Subgroups — #35197405

Order 20224.

7370 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777297	C₂	1	4	yes	maximal, complemented
2	#23777296	C₂	1	4	yes	maximal, complemented
3	#23777276	C₂	1	4	yes	maximal, complemented
4	#23777271	C₂	1	4	yes	maximal, complemented
5	#23777245	C₂	1	8	yes	maximal, complemented
6	#23777136	C₂	1	8	yes	maximal, complemented
7	#23777135	C₂	1	8	yes	maximal, complemented
8	#23777085	C₂	1	8	yes	maximal, complemented
9	#23776816	C₂	1	8	yes	maximal, complemented
10	#23776805	C₂	1	1	yes	maximal, characteristic, complemented
11	#23776729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#19099132	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#19099127	C₂	1	1	yes	maximal, characteristic, complemented
14	#23776601	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#19099037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11929624	C₂²	1	1	yes	characteristic
18	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
19	#19099298	C₂²	1	16	yes	complemented
20	#19099296	C₂²	1	16	yes	complemented
21	#19099285	C₂²	1	16	yes	complemented
22	#19099276	C₂²	1	16	yes	complemented
23	#19099261	C₂²	1	16	yes	complemented
24	#19099257	C₂²	1	16	yes	complemented
25	#19099242	C₂²	1	32	yes	complemented
26	#19099237	C₂²	1	32	yes	complemented
27	#19099234	C₂²	1	16	yes	complemented
28	#19099214	C₂²	1	16	yes	complemented
29	#19099209	C₂²	1	32	yes	complemented
30	#19099203	C₂²	1	32	yes	complemented
31	#19099194	C₂²	1	4	yes	complemented
32	#19099191	C₂²	1	4	yes	complemented
33	#19099191	C₂²	1	4	yes	complemented
34	#19099189	C₂²	1	4	yes	—
35	#19099185	C₂²	1	16	yes	complemented
36	#19099184	C₂²	1	16	yes	complemented
37	#19099168	C₂²	1	16	yes	complemented
38	#19099164	C₂²	1	16	yes	complemented
39	#19099146	C₂²	1	32	yes	complemented
40	#19099141	C₂²	1	4	yes	complemented
41	#19099137	C₂²	1	2	yes	complemented
42	#19099134	C₂²	1	2	yes	complemented
43	#19099132	C₂²	1	4	yes	—
44	#19099132	C₂²	1	4	yes	—
45	#19099132	C₂²	1	4	yes	complemented
46	#19099132	C₂²	1	4	yes	complemented
47	#19099130	C₂²	1	2	yes	complemented
48	#19099127	C₂²	1	4	yes	—
49	#19099127	C₂²	1	4	yes	—
50	#19099127	C₂²	1	4	yes	complemented
51	#19099127	C₂²	1	4	yes	complemented
52	#19099127	C₂²	1	2	yes	complemented
53	#19099122	C₂²	1	4	yes	—
54	#19099120	C₂²	1	4	yes	complemented
55	#19099116	C₂²	1	4	yes	complemented
56	#19099116	C₂²	1	4	yes	complemented
57	#19099113	C₂²	1	16	yes	complemented
58	#19099110	C₂²	1	16	yes	complemented
59	#19099109	C₂²	1	4	yes	complemented
60	C₂×#14579158	C₂²	1	2	yes	complemented
61	C₂×#14579157	C₂²	1	2	yes	complemented
62	#19099100	C₂²	1	16	yes	complemented
63	#19099097	C₂²	1	16	yes	complemented
64	C₂×#14579150	C₂²	1	2	yes	complemented
65	C₂×#14579149	C₂²	1	2	yes	complemented
66	#19099074	C₂²	1	4	yes	complemented
67	#19099072	C₂²	1	32	yes	complemented
68	#19099070	C₂²	1	4	yes	complemented
69	C₂×#14579136	C₂²	1	4	yes	complemented
70	C₂×#14579135	C₂²	1	4	yes	complemented
71	C₂×#14579131	C₂²	1	4	yes	—
72	C₂×#14579129	C₂²	1	4	yes	—
73	#19099044	C₂²	1	4	yes	complemented
74	#19099043	C₂²	1	4	yes	complemented
75	#19099040	C₂²	1	2	yes	complemented
76	#19099037	C₂²	1	4	yes	complemented
77	#19099037	C₂²	1	4	yes	complemented
78	#19099037	C₂²	1	4	yes	complemented
79	#19099037	C₂²	1	4	yes	complemented
