Subgroups — C₂×#23777590 #35195450

Order 20224.

8166 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777590	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099308	C₂	1	2	yes	maximal, complemented
3	C₂×#19099301	C₂	1	2	yes	maximal, complemented
4	C₂×#19099256	C₂	1	2	yes	maximal, complemented
5	C₂×#19099239	C₂	1	2	yes	maximal, complemented
6	C₂×#19099207	C₂	1	2	yes	maximal, complemented
7	C₂×#19099203	C₂	1	2	yes	maximal, complemented
8	C₂×#19099202	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×C₂²⋊D₇₉	C₂	1	2	yes	maximal, complemented
10	C₂×#19099163	C₂	1	2	yes	maximal, complemented
11	C₂×#19099160	C₂	1	2	yes	maximal, complemented
12	C₂×#19099158	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#19099150	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#19099145	C₂	1	2	yes	maximal, complemented
15	C₂×#19099140	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#19099122	C₂	1	2	yes	maximal, complemented
17	C₂×#19099121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#19099074	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#14579144	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#121×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#11929624	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#11929623	C₂²	1	2	yes	complemented
23	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
24	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
25	C₂²×D₄×D₇₉	C₂²	1	2	yes	complemented
26	#19099308	C₂²	1	32	yes	complemented
27	#19099301	C₂²	1	32	yes	complemented
28	#19099256	C₂²	1	32	yes	complemented
29	#19099239	C₂²	1	32	yes	complemented
30	#19099207	C₂²	1	32	yes	complemented
31	#19099203	C₂²	1	32	yes	complemented
32	#19099202	C₂²	1	32	yes	complemented
33	D₄×C₂²⋊D₇₉	C₂²	1	32	yes	complemented
34	#19099163	C₂²	1	32	yes	complemented
35	#19099160	C₂²	1	32	yes	complemented
36	#19099158	C₂²	1	16	yes	complemented
37	#19099150	C₂²	1	16	yes	complemented
38	#19099145	C₂²	1	32	yes	complemented
39	#19099140	C₂²	1	16	yes	complemented
40	#19099122	C₂²	1	32	yes	complemented
41	#19099121	C₂²	1	16	yes	complemented
42	C₂×#14579157	C₂²	1	2	yes	complemented
43	C₂×#14579156	C₂²	1	2	yes	complemented
44	C₂×#14579156	C₂²	1	2	yes	complemented
45	C₂×#14579154	C₂²	1	2	yes	complemented
46	C₂×#14579154	C₂²	1	2	yes	complemented
47	C₂×#14579151	C₂²	1	2	yes	complemented
48	C₂×#14579151	C₂²	1	2	yes	complemented
49	C₂×#14579148	C₂²	1	2	yes	complemented
50	C₂×#14579147	C₂²	1	2	yes	complemented
51	C₂×#14579147	C₂²	1	2	yes	complemented
52	#19099074	C₂²	1	16	yes	complemented
53	C₂×#14579146	C₂²	1	2	yes	complemented
54	C₂×#14579146	C₂²	1	2	yes	complemented
55	C₂×#14579145	C₂²	1	2	yes	complemented
56	C₂×#14579144	C₂²	1	2	yes	complemented
57	C₂×#14579144	C₂²	1	2	yes	complemented
58	C₂×#14579144	C₂²	1	2	yes	complemented
59	C₂×#14579144	C₂²	1	2	yes	complemented
60	C₂×#14579144	C₂²	1	2	yes	complemented
61	C₂×#14579144	C₂²	1	16	yes	complemented
62	C₂×#14579143	C₂²	1	2	yes	complemented
63	C₂×#14579143	C₂²	1	2	yes	complemented
64	C₂×#14579142	C₂²	1	2	yes	complemented
65	C₂×#14579142	C₂²	1	2	yes	complemented
66	C₂×#14579142	C₂²	1	2	yes	complemented
67	C₂×#14579142	C₂²	1	2	yes	complemented
68	C₂×#14579140	C₂²	1	2	yes	complemented
69	C₂×#14579140	C₂²	1	1	yes	characteristic, complemented
70	C₂×#14579140	C₂²	1	1	yes	characteristic, complemented
71	C₂×#14579139	C₂²	1	2	yes	complemented
72	C₂×#14579139	C₂²	1	2	yes	complemented
73	C₂×#14579138	C₂²	1	2	yes	complemented
74	C₂×#14579138	C₂²	1	2	yes	complemented
75	C₂×#14579135	C₂²	1	2	yes	—
76	C₂×#14579135	C₂²	1	1	yes	characteristic, complemented
77	C₂×#14579135	C₂²	1	1	yes	characteristic, complemented
78	C₂×#14579134	C₂²	1	2	yes	complemented
79	C₂×#14579134	C₂²	1	2	yes	complemented
80	C₂×#14579133	C₂²	1	2	yes	complemented
81	C₂×#14579133	C₂²	1	2	yes	complemented
82	C₂×#14579133	C₂²	1	2	yes	complemented
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×#14579133	C₂²	1	2	yes	complemented
87	C₂×#14579133	C₂²	1	2	yes	complemented
88	C₂×#14579132	C₂²	1	2	yes	complemented
89	C₂×#14579132	C₂²	1	2	yes	complemented
90	C₂×#14579131	C₂²	1	2	yes	complemented
91	C₂×#14579130	C₂²	1	2	yes	—
92	C₂×#14579130	C₂²	1	2	yes	complemented
93	C₂×#14579130	C₂²	1	2	yes	complemented
94	C₂×#14579129	C₂²	1	2	yes	complemented
95	C₂×#14579129	C₂²	1	2	yes	complemented
96	C₂×#14579129	C₂²	1	2	yes	complemented
97	C₂×#14579129	C₂²	1	2	yes	complemented
98	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
99	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
100	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
101	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
102	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
103	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
104	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
105	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
106	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
107	C₂×#14579117	C₂²	1	2	yes	complemented
108	C₂²×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	C₂²×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
110	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
111	C₂²×C₂²⋊Dic₇₉	C₂²	1	2	yes	complemented
112	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
115	C₂³×D₄×C₇₉	C₂²	1	2	yes	complemented
116	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
117	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
118	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
119	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
120	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
121	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
123	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic, complemented
124	C₂×#121×C₇₉	C₂²	1	16	yes	complemented
125	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
126	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
127	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
128	C₂⁴×D₇₉	C₂³	1	2	yes	—
129	C₂×#11929624	—	4	4	no	—
130	C₂×#11929624	C₂³	1	8	yes	complemented
131	C₂×#11929623	—	4	8	no	—
132	C₂×#11929623	C₂³	1	16	yes	complemented
133	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
135	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
136	C₂²×D₃₁₆	C₂³	1	2	yes	—
137	C₂²×C₂²⋊D₇₉	—	4	4	no	—
138	C₂²×C₂²⋊D₇₉	—	4	8	no	—
139	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
140	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
141	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
142	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
