂×Dic₇₉	C₂⁵	1	2	yes	—
603	C₂×Dic₇₉	C₂⁵	1	2	yes	—
604	C₂×Dic₇₉	C₂⁵	1	2	yes	—
605	C₂×Dic₇₉	C₂⁵	1	4	yes	—
606	C₂×Dic₇₉	C₂⁵	1	4	yes	—
607	C₂×Dic₇₉	C₂⁵	1	2	yes	—
608	D₃₁₆	—	2	16	no	—
609	D₃₁₆	—	2	8	no	—
610	C₄×D₇₉	—	2	8	no	—
611	C₄×D₇₉	—	2	8	no	—
612	C₄×D₇₉	—	2	8	no	—
613	C₄×D₇₉	—	2	8	no	—
614	C₄×D₇₉	—	2	8	no	—
615	C₄×D₇₉	—	4	4	no	—
616	C₄×D₇₉	—	4	8	no	—
617	C₄×D₇₉	—	4	4	no	—
618	C₄×D₇₉	—	4	8	no	—
619	C₄×D₇₉	—	4	8	no	—
620	C₄×D₇₉	C₂×#41	1	16	yes	complemented
621	Dic₁₅₈	—	2	8	no	—
622	Dic₁₅₈	—	4	8	no	—
623	Dic₁₅₈	—	4	8	no	—
624	C₂²×C₇₉	—	2	4	no	—
625	C₂²×C₇₉	—	2	4	no	—
626	C₂²×C₇₉	—	2	2	no	—
627	C₂²×C₇₉	—	2	4	no	—
628	C₂²×C₇₉	—	2	4	no	—
629	C₂²×C₇₉	—	2	2	no	—
630	C₂²×C₇₉	—	2	4	no	—
631	C₂²×C₇₉	—	2	4	no	—
632	C₂²×C₇₉	—	2	2	no	—
633	C₂²×C₇₉	—	4	4	no	—
634	C₂²×C₇₉	—	4	8	no	—
635	C₂²×C₇₉	—	4	8	no	—
636	C₂²×C₇₉	C₂²×#41	1	2	yes	—
637	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
638	C₂²×C₇₉	#585	1	2	yes	—
639	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
640	C₂×D₇₉	—	2	2	no	—
641	C₂×D₇₉	—	2	2	no	—
642	C₂×D₇₉	—	2	2	no	—
643	C₂×D₇₉	—	2	2	no	—
644	C₂×D₇₉	—	2	8	no	—
645	C₂×D₇₉	—	2	8	no	—
646	C₂×D₇₉	—	2	4	no	—
647	C₂×D₇₉	—	2	4	no	—
648	C₂×D₇₉	—	2	4	no	—
649	C₂×D₇₉	—	4	16	no	—
650	C₂×D₇₉	—	4	8	no	—
651	C₂×D₇₉	—	8	16	no	—
652	C₂×D₇₉	C₂²×#41	1	4	yes	—
653	C₂×D₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
654	C₄×C₇₉	—	2	2	no	—
655	C₄×C₇₉	—	2	2	no	—
656	C₄×C₇₉	—	2	4	no	—
657	C₄×C₇₉	—	2	2	no	—
658	C₄×C₇₉	—	2	2	no	—
659	C₄×C₇₉	—	2	4	no	—
660	C₄×C₇₉	—	2	2	no	—
661	C₄×C₇₉	C₂²×#41	1	4	yes	—
662	Dic₇₉	—	2	4	no	—
663	Dic₇₉	—	2	2	no	—
664	Dic₇₉	—	2	4	no	—
665	Dic₇₉	—	2	4	no	—
666	Dic₇₉	—	2	2	no	—
667	Dic₇₉	—	2	2	no	—
668	Dic₇₉	—	2	2	no	—
669	Dic₇₉	—	2	2	no	—
670	Dic₇₉	C₂²×#41	1	4	yes	—
671	C₂×#3494	—	79	1	no	maximal, Sylow
672	C₂×C₇₉	—	4	2	no	—
673	C₂×C₇₉	—	4	4	no	—
674	C₂×C₇₉	—	4	4	no	—
675	C₂×C₇₉	#3494	1	4	yes	complemented
676	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
677	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂×C₇₉	C₂×#585	1	1	yes	characteristic
679	D₇₉	—	2	4	no	—
680	D₇₉	—	2	4	no	—
681	D₇₉	—	4	4	no	—
682	#3494	—	79	32	no	—
683	C₂×#555	—	79	2	no	—
684	C₂×#553	—	79	2	no	—
685	C₂×#553	—	79	2	no	—
686	C₂×#551	—	79	2	no	—
687	C₂×#551	—	79	2	no	—
688	C₂×#547	—	79	2	no	—
689	C₂×#546	—	79	2	no	—
690	C₂×#546	—	79	2	no	—
691	C₂×#544	—	79	1	no	—
692	C₂×#542	—	79	1	no	—
693	C₂×#542	—	79	1	no	—
694	C₂×#540	—	79	1	no	—
695	C₂×#540	D₇₉	1	1	yes	characteristic, complemented
696	C₂×#535	—	79	1	no	—
697	C₂×#532	—	79	1	no	—
698	C₂×#532	—	79	1	no	—
699	C₂×#529	—	79	1	no	—
700	C₂×#529	—	79	1	no	—
701	C₂×#525	—	79	1	no	—
702	C₂²×#121	—	79	1	no	—
703	C₂×#520	—	79	1	no	—
704	C₂×#518	—	79	1	no	—
705	C₂²×#117	—	79	1	no	—
706	C₇₉	C₂×#3494	1	1	yes	characteristic, complemented, Sylow
707	C₂²×#41	—	79	2	no	—
708	C₂²×#41	—	79	1	no	—
709	C₂²×#41	—	79	2	no	—
710	C₂³×D₄	—	79	2	no	—
711	C₂³×D₄	—	79	1	no	—
712	C₂⁴×C₄	—	79	1	no	—
713	#555	—	79	32	no	—
714	#553	—	79	32	no	—
715	#553	—	79	32	no	—
716	#551	—	79	32	no	—
717	#551	—	79	32	no	—
718	#547	—	79	32	no	—
719	#546	—	79	32	no	—
720	#546	—	79	32	no	—
721	#544	—	79	16	no	—
722	#542	—	79	16	no	—
723	#542	—	79	16	no	—
724	#540	—	79	16	no	—
725	#540	C₂×D₇₉	1	16	yes	complemented
726	#535	—	79	16	no	—
727	#532	—	79	16	no	—
728	#532	—	79	16	no	—
729	C₂×C₄⋊Q₈	—	79	1	no	—
730	C₂×C₄⋊Q₈	—	79	2	no	—
731	C₂×C₄⋊Q₈	—	79	1	no	—
732	C₂×#127	—	79	1	no	—
733	C₂×#127	C₂×D₇₉	1	1	yes	characteristic, complemented
734	#529	—	79	16	no	—
735	#529	—	79	16	no	—
736	C₂×#126	—	79	2	no	—
737	C₂×#126	—	79	2	no	—
738	C₂×#126	—	79	2	no	—
739	C₂×#126	—	79	2	no	—