80	#19099037	C₂²	1	2	yes	complemented
81	#19099036	C₂²	1	4	yes	—
82	C₄×#11929624	C₂²	1	4	yes	complemented
83	#19099031	C₂²	1	4	yes	complemented
84	C₂×C₄×D₃₁₆	C₂²	1	4	yes	complemented
85	C₂×#14579123	C₂²	1	4	yes	complemented
86	C₂×#14579120	C₂²	1	1	yes	characteristic
87	C₂×#14579120	C₂²	1	1	yes	characteristic
88	#117×D₇₉	C₂²	1	4	yes	complemented
89	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	—
90	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
91	#520×C₇₉	C₂²	1	4	yes	complemented
92	#520×C₇₉	C₂²	1	4	yes	complemented
93	#519×C₇₉	C₂²	1	2	yes	complemented
94	#518×C₇₉	C₂²	1	4	yes	—
95	#518×C₇₉	C₂²	1	2	yes	complemented
96	C₄×#41×C₇₉	C₂²	1	4	yes	complemented
97	C₄×#41×C₇₉	C₂²	1	4	yes	complemented
98	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
99	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
100	C₂×#117×C₇₉	C₂²	1	4	yes	complemented
101	C₂⁴×D₇₉	C₂³	1	2	yes	—
102	C₂×#11929624	—	2	8	no	—
103	C₂×#11929624	C₂³	1	2	yes	—
104	C₂×#11929624	C₂³	1	2	yes	—
105	C₂×#11929624	C₂³	1	2	yes	—
106	C₂×#11929624	C₂³	1	2	yes	—
107	C₂×#11929624	C₂³	1	32	yes	complemented
108	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
109	C₂²×D₃₁₆	—	2	8	no	—
110	C₂²×D₃₁₆	C₂³	1	2	yes	—
111	C₂²×D₃₁₆	C₂³	1	2	yes	—
112	C₂²×D₃₁₆	C₂³	1	2	yes	—
113	C₂²×D₃₁₆	C₂³	1	2	yes	—
114	C₂²×D₃₁₆	C₂³	1	2	yes	—
115	C₂²×D₃₁₆	C₂³	1	2	yes	—
116	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
117	C₂²×D₃₁₆	C₂³	1	8	yes	—
118	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
119	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
120	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
121	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
122	#14579161	C₂³	1	8	yes	complemented
123	#14579160	C₂³	1	8	yes	complemented
124	#14579160	C₂³	1	8	yes	complemented
125	#14579159	C₂³	1	4	yes	complemented
126	#14579158	C₂³	1	8	yes	—
127	#14579158	C₂³	1	8	yes	—
128	#14579157	C₂³	1	8	yes	—
129	#14579157	C₂³	1	8	yes	—
130	#14579157	C₂³	1	4	yes	complemented
131	#14579156	C₂³	1	32	yes	complemented
132	#14579155	C₂³	1	32	yes	complemented
133	#14579153	C₂³	1	8	yes	complemented
134	#14579152	C₂³	1	8	yes	complemented
135	#14579152	C₂³	1	8	yes	complemented
136	#14579150	C₂³	1	8	yes	—
137	#14579150	C₂³	1	8	yes	—
138	#14579150	C₂³	1	4	yes	complemented
139	#14579149	C₂³	1	8	yes	—
140	#14579149	C₂³	1	8	yes	—
141	#14579149	C₂³	1	32	yes	complemented
142	#14579148	C₂³	1	4	yes	complemented
143	#14579147	C₂³	1	32	yes	complemented
144	#14579146	C₂³	1	32	yes	complemented
145	#14579146	C₂³	1	32	yes	complemented
146	#14579144	C₂³	1	8	yes	—
147	#14579144	C₂³	1	32	yes	complemented
148	#14579143	C₂³	1	32	yes	complemented
149	#14579142	C₂³	1	8	yes	—
150	#14579140	C₂³	1	16	yes	—
151	#14579140	C₂³	1	8	yes	complemented
152	#14579139	C₂³	1	32	yes	complemented
153	#14579138	C₂³	1	16	yes	—
154	#14579138	C₂³	1	16	yes	—
155	#14579137	C₂³	1	8	yes	complemented
156	#14579136	C₂³	1	16	yes	—
157	#14579136	C₂³	1	16	yes	—
158	#14579135	C₂³	1	16	yes	—
159	#14579135	C₂³	1	16	yes	—
160	#14579135	C₂³	1	8	yes	complemented
161	#14579135	C₂³	1	32	yes	complemented
162	#14579134	C₂³	1	32	yes	complemented
163	#14579134	C₂³	1	32	yes	complemented
164	#14579133	C₂³	1	16	yes	—
165	#14579132	C₂³	1	8	yes	complemented
166	#14579131	C₂³	1	16	yes	—
167	#14579131	C₂³	1	16	yes	—