143	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
144	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
145	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
146	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
147	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
148	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
149	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
150	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
151	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
152	C₂×D₄×D₇₉	—	4	8	no	—
153	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
154	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
155	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
156	C₂³×Dic₇₉	C₂³	1	2	yes	—
157	C₂³×Dic₇₉	C₂³	1	2	yes	—
158	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
159	C₂³×Dic₇₉	C₂³	1	2	yes	—
160	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
161	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
162	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
163	#14579157	C₂³	1	16	yes	complemented
164	#14579156	C₂³	1	16	yes	complemented
165	#14579156	C₂³	1	16	yes	complemented
166	#14579154	C₂³	1	16	yes	complemented
167	#14579154	C₂³	1	16	yes	complemented
168	#14579151	C₂³	1	16	yes	complemented
169	#14579151	C₂³	1	16	yes	complemented
170	#14579148	C₂³	1	16	yes	complemented
171	#14579147	C₂³	1	16	yes	complemented
172	#14579147	C₂³	1	16	yes	complemented
173	#14579146	C₂³	1	16	yes	complemented
174	#14579146	C₂³	1	16	yes	complemented
175	#14579145	C₂³	1	16	yes	complemented
176	#14579144	C₂³	1	16	yes	complemented
177	#14579144	C₂³	1	16	yes	complemented
178	#14579144	C₂³	1	16	yes	complemented
179	#14579144	C₂³	1	16	yes	complemented
180	#14579144	C₂³	1	16	yes	complemented
181	#14579143	C₂³	1	16	yes	complemented
182	#14579143	C₂³	1	16	yes	complemented
183	#14579142	C₂³	1	16	yes	complemented
184	#14579142	C₂³	1	16	yes	complemented
185	#14579142	C₂³	1	16	yes	complemented
186	#14579142	C₂³	1	16	yes	complemented
187	#14579140	C₂³	1	8	yes	complemented
188	#14579140	C₂³	1	16	yes	complemented
189	#14579140	C₂³	1	8	yes	complemented
190	#14579139	C₂³	1	16	yes	complemented
191	#14579139	C₂³	1	16	yes	complemented
192	#14579138	C₂³	1	16	yes	complemented
193	#14579138	C₂³	1	16	yes	complemented
194	#14579135	C₂³	1	16	yes	—
195	#14579135	C₂³	1	8	yes	complemented
196	#14579135	C₂³	1	8	yes	complemented
197	#14579134	C₂³	1	16	yes	complemented
198	#14579134	C₂³	1	16	yes	complemented
199	#14579133	C₂³	1	16	yes	complemented
200	#14579133	C₂³	1	16	yes	complemented
201	#14579133	C₂³	1	16	yes	complemented
202	#14579133	C₂³	1	16	yes	complemented
203	#14579133	C₂³	1	16	yes	complemented
204	#14579133	C₂³	1	16	yes	complemented
205	#14579133	C₂³	1	16	yes	complemented
206	#14579133	C₂³	1	16	yes	complemented
207	#14579132	C₂³	1	16	yes	complemented
208	#14579132	C₂³	1	16	yes	complemented
209	#14579131	C₂³	1	16	yes	complemented
210	#14579130	C₂³	1	16	yes	—
211	#14579130	C₂³	1	16	yes	complemented
212	#14579130	C₂³	1	16	yes	complemented
213	#14579129	C₂³	1	16	yes	complemented
214	#14579129	C₂³	1	16	yes	complemented
215	#14579129	C₂³	1	16	yes	complemented
216	#14579129	C₂³	1	16	yes	complemented
217	D₄×Dic₇₉	C₂³	1	16	yes	complemented
218	D₄×Dic₇₉	C₂³	1	16	yes	complemented
219	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
220	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
221	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
222	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
223	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
224	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
225	#14579120	C₂³	1	8	yes	complemented
226	#14579117	C₂³	1	16	yes	complemented
227	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
230	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
231	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
232	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
233	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
234	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
235	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
236	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
237	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
238	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
239	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
240	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
241	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	complemented
242	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	complemented
243	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
244	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
245	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
246	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
247	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
248	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
249	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
250	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
251	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
252	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
253	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
254	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	complemented
255	C₂×C₂²⋊Dic₇₉	C₂³	1	16	yes	complemented
256	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
257	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
258	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
259	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
260	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
261	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
262	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
263	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
264	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
265	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
266	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
267	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
268	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	complemented
269	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
270	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
271	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
272	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
273	C₂⁵×C₇₉	C₂³	1	2	yes	—
274	C₂²×D₄×C₇₉	—	4	4	no	—
275	C₂²×D₄×C₇₉	—	4	8	no	—
276	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
277	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