740	C₂×#125	—	79	1	no	—
741	C₂×#125	—	79	2	no	—
742	C₂×#125	C₂×D₇₉	1	1	yes	characteristic, complemented
743	C₂×#124	—	79	1	no	—
744	C₂×#124	—	79	2	no	—
745	C₂×#124	—	79	2	no	—
746	C₂×#124	—	79	2	no	—
747	C₂×#124	—	79	2	no	—
748	C₂×#124	—	79	1	no	—
749	#525	—	79	16	no	—
750	C₂×#123	—	79	2	no	—
751	C₂×#123	—	79	2	no	—
752	C₂×#123	—	79	2	no	—
753	C₂×#123	—	79	2	no	—
754	C₂×#123	—	79	2	no	—
755	C₂×#123	—	79	2	no	—
756	C₂×#123	—	79	2	no	—
757	C₂×#123	C₂×D₇₉	1	2	yes	complemented
758	C₂×#123	C₂×D₇₉	1	2	yes	complemented
759	C₂×C₂²⋊Q₈	—	79	1	no	—
760	C₂×C₂²⋊Q₈	—	79	1	no	—
761	C₂×C₂²⋊Q₈	—	79	2	no	—
762	C₂×C₂²⋊Q₈	—	79	2	no	—
763	C₂×C₂²⋊Q₈	—	79	2	no	—
764	C₂×C₂²⋊Q₈	—	79	2	no	—
765	C₂×#121	—	79	1	no	—
766	C₂×#121	—	79	2	no	—
767	C₂×#121	—	79	1	no	—
768	C₂×#121	—	79	2	no	—
769	C₂×#121	—	79	2	no	—
770	C₂×#121	—	79	2	no	—
771	C₂×#121	—	79	2	no	—
772	C₂×#121	—	79	2	no	—
773	C₂×#121	—	79	1	no	—
774	C₂×#121	—	79	16	no	—
775	C₂×#121	—	79	1	no	—
776	C₂×#121	—	79	2	no	—
777	C₂×#121	—	79	2	no	—
778	C₂×#121	C₂×D₇₉	1	1	yes	characteristic
779	C₂×#121	C₂×D₇₉	1	1	yes	characteristic, complemented
780	C₂×#121	C₂×D₇₉	1	2	yes	complemented
781	C₂×#121	C₂×D₇₉	1	2	yes	complemented
782	C₂×#120	—	79	2	no	—
783	C₂×#120	—	79	2	no	—
784	C₂×#120	—	79	2	no	—
785	#520	—	79	16	no	—
786	#518	—	79	16	no	—
787	C₂×C₄×Q₈	—	79	1	no	—
788	C₂×C₄×Q₈	—	79	1	no	—
789	C₂×C₄×D₄	—	79	1	no	—
790	C₂×C₄×D₄	—	79	1	no	—
791	C₂×C₄×D₄	—	79	2	no	—
792	C₂×C₄×D₄	—	79	2	no	—
793	C₂×C₄×D₄	—	79	2	no	—
794	C₂×C₄×D₄	—	79	2	no	—
795	C₂×C₄×D₄	—	79	2	no	—
796	C₂×C₄×D₄	—	79	2	no	—
797	C₂×C₄×D₄	—	79	1	no	—
798	C₂×C₄×D₄	—	79	2	no	—
799	C₂×C₄×D₄	—	79	2	no	—
800	C₂×C₄×D₄	—	79	2	no	—
801	C₂×C₄×D₄	—	79	2	no	—
802	C₂×C₄×D₄	—	79	1	no	—
803	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
804	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
805	C₂×#117	—	79	1	no	—
806	C₂×#117	—	79	2	no	—
807	C₂×#117	—	79	16	no	—
808	C₂×#117	—	79	1	no	—
809	C₂×#117	—	79	1	no	—
810	C₂×#117	—	79	1	no	—
811	C₂×#117	—	79	2	no	—
812	C₂×#117	—	79	1	no	—
813	C₂×#117	—	79	1	no	—
814	C₂×#117	—	79	2	no	—
815	C₂×#117	—	79	1	no	—
816	C₂×#117	—	79	1	no	—
817	C₂×#117	C₂×D₇₉	1	1	yes	characteristic, complemented
818	C₂²×C₄⋊C₄	—	79	2	no	—
819	C₂²×C₄⋊C₄	—	79	1	no	—
820	C₂²×C₄⋊C₄	—	79	1	no	—
821	C₂²×C₄⋊C₄	—	79	1	no	—
822	C₂²×C₂²⋊C₄	—	79	2	no	—
823	C₂²×C₂²⋊C₄	—	79	1	no	—
824	C₂²×C₂²⋊C₄	—	79	1	no	—
825	C₂²×C₂²⋊C₄	—	79	2	no	—
826	C₂²×C₂²⋊C₄	—	79	2	no	—
827	C₂²×C₄²	—	79	1	no	—
828	C₂²×C₄²	—	79	1	no	—
829	C₂⁵	—	79	2	no	—
830	C₂⁵	—	79	1	no	—
831	C₂×#41	—	316	8	no	—
832	C₂×#41	—	316	8	no	—
833	C₂×#41	—	79	16	no	—
834	C₂×#41	—	79	8	no	—
835	C₂×#41	—	79	16	no	—
836	C₂×#41	—	158	8	no	—
837	C₂²×Q₈	—	79	2	no	—
838	C₂²×Q₈	—	79	2	no	—
839	C₂²×Q₈	—	79	1	no	—
840	C₂²×D₄	—	316	8	no	—
841	C₂²×D₄	—	79	2	no	—
842	C₂²×D₄	—	79	2	no	—
843	C₂²×D₄	—	79	2	no	—
844	C₂²×D₄	—	79	16	no	—
845	C₂²×D₄	—	79	2	no	—
846	C₂²×D₄	—	79	2	no	—
847	C₂²×D₄	—	79	2	no	—
848	C₂²×D₄	—	79	2	no	—
849	C₂²×D₄	—	79	8	no	—
850	C₂²×D₄	—	79	1	no	—
851	C₂²×D₄	—	79	2	no	—
852	C₂²×D₄	—	158	8	no	—
853	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
854	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
855	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
856	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
857	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
858	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
859	C₂³×C₄	—	79	2	no	—
860	C₂³×C₄	—	79	2	no	—
861	C₂³×C₄	—	79	1	no	—
862	C₂³×C₄	—	79	1	no	—
863	C₂³×C₄	—	79	2	no	—
864	C₂³×C₄	—	79	2	no	—
865	C₂³×C₄	—	79	2	no	—
866	C₂³×C₄	—	79	1	no	—
867	C₂³×C₄	—	79	2	no	—