168	#14579130	C₂³	1	8	yes	—
169	#14579129	C₂³	1	16	yes	—
170	#14579129	C₂³	1	8	yes	—
171	#14579129	C₂³	1	16	yes	—
172	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
173	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
174	#14579126	C₂³	1	8	yes	complemented
175	C₄×D₃₁₆	C₂³	1	16	yes	—
176	C₄×D₃₁₆	C₂³	1	16	yes	—
177	C₄×D₃₁₆	C₂³	1	8	yes	complemented
178	C₄×D₃₁₆	C₂³	1	32	yes	complemented
179	#14579123	C₂³	1	16	yes	—
180	#14579123	C₂³	1	16	yes	—
181	#14579123	C₂³	1	8	yes	complemented
182	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
183	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
184	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
185	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	—
186	#14579120	C₂³	1	2	yes	—
187	#14579120	C₂³	1	2	yes	—
188	#14579120	C₂³	1	2	yes	—
189	#14579120	C₂³	1	2	yes	—
190	#14579120	C₂³	1	2	yes	—
191	#14579120	C₂³	1	2	yes	—
192	#14579120	C₂³	1	2	yes	—
193	#14579120	C₂³	1	2	yes	—
194	#14579119	C₂³	1	8	yes	complemented
195	#14579118	C₂³	1	8	yes	complemented
196	#14579118	C₂³	1	32	yes	complemented
197	#14579117	C₂³	1	8	yes	—
198	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
199	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
200	C₄⋊C₄×D₇₉	C₂³	1	8	yes	complemented
201	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
203	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
204	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
205	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
206	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
207	C₂²⋊C₄×D₇₉	C₂³	1	8	yes	—
208	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
209	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
210	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
211	C₄²×D₇₉	C₂³	1	8	yes	complemented
212	C₂×#41×C₇₉	—	2	8	no	—
213	C₂×#41×C₇₉	C₂³	1	2	yes	—
214	C₂×#41×C₇₉	C₂³	1	2	yes	—
215	C₂×#41×C₇₉	C₂³	1	2	yes	—
216	C₂×#41×C₇₉	C₂³	1	2	yes	—
217	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
218	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
219	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
220	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
221	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₇₉	C₂³	1	8	yes	complemented
223	C₄×Q₈×C₇₉	C₂³	1	8	yes	complemented
224	C₄×D₄×C₇₉	C₂³	1	16	yes	—
225	C₄×D₄×C₇₉	C₂³	1	16	yes	—
226	C₄×D₄×C₇₉	C₂³	1	8	yes	complemented
227	C₄×D₄×C₇₉	C₂³	1	8	yes	complemented
228	#117×C₇₉	C₂³	1	2	yes	—
229	#117×C₇₉	C₂³	1	2	yes	—
230	#117×C₇₉	C₂³	1	2	yes	—
231	#117×C₇₉	C₂³	1	2	yes	—
232	#117×C₇₉	C₂³	1	2	yes	—
233	#117×C₇₉	C₂³	1	2	yes	—
234	#117×C₇₉	C₂³	1	2	yes	—
235	#117×C₇₉	C₂³	1	2	yes	—
236	#117×C₇₉	C₂³	1	8	yes	—
237	#117×C₇₉	C₂³	1	8	yes	complemented
238	#117×C₇₉	C₂³	1	8	yes	complemented
239	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
240	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
241	C₂×C₄⋊C₄×C₇₉	C₂³	1	8	yes	complemented
242	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
243	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
244	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
245	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
246	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
247	C₂×C₄²×C₇₉	C₂³	1	8	yes	complemented
248	C₂³×D₇₉	—	2	8	no	—