278	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
279	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
280	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
281	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
282	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
283	C₂²×D₄×C₇₉	C₂³	1	16	yes	complemented
284	C₂²×D₄×C₇₉	C₂³	1	8	yes	complemented
285	C₂³×C₄×C₇₉	—	4	4	no	—
286	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
287	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
288	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
289	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
290	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
291	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
292	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
293	C₂³×C₄×C₇₉	C₂³	1	8	yes	complemented
294	#121×C₇₉	C₂³	1	8	yes	—
295	#121×C₇₉	C₂³	1	8	yes	complemented
296	#121×C₇₉	C₂³	1	8	yes	complemented
297	#121×C₇₉	C₂³	1	8	yes	complemented
298	#121×C₇₉	C₂³	1	16	yes	complemented
299	#121×C₇₉	C₂³	1	16	yes	complemented
300	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
303	C₂×C₄⋊C₄×C₇₉	C₂³	1	8	yes	complemented
304	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
305	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
306	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
307	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
308	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	complemented
309	C₂³×D₇₉	—	2	4	no	—
310	C₂³×D₇₉	—	4	4	no	—
311	C₂³×D₇₉	—	4	2	no	—
312	C₂³×D₇₉	—	4	4	no	—
313	C₂³×D₇₉	—	4	4	no	—
314	C₂³×D₇₉	—	4	2	no	—
315	C₂³×D₇₉	C₂⁴	1	2	yes	—
316	C₂³×D₇₉	C₂⁴	1	2	yes	—
317	C₂³×D₇₉	C₂⁴	1	4	yes	—
318	C₂³×D₇₉	C₂⁴	1	8	yes	—
319	#11929624	—	4	16	no	—
320	#11929623	—	4	32	no	—
321	C₂×Dic₁₅₈	—	4	4	no	—
322	C₂×Dic₁₅₈	—	4	2	no	—
323	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
324	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
325	C₂×D₃₁₆	—	4	2	no	—
326	C₂×D₃₁₆	—	4	4	no	—
327	C₂×D₃₁₆	C₂⁴	1	4	yes	—
328	C₂×D₃₁₆	C₂⁴	1	8	yes	—
329	C₂×C₂²⋊D₇₉	—	2	8	no	—
330	C₂×C₂²⋊D₇₉	—	2	8	no	—
331	C₂×C₂²⋊D₇₉	—	2	8	no	—
332	C₂×C₂²⋊D₇₉	—	4	16	no	—
333	C₂×C₂²⋊D₇₉	—	4	32	no	—
334	C₂×C₂²⋊D₇₉	—	4	4	no	—
335	C₂×C₂²⋊D₇₉	—	4	4	no	—
336	C₂×C₂²⋊D₇₉	—	4	4	no	—
337	C₂×C₂²⋊D₇₉	—	4	4	no	—
338	C₂×C₂²⋊D₇₉	—	4	4	no	—
339	C₂×C₂²⋊D₇₉	—	4	4	no	—
340	C₂×C₂²⋊D₇₉	—	4	4	no	—
341	C₂×C₂²⋊D₇₉	—	4	4	no	—
342	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
343	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
344	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
345	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
346	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
347	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
348	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
349	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
350	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
351	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
352	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
353	D₄×D₇₉	—	4	32	no	—
354	C₂²×Dic₇₉	—	2	4	no	—
355	C₂²×Dic₇₉	—	4	4	no	—
356	C₂²×Dic₇₉	—	4	2	no	—
357	C₂²×Dic₇₉	—	4	4	no	—
358	C₂²×Dic₇₉	—	4	2	no	—
359	C₂²×Dic₇₉	—	4	4	no	—
360	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
361	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
362	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
363	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
364	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
365	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
366	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
367	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
368	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
369	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
370	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
371	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
372	C₂×C₄×D₇₉	—	4	4	no	—
373	C₂×C₄×D₇₉	—	4	4	no	—
374	C₂×C₄×D₇₉	—	4	4	no	—
375	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
376	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
377	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
378	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
379	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
380	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
381	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
382	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
383	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
384	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
385	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
386	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
387	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
388	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
389	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
390	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
391	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
392	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
393	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
394	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
395	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
396	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
397	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
398	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
399	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
400	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
401	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
402	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
403	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
404	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
405	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
406	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
407	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
408	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
409	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
410	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
411	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
412	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
413	C₄×Dic₇₉	C₂⁴	1	8	yes	—
414	C₄×Dic₇₉	C₂⁴	1	8	yes	—
415	C₄×Dic₇₉	C₂⁴	1	8	yes	—
416	C₂⁴×C₇₉	—	2	4	no	—
417	C₂⁴×C₇₉	—	2	4	no	—
418	C₂⁴×C₇₉	—	2	8	no	—
419	C₂⁴×C₇₉	—	4	2	no	—
420	C₂⁴×C₇₉	—	4	4	no	—
421	C₂⁴×C₇₉	—	4	4	no	—
422	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
423	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