868	C₂³×C₄	—	79	1	no	—
869	C₂³×C₄	—	79	1	no	—
870	C₂³×C₄	—	79	1	no	—
871	C₂³×C₄	—	79	1	no	—
872	C₂³×C₄	—	79	1	no	—
873	C₂³×C₄	—	79	8	no	—
874	C₂³×C₄	—	79	1	no	—
875	C₂³×C₄	—	158	8	no	—
876	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
877	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
878	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
879	C₄⋊Q₈	—	79	8	no	—
880	C₄⋊Q₈	—	79	16	no	—
881	C₄⋊Q₈	—	79	8	no	—
882	#127	—	79	8	no	—
883	#127	C₂²×D₇₉	1	8	yes	complemented
884	#126	—	79	16	no	—
885	#126	—	79	16	no	—
886	#126	—	79	16	no	—
887	#126	—	79	16	no	—
888	#125	—	79	8	no	—
889	#125	—	79	16	no	—
890	#125	C₂²×D₇₉	1	8	yes	complemented
891	#124	—	79	8	no	—
892	#124	—	79	16	no	—
893	#124	—	79	16	no	—
894	#124	—	79	16	no	—
895	#124	—	79	16	no	—
896	#124	—	79	8	no	—
897	#123	—	79	16	no	—
898	#123	—	79	16	no	—
899	#123	—	79	16	no	—
900	#123	—	79	16	no	—
901	#123	—	79	16	no	—
902	#123	—	79	16	no	—
903	#123	—	79	16	no	—
904	#123	C₂²×D₇₉	1	16	yes	complemented
905	#123	C₂²×D₇₉	1	16	yes	complemented
906	C₂²⋊Q₈	—	79	8	no	—
907	C₂²⋊Q₈	—	79	8	no	—
908	C₂²⋊Q₈	—	79	16	no	—
909	C₂²⋊Q₈	—	79	16	no	—
910	C₂²⋊Q₈	—	79	16	no	—
911	C₂²⋊Q₈	—	79	16	no	—
912	#121	—	79	8	no	—
913	#121	—	79	16	no	—
914	#121	—	79	8	no	—
915	#121	—	79	16	no	—
916	#121	—	79	16	no	—
917	#121	—	79	16	no	—
918	#121	—	79	16	no	—
919	#121	—	79	16	no	—
920	#121	—	79	8	no	—
921	#121	—	79	8	no	—
922	#121	—	79	16	no	—
923	#121	—	79	16	no	—
924	#121	C₂²×D₇₉	1	8	yes	—
925	#121	C₂²×D₇₉	1	8	yes	complemented
926	#121	C₂²×D₇₉	1	16	yes	complemented
927	#121	C₂²×D₇₉	1	16	yes	complemented
928	#120	—	79	16	no	—
929	#120	—	79	16	no	—
930	#120	—	79	16	no	—
931	C₄×Q₈	—	79	8	no	—
932	C₄×Q₈	—	79	8	no	—
933	C₄×D₄	—	79	8	no	—
934	C₄×D₄	—	79	8	no	—
935	C₄×D₄	—	79	16	no	—
936	C₄×D₄	—	79	16	no	—
937	C₄×D₄	—	79	16	no	—
938	C₄×D₄	—	79	16	no	—
939	C₄×D₄	—	79	16	no	—
940	C₄×D₄	—	79	16	no	—
941	C₄×D₄	—	79	8	no	—
942	C₄×D₄	—	79	16	no	—
943	C₄×D₄	—	79	16	no	—
944	C₄×D₄	—	79	16	no	—
945	C₄×D₄	—	79	16	no	—
946	C₄×D₄	—	79	8	no	—
947	C₄×D₄	C₂²×D₇₉	1	8	yes	complemented
948	C₄×D₄	C₂²×D₇₉	1	8	yes	complemented
949	#117	—	79	8	no	—
950	#117	—	79	16	no	—
951	#117	—	79	8	no	—
952	#117	—	79	8	no	—
953	#117	—	79	8	no	—
954	#117	—	79	16	no	—
955	#117	—	79	8	no	—
956	#117	—	79	8	no	—
957	#117	—	79	16	no	—
958	#117	—	79	8	no	—
959	#117	—	79	8	no	—
960	#117	C₂²×D₇₉	1	8	yes	complemented
961	C₂×C₄⋊C₄	—	79	1	no	—
962	C₂×C₄⋊C₄	—	79	2	no	—
963	C₂×C₄⋊C₄	—	79	1	no	—
964	C₂×C₄⋊C₄	—	79	1	no	—
965	C₂×C₄⋊C₄	—	79	1	no	—
966	C₂×C₄⋊C₄	—	79	1	no	—
967	C₂×C₄⋊C₄	—	79	1	no	—
968	C₂×C₄⋊C₄	—	79	1	no	—
969	C₂×C₄⋊C₄	—	79	2	no	—
970	C₂×C₄⋊C₄	—	79	2	no	—
971	C₂×C₄⋊C₄	—	79	16	no	—
972	C₂×C₄⋊C₄	—	79	2	no	—
973	C₂×C₄⋊C₄	—	79	1	no	—
974	C₂×C₄⋊C₄	—	79	2	no	—
975	C₂×C₄⋊C₄	—	79	2	no	—
976	C₂×C₄⋊C₄	—	79	2	no	—
977	C₂×C₄⋊C₄	—	79	2	no	—
978	C₂×C₄⋊C₄	—	79	2	no	—
979	C₂×C₄⋊C₄	—	79	8	no	—
980	C₂×C₄⋊C₄	—	79	8	no	—
981	C₂×C₄⋊C₄	—	79	8	no	—
982	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
983	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
984	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
985	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
986	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
987	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
988	C₂×C₂²⋊C₄	—	79	1	no	—
989	C₂×C₂²⋊C₄	—	79	1	no	—
990	C₂×C₂²⋊C₄	—	79	2	no	—
991	C₂×C₂²⋊C₄	—	79	2	no	—
992	C₂×C₂²⋊C₄	—	79	2	no	—
993	C₂×C₂²⋊C₄	—	79	2	no	—
994	C₂×C₂²⋊C₄	—	79	2	no	—
995	C₂×C₂²⋊C₄	—	79	2	no	—
996	C₂×C₂²⋊C₄	—	79	2	no	—
997	C₂×C₂²⋊C₄	—	79	1	no	—
998	C₂×C₂²⋊C₄	—	79	1	no	—
999	C₂×C₂²⋊C₄	—	79	2	no	—
