Subgroups — C₂×#23777635 #35195506

Order 20224.

8890 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777635	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099301	C₂	1	4	yes	maximal, complemented
3	C₂×#19099265	C₂	1	2	yes	maximal, complemented
4	C₂×#19099261	C₂	1	2	yes	maximal, complemented
5	C₂×#19099197	C₂	1	2	yes	maximal, complemented
6	C₂×D₄×C₂²⋊D₇₉	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×C₂²⋊D₇₉	C₂	1	4	yes	maximal, complemented
8	C₂×#19099166	C₂	1	2	yes	maximal, complemented
9	C₂×#19099151	C₂	1	2	yes	maximal, complemented
10	C₂×#19099150	C₂	1	2	yes	maximal, complemented
11	C₂×#19099129	C₂	1	2	yes	maximal, complemented
12	C₂×#19099125	C₂	1	2	yes	maximal, complemented
13	C₂×#19099121	C₂	1	2	yes	maximal, complemented
14	C₂×#19099074	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#14579135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#121×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11929624	C₂²	1	1	yes	characteristic, complemented
18	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
20	C₂³×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
21	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₇₉	C₂²	1	2	yes	complemented
23	#19099301	C₂²	1	64	yes	complemented
24	#19099265	C₂²	1	32	yes	complemented
25	#19099261	C₂²	1	32	yes	complemented
26	#19099197	C₂²	1	32	yes	complemented
27	D₄×C₂²⋊D₇₉	C₂²	1	64	yes	complemented
28	D₄×C₂²⋊D₇₉	C₂²	1	32	yes	complemented
29	#19099166	C₂²	1	32	yes	complemented
30	#19099151	C₂²	1	32	yes	complemented
31	#19099150	C₂²	1	32	yes	complemented
32	#19099129	C₂²	1	32	yes	complemented
33	#19099125	C₂²	1	32	yes	complemented
34	#19099121	C₂²	1	32	yes	complemented
35	C₂×#14579157	C₂²	1	2	yes	complemented
36	C₂×#14579157	C₂²	1	4	yes	complemented
37	C₂×#14579156	C₂²	1	4	yes	complemented
38	C₂×#14579154	C₂²	1	4	yes	complemented
39	C₂×#14579152	C₂²	1	2	yes	complemented
40	C₂×#14579147	C₂²	1	4	yes	complemented
41	#19099074	C₂²	1	16	yes	complemented
42	C₂×#14579146	C₂²	1	4	yes	complemented
43	C₂×#14579145	C₂²	1	4	yes	complemented
44	C₂×#14579145	C₂²	1	4	yes	complemented
45	C₂×#14579144	C₂²	1	2	yes	complemented
46	C₂×#14579143	C₂²	1	4	yes	complemented
47	C₂×#14579140	C₂²	1	1	yes	characteristic, complemented
48	C₂×#14579140	C₂²	1	1	yes	characteristic, complemented
49	C₂×#14579136	C₂²	1	2	yes	complemented
50	C₂×#14579135	C₂²	1	2	yes	complemented
51	C₂×#14579135	C₂²	1	4	yes	complemented
52	C₂×#14579135	C₂²	1	2	yes	complemented
53	C₂×#14579135	C₂²	1	2	yes	complemented
54	C₂×#14579135	C₂²	1	2	yes	complemented
55	C₂×#14579135	C₂²	1	1	yes	characteristic, complemented
56	C₂×#14579135	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14579135	C₂²	1	16	yes	complemented
58	C₂×#14579134	C₂²	1	4	yes	complemented
59	C₂×#14579133	C₂²	1	4	yes	complemented
60	C₂×#14579133	C₂²	1	4	yes	complemented
61	C₂×#14579133	C₂²	1	4	yes	complemented
62	C₂×#14579132	C₂²	1	2	yes	complemented
63	C₂×#14579132	C₂²	1	4	yes	complemented
64	C₂×#14579131	C₂²	1	4	yes	complemented
65	C₂×#14579131	C₂²	1	4	yes	complemented
66	C₂×#14579130	C₂²	1	2	yes	complemented
67	C₂×#14579130	C₂²	1	4	yes	complemented
68	C₂×#14579129	C₂²	1	4	yes	complemented
69	C₂×#14579129	C₂²	1	4	yes	complemented
70	C₂×#14579129	C₂²	1	4	yes	complemented
71	C₂×D₄×Dic₇₉	C₂²	1	4	yes	complemented
72	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
73	C₂×#14579123	C₂²	1	2	yes	complemented
74	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
75	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
76	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
77	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
78	C₂×#14579119	C₂²	1	2	yes	complemented
79	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
80	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
81	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
82	C₂³×D₄×C₇₉	C₂²	1	2	yes	complemented
83	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
84	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
85	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
86	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
87	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
88	C₂×#121×C₇₉	C₂²	1	16	yes	complemented
89	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
90	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
91	C₂⁴×D₇₉	C₂³	1	2	yes	—
92	C₂⁴×D₇₉	C₂³	1	4	yes	—
93	C₂×#11929624	—	4	4	no	—
94	C₂×#11929624	C₂³	1	8	yes	complemented
95	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
96	C₂²×D₃₁₆	—	4	4	no	—
97	C₂²×D₃₁₆	C₂³	1	2	yes	—
98	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
99	C₂²×D₃₁₆	C₂³	1	2	yes	—