424	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
425	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
426	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
427	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
428	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
429	C₂×D₄×C₇₉	—	2	8	no	—
430	C₂×D₄×C₇₉	—	2	8	no	—
431	C₂×D₄×C₇₉	—	4	4	no	—
432	C₂×D₄×C₇₉	—	4	4	no	—
433	C₂×D₄×C₇₉	—	4	2	no	—
434	C₂×D₄×C₇₉	—	4	4	no	—
435	C₂×D₄×C₇₉	—	4	2	no	—
436	C₂×D₄×C₇₉	—	4	16	no	—
437	C₂×D₄×C₇₉	—	4	32	no	—
438	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
439	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
440	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
441	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
442	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
443	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
444	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
445	C₂²×C₄×C₇₉	—	2	4	no	—
446	C₂²×C₄×C₇₉	—	2	4	no	—
447	C₂²×C₄×C₇₉	—	4	2	no	—
448	C₂²×C₄×C₇₉	—	4	2	no	—
449	C₂²×C₄×C₇₉	—	4	2	no	—
450	C₂²×C₄×C₇₉	—	4	2	no	—
451	C₂²×C₄×C₇₉	—	4	16	no	—
452	C₂²×C₄×C₇₉	—	4	4	no	—
453	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
455	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
456	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
458	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
461	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
462	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
463	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
464	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
465	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
466	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
467	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
468	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
469	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
470	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
471	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
472	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
473	C₂³×C₇₉	—	2	2	no	—
474	C₂³×C₇₉	—	2	2	no	—
475	C₂³×C₇₉	—	2	2	no	—
476	C₂³×C₇₉	—	2	2	no	—
477	C₂³×C₇₉	—	2	4	no	—
478	C₂³×C₇₉	—	2	4	no	—
479	C₂³×C₇₉	—	2	8	no	—
480	C₂³×C₇₉	—	2	2	no	—
481	C₂³×C₇₉	—	2	4	no	—
482	C₂³×C₇₉	—	2	4	no	—
483	C₂³×C₇₉	—	2	8	no	—
484	C₂³×C₇₉	—	2	2	no	—
485	C₂³×C₇₉	—	2	4	no	—
486	C₂³×C₇₉	—	2	2	no	—
487	C₂³×C₇₉	—	2	4	no	—
488	C₂³×C₇₉	—	2	16	no	—
489	C₂³×C₇₉	—	4	4	no	—
490	C₂³×C₇₉	—	4	8	no	—
491	C₂³×C₇₉	—	4	8	no	—
492	C₂³×C₇₉	—	4	16	no	—
493	C₂³×C₇₉	—	8	16	no	—
494	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
495	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
496	C₂³×C₇₉	C₂⁵	1	4	yes	—
497	C₂³×C₇₉	C₂⁵	1	2	yes	—
498	C₂³×C₇₉	C₂⁵	1	4	yes	—
499	C₂³×C₇₉	C₂⁵	1	2	yes	—
500	C₂³×C₇₉	C₂⁵	1	2	yes	—
501	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
502	C₂²×D₇₉	—	2	4	no	—
503	C₂²×D₇₉	—	2	4	no	—
504	C₂²×D₇₉	—	2	4	no	—
505	C₂²×D₇₉	—	2	4	no	—
506	C₂²×D₇₉	—	2	4	no	—
507	C₂²×D₇₉	—	2	4	no	—
508	C₂²×D₇₉	—	2	8	no	—
509	C₂²×D₇₉	—	4	8	no	—
510	C₂²×D₇₉	—	4	4	no	—
511	C₂²×D₇₉	—	4	8	no	—
512	C₂²×D₇₉	—	4	8	no	—
513	C₂²×D₇₉	—	4	4	no	—
514	C₂²×D₇₉	—	8	8	no	—
515	C₂²×D₇₉	—	8	16	no	—
516	C₂²×D₇₉	C₂⁵	1	4	yes	—
517	C₂²×D₇₉	C₂⁵	1	4	yes	—
518	D₄×C₇₉	—	2	16	no	—
519	D₄×C₇₉	—	2	16	no	—
520	D₄×C₇₉	—	4	4	no	—
521	D₄×C₇₉	—	4	8	no	—
522	D₄×C₇₉	—	4	4	no	—
523	D₄×C₇₉	—	4	8	no	—
524	D₄×C₇₉	—	4	8	no	—
525	C₂×C₄×C₇₉	—	2	2	no	—
526	C₂×C₄×C₇₉	—	2	4	no	—
527	C₂×C₄×C₇₉	—	2	4	no	—
528	C₂×C₄×C₇₉	—	2	2	no	—
529	C₂×C₄×C₇₉	—	2	8	no	—
530	C₂×C₄×C₇₉	—	2	8	no	—
531	C₂×C₄×C₇₉	—	2	2	no	—
532	C₂×C₄×C₇₉	—	2	2	no	—
533	C₂×C₄×C₇₉	—	4	4	no	—
534	C₂×C₄×C₇₉	—	4	4	no	—
535	C₂×C₄×C₇₉	—	4	4	no	—
536	C₂×C₄×C₇₉	—	4	4	no	—
537	C₂×C₄×C₇₉	—	4	8	no	—
538	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
539	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
540	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
541	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
542	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
543	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
544	C₂²⋊D₇₉	—	2	16	no	—
545	C₂²⋊D₇₉	—	2	16	no	—
546	C₂²⋊D₇₉	—	2	16	no	—
547	C₂²⋊D₇₉	—	4	8	no	—
548	C₂²⋊D₇₉	—	4	8	no	—
549	C₂²⋊D₇₉	—	4	8	no	—
550	C₂²⋊D₇₉	—	4	8	no	—
551	C₂²⋊D₇₉	—	4	8	no	—
552	C₂²⋊D₇₉	—	4	8	no	—
553	C₂²⋊D₇₉	—	4	8	no	—
554	C₂²⋊D₇₉	—	4	8	no	—
555	C₂×Dic₇₉	—	2	4	no	—
556	C₂×Dic₇₉	—	2	4	no	—
557	C₂×Dic₇₉	—	2	4	no	—
558	C₂×Dic₇₉	—	2	8	no	—
559	C₂×Dic₇₉	—	2	4	no	—
560	C₂×Dic₇₉	—	2	4	no	—
561	C₂×Dic₇₉	—	2	4	no	—
562	C₂×Dic₇₉	—	4	8	no	—
563	C₂×Dic₇₉	—	4	4	no	—
564	C₂×Dic₇₉	—	4	4	no	—
565	C₂×Dic₇₉	—	4	8	no	—
566	C₂×Dic₇₉	—	4	8	no	—
567	C₂×Dic₇₉	C₂⁵	1	4	yes	—
568	C₂×Dic₇₉	C₂⁵	1	4	yes	—
569	C₂×Dic₇₉	C₂⁵	1	4	yes	—
570	C₂×Dic₇₉	C₂⁵	1	4	yes	—
571	C₂×Dic₇₉	C₂⁵	1	4	yes	—
572	C₂×Dic₇₉	C₂⁵	1	4	yes	—
573	D₃₁₆	—	4	8	no	—
574	D₃₁₆	—	4	4	no	—
575	C₄×D₇₉	—	4	8	no	—
576	C₄×D₇₉	—	4	8	no	—
577	C₄×D₇₉	—	4	8	no	—
578	Dic₁₅₈	—	4	8	no	—
579	Dic₁₅₈	—	4	4	no	—
580	C₂²×C₇₉	—	2	2	no	—
581	C₂²×C₇₉	—	2	2	no	—
582	C₂²×C₇₉	—	2	2	no	—
583	C₂²×C₇₉	—	2	2	no	—
584	C₂²×C₇₉	—	2	8	no	—
585	C₂²×C₇₉	—	2	8	no	—
586	C₂²×C₇₉	—	2	2	no	—
587	C₂²×C₇₉	—	2	4	no	—
588	C₂²×C₇₉	—	2	4	no	—
589	C₂²×C₇₉	—	2	4	no	—
590	C₂²×C₇₉	—	2	2	no	—
591	C₂²×C₇₉	—	2	4	no	—
592	C₂²×C₇₉	—	2	2	no	—
593	C₂²×C₇₉	—	2	4	no	—
594	C₂²×C₇₉	—	2	4	no	—
595	C₂²×C₇₉	—	4	16	no	—
596	C₂²×C₇₉	—	4	8	no	—
597	C₂²×C₇₉	—	4	4	no	—
598	C₂²×C₇₉	—	4	8	no	—
599	C₂²×C₇₉	—	8	16	no	—
600	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
601	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
602	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
603	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
604	C₂²×C₇₉	#585	1	2	yes	—
605	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
606	C₂×D₇₉	—	2	4	no	—
607	C₂×D₇₉	—	2	4	no	—
608	C₂×D₇₉	—	2	4	no	—
609	C₂×D₇₉	—	2	4	no	—
610	C₂×D₇₉	—	2	4	no	—
611	C₂×D₇₉	—	2	4	no	—
612	C₂×D₇₉	—	4	8	no	—
613	C₂×D₇₉	—	4	8	no	—
614	C₂×D₇₉	—	8	8	no	—
615	C₂×D₇₉	—	8	16	no	—
616	C₄×C₇₉	—	2	2	no	—
617	C₄×C₇₉	—	2	2	no	—
618	C₄×C₇₉	—	2	2	no	—
619	C₄×C₇₉	—	2	2	no	—
620	C₄×C₇₉	—	2	4	no	—
621	C₄×C₇₉	—	2	4	no	—
622	Dic₇₉	—	2	4	no	—
623	Dic₇₉	—	2	4	no	—
624	Dic₇₉	—	2	4	no	—
625	Dic₇₉	—	2	4	no	—
626	Dic₇₉	—	2	4	no	—
627	Dic₇₉	—	2	4	no	—
628	C₂×#3534	—	79	1	no	maximal, Sylow
629	C₂×C₇₉	—	2	4	no	—
630	C₂×C₇₉	—	2	4	no	—
631	C₂×C₇₉	—	4	4	no	—
632	C₂×C₇₉	—	4	2	no	—
633	C₂×C₇₉	—	4	4	no	—
634	C₂×C₇₉	#3534	1	4	yes	complemented
635	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
636	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