1000	C₂×C₂²⋊C₄	—	79	1	no	—
1001	C₂×C₂²⋊C₄	—	79	1	no	—
1002	C₂×C₂²⋊C₄	—	79	2	no	—
1003	C₂×C₂²⋊C₄	—	79	2	no	—
1004	C₂×C₂²⋊C₄	—	79	2	no	—
1005	C₂×C₂²⋊C₄	—	79	16	no	—
1006	C₂×C₂²⋊C₄	—	79	2	no	—
1007	C₂×C₂²⋊C₄	—	79	2	no	—
1008	C₂×C₂²⋊C₄	—	79	2	no	—
1009	C₂×C₂²⋊C₄	—	79	2	no	—
1010	C₂×C₂²⋊C₄	—	79	8	no	—
1011	C₂×C₂²⋊C₄	—	79	8	no	—
1012	C₂×C₂²⋊C₄	—	79	16	no	—
1013	C₂×C₂²⋊C₄	—	79	16	no	—
1014	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
1015	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
1016	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
1017	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
1018	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
1019	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
1020	C₂×C₄²	—	79	1	no	—
1021	C₂×C₄²	—	79	1	no	—
1022	C₂×C₄²	—	79	1	no	—
1023	C₂×C₄²	—	79	2	no	—
1024	C₂×C₄²	—	79	2	no	—
1025	C₂×C₄²	—	79	1	no	—
1026	C₂×C₄²	—	79	1	no	—
1027	C₂×C₄²	—	79	1	no	—
1028	C₂×C₄²	—	79	2	no	—
1029	C₂×C₄²	—	79	8	no	—
1030	C₂×C₄²	—	79	8	no	—
1031	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
1032	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
1033	C₂⁴	—	316	2	no	—
1034	C₂⁴	—	316	4	no	—
1035	C₂⁴	—	316	4	no	—
1036	C₂⁴	—	79	8	no	—
1037	C₂⁴	—	79	4	no	—
1038	C₂⁴	—	79	1	no	—
1039	C₂⁴	—	79	1	no	—
1040	C₂⁴	—	79	2	no	—
1041	C₂⁴	—	158	4	no	—
1042	C₂⁴	—	158	4	no	—
1043	C₂⁴	—	158	8	no	—
1044	C₂⁴	C₂³×D₇₉	1	2	yes	—
1045	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
1046	C₂⁴	C₂³×D₇₉	1	2	yes	—
1047	#41	—	316	32	no	—
1048	#41	—	316	32	no	—
1049	#41	—	158	32	no	—
1050	C₂×Q₈	—	316	4	no	—
1051	C₂×Q₈	—	316	4	no	—
1052	C₂×Q₈	—	79	8	no	—
1053	C₂×Q₈	—	79	8	no	—
1054	C₂×Q₈	—	79	4	no	—
1055	C₂×Q₈	—	158	4	no	—
1056	C₂×D₄	—	2	4	no	—
1057	C₂×D₄	—	2	4	no	—
1058	C₂×D₄	—	4	4	no	—
1059	C₂×D₄	—	4	4	no	—
1060	C₂×D₄	—	4	4	no	—
1061	C₂×D₄	—	4	4	no	—
1062	C₂×D₄	—	316	32	no	—
1063	C₂×D₄	—	316	4	no	—
1064	C₂×D₄	—	316	4	no	—
1065	C₂×D₄	—	316	4	no	—
1066	C₂×D₄	—	79	8	no	—
1067	C₂×D₄	—	79	8	no	—
1068	C₂×D₄	—	79	8	no	—
1069	C₂×D₄	—	79	8	no	—
1070	C₂×D₄	—	79	8	no	—
1071	C₂×D₄	—	79	8	no	—
1072	C₂×D₄	—	79	8	no	—
1073	C₂×D₄	—	79	4	no	—
1074	C₂×D₄	—	79	8	no	—
1075	C₂×D₄	—	158	8	no	—
1076	C₂×D₄	—	158	32	no	—
1077	C₂×D₄	—	158	8	no	—
1078	C₂×D₄	—	158	8	no	—
1079	C₂×D₄	—	158	8	no	—
1080	C₂×D₄	—	158	8	no	—
1081	C₂×D₄	—	158	4	no	—
1082	C₂×D₄	C₂³×D₇₉	1	4	yes	—
1083	C₂×D₄	C₂³×D₇₉	1	4	yes	—
1084	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1085	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1086	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1087	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1088	C₂²×C₄	—	2	4	no	—
1089	C₂²×C₄	—	4	4	no	—
1090	C₂²×C₄	—	4	4	no	—
1091	C₂²×C₄	—	316	2	no	—
1092	C₂²×C₄	—	316	4	no	—
1093	C₂²×C₄	—	316	2	no	—
1094	C₂²×C₄	—	316	4	no	—
1095	C₂²×C₄	—	316	4	no	—
1096	C₂²×C₄	—	316	4	no	—
1097	C₂²×C₄	—	316	4	no	—
1098	C₂²×C₄	—	79	8	no	—
1099	C₂²×C₄	—	79	8	no	—
1100	C₂²×C₄	—	79	4	no	—
1101	C₂²×C₄	—	79	4	no	—
1102	C₂²×C₄	—	79	8	no	—
1103	C₂²×C₄	—	79	8	no	—
1104	C₂²×C₄	—	79	8	no	—
1105	C₂²×C₄	—	79	1	no	—
1106	C₂²×C₄	—	79	8	no	—
1107	C₂²×C₄	—	79	4	no	—
1108	C₂²×C₄	—	79	8	no	—
1109	C₂²×C₄	—	79	4	no	—
1110	C₂²×C₄	—	79	1	no	—
1111	C₂²×C₄	—	79	1	no	—
1112	C₂²×C₄	—	79	2	no	—
1113	C₂²×C₄	—	79	1	no	—
1114	C₂²×C₄	—	79	1	no	—
1115	C₂²×C₄	—	79	1	no	—
1116	C₂²×C₄	—	79	2	no	—
1117	C₂²×C₄	—	79	2	no	—
1118	C₂²×C₄	—	79	4	no	—
1119	C₂²×C₄	—	79	4	no	—
1120	C₂²×C₄	—	79	4	no	—
1121	C₂²×C₄	—	79	4	no	—
1122	C₂²×C₄	—	79	4	no	—
1123	C₂²×C₄	—	158	4	no	—
1124	C₂²×C₄	—	158	32	no	—
1125	C₂²×C₄	—	158	4	no	—
1126	C₂²×C₄	—	158	4	no	—
1127	C₂²×C₄	—	158	4	no	—