100	C₂²×D₃₁₆	C₂³	1	4	yes	—
101	C₂²×D₃₁₆	C₂³	1	8	yes	complemented
102	C₂²×C₂²⋊D₇₉	—	4	8	no	—
103	C₂²×C₂²⋊D₇₉	—	4	16	no	—
104	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
106	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
108	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
109	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
112	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
113	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
114	C₂²×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
115	C₂×D₄×D₇₉	—	4	8	no	—
116	C₂×D₄×D₇₉	—	4	16	no	—
117	C₂×D₄×D₇₉	C₂³	1	32	yes	complemented
118	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
119	C₂³×Dic₇₉	C₂³	1	2	yes	—
120	C₂³×Dic₇₉	C₂³	1	4	yes	—
121	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
122	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
123	#14579157	C₂³	1	16	yes	complemented
124	#14579157	C₂³	1	32	yes	complemented
125	#14579156	C₂³	1	32	yes	complemented
126	#14579154	C₂³	1	32	yes	complemented
127	#14579152	C₂³	1	16	yes	complemented
128	#14579147	C₂³	1	32	yes	complemented
129	#14579146	C₂³	1	32	yes	complemented
130	#14579145	C₂³	1	32	yes	complemented
131	#14579145	C₂³	1	32	yes	complemented
132	#14579144	C₂³	1	16	yes	complemented
133	#14579143	C₂³	1	32	yes	complemented
134	#14579140	C₂³	1	8	yes	complemented
135	#14579140	C₂³	1	8	yes	complemented
136	#14579136	C₂³	1	16	yes	complemented
137	#14579135	C₂³	1	16	yes	complemented
138	#14579135	C₂³	1	16	yes	complemented
139	#14579135	C₂³	1	16	yes	complemented
140	#14579135	C₂³	1	32	yes	complemented
141	#14579135	C₂³	1	16	yes	complemented
142	#14579135	C₂³	1	8	yes	complemented
143	#14579135	C₂³	1	8	yes	complemented
144	#14579134	C₂³	1	32	yes	complemented
145	#14579133	C₂³	1	32	yes	complemented
146	#14579133	C₂³	1	32	yes	complemented
147	#14579133	C₂³	1	32	yes	complemented
148	#14579132	C₂³	1	32	yes	complemented
149	#14579132	C₂³	1	16	yes	complemented
150	#14579131	C₂³	1	32	yes	complemented
151	#14579131	C₂³	1	32	yes	complemented
152	#14579130	C₂³	1	32	yes	complemented
153	#14579130	C₂³	1	16	yes	complemented
154	#14579129	C₂³	1	32	yes	complemented
155	#14579129	C₂³	1	32	yes	complemented
156	#14579129	C₂³	1	32	yes	complemented
157	D₄×Dic₇₉	C₂³	1	32	yes	complemented
158	D₄×Dic₇₉	C₂³	1	16	yes	complemented
159	#14579123	C₂³	1	16	yes	complemented
160	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
161	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
162	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
163	#14579120	C₂³	1	8	yes	complemented
164	#14579119	C₂³	1	16	yes	complemented
165	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
166	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
167	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
170	C₂×C₄⋊Dic₇₉	C₂³	1	8	yes	complemented
171	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
172	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
173	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
174	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
178	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
179	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
180	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
181	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
182	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
183	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
184	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
185	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
186	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	complemented
187	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
188	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
189	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
190	C₂⁵×C₇₉	C₂³	1	2	yes	—
191	C₂²×D₄×C₇₉	—	4	4	no	—
192	C₂²×D₄×C₇₉	—	4	8	no	—
193	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
194	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
195	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
196	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
197	C₂²×D₄×C₇₉	C₂³	1	8	yes	complemented
198	C₂²×D₄×C₇₉	C₂³	1	16	yes	complemented
199	C₂³×C₄×C₇₉	—	4	4	no	—
200	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
205	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₇₉	C₂³	1	8	yes	complemented
208	#121×C₇₉	C₂³	1	16	yes	complemented
209	#121×C₇₉	C₂³	1	16	yes	complemented
210	#121×C₇₉	C₂³	1	16	yes	complemented
211	#121×C₇₉	C₂³	1	16	yes	complemented
212	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
214	C₂×C₄⋊C₄×C₇₉	C₂³	1	8	yes	complemented
215	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