637	C₂×C₇₉	C₂×#585	1	1	yes	characteristic
638	D₇₉	—	4	4	no	—
639	D₇₉	—	4	4	no	—
640	#3534	—	79	32	no	—
641	C₂×#562	—	79	2	no	—
642	C₂×#560	—	79	2	no	—
643	C₂×#553	—	79	2	no	—
644	C₂×#551	—	79	2	no	—
645	C₂×#546	—	79	2	no	—
646	C₂×#546	—	79	2	no	—
647	C₂×#546	—	79	2	no	—
648	C₂×D₄²	—	79	2	no	—
649	C₂×#540	—	79	2	no	—
650	C₂×#539	—	79	1	no	—
651	C₂×#539	—	79	2	no	—
652	C₂×#538	—	79	2	no	—
653	C₂×#538	—	79	1	no	—
654	C₂×#537	—	79	1	no	—
655	C₂×#534	—	79	2	no	—
656	C₂×#534	—	79	1	no	—
657	C₂×#525	—	79	1	no	—
658	C₂²×#123	—	79	1	no	—
659	C₂²×#121	D₇₉	1	1	yes	characteristic, complemented
660	C₇₉	C₂×#3534	1	1	yes	characteristic, complemented, Sylow
661	C₂²×#41	—	79	2	no	—
662	C₂²×#41	—	79	1	no	—
663	C₂³×D₄	—	79	1	no	—
664	C₂³×D₄	—	79	2	no	—
665	C₂³×D₄	—	79	2	no	—
666	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
667	C₂³×D₄	C₂×D₇₉	1	2	yes	complemented
668	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
669	#562	—	79	32	no	—
670	#560	—	79	32	no	—
671	#553	—	79	32	no	—
672	#551	—	79	32	no	—
673	#546	—	79	32	no	—
674	#546	—	79	32	no	—
675	#546	—	79	32	no	—
676	D₄²	—	79	32	no	—
677	#540	—	79	32	no	—
678	#539	—	79	16	no	—
679	#539	—	79	32	no	—
680	#538	—	79	32	no	—
681	#538	—	79	16	no	—
682	#537	—	79	16	no	—
683	#534	—	79	32	no	—
684	#534	—	79	16	no	—
685	C₂×#127	—	79	2	no	—
686	C₂×#126	—	79	2	no	—
687	C₂×#126	—	79	2	no	—
688	C₂×#126	—	79	2	no	—
689	C₂×#126	—	79	2	no	—
690	C₂×#125	—	79	2	no	—
691	C₂×#125	—	79	2	no	—
692	C₂×#124	—	79	2	no	—
693	C₂×#124	—	79	2	no	—
694	C₂×#124	—	79	2	no	—
695	#525	—	79	16	no	—
696	C₂×#123	—	79	2	no	—
697	C₂×#123	—	79	2	no	—
698	C₂×#123	—	79	2	no	—
699	C₂×#123	—	79	2	no	—
700	C₂×#123	—	79	2	no	—
701	C₂×#123	—	79	2	no	—
702	C₂×#123	—	79	2	no	—
703	C₂×#123	—	79	2	no	—
704	C₂×#123	—	79	2	no	—
705	C₂×#123	—	79	16	no	—
706	C₂×#123	—	79	2	no	—
707	C₂×#123	—	79	2	no	—
708	C₂×#123	—	79	2	no	—
709	C₂×#123	—	79	2	no	—
710	C₂×#123	—	79	2	no	—
711	C₂×C₂²⋊Q₈	—	79	1	no	—
712	C₂×C₂²⋊Q₈	—	79	1	no	—
713	C₂×C₂²⋊Q₈	—	79	2	no	—
714	C₂×C₂²⋊Q₈	—	79	2	no	—
715	C₂×C₂²⋊Q₈	—	79	2	no	—
716	C₂×C₂²⋊Q₈	—	79	2	no	—
717	C₂×C₂²⋊Q₈	—	79	2	no	—
718	C₂×#121	—	79	2	no	—
719	C₂×#121	—	79	2	no	—
720	C₂×#121	—	79	2	no	—
721	C₂×#121	—	79	2	no	—
722	C₂×#121	—	79	2	no	—
723	C₂×#121	—	79	2	no	—
724	C₂×#121	—	79	2	no	—
725	C₂×#121	—	79	2	no	—
726	C₂×#121	—	79	2	no	—
727	C₂×#121	—	79	2	no	—
728	C₂×#121	—	79	1	no	—
729	C₂×#121	—	79	1	no	—
730	C₂×#121	—	79	2	no	—
731	C₂×#121	—	79	2	no	—
732	C₂×#121	—	79	2	no	—
733	C₂×#121	C₂×D₇₉	1	1	yes	characteristic
734	C₂×#121	C₂×D₇₉	1	1	yes	characteristic, complemented
735	C₂×#121	C₂×D₇₉	1	1	yes	characteristic, complemented
736	C₂×#121	C₂×D₇₉	1	1	yes	characteristic, complemented
737	C₂×#121	C₂×D₇₉	1	2	yes	complemented
738	C₂×#121	C₂×D₇₉	1	2	yes	complemented
739	C₂×#121	C₂×D₇₉	1	16	yes	complemented
740	C₂×#120	—	79	2	no	—
741	C₂×#120	—	79	2	no	—
742	C₂×#120	—	79	2	no	—
743	C₂×#120	—	79	2	no	—
744	C₂×#120	—	79	2	no	—
745	C₂×#120	—	79	2	no	—
746	C₂×#120	—	79	2	no	—
747	C₂×#120	—	79	2	no	—
748	C₂×C₄×D₄	—	79	2	no	—
749	C₂×C₄×D₄	—	79	2	no	—
750	C₂×C₄×D₄	—	79	2	no	—
751	C₂×C₄×D₄	—	79	2	no	—
752	C₂×C₄×D₄	—	79	2	no	—
753	C₂×C₄×D₄	—	79	2	no	—
754	C₂×C₄×D₄	—	79	2	no	—
755	C₂×C₄×D₄	—	79	2	no	—
756	C₂×#117	—	79	1	no	—
757	C₂×#117	—	79	2	no	—
758	C₂²×C₄⋊C₄	—	79	1	no	—
759	C₂²×C₄⋊C₄	—	79	1	no	—
760	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
761	C₂²×C₂²⋊C₄	—	79	1	no	—
762	C₂²×C₂²⋊C₄	—	79	2	no	—
763	C₂²×C₂²⋊C₄	—	79	1	no	—
764	C₂²×C₂²⋊C₄	—	79	1	no	—
765	C₂²×C₂²⋊C₄	—	79	2	no	—
766	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
767	C₂⁵	—	79	2	no	—
768	C₂⁵	—	79	1	no	—
769	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
770	C₂⁵	C₂²×D₇₉	1	2	yes	—
771	C₂×#41	—	316	4	no	—
772	C₂×#41	—	316	8	no	—
773	C₂×#41	—	79	16	no	—
774	C₂×#41	—	79	8	no	—
775	C₂²×Q₈	—	79	1	no	—
776	C₂²×Q₈	—	79	2	no	—
777	C₂²×D₄	—	4	4	no	—
778	C₂²×D₄	—	4	8	no	—
779	C₂²×D₄	—	316	8	no	—
780	C₂²×D₄	—	316	4	no	—
781	C₂²×D₄	—	316	8	no	—
782	C₂²×D₄	—	79	2	no	—
783	C₂²×D₄	—	79	2	no	—
784	C₂²×D₄	—	79	2	no	—
785	C₂²×D₄	—	79	2	no	—
786	C₂²×D₄	—	79	2	no	—
787	C₂²×D₄	—	79	2	no	—
788	C₂²×D₄	—	79	2	no	—
789	C₂²×D₄	—	79	2	no	—
790	C₂²×D₄	—	79	8	no	—
791	C₂²×D₄	—	79	16	no	—
792	C₂²×D₄	—	79	16	no	—
793	C₂²×D₄	—	79	2	no	—
794	C₂²×D₄	—	79	2	no	—
795	C₂²×D₄	—	79	2	no	—
796	C₂²×D₄	—	79	1	no	—
797	C₂²×D₄	—	79	2	no	—
798	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
799	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
800	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
801	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
802	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
803	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
804	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
805	C₂²×D₄	C₂²×D₇₉	1	8	yes	complemented
806	C₂²×D₄	C₂²×D₇₉	1	16	yes	complemented
807	C₂³×C₄	—	4	4	no	—
808	C₂³×C₄	—	79	1	no	—
809	C₂³×C₄	—	79	2	no	—
810	C₂³×C₄	—	79	2	no	—
811	C₂³×C₄	—	79	1	no	—
812	C₂³×C₄	—	79	2	no	—
813	C₂³×C₄	—	79	2	no	—
814	C₂³×C₄	—	79	2	no	—
815	C₂³×C₄	—	79	2	no	—
816	C₂³×C₄	—	79	1	no	—
817	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
818	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
819	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
820	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
821	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
822	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
823	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
824	C₂³×C₄	C₂²×D₇₉	1	8	yes	complemented
825	#127	—	79	16	no	—
826	#126	—	79	16	no	—
827	#126	—	79	16	no	—
828	#126	—	79	16	no	—
829	#126	—	79	16	no	—
830	#125	—	79	16	no	—
831	#125	—	79	16	no	—
832	#124	—	79	16	no	—
833	#124	—	79	16	no	—
834	#124	—	79	16	no	—
835	#123	—	79	16	no	—
836	#123	—	79	16	no	—
837	#123	—	79	16	no	—
838	#123	—	79	16	no	—
839	#123	—	79	16	no	—
840	#123	—	79	16	no	—
841	#123	—	79	16	no	—
842	#123	—	79	16	no	—
843	#123	—	79	16	no	—
844	#123	—	79	16	no	—
845	#123	—	79	16	no	—
846	#123	—	79	16	no	—
847	#123	—	79	16	no	—
848	#123	—	79	16	no	—
849	C₂²⋊Q₈	—	79	8	no	—
850	C₂²⋊Q₈	—	79	8	no	—
851	C₂²⋊Q₈	—	79	16	no	—
852	C₂²⋊Q₈	—	79	16	no	—
853	C₂²⋊Q₈	—	79	16	no	—
854	C₂²⋊Q₈	—	79	16	no	—
855	C₂²⋊Q₈	—	79	16	no	—
856	#121	—	79	16	no	—
857	#121	—	79	16	no	—
858	#121	—	79	16	no	—
859	#121	—	79	16	no	—
860	#121	—	79	16	no	—
861	#121	—	79	16	no	—
862	#121	—	79	16	no	—
863	#121	—	79	16	no	—
864	#121	—	79	16	no	—
865	#121	—	79	16	no	—
866	#121	—	79	8	no	—
867	#121	—	79	8	no	—
868	#121	—	79	16	no	—
869	#121	—	79	16	no	—
870	#121	—	79	16	no	—