1128	C₂²×C₄	—	158	4	no	—
1129	C₂²×C₄	—	158	8	no	—
1130	C₂²×C₄	—	158	4	no	—
1131	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
1132	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1133	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1134	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1135	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1136	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
1137	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
1138	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1139	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
1140	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
1141	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1142	C₄⋊C₄	—	79	4	no	—
1143	C₄⋊C₄	—	79	8	no	—
1144	C₄⋊C₄	—	79	4	no	—
1145	C₄⋊C₄	—	79	4	no	—
1146	C₄⋊C₄	—	79	4	no	—
1147	C₄⋊C₄	—	79	8	no	—
1148	C₄⋊C₄	—	79	8	no	—
1149	C₄⋊C₄	—	79	8	no	—
1150	C₄⋊C₄	—	79	8	no	—
1151	C₄⋊C₄	—	79	8	no	—
1152	C₄⋊C₄	—	79	4	no	—
1153	C₄⋊C₄	—	79	4	no	—
1154	C₄⋊C₄	—	79	4	no	—
1155	C₄⋊C₄	—	79	8	no	—
1156	C₄⋊C₄	—	79	4	no	—
1157	C₄⋊C₄	—	79	8	no	—
1158	C₄⋊C₄	—	79	8	no	—
1159	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
1160	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
1161	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
1162	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
1163	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
1164	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
1165	C₂²⋊C₄	—	79	4	no	—
1166	C₂²⋊C₄	—	79	4	no	—
1167	C₂²⋊C₄	—	79	8	no	—
1168	C₂²⋊C₄	—	79	8	no	—
1169	C₂²⋊C₄	—	79	8	no	—
1170	C₂²⋊C₄	—	79	8	no	—
1171	C₂²⋊C₄	—	79	8	no	—
1172	C₂²⋊C₄	—	79	8	no	—
1173	C₂²⋊C₄	—	79	8	no	—
1174	C₂²⋊C₄	—	79	4	no	—
1175	C₂²⋊C₄	—	79	4	no	—
1176	C₂²⋊C₄	—	79	8	no	—
1177	C₂²⋊C₄	—	79	4	no	—
1178	C₂²⋊C₄	—	79	4	no	—
1179	C₂²⋊C₄	—	79	8	no	—
1180	C₂²⋊C₄	—	79	8	no	—
1181	C₂²⋊C₄	—	79	8	no	—
1182	C₂²⋊C₄	—	79	8	no	—
1183	C₂²⋊C₄	—	79	8	no	—
1184	C₂²⋊C₄	—	79	8	no	—
1185	C₂²⋊C₄	—	79	8	no	—
1186	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
1187	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
1188	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
1189	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
1190	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
1191	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
1192	C₄²	—	79	4	no	—
1193	C₄²	—	79	4	no	—
1194	C₄²	—	79	4	no	—
1195	C₄²	—	79	4	no	—
1196	C₄²	—	79	4	no	—
1197	C₄²	—	79	4	no	—
1198	C₄²	—	79	8	no	—
1199	C₄²	—	79	8	no	—
1200	C₄²	—	79	8	no	—
1201	C₄²	C₂³×D₇₉	1	4	yes	—
1202	C₄²	C₂³×D₇₉	1	4	yes	—
1203	C₂³	—	2	4	no	—
1204	C₂³	—	2	4	no	—
1205	C₂³	—	2	2	no	—
1206	C₂³	—	2	4	no	—
1207	C₂³	—	2	4	no	—
1208	C₂³	—	2	2	no	—
1209	C₂³	—	2	2	no	—
1210	C₂³	—	2	4	no	—
1211	C₂³	—	2	4	no	—
1212	C₂³	—	316	4	no	—
1213	C₂³	—	316	8	no	—
1214	C₂³	—	316	8	no	—
1215	C₂³	—	316	16	no	—
1216	C₂³	—	79	4	no	—
1217	C₂³	—	79	2	no	—
1218	C₂³	—	79	2	no	—
1219	C₂³	—	79	4	no	—
1220	C₂³	—	79	4	no	—
1221	C₂³	—	632	16	no	—
1222	C₂³	—	158	8	no	—
1223	C₂³	—	158	8	no	—
1224	C₂³	—	158	16	no	—
1225	C₂³	—	158	4	no	—
1226	C₂³	—	158	4	no	—
1227	C₂³	—	158	4	no	—
1228	C₂³	—	158	2	no	—
1229	C₂³	—	158	2	no	—
1230	C₂³	—	158	2	no	—
1231	C₂³	—	158	2	no	—
1232	C₂³	C₂⁴×D₇₉	1	2	yes	—
1233	C₂³	C₂⁴×D₇₉	1	4	yes	—
1234	C₂³	C₂⁴×D₇₉	1	4	yes	—
1235	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
1236	Q₈	—	316	8	no	—
1237	Q₈	—	316	8	no	—
1238	Q₈	—	158	8	no	—
1239	D₄	—	2	8	no	—
1240	D₄	—	2	8	no	—
1241	D₄	—	4	8	no	—
1242	D₄	—	4	8	no	—
1243	D₄	—	4	8	no	—
1244	D₄	—	4	8	no	—
1245	D₄	—	316	8	no	—
1246	D₄	—	316	8	no	—