249	C₂³×D₇₉	—	8	4	no	—
250	C₂³×D₇₉	C₂⁴	1	4	yes	—
251	C₂³×D₇₉	C₂⁴	1	4	yes	—
252	C₂³×D₇₉	C₂⁴	1	4	yes	—
253	C₂³×D₇₉	C₂⁴	1	2	yes	—
254	#11929624	—	2	8	no	—
255	#11929624	—	2	8	no	—
256	#11929624	—	2	8	no	—
257	#11929624	—	2	8	no	—
258	#11929624	—	8	32	no	—
259	C₂×Dic₁₅₈	—	2	4	no	—
260	C₂×Dic₁₅₈	C₂⁴	1	2	yes	—
261	C₂×Dic₁₅₈	C₂⁴	1	2	yes	—
262	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
263	C₂×D₃₁₆	—	2	4	no	—
264	C₂×D₃₁₆	—	2	8	no	—
265	C₂×D₃₁₆	—	2	8	no	—
266	C₂×D₃₁₆	—	2	8	no	—
267	C₂×D₃₁₆	—	2	8	no	—
268	C₂×D₃₁₆	—	2	8	no	—
269	C₂×D₃₁₆	—	2	8	no	—
270	C₂×D₃₁₆	—	8	8	no	—
271	C₂×D₃₁₆	C₂⁴	1	2	yes	—
272	C₂×D₃₁₆	C₂⁴	1	2	yes	—
273	C₂×D₃₁₆	C₂⁴	1	4	yes	—
274	C₂×D₃₁₆	C₂⁴	1	4	yes	—
275	C₂×D₃₁₆	C₂⁴	1	4	yes	—
276	C₂×D₃₁₆	C₂⁴	1	4	yes	—
277	C₂×D₃₁₆	C₂⁴	1	32	yes	—
278	C₂×C₂²⋊D₇₉	—	2	8	no	—
279	C₂×C₂²⋊D₇₉	—	8	8	no	—
280	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
281	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
282	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
283	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
284	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
285	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
286	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
287	C₂×C₄×D₇₉	—	2	8	no	—
288	C₂×C₄×D₇₉	—	8	8	no	—
289	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
290	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
291	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
292	C₂×C₄×D₇₉	C₂⁴	1	32	yes	—
293	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
294	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
295	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
296	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
297	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
298	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
299	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
300	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
301	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
302	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
303	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
304	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
305	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
306	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
307	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
308	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
309	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
310	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
311	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
312	C₄×Dic₇₉	C₂⁴	1	4	yes	—
313	C₄×Dic₇₉	C₂⁴	1	16	yes	—
314	C₄×Dic₇₉	C₂⁴	1	4	yes	—
315	C₄×Dic₇₉	C₂⁴	1	4	yes	—
316	C₄×Dic₇₉	C₂⁴	1	4	yes	—
317	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
318	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
319	#41×C₇₉	—	2	8	no	—
320	#41×C₇₉	—	2	8	no	—
321	#41×C₇₉	—	2	8	no	—
322	#41×C₇₉	—	2	8	no	—
323	C₂×Q₈×C₇₉	—	2	4	no	—
324	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
326	C₂×D₄×C₇₉	—	2	8	no	—
327	C₂×D₄×C₇₉	—	2	4	no	—
328	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
329	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
330	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