216	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	complemented
218	C₂³×D₇₉	—	2	8	no	—
219	C₂³×D₇₉	—	4	8	no	—
220	C₂³×D₇₉	—	4	8	no	—
221	C₂³×D₇₉	—	4	4	no	—
222	C₂³×D₇₉	—	4	8	no	—
223	C₂³×D₇₉	—	4	4	no	—
224	C₂³×D₇₉	C₂⁴	1	2	yes	—
225	C₂³×D₇₉	C₂⁴	1	4	yes	—
226	C₂³×D₇₉	C₂⁴	1	8	yes	—
227	C₂³×D₇₉	C₂⁴	1	16	yes	—
228	#11929624	—	4	16	no	—
229	C₂×Dic₁₅₈	—	4	2	no	—
230	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
231	C₂×D₃₁₆	—	2	8	no	—
232	C₂×D₃₁₆	—	4	2	no	—
233	C₂×D₃₁₆	—	4	8	no	—
234	C₂×D₃₁₆	—	4	4	no	—
235	C₂×D₃₁₆	—	4	16	no	—
236	C₂×D₃₁₆	C₂⁴	1	8	yes	—
237	C₂×D₃₁₆	C₂⁴	1	4	yes	—
238	C₂×D₃₁₆	C₂⁴	1	8	yes	—
239	C₂×D₃₁₆	C₂⁴	1	16	yes	—
240	C₂×C₂²⋊D₇₉	—	2	8	no	—
241	C₂×C₂²⋊D₇₉	—	2	16	no	—
242	C₂×C₂²⋊D₇₉	—	2	8	no	—
243	C₂×C₂²⋊D₇₉	—	4	32	no	—
244	C₂×C₂²⋊D₇₉	—	4	64	no	—
245	C₂×C₂²⋊D₇₉	—	4	4	no	—
246	C₂×C₂²⋊D₇₉	—	4	8	no	—
247	C₂×C₂²⋊D₇₉	—	4	8	no	—
248	C₂×C₂²⋊D₇₉	—	4	8	no	—
249	C₂×C₂²⋊D₇₉	—	4	8	no	—
250	C₂×C₂²⋊D₇₉	—	4	8	no	—
251	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
252	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
253	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
254	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
255	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
256	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
257	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
258	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
259	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
260	D₄×D₇₉	—	4	64	no	—
261	D₄×D₇₉	—	4	32	no	—
262	C₂²×Dic₇₉	—	4	4	no	—
263	C₂²×Dic₇₉	—	4	8	no	—
264	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
265	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
266	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
267	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
268	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
269	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
270	C₂×C₄×D₇₉	—	2	8	no	—
271	C₂×C₄×D₇₉	—	4	8	no	—
272	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
273	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
274	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
275	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
276	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
277	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
278	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
279	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
280	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
281	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
282	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
283	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
284	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
285	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
286	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
287	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
288	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
289	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
290	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
291	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
292	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
293	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
294	C₄×Dic₇₉	C₂⁴	1	16	yes	—
295	C₄×Dic₇₉	C₂⁴	1	8	yes	—
296	C₂⁴×C₇₉	—	2	4	no	—
297	C₂⁴×C₇₉	—	2	4	no	—
298	C₂⁴×C₇₉	—	2	8	no	—
299	C₂⁴×C₇₉	—	4	2	no	—
300	C₂⁴×C₇₉	—	4	4	no	—
301	C₂⁴×C₇₉	—	4	4	no	—
302	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
303	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
304	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
305	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
306	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
307	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
308	C₂×D₄×C₇₉	—	2	16	no	—
309	C₂×D₄×C₇₉	—	2	8	no	—
310	C₂×D₄×C₇₉	—	4	16	no	—
311	C₂×D₄×C₇₉	—	4	8	no	—
312	C₂×D₄×C₇₉	—	4	4	no	—
313	C₂×D₄×C₇₉	—	4	32	no	—
314	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
315	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
316	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
317	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
318	C₂²×C₄×C₇₉	—	2	4	no	—
319	C₂²×C₄×C₇₉	—	2	4	no	—
320	C₂²×C₄×C₇₉	—	2	4	no	—
321	C₂²×C₄×C₇₉	—	4	16	no	—
322	C₂²×C₄×C₇₉	—	4	2	no	—
323	C₂²×C₄×C₇₉	—	4	2	no	—
324	C₂²×C₄×C₇₉	—	4	2	no	—
325	C₂²×C₄×C₇₉	—	4	4	no	—
326	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
330	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
333	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