1247	D₄	—	316	8	no	—
1248	D₄	—	158	16	no	—
1249	D₄	—	158	16	no	—
1250	D₄	—	158	16	no	—
1251	D₄	—	158	16	no	—
1252	D₄	—	158	16	no	—
1253	D₄	—	158	8	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	4	no	—
1256	C₂×C₄	—	2	2	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	2	4	no	—
1259	C₂×C₄	—	2	2	no	—
1260	C₂×C₄	—	2	2	no	—
1261	C₂×C₄	—	2	8	no	—
1262	C₂×C₄	—	4	8	no	—
1263	C₂×C₄	—	4	8	no	—
1264	C₂×C₄	—	316	8	no	—
1265	C₂×C₄	—	316	8	no	—
1266	C₂×C₄	—	316	4	no	—
1267	C₂×C₄	—	316	8	no	—
1268	C₂×C₄	—	316	4	no	—
1269	C₂×C₄	—	316	8	no	—
1270	C₂×C₄	—	316	8	no	—
1271	C₂×C₄	—	79	2	no	—
1272	C₂×C₄	—	79	4	no	—
1273	C₂×C₄	—	79	16	no	—
1274	C₂×C₄	—	79	2	no	—
1275	C₂×C₄	—	79	2	no	—
1276	C₂×C₄	—	79	4	no	—
1277	C₂×C₄	—	79	2	no	—
1278	C₂×C₄	—	79	2	no	—
1279	C₂×C₄	—	79	2	no	—
1280	C₂×C₄	—	79	4	no	—
1281	C₂×C₄	—	79	4	no	—
1282	C₂×C₄	—	158	8	no	—
1283	C₂×C₄	—	158	8	no	—
1284	C₂×C₄	—	158	8	no	—
1285	C₂×C₄	—	158	8	no	—
1286	C₂×C₄	—	158	8	no	—
1287	C₂×C₄	—	158	16	no	—
1288	C₂×C₄	—	158	2	no	—
1289	C₂×C₄	—	158	4	no	—
1290	C₂×C₄	—	158	4	no	—
1291	C₂×C₄	—	158	2	no	—
1292	C₂×C₄	—	158	2	no	—
1293	C₂×C₄	—	158	2	no	—
1294	C₂×C₄	—	158	2	no	—
1295	C₂×C₄	—	158	4	no	—
1296	C₂×C₄	—	158	8	no	—
1297	C₂×C₄	#41×D₇₉	1	4	yes	—
1298	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1299	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1300	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1301	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1302	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
1303	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
1304	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1305	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1306	C₂²	—	2	2	no	—
1307	C₂²	—	2	4	no	—
1308	C₂²	—	2	4	no	—
1309	C₂²	—	2	4	no	—
1310	C₂²	—	2	4	no	—
1311	C₂²	—	2	2	no	—
1312	C₂²	—	2	4	no	—
1313	C₂²	—	2	4	no	—
1314	C₂²	—	2	2	no	—
1315	C₂²	—	4	4	no	—
1316	C₂²	—	4	8	no	—
1317	C₂²	—	4	8	no	—
1318	C₂²	—	316	16	no	—
1319	C₂²	—	316	8	no	—
1320	C₂²	—	79	4	no	—
1321	C₂²	—	79	4	no	—
1322	C₂²	—	632	16	no	—
1323	C₂²	—	158	4	no	—
1324	C₂²	—	158	4	no	—
1325	C₂²	—	158	4	no	—
1326	C₂²	—	158	8	no	—
1327	C₂²	—	158	8	no	—
1328	C₂²	—	158	2	no	—
1329	C₂²	—	158	2	no	—
1330	C₂²	—	158	2	no	—
1331	C₂²	—	158	2	no	—
1332	C₂²	C₂×#41×D₇₉	1	2	yes	—
1333	C₂²	H(5,𝔽₂)×D₇₉	1	2	yes	—
1334	C₂²	#19099398	1	2	yes	—
1335	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
1336	C₄	—	2	2	no	—
1337	C₄	—	2	2	no	—
1338	C₄	—	2	4	no	—
1339	C₄	—	2	2	no	—
1340	C₄	—	2	2	no	—
1341	C₄	—	2	4	no	—
1342	C₄	—	2	2	no	—
1343	C₄	—	79	4	no	—
1344	C₄	—	158	2	no	—
1345	C₄	—	158	4	no	—
1346	C₄	—	158	2	no	—
1347	C₄	—	158	4	no	—
1348	C₄	—	158	4	no	—
1349	C₄	—	158	2	no	—
1350	C₄	—	158	2	no	—
1351	C₄	—	158	2	no	—
1352	C₄	C₂×#41×D₇₉	1	4	yes	—
1353	C₂	—	4	2	no	—
1354	C₂	—	4	4	no	—
1355	C₂	—	4	4	no	—
1356	C₂	—	316	4	no	—
1357	C₂	—	158	4	no	—
1358	C₂	—	158	4	no	—
1359	C₂	#23777127	1	4	yes	direct product factor
1360	C₂	C₂²×#41×D₇₉	1	1	yes	characteristic
1361	C₂	C₂×H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
1362	C₂	C₂×#19099398	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#540×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#540	D₇₉
hypocenter	C₇₉	C₂×#3494
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#540

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #23777127	C₂	direct (N × H)
2. C₂×#19099277	C₂	semidirect
3. C₂×#19099258	C₂	semidirect
4. C₂×#19099256	C₂	semidirect
5. C₂×#19099241	C₂	semidirect
6. C₂×#19099236	C₂	semidirect
7. C₂×#19099211	C₂	semidirect
8. C₂×#19099210	C₂	semidirect