871	#121	C₂²×D₇₉	1	8	yes	—
872	#121	C₂²×D₇₉	1	8	yes	complemented
873	#121	C₂²×D₇₉	1	8	yes	complemented
874	#121	C₂²×D₇₉	1	8	yes	complemented
875	#121	C₂²×D₇₉	1	16	yes	complemented
876	#121	C₂²×D₇₉	1	16	yes	complemented
877	#120	—	79	16	no	—
878	#120	—	79	16	no	—
879	#120	—	79	16	no	—
880	#120	—	79	16	no	—
881	#120	—	79	16	no	—
882	#120	—	79	16	no	—
883	#120	—	79	16	no	—
884	#120	—	79	16	no	—
885	C₄×D₄	—	79	16	no	—
886	C₄×D₄	—	79	16	no	—
887	C₄×D₄	—	79	16	no	—
888	C₄×D₄	—	79	16	no	—
889	C₄×D₄	—	79	16	no	—
890	C₄×D₄	—	79	16	no	—
891	C₄×D₄	—	79	16	no	—
892	C₄×D₄	—	79	16	no	—
893	#117	—	79	8	no	—
894	#117	—	79	16	no	—
895	C₂×C₄⋊C₄	—	79	2	no	—
896	C₂×C₄⋊C₄	—	79	2	no	—
897	C₂×C₄⋊C₄	—	79	2	no	—
898	C₂×C₄⋊C₄	—	79	2	no	—
899	C₂×C₄⋊C₄	—	79	8	no	—
900	C₂×C₄⋊C₄	—	79	8	no	—
901	C₂×C₄⋊C₄	—	79	1	no	—
902	C₂×C₄⋊C₄	—	79	2	no	—
903	C₂×C₄⋊C₄	—	79	1	no	—
904	C₂×C₄⋊C₄	—	79	2	no	—
905	C₂×C₄⋊C₄	—	79	2	no	—
906	C₂×C₄⋊C₄	—	79	2	no	—
907	C₂×C₄⋊C₄	—	79	2	no	—
908	C₂×C₄⋊C₄	—	79	2	no	—
909	C₂×C₄⋊C₄	—	79	2	no	—
910	C₂×C₄⋊C₄	—	79	2	no	—
911	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
912	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
913	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
914	C₂×C₄⋊C₄	C₂²×D₇₉	1	8	yes	complemented
915	C₂×C₂²⋊C₄	—	79	2	no	—
916	C₂×C₂²⋊C₄	—	79	2	no	—
917	C₂×C₂²⋊C₄	—	79	2	no	—
918	C₂×C₂²⋊C₄	—	79	2	no	—
919	C₂×C₂²⋊C₄	—	79	2	no	—
920	C₂×C₂²⋊C₄	—	79	2	no	—
921	C₂×C₂²⋊C₄	—	79	8	no	—
922	C₂×C₂²⋊C₄	—	79	16	no	—
923	C₂×C₂²⋊C₄	—	79	2	no	—
924	C₂×C₂²⋊C₄	—	79	2	no	—
925	C₂×C₂²⋊C₄	—	79	2	no	—
926	C₂×C₂²⋊C₄	—	79	2	no	—
927	C₂×C₂²⋊C₄	—	79	2	no	—
928	C₂×C₂²⋊C₄	—	79	2	no	—
929	C₂×C₂²⋊C₄	—	79	2	no	—
930	C₂×C₂²⋊C₄	—	79	2	no	—
931	C₂×C₂²⋊C₄	—	79	2	no	—
932	C₂×C₂²⋊C₄	—	79	2	no	—
933	C₂×C₂²⋊C₄	—	79	8	no	—
934	C₂×C₂²⋊C₄	—	79	8	no	—
935	C₂×C₂²⋊C₄	—	79	2	no	—
936	C₂×C₂²⋊C₄	—	79	2	no	—
937	C₂×C₂²⋊C₄	—	79	2	no	—
938	C₂×C₂²⋊C₄	—	79	2	no	—
939	C₂×C₂²⋊C₄	—	79	2	no	—
940	C₂×C₂²⋊C₄	—	79	16	no	—
941	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
942	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
943	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
944	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
945	C₂×C₂²⋊C₄	C₂²×D₇₉	1	16	yes	complemented
946	C₂×C₄²	—	79	2	no	—
947	C₂×C₄²	—	79	2	no	—
948	C₂×C₄²	—	79	2	no	—
949	C₂⁴	—	2	4	no	—
950	C₂⁴	—	2	4	no	—
951	C₂⁴	—	2	8	no	—
952	C₂⁴	—	4	2	no	—
953	C₂⁴	—	4	4	no	—
954	C₂⁴	—	4	4	no	—
955	C₂⁴	—	316	2	no	—
956	C₂⁴	—	316	4	no	—
957	C₂⁴	—	316	4	no	—
958	C₂⁴	—	316	2	no	—
959	C₂⁴	—	316	4	no	—
960	C₂⁴	—	79	8	no	—
961	C₂⁴	—	79	4	no	—
962	C₂⁴	—	79	2	no	—
963	C₂⁴	—	79	2	no	—
964	C₂⁴	—	158	4	no	—
965	C₂⁴	C₂³×D₇₉	1	2	yes	—
966	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
967	C₂⁴	C₂³×D₇₉	1	2	yes	—
968	C₂⁴	C₂³×D₇₉	1	4	yes	—
969	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
970	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
971	C₂⁴	C₂³×D₇₉	1	8	yes	—
972	#41	—	316	16	no	—
973	#41	—	316	32	no	—
974	C₂×Q₈	—	316	2	no	—
975	C₂×Q₈	—	316	4	no	—
976	C₂×Q₈	—	79	4	no	—
977	C₂×Q₈	—	79	8	no	—
978	C₂×D₄	—	2	8	no	—
979	C₂×D₄	—	2	8	no	—
980	C₂×D₄	—	4	2	no	—
981	C₂×D₄	—	4	4	no	—
982	C₂×D₄	—	4	2	no	—
983	C₂×D₄	—	4	4	no	—
984	C₂×D₄	—	4	4	no	—
985	C₂×D₄	—	4	16	no	—
986	C₂×D₄	—	4	32	no	—
987	C₂×D₄	—	316	4	no	—
988	C₂×D₄	—	316	2	no	—
989	C₂×D₄	—	316	32	no	—
990	C₂×D₄	—	316	16	no	—
991	C₂×D₄	—	316	32	no	—
992	C₂×D₄	—	316	4	no	—
993	C₂×D₄	—	316	4	no	—
994	C₂×D₄	—	316	4	no	—
995	C₂×D₄	—	316	4	no	—
996	C₂×D₄	—	316	4	no	—
997	C₂×D₄	—	316	4	no	—
998	C₂×D₄	—	316	4	no	—
999	C₂×D₄	—	316	4	no	—
1000	C₂×D₄	—	79	8	no	—
1001	C₂×D₄	—	79	8	no	—
1002	C₂×D₄	—	79	8	no	—
1003	C₂×D₄	—	79	8	no	—
1004	C₂×D₄	—	79	8	no	—
1005	C₂×D₄	—	79	8	no	—
1006	C₂×D₄	—	79	8	no	—
1007	C₂×D₄	—	79	8	no	—
1008	C₂×D₄	—	79	8	no	—
1009	C₂×D₄	—	79	8	no	—
1010	C₂×D₄	—	79	8	no	—
1011	C₂×D₄	—	79	4	no	—
1012	C₂×D₄	—	79	8	no	—
1013	C₂×D₄	—	158	8	no	—
1014	C₂×D₄	—	158	8	no	—
1015	C₂×D₄	—	158	8	no	—
1016	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1017	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1018	C₂×D₄	C₂³×D₇₉	1	4	yes	—
1019	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1020	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1021	C₂×D₄	C₂³×D₇₉	1	4	yes	—
1022	C₂×D₄	C₂³×D₇₉	1	8	yes	—
1023	C₂²×C₄	—	2	4	no	—
1024	C₂²×C₄	—	2	4	no	—
1025	C₂²×C₄	—	4	2	no	—
1026	C₂²×C₄	—	4	2	no	—
1027	C₂²×C₄	—	4	2	no	—
1028	C₂²×C₄	—	4	2	no	—
1029	C₂²×C₄	—	4	16	no	—
1030	C₂²×C₄	—	4	4	no	—
1031	C₂²×C₄	—	316	4	no	—
1032	C₂²×C₄	—	316	4	no	—
1033	C₂²×C₄	—	316	4	no	—
1034	C₂²×C₄	—	316	2	no	—
1035	C₂²×C₄	—	316	4	no	—
1036	C₂²×C₄	—	316	2	no	—
1037	C₂²×C₄	—	316	4	no	—
1038	C₂²×C₄	—	316	4	no	—
1039	C₂²×C₄	—	79	4	no	—
1040	C₂²×C₄	—	79	8	no	—
1041	C₂²×C₄	—	79	8	no	—
1042	C₂²×C₄	—	79	4	no	—
1043	C₂²×C₄	—	79	8	no	—
1044	C₂²×C₄	—	79	8	no	—
1045	C₂²×C₄	—	79	8	no	—
1046	C₂²×C₄	—	79	8	no	—
1047	C₂²×C₄	—	79	4	no	—
1048	C₂²×C₄	—	79	2	no	—
1049	C₂²×C₄	—	79	2	no	—
1050	C₂²×C₄	—	79	2	no	—
1051	C₂²×C₄	—	79	2	no	—
1052	C₂²×C₄	—	79	2	no	—
1053	C₂²×C₄	—	79	2	no	—
1054	C₂²×C₄	—	158	4	no	—
1055	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
1056	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
1057	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1058	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
1059	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
1060	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1061	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1062	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
1063	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
1064	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
1065	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
1066	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
1067	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
1068	C₄⋊C₄	—	79	8	no	—
1069	C₄⋊C₄	—	79	8	no	—
1070	C₄⋊C₄	—	79	8	no	—
1071	C₄⋊C₄	—	79	8	no	—
1072	C₄⋊C₄	—	79	8	no	—
1073	C₄⋊C₄	—	79	8	no	—
1074	C₄⋊C₄	—	79	8	no	—
1075	C₄⋊C₄	—	79	8	no	—
1076	C₄⋊C₄	—	79	8	no	—
1077	C₄⋊C₄	—	79	8	no	—
1078	C₄⋊C₄	—	79	4	no	—
1079	C₄⋊C₄	—	79	4	no	—
1080	C₄⋊C₄	—	79	8	no	—
1081	C₄⋊C₄	—	79	8	no	—
1082	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
1083	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
1084	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
1085	C₂²⋊C₄	—	79	8	no	—
1086	C₂²⋊C₄	—	79	8	no	—
1087	C₂²⋊C₄	—	79	8	no	—
1088	C₂²⋊C₄	—	79	8	no	—
1089	C₂²⋊C₄	—	79	8	no	—
1090	C₂²⋊C₄	—	79	8	no	—
1091	C₂²⋊C₄	—	79	8	no	—
1092	C₂²⋊C₄	—	79	8	no	—
1093	C₂²⋊C₄	—	79	8	no	—
1094	C₂²⋊C₄	—	79	8	no	—
1095	C₂²⋊C₄	—	79	8	no	—