331	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₇₉	—	2	8	no	—
333	C₂²×C₄×C₇₉	#41	1	8	yes	complemented
334	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
335	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
336	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
338	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
339	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
346	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
347	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
348	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
349	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
350	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
351	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
352	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
353	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
354	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
355	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
356	C₄²×C₇₉	C₂⁴	1	4	yes	—
357	C₄²×C₇₉	C₂⁴	1	4	yes	—
358	C₄²×C₇₉	C₂⁴	1	4	yes	—
359	C₄²×C₇₉	C₂⁴	1	4	yes	—
360	C₄²×C₇₉	C₂⁴	1	16	yes	—
361	C₂³×C₇₉	—	2	4	no	—
362	C₂³×C₇₉	—	4	2	no	—
363	C₂³×C₇₉	—	4	4	no	—
364	C₂³×C₇₉	C₂×#41	1	4	yes	—
365	C₂³×C₇₉	C₂⁵	1	4	yes	—
366	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
367	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
368	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
369	C₂²×D₇₉	—	2	8	no	—
370	C₂²×D₇₉	—	2	4	no	—
371	C₂²×D₇₉	—	2	8	no	—
372	C₂²×D₇₉	—	2	8	no	—
373	C₂²×D₇₉	—	4	8	no	—
374	C₂²×D₇₉	—	4	8	no	—
375	C₂²×D₇₉	—	4	4	no	—
376	C₂²×D₇₉	—	4	8	no	—
377	C₂²×D₇₉	—	8	16	no	—
378	C₂²×D₇₉	C₂⁵	1	8	yes	—
379	C₂²×D₇₉	C₂⁵	1	4	yes	—
380	Q₈×C₇₉	—	2	4	no	—
381	Q₈×C₇₉	—	2	4	no	—
382	D₄×C₇₉	—	2	8	no	—
383	D₄×C₇₉	—	2	8	no	—
384	D₄×C₇₉	—	2	4	no	—
385	D₄×C₇₉	—	2	4	no	—
386	C₂×C₄×C₇₉	—	2	4	no	—
387	C₂×C₄×C₇₉	—	2	8	no	—
388	C₂×C₄×C₇₉	—	2	8	no	—
389	C₂×C₄×C₇₉	—	4	4	no	—
390	C₂×C₄×C₇₉	—	4	4	no	—
391	C₂×C₄×C₇₉	—	4	16	no	—
392	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
393	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
394	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
395	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
396	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
397	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
398	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
399	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
400	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
401	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
402	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
403	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
404	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
405	C₂²⋊D₇₉	—	2	8	no	—
406	C₂²⋊D₇₉	—	2	8	no	—
407	C₂²⋊D₇₉	—	4	32	no	—
408	C₂²⋊D₇₉	—	4	16	no	—
409	C₂×Dic₇₉	—	2	4	no	—
410	C₂×Dic₇₉	—	4	4	no	—
411	C₂×Dic₇₉	—	4	4	no	—
412	C₂×Dic₇₉	C₂⁵	1	4	yes	—
413	C₂×Dic₇₉	C₂⁵	1	8	yes	—
414	C₂×Dic₇₉	C₂⁵	1	8	yes	—
415	D₃₁₆	—	2	8	no	—
416	D₃₁₆	—	2	8	no	—
417	D₃₁₆	—	2	8	no	—
418	D₃₁₆	—	2	8	no	—
419	D₃₁₆	—	2	4	no	—
420	D₃₁₆	—	2	4	no	—
421	D₃₁₆	—	4	32	no	—
422	C₄×D₇₉	—	2	8	no	—
423	C₄×D₇₉	—	2	8	no	—
424	C₄×D₇₉	—	4	32	no	—
425	C₄×D₇₉	—	4	16	no	—
426	Dic₁₅₈	—	2	4	no	—
427	Dic₁₅₈	—	2	4	no	—
428	Dic₁₅₈	—	4	16	no	—
429	C₂²×C₇₉	—	2	2	no	—