334	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
335	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
336	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
337	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
338	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
339	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
340	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
341	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
342	C₂³×C₇₉	—	2	2	no	—
343	C₂³×C₇₉	—	2	2	no	—
344	C₂³×C₇₉	—	2	2	no	—
345	C₂³×C₇₉	—	2	2	no	—
346	C₂³×C₇₉	—	2	8	no	—
347	C₂³×C₇₉	—	2	8	no	—
348	C₂³×C₇₉	—	2	2	no	—
349	C₂³×C₇₉	—	2	2	no	—
350	C₂³×C₇₉	—	2	8	no	—
351	C₂³×C₇₉	—	2	8	no	—
352	C₂³×C₇₉	—	2	8	no	—
353	C₂³×C₇₉	—	2	2	no	—
354	C₂³×C₇₉	—	2	16	no	—
355	C₂³×C₇₉	—	4	4	no	—
356	C₂³×C₇₉	—	4	8	no	—
357	C₂³×C₇₉	—	4	8	no	—
358	C₂³×C₇₉	—	4	16	no	—
359	C₂³×C₇₉	—	8	16	no	—
360	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
361	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
362	C₂³×C₇₉	C₂⁵	1	8	yes	—
363	C₂³×C₇₉	C₂⁵	1	2	yes	—
364	C₂³×C₇₉	C₂⁵	1	2	yes	—
365	C₂³×C₇₉	C₂⁵	1	2	yes	—
366	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
367	C₂²×D₇₉	—	2	4	no	—
368	C₂²×D₇₉	—	2	8	no	—
369	C₂²×D₇₉	—	2	4	no	—
370	C₂²×D₇₉	—	2	8	no	—
371	C₂²×D₇₉	—	2	4	no	—
372	C₂²×D₇₉	—	2	8	no	—
373	C₂²×D₇₉	—	2	16	no	—
374	C₂²×D₇₉	—	4	16	no	—
375	C₂²×D₇₉	—	4	16	no	—
376	C₂²×D₇₉	—	4	8	no	—
377	C₂²×D₇₉	—	4	16	no	—
378	C₂²×D₇₉	—	4	8	no	—
379	C₂²×D₇₉	—	8	16	no	—
380	C₂²×D₇₉	—	8	32	no	—
381	C₂²×D₇₉	C₂⁵	1	4	yes	—
382	C₂²×D₇₉	C₂⁵	1	8	yes	—
383	D₄×C₇₉	—	2	32	no	—
384	D₄×C₇₉	—	2	16	no	—
385	D₄×C₇₉	—	4	8	no	—
386	D₄×C₇₉	—	4	16	no	—
387	C₂×C₄×C₇₉	—	2	8	no	—
388	C₂×C₄×C₇₉	—	2	2	no	—
389	C₂×C₄×C₇₉	—	2	2	no	—
390	C₂×C₄×C₇₉	—	2	2	no	—
391	C₂×C₄×C₇₉	—	2	8	no	—
392	C₂×C₄×C₇₉	—	2	8	no	—
393	C₂×C₄×C₇₉	—	2	8	no	—
394	C₂×C₄×C₇₉	—	4	4	no	—
395	C₂×C₄×C₇₉	—	4	4	no	—
396	C₂×C₄×C₇₉	—	4	4	no	—
397	C₂×C₄×C₇₉	—	4	8	no	—
398	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
399	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
400	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
401	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
402	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
403	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
404	C₂²⋊D₇₉	—	2	16	no	—
405	C₂²⋊D₇₉	—	2	32	no	—
406	C₂²⋊D₇₉	—	2	16	no	—
407	C₂²⋊D₇₉	—	4	16	no	—
408	C₂²⋊D₇₉	—	4	16	no	—
409	C₂²⋊D₇₉	—	4	16	no	—
410	C₂²⋊D₇₉	—	4	16	no	—
411	C₂²⋊D₇₉	—	4	16	no	—
412	C₂²⋊D₇₉	—	4	8	no	—
413	C₂×Dic₇₉	—	2	4	no	—
414	C₂×Dic₇₉	—	2	4	no	—
415	C₂×Dic₇₉	—	2	8	no	—
416	C₂×Dic₇₉	—	2	4	no	—
417	C₂×Dic₇₉	—	4	8	no	—
418	C₂×Dic₇₉	—	4	16	no	—
419	C₂×Dic₇₉	C₂⁵	1	4	yes	—
420	C₂×Dic₇₉	C₂⁵	1	8	yes	—
421	C₂×Dic₇₉	C₂⁵	1	4	yes	—
422	C₂×Dic₇₉	C₂⁵	1	4	yes	—
423	D₃₁₆	—	2	16	no	—
424	D₃₁₆	—	4	16	no	—
425	D₃₁₆	—	4	8	no	—
426	D₃₁₆	—	4	4	no	—
427	C₄×D₇₉	—	2	16	no	—
428	C₄×D₇₉	—	4	16	no	—
429	Dic₁₅₈	—	4	4	no	—
430	C₂²×C₇₉	—	2	2	no	—
431	C₂²×C₇₉	—	2	2	no	—
432	C₂²×C₇₉	—	2	2	no	—
433	C₂²×C₇₉	—	2	2	no	—
434	C₂²×C₇₉	—	2	8	no	—
435	C₂²×C₇₉	—	2	8	no	—
436	C₂²×C₇₉	—	2	2	no	—
437	C₂²×C₇₉	—	2	2	no	—
438	C₂²×C₇₉	—	2	8	no	—
439	C₂²×C₇₉	—	2	8	no	—
440	C₂²×C₇₉	—	2	8	no	—
441	C₂²×C₇₉	—	2	2	no	—
442	C₂²×C₇₉	—	4	16	no	—
443	C₂²×C₇₉	—	4	16	no	—
444	C₂²×C₇₉	—	4	4	no	—
445	C₂²×C₇₉	—	8	16	no	—
446	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
447	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
448	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
450	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
451	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
452	C₂×D₇₉	—	2	4	no	—
453	C₂×D₇₉	—	2	8	no	—
454	C₂×D₇₉	—	2	4	no	—
455	C₂×D₇₉	—	2	8	no	—
456	C₂×D₇₉	—	2	4	no	—
457	C₂×D₇₉	—	2	8	no	—
458	C₂×D₇₉	—	4	8	no	—
459	C₂×D₇₉	—	4	16	no	—
460	C₂×D₇₉	—	8	16	no	—
461	C₂×D₇₉	—	8	32	no	—
462	C₄×C₇₉	—	2	2	no	—
463	C₄×C₇₉	—	2	2	no	—
464	C₄×C₇₉	—	2	2	no	—
465	C₄×C₇₉	—	2	8	no	—
466	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
467	Dic₇₉	—	2	4	no	—
468	Dic₇₉	—	2	8	no	—
469	Dic₇₉	—	2	4	no	—
470	Dic₇₉	—	2	4	no	—
471	C₂×#3537	—	79	1	no	maximal, Sylow
472	C₂×C₇₉	—	2	4	no	—
473	C₂×C₇₉	—	2	4	no	—
474	C₂×C₇₉	—	4	8	no	—
475	C₂×C₇₉	—	4	2	no	—
476	C₂×C₇₉	#3537	1	4	yes	complemented
477	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
480	D₇₉	—	4	4	no	—
481	D₇₉	—	4	8	no	—
482	#3537	—	79	32	no	—
483	C₂×#560	—	79	4	no	—
484	C₂×#553	—	79	2	no	—
485	C₂×#553	—	79	2	no	—
486	C₂×D₄²	—	79	4	no	—
487	C₂×D₄²	—	79	2	no	—
488	C₂×D₄²	—	79	2	no	—
489	C₂×#540	—	79	2	no	—
490	C₂×#538	—	79	2	no	—
491	C₂×#538	—	79	2	no	—
492	C₂×#535	—	79	2	no	—
493	C₂×#534	—	79	2	no	—
494	C₂×#534	—	79	2	no	—
495	C₂×#525	—	79	1	no	—
496	C₂²×#121	—	79	1	no	—