9. C₂×#19099202	C₂	semidirect
10. C₂×#19099193	C₂	semidirect
11. C₂×#19099184	C₂	semidirect
12. C₂×#19099180	C₂	semidirect
13. C₂×#19099166	C₂	semidirect
14. C₂×#19099126	C₂	semidirect
15. C₂×#19099111	C₂	semidirect
16. C₂×#19099110	C₂	semidirect
17. C₂×#19099098	C₂	semidirect
18. C₂×#19099095	C₂	semidirect
19. C₂×#19099073	C₂	semidirect
20. C₂×#121×D₇₉	C₂	semidirect
21. C₂×#19099042	C₂	semidirect
22. C₂×#19099035	C₂	semidirect
23. C₂×#117×D₇₉	C₂	semidirect
24. C₂×#540×C₇₉	C₂	semidirect
25. C₂²×#11929624	C₂²	semidirect
27. C₂²×#11929623	C₂²	semidirect
31. #19099277	C₂²	semidirect
32. #19099258	C₂²	semidirect
33. #19099256	C₂²	semidirect
34. #19099241	C₂²	semidirect
35. #19099236	C₂²	semidirect
36. #19099211	C₂²	semidirect
37. #19099210	C₂²	semidirect
38. #19099202	C₂²	semidirect
39. #19099193	C₂²	semidirect
40. #19099184	C₂²	semidirect
41. #19099180	C₂²	semidirect
42. #19099166	C₂²	semidirect
43. #19099126	C₂²	semidirect
44. #19099111	C₂²	semidirect
45. #19099110	C₂²	semidirect
46. C₂×#14579161	C₂²	semidirect
47. C₂×#14579160	C₂²	semidirect
48. C₂×#14579160	C₂²	semidirect
49. C₂×#14579157	C₂²	semidirect
50. #19099098	C₂²	semidirect
51. #19099095	C₂²	semidirect
52. C₂×#14579156	C₂²	semidirect
53. C₂×#14579156	C₂²	semidirect
54. C₂×#14579154	C₂²	semidirect
55. C₂×#14579154	C₂²	semidirect
56. C₂×#14579152	C₂²	semidirect
57. C₂×#14579151	C₂²	semidirect
58. C₂×#14579149	C₂²	semidirect
59. C₂×#14579148	C₂²	semidirect
60. C₂×#14579148	C₂²	semidirect
61. C₂×#14579148	C₂²	semidirect
62. C₂×#14579147	C₂²	semidirect
63. C₂×#14579147	C₂²	semidirect
64. #19099073	C₂²	semidirect
65. C₂×#14579146	C₂²	semidirect
66. C₂×#14579145	C₂²	semidirect
68. C₂×#14579143	C₂²	semidirect
69. C₂×#14579143	C₂²	semidirect
70. C₂×#14579143	C₂²	semidirect
71. C₂×#14579142	C₂²	semidirect
73. C₂×#14579141	C₂²	semidirect
74. C₂×#14579140	C₂²	semidirect
76. C₂×#14579139	C₂²	semidirect
77. C₂×#14579138	C₂²	semidirect
81. C₂×#14579134	C₂²	semidirect
83. C₂×#14579133	C₂²	semidirect
84. C₂×#14579133	C₂²	semidirect
85. C₂×#14579133	C₂²	semidirect
87. C₂×#14579132	C₂²	semidirect
88. C₂×#14579132	C₂²	semidirect
89. C₂×#14579132	C₂²	semidirect
90. #121×D₇₉	C₂²	semidirect
94. #19099042	C₂²	semidirect
95. #19099035	C₂²	semidirect
96. C₂×C₄×Dic₁₅₈	C₂²	semidirect
97. C₂×#14579126	C₂²	semidirect
98. C₂×C₄×D₃₁₆	C₂²	semidirect
99. C₂×D₄×Dic₇₉	C₂²	semidirect
100. C₂×D₄×Dic₇₉	C₂²	semidirect
101. C₂×D₄×Dic₇₉	C₂²	semidirect
102. C₂×D₄×Dic₇₉	C₂²	semidirect
103. C₂×#14579123	C₂²	semidirect
104. C₂×#14579123	C₂²	semidirect
106. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
107. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
108. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
110. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
111. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
112. C₂×#14579120	C₂²	semidirect
113. C₂×#14579120	C₂²	semidirect
117. C₂×#14579119	C₂²	semidirect
120. C₂×#14579117	C₂²	semidirect
121. C₂×#14579117	C₂²	semidirect
122. C₂×#14579117	C₂²	semidirect
123. #117×D₇₉	C₂²	semidirect
124. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
126. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
127. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
133. C₂×C₄²×D₇₉	C₂²	semidirect
134. C₂×C₄²×D₇₉	C₂²	semidirect
135. #540×C₇₉	C₂²	semidirect
136. C₂×#127×C₇₉	C₂²	semidirect
137. C₂×#125×C₇₉	C₂²	semidirect
138. C₂×#123×C₇₉	C₂²	semidirect
139. C₂×#123×C₇₉	C₂²	semidirect
141. C₂×#121×C₇₉	C₂²	semidirect
142. C₂×#121×C₇₉	C₂²	semidirect
143. C₂×#121×C₇₉	C₂²	semidirect
144. C₂×C₄×D₄×C₇₉	C₂²	semidirect