1096	C₂²⋊C₄	—	79	8	no	—
1097	C₂²⋊C₄	—	79	8	no	—
1098	C₂²⋊C₄	—	79	8	no	—
1099	C₂²⋊C₄	—	79	8	no	—
1100	C₂²⋊C₄	—	79	8	no	—
1101	C₂²⋊C₄	—	79	8	no	—
1102	C₂²⋊C₄	—	79	8	no	—
1103	C₂²⋊C₄	—	79	8	no	—
1104	C₂²⋊C₄	—	79	8	no	—
1105	C₂²⋊C₄	—	79	8	no	—
1106	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
1107	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
1108	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
1109	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
1110	C₄²	—	79	8	no	—
1111	C₄²	—	79	8	no	—
1112	C₄²	—	79	8	no	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	2	no	—
1115	C₂³	—	2	2	no	—
1116	C₂³	—	2	2	no	—
1117	C₂³	—	2	8	no	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	2	4	no	—
1120	C₂³	—	2	4	no	—
1121	C₂³	—	2	4	no	—
1122	C₂³	—	2	8	no	—
1123	C₂³	—	2	2	no	—
1124	C₂³	—	2	4	no	—
1125	C₂³	—	2	4	no	—
1126	C₂³	—	2	2	no	—
1127	C₂³	—	2	4	no	—
1128	C₂³	—	2	16	no	—
1129	C₂³	—	4	4	no	—
1130	C₂³	—	4	8	no	—
1131	C₂³	—	4	8	no	—
1132	C₂³	—	4	16	no	—
1133	C₂³	—	8	16	no	—
1134	C₂³	—	316	4	no	—
1135	C₂³	—	316	8	no	—
1136	C₂³	—	316	8	no	—
1137	C₂³	—	316	4	no	—
1138	C₂³	—	316	8	no	—
1139	C₂³	—	79	4	no	—
1140	C₂³	—	79	4	no	—
1141	C₂³	—	632	8	no	—
1142	C₂³	—	632	16	no	—
1143	C₂³	—	158	4	no	—
1144	C₂³	—	158	4	no	—
1145	C₂³	—	158	4	no	—
1146	C₂³	—	158	4	no	—
1147	C₂³	—	158	4	no	—
1148	C₂³	—	158	4	no	—
1149	C₂³	—	158	8	no	—
1150	C₂³	#14579206	1	4	yes	—
1151	C₂³	#14579206	1	4	yes	—
1152	C₂³	C₂⁴×D₇₉	1	4	yes	—
1153	C₂³	C₂⁴×D₇₉	1	2	yes	—
1154	C₂³	C₂⁴×D₇₉	1	4	yes	—
1155	C₂³	C₂⁴×D₇₉	1	2	yes	—
1156	C₂³	C₂⁴×D₇₉	1	2	yes	—
1157	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
1158	Q₈	—	316	4	no	—
1159	Q₈	—	316	8	no	—
1160	D₄	—	2	16	no	—
1161	D₄	—	2	16	no	—
1162	D₄	—	4	4	no	—
1163	D₄	—	4	8	no	—
1164	D₄	—	4	4	no	—
1165	D₄	—	4	8	no	—
1166	D₄	—	4	8	no	—
1167	D₄	—	316	8	no	—
1168	D₄	—	316	4	no	—
1169	D₄	—	316	8	no	—
1170	D₄	—	316	8	no	—
1171	D₄	—	316	8	no	—
1172	D₄	—	316	8	no	—
1173	D₄	—	316	8	no	—
1174	D₄	—	316	8	no	—
1175	D₄	—	316	8	no	—
1176	D₄	—	316	8	no	—
1177	D₄	—	158	16	no	—
1178	D₄	—	158	16	no	—
1179	D₄	—	158	16	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	8	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	8	no	—
1186	C₂×C₄	—	2	4	no	—
1187	C₂×C₄	—	2	4	no	—
1188	C₂×C₄	—	4	4	no	—
1189	C₂×C₄	—	4	4	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	4	no	—
1192	C₂×C₄	—	4	8	no	—
1193	C₂×C₄	—	316	8	no	—
1194	C₂×C₄	—	316	8	no	—
1195	C₂×C₄	—	316	8	no	—
1196	C₂×C₄	—	316	4	no	—
1197	C₂×C₄	—	316	8	no	—
1198	C₂×C₄	—	316	8	no	—
1199	C₂×C₄	—	316	4	no	—
1200	C₂×C₄	—	316	8	no	—
1201	C₂×C₄	—	79	4	no	—
1202	C₂×C₄	—	79	4	no	—
1203	C₂×C₄	—	79	4	no	—
1204	C₂×C₄	—	79	4	no	—
1205	C₂×C₄	—	79	4	no	—
1206	C₂×C₄	—	79	4	no	—
1207	C₂×C₄	—	158	4	no	—
1208	C₂×C₄	—	158	4	no	—
1209	C₂×C₄	—	158	4	no	—
1210	C₂×C₄	—	158	4	no	—
1211	C₂×C₄	—	158	8	no	—
1212	C₂×C₄	—	158	4	no	—
1213	C₂×C₄	—	158	4	no	—
1214	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1215	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
1216	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
1217	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1218	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1219	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1220	C₂²	—	2	8	no	—
1221	C₂²	—	2	8	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	4	no	—
1228	C₂²	—	2	4	no	—
1229	C₂²	—	2	4	no	—
1230	C₂²	—	2	2	no	—
1231	C₂²	—	2	4	no	—
1232	C₂²	—	2	4	no	—
1233	C₂²	—	2	2	no	—
1234	C₂²	—	2	4	no	—
1235	C₂²	—	4	16	no	—
1236	C₂²	—	4	4	no	—
1237	C₂²	—	4	8	no	—
1238	C₂²	—	4	8	no	—
1239	C₂²	—	8	16	no	—
1240	C₂²	—	316	8	no	—
1241	C₂²	—	316	8	no	—
1242	C₂²	—	632	8	no	—
1243	C₂²	—	632	16	no	—
1244	C₂²	—	158	4	no	—
1245	C₂²	—	158	4	no	—
1246	C₂²	—	158	4	no	—
1247	C₂²	—	158	4	no	—
1248	C₂²	—	158	4	no	—
1249	C₂²	—	158	4	no	—
1250	C₂²	C₂×#14579206	1	4	yes	—
1251	C₂²	C₂×#14579206	1	4	yes	—
1252	C₂²	C₂×#14579206	1	2	yes	—
1253	C₂²	C₂×#14579206	1	2	yes	—
1254	C₂²	#19099399	1	2	yes	—
1255	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
1256	C₄	—	2	2	no	—
1257	C₄	—	2	2	no	—
1258	C₄	—	2	2	no	—
1259	C₄	—	2	2	no	—
1260	C₄	—	2	4	no	—
1261	C₄	—	2	4	no	—
1262	C₄	—	158	4	no	—
1263	C₄	—	158	4	no	—
1264	C₄	—	158	4	no	—
1265	C₄	—	158	4	no	—
1266	C₄	—	158	4	no	—
1267	C₄	—	158	4	no	—
1268	C₂	—	2	4	no	—
1269	C₂	—	2	4	no	—
1270	C₂	—	4	2	no	—
1271	C₂	—	4	4	no	—
1272	C₂	—	4	4	no	—
1273	C₂	—	316	4	no	—
1274	C₂	—	316	4	no	—
1275	C₂	#23777590	1	4	yes	direct product factor
1276	C₂	C₂²×#14579206	1	1	yes	characteristic
1277	C₂	C₂²×#14579206	1	1	yes	characteristic
1278	C₂	C₂×#19099399	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂²×#121×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂²×#121	D₇₉
hypocenter	C₇₉	C₂×#3534
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. #23777590	C₂	direct (N × H)
2. C₂×#19099308	C₂	semidirect
3. C₂×#19099301	C₂	semidirect
4. C₂×#19099256	C₂	semidirect
5. C₂×#19099239	C₂	semidirect
6. C₂×#19099207	C₂	semidirect
7. C₂×#19099203	C₂	semidirect
8. C₂×#19099202	C₂	semidirect
9. C₂×D₄×C₂²⋊D₇₉	C₂	semidirect
10. C₂×#19099163	C₂	semidirect
11. C₂×#19099160	C₂	semidirect
12. C₂×#19099158	C₂	semidirect
13. C₂×#19099150	C₂	semidirect
14. C₂×#19099145	C₂	semidirect
15. C₂×#19099140	C₂	semidirect
16. C₂×#19099122	C₂	semidirect
17. C₂×#19099121	C₂	semidirect
18. C₂×#19099074	C₂	semidirect
19. C₂²×#14579144	C₂	semidirect
20. C₂²×#121×C₇₉	C₂	semidirect
21. C₂²×#11929624	C₂²	semidirect
22. C₂²×#11929623	C₂²	semidirect
24. C₂³×C₂²⋊D₇₉	C₂²	semidirect
25. C₂²×D₄×D₇₉	C₂²	semidirect
26. #19099308	C₂²	semidirect
27. #19099301	C₂²	semidirect
28. #19099256	C₂²	semidirect
29. #19099239	C₂²	semidirect
30. #19099207	C₂²	semidirect
31. #19099203	C₂²	semidirect
32. #19099202	C₂²	semidirect
33. D₄×C₂²⋊D₇₉	C₂²	semidirect
34. #19099163	C₂²	semidirect
35. #19099160	C₂²	semidirect
36. #19099158	C₂²	semidirect
37. #19099150	C₂²	semidirect
38. #19099145	C₂²	semidirect
39. #19099140	C₂²	semidirect
40. #19099122	C₂²	semidirect
41. #19099121	C₂²	semidirect
42. C₂×#14579157	C₂²	semidirect
43. C₂×#14579156	C₂²	semidirect
44. C₂×#14579156	C₂²	semidirect
45. C₂×#14579154	C₂²	semidirect
46. C₂×#14579154	C₂²	semidirect
47. C₂×#14579151	C₂²	semidirect
48. C₂×#14579151	C₂²	semidirect
49. C₂×#14579148	C₂²	semidirect
50. C₂×#14579147	C₂²	semidirect
51. C₂×#14579147	C₂²	semidirect
52. #19099074	C₂²	semidirect
53. C₂×#14579146	C₂²	semidirect
54. C₂×#14579146	C₂²	semidirect
55. C₂×#14579145	C₂²	semidirect
56. C₂×#14579144	C₂²	semidirect
57. C₂×#14579144	C₂²	semidirect
58. C₂×#14579144	C₂²	semidirect
59. C₂×#14579144	C₂²	semidirect