497	C₂²×#121	D₇₉	1	1	yes	characteristic, complemented
498	C₇₉	C₂×#3537	1	1	yes	characteristic, complemented, Sylow
499	C₂²×#41	—	79	1	no	—
500	C₂³×D₄	—	79	2	no	—
501	C₂³×D₄	—	79	4	no	—
502	C₂³×D₄	—	79	4	no	—
503	C₂³×D₄	—	79	2	no	—
504	C₂³×D₄	—	79	1	no	—
505	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
506	C₂³×D₄	C₂×D₇₉	1	2	yes	complemented
507	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
508	#560	—	79	64	no	—
509	#553	—	79	32	no	—
510	#553	—	79	32	no	—
511	D₄²	—	79	64	no	—
512	D₄²	—	79	32	no	—
513	D₄²	—	79	32	no	—
514	#540	—	79	32	no	—
515	#538	—	79	32	no	—
516	#538	—	79	32	no	—
517	#535	—	79	32	no	—
518	#534	—	79	32	no	—
519	#534	—	79	32	no	—
520	C₂×#127	—	79	4	no	—
521	C₂×#127	—	79	2	no	—
522	C₂×#126	—	79	4	no	—
523	C₂×#126	—	79	4	no	—
524	C₂×#125	—	79	2	no	—
525	C₂×#124	—	79	4	no	—
526	#525	—	79	16	no	—
527	C₂×#123	—	79	2	no	—
528	C₂×#123	—	79	4	no	—
529	C₂×#123	—	79	4	no	—
530	C₂×#123	—	79	4	no	—
531	C₂×#123	—	79	4	no	—
532	C₂×C₂²⋊Q₈	—	79	1	no	—
533	C₂×C₂²⋊Q₈	—	79	1	no	—
534	C₂×#121	—	79	4	no	—
535	C₂×#121	—	79	2	no	—
536	C₂×#121	—	79	4	no	—
537	C₂×#121	—	79	4	no	—
538	C₂×#121	—	79	4	no	—
539	C₂×#121	—	79	2	no	—
540	C₂×#121	—	79	2	no	—
541	C₂×#121	—	79	2	no	—
542	C₂×#121	—	79	2	no	—
543	C₂×#121	—	79	1	no	—
544	C₂×#121	—	79	1	no	—
545	C₂×#121	—	79	4	no	—
546	C₂×#121	—	79	16	no	—
547	C₂×#121	—	79	2	no	—
548	C₂×#121	—	79	4	no	—
549	C₂×#121	C₂×D₇₉	1	2	yes	complemented
550	C₂×#121	C₂×D₇₉	1	2	yes	complemented
551	C₂×#121	C₂×D₇₉	1	2	yes	complemented
552	C₂×#121	C₂×D₇₉	1	2	yes	complemented
553	C₂×#121	C₂×D₇₉	1	16	yes	complemented
554	C₂×#120	—	79	2	no	—
555	C₂×#120	—	79	4	no	—
556	C₂×#120	—	79	4	no	—
557	C₂×#120	—	79	4	no	—
558	C₂×#120	—	79	4	no	—
559	C₂×#120	—	79	4	no	—
560	C₂×#120	—	79	4	no	—
561	C₂×C₄×D₄	—	79	4	no	—
562	C₂×C₄×D₄	—	79	2	no	—
563	C₂×C₄×D₄	—	79	2	no	—
564	C₂×C₄×D₄	—	79	2	no	—
565	C₂×C₄×D₄	—	79	4	no	—
566	C₂×C₄×D₄	—	79	2	no	—
567	C₂×#117	—	79	1	no	—
568	C₂×#117	—	79	2	no	—
569	C₂²×C₄⋊C₄	—	79	1	no	—
570	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
571	C₂²×C₂²⋊C₄	—	79	2	no	—
572	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
573	C₂⁵	—	79	4	no	—
574	C₂⁵	—	79	2	no	—
575	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
576	C₂⁵	C₂²×D₇₉	1	2	yes	—
577	C₂×#41	—	316	4	no	—
578	C₂×#41	—	79	8	no	—
579	C₂²×Q₈	—	79	1	no	—
580	C₂²×D₄	—	4	4	no	—
581	C₂²×D₄	—	4	8	no	—
582	C₂²×D₄	—	316	4	no	—
583	C₂²×D₄	—	316	16	no	—
584	C₂²×D₄	—	316	8	no	—
585	C₂²×D₄	—	316	16	no	—
586	C₂²×D₄	—	316	8	no	—
587	C₂²×D₄	—	79	2	no	—
588	C₂²×D₄	—	79	4	no	—
589	C₂²×D₄	—	79	4	no	—
590	C₂²×D₄	—	79	4	no	—
591	C₂²×D₄	—	79	4	no	—
592	C₂²×D₄	—	79	4	no	—
593	C₂²×D₄	—	79	16	no	—
594	C₂²×D₄	—	79	32	no	—
595	C₂²×D₄	—	79	32	no	—
596	C₂²×D₄	—	79	16	no	—
597	C₂²×D₄	—	79	2	no	—
598	C₂²×D₄	—	79	2	no	—
599	C₂²×D₄	—	79	4	no	—
600	C₂²×D₄	—	79	1	no	—
601	C₂²×D₄	—	79	2	no	—
602	C₂²×D₄	—	79	4	no	—
603	C₂²×D₄	—	79	8	no	—
604	C₂²×D₄	—	79	2	no	—
605	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
606	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
607	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
608	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
609	C₂²×D₄	C₂²×D₇₉	1	8	yes	complemented
610	C₂²×D₄	C₂²×D₇₉	1	16	yes	complemented
611	C₂³×C₄	—	4	4	no	—
612	C₂³×C₄	—	79	2	no	—
613	C₂³×C₄	—	79	4	no	—
614	C₂³×C₄	—	79	4	no	—
615	C₂³×C₄	—	79	2	no	—
616	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
617	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
618	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
619	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
620	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
621	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
622	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
623	C₂³×C₄	C₂²×D₇₉	1	8	yes	complemented
624	#127	—	79	32	no	—
625	#127	—	79	16	no	—
626	#126	—	79	32	no	—
627	#126	—	79	32	no	—
628	#125	—	79	16	no	—
629	#124	—	79	32	no	—
630	#123	—	79	16	no	—
631	#123	—	79	32	no	—
632	#123	—	79	32	no	—
633	#123	—	79	32	no	—
634	#123	—	79	32	no	—
635	C₂²⋊Q₈	—	79	8	no	—
636	C₂²⋊Q₈	—	79	8	no	—
637	#121	—	79	32	no	—
638	#121	—	79	16	no	—
639	#121	—	79	32	no	—
640	#121	—	79	32	no	—
641	#121	—	79	32	no	—
642	#121	—	79	16	no	—
643	#121	—	79	16	no	—
644	#121	—	79	16	no	—
645	#121	—	79	16	no	—
646	#121	—	79	8	no	—
647	#121	—	79	8	no	—
648	#121	—	79	32	no	—
649	#121	—	79	16	no	—
650	#121	—	79	32	no	—
651	#121	C₂²×D₇₉	1	16	yes	complemented
652	#121	C₂²×D₇₉	1	16	yes	complemented
653	#121	C₂²×D₇₉	1	16	yes	complemented
654	#121	C₂²×D₇₉	1	16	yes	complemented
655	#120	—	79	16	no	—
656	#120	—	79	32	no	—
657	#120	—	79	32	no	—