145. C₂×C₄×D₄×C₇₉	C₂²	semidirect
146. C₂×#117×C₇₉	C₂²	semidirect
150. C₂×#11929624	C₂³	semidirect
154. C₂×#11929623	C₂³	semidirect
188. #14579161	C₂³	semidirect
189. #14579160	C₂³	semidirect
190. #14579160	C₂³	semidirect
191. #14579157	C₂³	semidirect
192. #14579156	C₂³	semidirect
193. #14579156	C₂³	semidirect
194. #14579154	C₂³	semidirect
195. #14579154	C₂³	semidirect
196. #14579152	C₂³	semidirect
197. #14579151	C₂³	semidirect
198. #14579149	C₂³	semidirect
199. #14579148	C₂³	semidirect
200. #14579148	C₂³	semidirect
201. #14579148	C₂³	semidirect
202. #14579147	C₂³	semidirect
203. #14579147	C₂³	semidirect
204. #14579146	C₂³	semidirect
205. #14579145	C₂³	semidirect
207. #14579143	C₂³	semidirect
208. #14579143	C₂³	semidirect
209. #14579143	C₂³	semidirect
210. #14579142	C₂³	semidirect
212. #14579141	C₂³	semidirect
213. #14579140	C₂³	semidirect
215. #14579139	C₂³	semidirect
216. #14579138	C₂³	semidirect
220. #14579134	C₂³	semidirect
222. #14579133	C₂³	semidirect
223. #14579133	C₂³	semidirect
224. #14579133	C₂³	semidirect
226. #14579132	C₂³	semidirect
227. #14579132	C₂³	semidirect
228. #14579132	C₂³	semidirect
232. C₄×Dic₁₅₈	C₂³	semidirect
233. #14579126	C₂³	semidirect
234. C₄×D₃₁₆	C₂³	semidirect
235. D₄×Dic₇₉	C₂³	semidirect
236. D₄×Dic₇₉	C₂³	semidirect
237. D₄×Dic₇₉	C₂³	semidirect
238. D₄×Dic₇₉	C₂³	semidirect
239. #14579123	C₂³	semidirect
240. #14579123	C₂³	semidirect
242. C₄×C₂²⋊D₇₉	C₂³	semidirect
243. C₄×C₂²⋊D₇₉	C₂³	semidirect
244. C₄×C₂²⋊D₇₉	C₂³	semidirect
246. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
247. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
248. #14579120	C₂³	semidirect
249. #14579120	C₂³	semidirect
253. #14579119	C₂³	semidirect
256. #14579117	C₂³	semidirect
257. #14579117	C₂³	semidirect
258. #14579117	C₂³	semidirect
276. C₂×Dic₇₉⋊C₄	C₂³	semidirect
278. C₄⋊C₄×D₇₉	C₂³	semidirect
279. C₄⋊C₄×D₇₉	C₂³	semidirect
315. C₄²×D₇₉	C₂³	semidirect
316. C₄²×D₇₉	C₂³	semidirect
326. #127×C₇₉	C₂³	semidirect
327. #125×C₇₉	C₂³	semidirect
328. #123×C₇₉	C₂³	semidirect
329. #123×C₇₉	C₂³	semidirect
331. #121×C₇₉	C₂³	semidirect
332. #121×C₇₉	C₂³	semidirect
333. #121×C₇₉	C₂³	semidirect
334. C₄×D₄×C₇₉	C₂³	semidirect
335. C₄×D₄×C₇₉	C₂³	semidirect
336. #117×C₇₉	C₂³	semidirect
419. C₂×C₄×D₇₉	#41	semidirect
620. C₄×D₇₉	C₂×#41	semidirect
675. C₂×C₇₉	#3494	semidirect
695. C₂×#540	D₇₉	semidirect
706. C₇₉	C₂×#3494	semidirect
725. #540	C₂×D₇₉	semidirect
733. C₂×#127	C₂×D₇₉	semidirect
742. C₂×#125	C₂×D₇₉	semidirect
757. C₂×#123	C₂×D₇₉	semidirect
758. C₂×#123	C₂×D₇₉	semidirect
779. C₂×#121	C₂×D₇₉	semidirect
780. C₂×#121	C₂×D₇₉	semidirect
781. C₂×#121	C₂×D₇₉	semidirect
803. C₂×C₄×D₄	C₂×D₇₉	semidirect
804. C₂×C₄×D₄	C₂×D₇₉	semidirect
817. C₂×#117	C₂×D₇₉	semidirect
883. #127	C₂²×D₇₉	semidirect
890. #125	C₂²×D₇₉	semidirect
904. #123	C₂²×D₇₉	semidirect
905. #123	C₂²×D₇₉	semidirect
925. #121	C₂²×D₇₉	semidirect
926. #121	C₂²×D₇₉	semidirect
927. #121	C₂²×D₇₉	semidirect
947. C₄×D₄	C₂²×D₇₉	semidirect
948. C₄×D₄	C₂²×D₇₉	semidirect
960. #117	C₂²×D₇₉	semidirect
1359. C₂	#23777127	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23777127	2
C₂×#19099277	2
C₂×#19099258	2
C₂×#19099256	2
C₂×#19099241	2
C₂×#19099236	2
C₂×#19099211	2
C₂×#19099210	2
C₂×#19099202	2
C₂×#19099193	2
C₂×#19099184	2
C₂×#19099180	2
C₂×#19099166	2
C₂×#19099126	2
C₂×#19099111	2
C₂×#19099110	2
C₂×#19099098	2
C₂×#19099095	2
C₂×#19099073	2
C₂×#121×D₇₉	2
C₂×#19099042	2
C₂×#19099035	2
C₂×#117×D₇₉	2
C₂×#540×C₇₉	2
C₂×#3494	79

Subgroups — C2×#23777127 #35196611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777127 #35196611