60. C₂×#14579144	C₂²	semidirect
61. C₂×#14579144	C₂²	semidirect
62. C₂×#14579143	C₂²	semidirect
63. C₂×#14579143	C₂²	semidirect
64. C₂×#14579142	C₂²	semidirect
65. C₂×#14579142	C₂²	semidirect
66. C₂×#14579142	C₂²	semidirect
67. C₂×#14579142	C₂²	semidirect
68. C₂×#14579140	C₂²	semidirect
69. C₂×#14579140	C₂²	semidirect
70. C₂×#14579140	C₂²	semidirect
71. C₂×#14579139	C₂²	semidirect
72. C₂×#14579139	C₂²	semidirect
73. C₂×#14579138	C₂²	semidirect
74. C₂×#14579138	C₂²	semidirect
76. C₂×#14579135	C₂²	semidirect
77. C₂×#14579135	C₂²	semidirect
78. C₂×#14579134	C₂²	semidirect
79. C₂×#14579134	C₂²	semidirect
80. C₂×#14579133	C₂²	semidirect
81. C₂×#14579133	C₂²	semidirect
82. C₂×#14579133	C₂²	semidirect
83. C₂×#14579133	C₂²	semidirect
84. C₂×#14579133	C₂²	semidirect
85. C₂×#14579133	C₂²	semidirect
86. C₂×#14579133	C₂²	semidirect
87. C₂×#14579133	C₂²	semidirect
88. C₂×#14579132	C₂²	semidirect
89. C₂×#14579132	C₂²	semidirect
90. C₂×#14579131	C₂²	semidirect
92. C₂×#14579130	C₂²	semidirect
93. C₂×#14579130	C₂²	semidirect
94. C₂×#14579129	C₂²	semidirect
95. C₂×#14579129	C₂²	semidirect
96. C₂×#14579129	C₂²	semidirect
97. C₂×#14579129	C₂²	semidirect
98. C₂×D₄×Dic₇₉	C₂²	semidirect
99. C₂×D₄×Dic₇₉	C₂²	semidirect
100. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
101. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
102. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
103. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
104. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
105. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
106. C₂×#14579120	C₂²	semidirect
107. C₂×#14579117	C₂²	semidirect
108. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
109. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
110. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
111. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
112. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
113. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
114. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
115. C₂³×D₄×C₇₉	C₂²	semidirect
116. C₂³×D₄×C₇₉	C₂²	semidirect
117. C₂⁴×C₄×C₇₉	C₂²	semidirect
119. C₂×#121×C₇₉	C₂²	semidirect
120. C₂×#121×C₇₉	C₂²	semidirect
121. C₂×#121×C₇₉	C₂²	semidirect
122. C₂×#121×C₇₉	C₂²	semidirect
123. C₂×#121×C₇₉	C₂²	semidirect
124. C₂×#121×C₇₉	C₂²	semidirect
125. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
126. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
130. C₂×#11929624	C₂³	semidirect
132. C₂×#11929623	C₂³	semidirect
151. C₂²×C₂²⋊D₇₉	C₂³	semidirect
153. C₂×D₄×D₇₉	C₂³	semidirect
163. #14579157	C₂³	semidirect
164. #14579156	C₂³	semidirect
165. #14579156	C₂³	semidirect
166. #14579154	C₂³	semidirect
167. #14579154	C₂³	semidirect
168. #14579151	C₂³	semidirect
169. #14579151	C₂³	semidirect
170. #14579148	C₂³	semidirect
171. #14579147	C₂³	semidirect
172. #14579147	C₂³	semidirect
173. #14579146	C₂³	semidirect
174. #14579146	C₂³	semidirect
175. #14579145	C₂³	semidirect
176. #14579144	C₂³	semidirect
177. #14579144	C₂³	semidirect
178. #14579144	C₂³	semidirect
179. #14579144	C₂³	semidirect
180. #14579144	C₂³	semidirect
181. #14579143	C₂³	semidirect
182. #14579143	C₂³	semidirect
183. #14579142	C₂³	semidirect
184. #14579142	C₂³	semidirect
185. #14579142	C₂³	semidirect
186. #14579142	C₂³	semidirect
187. #14579140	C₂³	semidirect
188. #14579140	C₂³	semidirect
189. #14579140	C₂³	semidirect
190. #14579139	C₂³	semidirect
191. #14579139	C₂³	semidirect
192. #14579138	C₂³	semidirect
193. #14579138	C₂³	semidirect
195. #14579135	C₂³	semidirect
196. #14579135	C₂³	semidirect
197. #14579134	C₂³	semidirect
198. #14579134	C₂³	semidirect
199. #14579133	C₂³	semidirect
200. #14579133	C₂³	semidirect
201. #14579133	C₂³	semidirect
202. #14579133	C₂³	semidirect
203. #14579133	C₂³	semidirect
204. #14579133	C₂³	semidirect
205. #14579133	C₂³	semidirect
206. #14579133	C₂³	semidirect
207. #14579132	C₂³	semidirect
208. #14579132	C₂³	semidirect
209. #14579131	C₂³	semidirect
211. #14579130	C₂³	semidirect
212. #14579130	C₂³	semidirect
213. #14579129	C₂³	semidirect
214. #14579129	C₂³	semidirect
215. #14579129	C₂³	semidirect
216. #14579129	C₂³	semidirect
217. D₄×Dic₇₉	C₂³	semidirect
218. D₄×Dic₇₉	C₂³	semidirect
219. C₄×C₂²⋊D₇₉	C₂³	semidirect
220. C₄×C₂²⋊D₇₉	C₂³	semidirect
221. C₄×C₂²⋊D₇₉	C₂³	semidirect
222. C₄×C₂²⋊D₇₉	C₂³	semidirect
223. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
224. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
225. #14579120	C₂³	semidirect
226. #14579117	C₂³	semidirect
241. C₂×Dic₇₉⋊C₄	C₂³	semidirect
242. C₂×Dic₇₉⋊C₄	C₂³	semidirect
254. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
255. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
266. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
267. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
268. C₂²⋊C₄×D₇₉	C₂³	semidirect
283. C₂²×D₄×C₇₉	C₂³	semidirect
284. C₂²×D₄×C₇₉	C₂³	semidirect
293. C₂³×C₄×C₇₉	C₂³	semidirect
295. #121×C₇₉	C₂³	semidirect
296. #121×C₇₉	C₂³	semidirect
297. #121×C₇₉	C₂³	semidirect
298. #121×C₇₉	C₂³	semidirect
299. #121×C₇₉	C₂³	semidirect
303. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
308. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
634. C₂×C₇₉	#3534	semidirect
659. C₂²×#121	D₇₉	semidirect
660. C₇₉	C₂×#3534	semidirect
666. C₂³×D₄	C₂×D₇₉	semidirect
667. C₂³×D₄	C₂×D₇₉	semidirect
668. C₂⁴×C₄	C₂×D₇₉	semidirect
734. C₂×#121	C₂×D₇₉	semidirect
735. C₂×#121	C₂×D₇₉	semidirect
736. C₂×#121	C₂×D₇₉	semidirect
737. C₂×#121	C₂×D₇₉	semidirect
738. C₂×#121	C₂×D₇₉	semidirect
739. C₂×#121	C₂×D₇₉	semidirect
760. C₂²×C₄⋊C₄	C₂×D₇₉	semidirect
766. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
805. C₂²×D₄	C₂²×D₇₉	semidirect
806. C₂²×D₄	C₂²×D₇₉	semidirect
824. C₂³×C₄	C₂²×D₇₉	semidirect
872. #121	C₂²×D₇₉	semidirect
873. #121	C₂²×D₇₉	semidirect
874. #121	C₂²×D₇₉	semidirect
875. #121	C₂²×D₇₉	semidirect
876. #121	C₂²×D₇₉	semidirect
914. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
945. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
1275. C₂	#23777590	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777590	2
C₂×#19099308	2
C₂×#19099301	2
C₂×#19099256	2
C₂×#19099239	2
C₂×#19099207	2
C₂×#19099203	2
C₂×#19099202	2
C₂×D₄×C₂²⋊D₇₉	2
C₂×#19099163	2
C₂×#19099160	2
C₂×#19099158	2
C₂×#19099150	2
C₂×#19099145	2
C₂×#19099140	2
C₂×#19099122	2
C₂×#19099121	2
C₂×#19099074	2
C₂²×#14579144	2
C₂²×#121×C₇₉	2
C₂×#3534	79

Subgroups — C2×#23777590 #35195450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777590 #35195450