658	#120	—	79	32	no	—
659	#120	—	79	32	no	—
660	#120	—	79	32	no	—
661	#120	—	79	32	no	—
662	C₄×D₄	—	79	32	no	—
663	C₄×D₄	—	79	16	no	—
664	C₄×D₄	—	79	16	no	—
665	C₄×D₄	—	79	16	no	—
666	C₄×D₄	—	79	32	no	—
667	C₄×D₄	—	79	16	no	—
668	#117	—	79	8	no	—
669	#117	—	79	16	no	—
670	C₂×C₄⋊C₄	—	79	2	no	—
671	C₂×C₄⋊C₄	—	79	2	no	—
672	C₂×C₄⋊C₄	—	79	8	no	—
673	C₂×C₄⋊C₄	—	79	1	no	—
674	C₂×C₄⋊C₄	—	79	1	no	—
675	C₂×C₄⋊C₄	—	79	2	no	—
676	C₂×C₄⋊C₄	—	79	2	no	—
677	C₂×C₄⋊C₄	—	79	4	no	—
678	C₂×C₄⋊C₄	—	79	4	no	—
679	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
680	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
681	C₂×C₄⋊C₄	C₂²×D₇₉	1	8	yes	complemented
682	C₂×C₂²⋊C₄	—	79	2	no	—
683	C₂×C₂²⋊C₄	—	79	2	no	—
684	C₂×C₂²⋊C₄	—	79	2	no	—
685	C₂×C₂²⋊C₄	—	79	4	no	—
686	C₂×C₂²⋊C₄	—	79	4	no	—
687	C₂×C₂²⋊C₄	—	79	4	no	—
688	C₂×C₂²⋊C₄	—	79	4	no	—
689	C₂×C₂²⋊C₄	—	79	16	no	—
690	C₂×C₂²⋊C₄	—	79	4	no	—
691	C₂×C₂²⋊C₄	—	79	4	no	—
692	C₂×C₂²⋊C₄	—	79	4	no	—
693	C₂×C₂²⋊C₄	—	79	2	no	—
694	C₂×C₂²⋊C₄	—	79	2	no	—
695	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
696	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
697	C₂×C₂²⋊C₄	C₂²×D₇₉	1	16	yes	complemented
698	C₂×C₄²	—	79	2	no	—
699	C₂×C₄²	—	79	4	no	—
700	C₂⁴	—	2	4	no	—
701	C₂⁴	—	2	4	no	—
702	C₂⁴	—	2	8	no	—
703	C₂⁴	—	4	2	no	—
704	C₂⁴	—	4	4	no	—
705	C₂⁴	—	4	4	no	—
706	C₂⁴	—	316	4	no	—
707	C₂⁴	—	316	4	no	—
708	C₂⁴	—	316	8	no	—
709	C₂⁴	—	316	8	no	—
710	C₂⁴	—	316	8	no	—
711	C₂⁴	—	79	16	no	—
712	C₂⁴	—	79	8	no	—
713	C₂⁴	—	79	4	no	—
714	C₂⁴	—	79	2	no	—
715	C₂⁴	—	158	8	no	—
716	C₂⁴	C₂³×D₇₉	1	4	yes	—
717	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
718	C₂⁴	C₂³×D₇₉	1	4	yes	—
719	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
720	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
721	C₂⁴	C₂³×D₇₉	1	8	yes	—
722	#41	—	316	16	no	—
723	C₂×Q₈	—	316	2	no	—
724	C₂×Q₈	—	79	4	no	—
725	C₂×D₄	—	2	16	no	—
726	C₂×D₄	—	2	8	no	—
727	C₂×D₄	—	4	16	no	—
728	C₂×D₄	—	4	4	no	—
729	C₂×D₄	—	4	8	no	—
730	C₂×D₄	—	4	32	no	—
731	C₂×D₄	—	316	4	no	—
732	C₂×D₄	—	316	8	no	—
733	C₂×D₄	—	316	2	no	—
734	C₂×D₄	—	316	16	no	—
735	C₂×D₄	—	316	64	no	—
736	C₂×D₄	—	316	32	no	—
737	C₂×D₄	—	316	64	no	—
738	C₂×D₄	—	316	32	no	—
739	C₂×D₄	—	316	8	no	—
740	C₂×D₄	—	316	8	no	—
741	C₂×D₄	—	316	8	no	—
742	C₂×D₄	—	316	8	no	—
743	C₂×D₄	—	316	8	no	—
744	C₂×D₄	—	316	4	no	—
745	C₂×D₄	—	79	8	no	—
746	C₂×D₄	—	79	16	no	—
747	C₂×D₄	—	79	16	no	—
748	C₂×D₄	—	79	16	no	—
749	C₂×D₄	—	79	16	no	—
750	C₂×D₄	—	79	16	no	—
751	C₂×D₄	—	79	8	no	—
752	C₂×D₄	—	79	8	no	—
753	C₂×D₄	—	79	16	no	—
754	C₂×D₄	—	79	4	no	—
755	C₂×D₄	—	79	8	no	—
756	C₂×D₄	—	79	16	no	—
757	C₂×D₄	—	79	8	no	—
758	C₂×D₄	—	158	8	no	—
759	C₂×D₄	—	158	16	no	—
760	C₂×D₄	—	158	8	no	—
761	C₂×D₄	—	158	8	no	—
762	C₂×D₄	C₂³×D₇₉	1	16	yes	—
763	C₂×D₄	C₂³×D₇₉	1	8	yes	—
764	C₂×D₄	C₂³×D₇₉	1	8	yes	—
765	C₂×D₄	C₂³×D₇₉	1	16	yes	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	4	16	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	4	no	—
774	C₂²×C₄	—	316	8	no	—
775	C₂²×C₄	—	316	4	no	—
776	C₂²×C₄	—	316	8	no	—
777	C₂²×C₄	—	79	8	no	—
778	C₂²×C₄	—	79	16	no	—
779	C₂²×C₄	—	79	16	no	—
780	C₂²×C₄	—	79	2	no	—
781	C₂²×C₄	—	79	2	no	—
782	C₂²×C₄	—	79	2	no	—
783	C₂²×C₄	—	79	4	no	—
784	C₂²×C₄	—	79	8	no	—
785	C₂²×C₄	—	158	8	no	—
786	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
787	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
788	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
789	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
790	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
791	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
792	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
793	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
794	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
795	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
796	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
797	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
798	C₄⋊C₄	—	79	8	no	—
799	C₄⋊C₄	—	79	8	no	—
800	C₄⋊C₄	—	79	16	no	—
801	C₄⋊C₄	—	79	8	no	—
802	C₄⋊C₄	—	79	8	no	—
803	C₄⋊C₄	—	79	4	no	—
804	C₄⋊C₄	—	79	4	no	—
805	C₄⋊C₄	—	79	16	no	—
806	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
807	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
808	C₂²⋊C₄	—	79	8	no	—
809	C₂²⋊C₄	—	79	8	no	—
810	C₂²⋊C₄	—	79	8	no	—
811	C₂²⋊C₄	—	79	16	no	—
812	C₂²⋊C₄	—	79	16	no	—
813	C₂²⋊C₄	—	79	16	no	—
814	C₂²⋊C₄	—	79	16	no	—
815	C₂²⋊C₄	—	79	16	no	—
816	C₂²⋊C₄	—	79	16	no	—
817	C₂²⋊C₄	—	79	16	no	—
818	C₂²⋊C₄	—	79	8	no	—
819	C₂²⋊C₄	—	79	8	no	—
820	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
821	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
822	C₄²	—	79	8	no	—
823	C₄²	—	79	16	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	8	no	—
830	C₂³	—	2	8	no	—
831	C₂³	—	2	8	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	8	no	—
834	C₂³	—	2	8	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	16	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	8	no	—
839	C₂³	—	4	8	no	—
840	C₂³	—	4	16	no	—
841	C₂³	—	8	16	no	—
842	C₂³	—	316	8	no	—
843	C₂³	—	316	8	no	—
844	C₂³	—	316	16	no	—
845	C₂³	—	316	16	no	—
846	C₂³	—	316	16	no	—
847	C₂³	—	79	8	no	—
848	C₂³	—	79	4	no	—
849	C₂³	—	632	16	no	—
850	C₂³	—	632	32	no	—
851	C₂³	—	158	8	no	—
852	C₂³	—	158	4	no	—
853	C₂³	—	158	4	no	—
854	C₂³	—	158	8	no	—
855	C₂³	—	158	8	no	—
856	C₂³	—	158	4	no	—
857	C₂³	—	158	16	no	—
858	C₂³	#14579206	1	4	yes	—
859	C₂³	#14579207	1	4	yes	—
860	C₂³	C₂⁴×D₇₉	1	8	yes	—
861	C₂³	C₂⁴×D₇₉	1	2	yes	—
862	C₂³	C₂⁴×D₇₉	1	2	yes	—
863	C₂³	C₂⁴×D₇₉	1	2	yes	—
864	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
865	Q₈	—	316	4	no	—
866	D₄	—	2	32	no	—
867	D₄	—	2	16	no	—
868	D₄	—	4	8	no	—
869	D₄	—	4	16	no	—
870	D₄	—	316	8	no	—
871	D₄	—	316	16	no	—
872	D₄	—	316	4	no	—
873	D₄	—	316	16	no	—
874	D₄	—	316	16	no	—
875	D₄	—	316	16	no	—
876	D₄	—	316	16	no	—
877	D₄	—	316	16	no	—
878	D₄	—	316	8	no	—
879	D₄	—	158	16	no	—
880	D₄	—	158	32	no	—
881	D₄	—	158	16	no	—
882	D₄	—	158	16	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	8	no	—
887	C₂×C₄	—	2	8	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	316	16	no	—
895	C₂×C₄	—	316	8	no	—
896	C₂×C₄	—	316	16	no	—
897	C₂×C₄	—	79	4	no	—
898	C₂×C₄	—	79	4	no	—
899	C₂×C₄	—	79	4	no	—
900	C₂×C₄	—	79	8	no	—
901	C₂×C₄	—	158	4	no	—
902	C₂×C₄	—	158	4	no	—
903	C₂×C₄	—	158	8	no	—
904	C₂×C₄	—	158	4	no	—
905	C₂×C₄	—	158	16	no	—
906	C₂×C₄	#14579206	1	4	yes	—
907	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
908	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
909	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
910	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
911	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
912	C₂²	—	2	8	no	—
913	C₂²	—	2	8	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	8	no	—
920	C₂²	—	2	8	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	8	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	4	16	no	—
925	C₂²	—	4	4	no	—
926	C₂²	—	4	16	no	—
927	C₂²	—	8	16	no	—
928	C₂²	—	316	16	no	—
929	C₂²	—	316	8	no	—
930	C₂²	—	632	16	no	—
931	C₂²	—	632	32	no	—
932	C₂²	—	158	8	no	—
933	C₂²	—	158	4	no	—
934	C₂²	—	158	4	no	—
935	C₂²	—	158	8	no	—
936	C₂²	—	158	8	no	—
937	C₂²	—	158	4	no	—
938	C₂²	C₂×#14579206	1	4	yes	—
939	C₂²	C₂×#14579206	1	2	yes	—
940	C₂²	C₂×#14579206	1	2	yes	—
941	C₂²	C₂×#14579207	1	4	yes	—
942	C₂²	C₂×#14579207	1	2	yes	—
943	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	8	no	—
948	C₄	—	158	4	no	—
949	C₄	—	158	4	no	—
950	C₄	—	158	8	no	—
951	C₄	—	158	4	no	—
952	C₄	C₂×#14579206	1	4	yes	—
953	C₂	—	2	4	no	—
954	C₂	—	2	4	no	—
955	C₂	—	4	2	no	—
956	C₂	—	4	8	no	—
957	C₂	—	316	8	no	—
958	C₂	—	316	4	no	—
959	C₂	#23777635	1	4	yes	direct product factor
960	C₂	C₂²×#14579206	1	1	yes	characteristic
961	C₂	C₂²×#14579206	1	1	yes	characteristic
962	C₂	C₂²×#14579207	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×#3537
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. #23777635	C₂	direct (N × H)
2. C₂×#19099301	C₂	semidirect
3. C₂×#19099265	C₂	semidirect
4. C₂×#19099261	C₂	semidirect
5. C₂×#19099197	C₂	semidirect
6. C₂×D₄×C₂²⋊D₇₉	C₂	semidirect
7. C₂×D₄×C₂²⋊D₇₉	C₂	semidirect
8. C₂×#19099166	C₂	semidirect
9. C₂×#19099151	C₂	semidirect
10. C₂×#19099150	C₂	semidirect
11. C₂×#19099129	C₂	semidirect
12. C₂×#19099125	C₂	semidirect
13. C₂×#19099121	C₂	semidirect
14. C₂×#19099074	C₂	semidirect
15. C₂²×#14579135	C₂	semidirect
16. C₂²×#121×C₇₉	C₂	semidirect
17. C₂²×#11929624	C₂²	semidirect
18. C₂³×D₃₁₆	C₂²	semidirect
19. C₂³×C₂²⋊D₇₉	C₂²	semidirect
20. C₂³×C₂²⋊D₇₉	C₂²	semidirect
21. C₂²×D₄×D₇₉	C₂²	semidirect
22. C₂²×D₄×D₇₉	C₂²	semidirect
23. #19099301	C₂²	semidirect
24. #19099265	C₂²	semidirect
25. #19099261	C₂²	semidirect
26. #19099197	C₂²	semidirect
27. D₄×C₂²⋊D₇₉	C₂²	semidirect
28. D₄×C₂²⋊D₇₉	C₂²	semidirect
29. #19099166	C₂²	semidirect
30. #19099151	C₂²	semidirect
31. #19099150	C₂²	semidirect
32. #19099129	C₂²	semidirect
33. #19099125	C₂²	semidirect
34. #19099121	C₂²	semidirect
35. C₂×#14579157	C₂²	semidirect
36. C₂×#14579157	C₂²	semidirect
37. C₂×#14579156	C₂²	semidirect
38. C₂×#14579154	C₂²	semidirect
39. C₂×#14579152	C₂²	semidirect
40. C₂×#14579147	C₂²	semidirect
41. #19099074	C₂²	semidirect
42. C₂×#14579146	C₂²	semidirect
43. C₂×#14579145	C₂²	semidirect
44. C₂×#14579145	C₂²	semidirect
45. C₂×#14579144	C₂²	semidirect
46. C₂×#14579143	C₂²	semidirect
47. C₂×#14579140	C₂²	semidirect
48. C₂×#14579140	C₂²	semidirect
49. C₂×#14579136	C₂²	semidirect
50. C₂×#14579135	C₂²	semidirect
51. C₂×#14579135	C₂²	semidirect
52. C₂×#14579135	C₂²	semidirect
53. C₂×#14579135	C₂²	semidirect
54. C₂×#14579135	C₂²	semidirect
55. C₂×#14579135	C₂²	semidirect
56. C₂×#14579135	C₂²	semidirect
57. C₂×#14579135	C₂²	semidirect
58. C₂×#14579134	C₂²	semidirect
59. C₂×#14579133	C₂²	semidirect
60. C₂×#14579133	C₂²	semidirect
61. C₂×#14579133	C₂²	semidirect
62. C₂×#14579132	C₂²	semidirect
63. C₂×#14579132	C₂²	semidirect
64. C₂×#14579131	C₂²	semidirect
65. C₂×#14579131	C₂²	semidirect
66. C₂×#14579130	C₂²	semidirect
67. C₂×#14579130	C₂²	semidirect
68. C₂×#14579129	C₂²	semidirect
69. C₂×#14579129	C₂²	semidirect
70. C₂×#14579129	C₂²	semidirect
71. C₂×D₄×Dic₇₉	C₂²	semidirect
72. C₂×D₄×Dic₇₉	C₂²	semidirect
73. C₂×#14579123	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
75. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
77. C₂×#14579120	C₂²	semidirect
78. C₂×#14579119	C₂²	semidirect
79. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
80. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
81. C₂³×D₄×C₇₉	C₂²	semidirect
82. C₂³×D₄×C₇₉	C₂²	semidirect
83. C₂⁴×C₄×C₇₉	C₂²	semidirect
84. C₂×#121×C₇₉	C₂²	semidirect
85. C₂×#121×C₇₉	C₂²	semidirect
86. C₂×#121×C₇₉	C₂²	semidirect
87. C₂×#121×C₇₉	C₂²	semidirect
88. C₂×#121×C₇₉	C₂²	semidirect
89. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
90. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
94. C₂×#11929624	C₂³	semidirect
101. C₂²×D₃₁₆	C₂³	semidirect
113. C₂²×C₂²⋊D₇₉	C₂³	semidirect
114. C₂²×C₂²⋊D₇₉	C₂³	semidirect
117. C₂×D₄×D₇₉	C₂³	semidirect
118. C₂×D₄×D₇₉	C₂³	semidirect
123. #14579157	C₂³	semidirect
124. #14579157	C₂³	semidirect
125. #14579156	C₂³	semidirect
126. #14579154	C₂³	semidirect
127. #14579152	C₂³	semidirect
128. #14579147	C₂³	semidirect
129. #14579146	C₂³	semidirect
130. #14579145	C₂³	semidirect
131. #14579145	C₂³	semidirect
132. #14579144	C₂³	semidirect
133. #14579143	C₂³	semidirect
134. #14579140	C₂³	semidirect
135. #14579140	C₂³	semidirect
136. #14579136	C₂³	semidirect
137. #14579135	C₂³	semidirect
138. #14579135	C₂³	semidirect
139. #14579135	C₂³	semidirect
140. #14579135	C₂³	semidirect
141. #14579135	C₂³	semidirect
142. #14579135	C₂³	semidirect
143. #14579135	C₂³	semidirect
144. #14579134	C₂³	semidirect
145. #14579133	C₂³	semidirect
146. #14579133	C₂³	semidirect
147. #14579133	C₂³	semidirect
148. #14579132	C₂³	semidirect
149. #14579132	C₂³	semidirect
150. #14579131	C₂³	semidirect
151. #14579131	C₂³	semidirect
152. #14579130	C₂³	semidirect
153. #14579130	C₂³	semidirect
154. #14579129	C₂³	semidirect
155. #14579129	C₂³	semidirect
156. #14579129	C₂³	semidirect
157. D₄×Dic₇₉	C₂³	semidirect
158. D₄×Dic₇₉	C₂³	semidirect
159. #14579123	C₂³	semidirect
160. C₄×C₂²⋊D₇₉	C₂³	semidirect
161. C₄×C₂²⋊D₇₉	C₂³	semidirect
162. C₄×C₂²⋊D₇₉	C₂³	semidirect
163. #14579120	C₂³	semidirect
164. #14579119	C₂³	semidirect
170. C₂×C₄⋊Dic₇₉	C₂³	semidirect
186. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
197. C₂²×D₄×C₇₉	C₂³	semidirect
198. C₂²×D₄×C₇₉	C₂³	semidirect
207. C₂³×C₄×C₇₉	C₂³	semidirect
208. #121×C₇₉	C₂³	semidirect
209. #121×C₇₉	C₂³	semidirect
210. #121×C₇₉	C₂³	semidirect
211. #121×C₇₉	C₂³	semidirect
214. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
217. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
476. C₂×C₇₉	#3537	semidirect
497. C₂²×#121	D₇₉	semidirect
498. C₇₉	C₂×#3537	semidirect
505. C₂³×D₄	C₂×D₇₉	semidirect
506. C₂³×D₄	C₂×D₇₉	semidirect
507. C₂⁴×C₄	C₂×D₇₉	semidirect
549. C₂×#121	C₂×D₇₉	semidirect
550. C₂×#121	C₂×D₇₉	semidirect
551. C₂×#121	C₂×D₇₉	semidirect
552. C₂×#121	C₂×D₇₉	semidirect
553. C₂×#121	C₂×D₇₉	semidirect
570. C₂²×C₄⋊C₄	C₂×D₇₉	semidirect
572. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
609. C₂²×D₄	C₂²×D₇₉	semidirect
610. C₂²×D₄	C₂²×D₇₉	semidirect
623. C₂³×C₄	C₂²×D₇₉	semidirect
651. #121	C₂²×D₇₉	semidirect
652. #121	C₂²×D₇₉	semidirect
653. #121	C₂²×D₇₉	semidirect
654. #121	C₂²×D₇₉	semidirect
681. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
697. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
959. C₂	#23777635	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777635	2
C₂×#19099301	2
C₂×#19099265	2
C₂×#19099261	2
C₂×#19099197	2
C₂×D₄×C₂²⋊D₇₉	2
C₂×#19099166	2
C₂×#19099151	2
C₂×#19099150	2
C₂×#19099129	2
C₂×#19099125	2
C₂×#19099121	2
C₂×#19099074	2
C₂²×#14579135	2
C₂²×#121×C₇₉	2
C₂×#3537	79

Subgroups — C2×#23777635 #35195506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777635 #35195506