430	C₂²×C₇₉	—	2	2	no	—
431	C₂²×C₇₉	—	2	2	no	—
432	C₂²×C₇₉	—	2	4	no	—
433	C₂²×C₇₉	—	2	8	no	—
434	C₂²×C₇₉	—	4	4	no	—
435	C₂²×C₇₉	—	8	4	no	—
436	C₂²×C₇₉	C₂²×#41	1	2	yes	—
437	C₂²×C₇₉	C₂²×#41	1	2	yes	—
438	C₂²×C₇₉	C₂²×#41	1	2	yes	—
439	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
440	C₂×D₇₉	—	2	4	no	—
441	C₂×D₇₉	—	2	8	no	—
442	C₂×D₇₉	—	2	16	no	—
443	C₂×D₇₉	—	2	8	no	—
444	C₂×D₇₉	—	4	16	no	—
445	C₂×D₇₉	—	8	4	no	—
446	C₂×D₇₉	—	8	8	no	—
447	C₂×D₇₉	—	8	8	no	—
448	C₄×C₇₉	—	2	4	no	—
449	C₄×C₇₉	—	2	8	no	—
450	C₄×C₇₉	—	2	8	no	—
451	C₄×C₇₉	C₂²×#41	1	2	yes	—
452	C₄×C₇₉	C₂²×#41	1	2	yes	—
453	C₄×C₇₉	C₂²×#41	1	2	yes	—
454	C₄×C₇₉	C₂²×#41	1	2	yes	—
455	Dic₇₉	—	2	4	no	—
456	Dic₇₉	—	2	8	no	—
457	Dic₇₉	—	2	8	no	—
458	#62855	—	79	1	no	maximal, Sylow
459	C₂×C₇₉	—	2	2	no	—
460	C₂×C₇₉	—	2	2	no	—
461	C₂×C₇₉	—	2	2	no	—
462	C₂×C₇₉	—	4	4	no	—
463	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
464	C₂×C₇₉	H(7,𝔽₂)	1	2	yes	—
465	D₇₉	—	4	8	no	—
466	D₇₉	—	4	4	no	—
467	#3510	—	79	4	no	—
468	#3510	—	79	4	no	—
469	#3508	—	79	4	no	—
470	#3508	—	79	4	no	—
471	#3506	—	79	8	no	—
472	#3494	—	79	8	no	—
473	#3494	—	79	8	no	—
474	#3490	—	79	8	no	—
475	#3460	—	79	8	no	—
476	#3458	—	79	1	no	—
477	#3449	—	79	1	no	—
478	C₂×#535	—	79	1	no	—
479	C₂×#535	—	79	1	no	—
480	#3428	—	79	1	no	—
481	#3428	D₇₉	1	1	yes	characteristic, complemented
482	C₂×#518	—	79	1	no	—
483	C₇₉	#62855	1	1	yes	characteristic, complemented, Sylow
484	C₂²×#41	—	79	1	no	—
485	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
486	C₂³×D₄	—	79	1	no	—
487	#559	—	79	16	no	—
488	#559	—	79	16	no	—
489	#556	—	79	16	no	—
490	#555	—	79	16	no	—
491	#553	—	79	16	no	—
492	#553	—	79	16	no	—
493	#551	—	79	32	no	—
494	#551	—	79	32	no	—
495	#550	—	79	16	no	—
496	#547	—	79	16	no	—
497	#546	—	79	32	no	—
498	#546	—	79	32	no	—
499	#544	—	79	4	no	—
500	#544	—	79	4	no	—
501	#544	—	79	4	no	—
502	#543	—	79	4	no	—
503	#542	—	79	16	no	—
504	#542	—	79	16	no	—
505	#540	—	79	16	no	—
506	#540	—	79	16	no	—
507	#538	—	79	32	no	—
508	#537	—	79	4	no	—
509	#536	—	79	2	no	—
510	#536	—	79	2	no	—
511	#535	—	79	4	no	—
512	#535	—	79	4	no	—
513	#535	—	79	4	no	—
514	#535	—	79	4	no	—
515	#535	—	79	2	no	—
516	#535	—	79	2	no	—
517	#535	—	79	4	no	—
518	#535	—	79	4	no	—
519	#535	—	79	4	no	—
520	#535	—	79	4	no	—
521	#534	—	79	4	no	—
522	#533	—	79	4	no	—
523	#533	—	79	4	no	—
524	#533	—	79	4	no	—
525	#532	—	79	4	no	—
526	#532	—	79	16	no	—
527	#532	—	79	16	no	—
528	C₂×#127	—	79	2	no	—
529	C₂×#127	—	79	2	no	—
530	#529	—	79	16	no	—
531	#529	—	79	16	no	—
532	C₂×#124	—	79	2	no	—
533	C₂×#124	—	79	2	no	—
534	#525	—	79	4	no	—
535	#525	—	79	4	no	—
536	#525	—	79	32	no	—
537	C₂×#121	—	79	4	no	—
538	C₂×#121	—	79	4	no	—
539	C₂×#120	—	79	4	no	—
540	C₂×#120	—	79	4	no	—
541	#520	—	79	4	no	—
542	#520	—	79	4	no	—
543	#520	C₂×D₇₉	1	4	yes	complemented
544	#520	C₂×D₇₉	1	4	yes	complemented
545	#519	—	79	2	no	—
546	#519	C₂×D₇₉	1	2	yes	complemented
547	#518	—	79	4	no	—
548	#518	—	79	4	no	—
549	#518	—	79	4	no	—
550	#518	—	79	4	no	—
551	#518	—	79	2	no	—
552	#518	—	79	4	no	—
553	#518	C₂×D₇₉	1	4	yes	—
554	#518	C₂×D₇₉	1	2	yes	complemented
555	C₄×#41	—	79	4	no	—
556	C₄×#41	—	79	4	no	—
557	C₄×#41	C₂×D₇₉	1	4	yes	complemented
558	C₄×#41	C₂×D₇₉	1	4	yes	complemented
559	C₂×C₄×D₄	—	79	4	no	—
560	C₂×C₄×D₄	—	79	4	no	—
561	C₂×#117	—	79	1	no	—
562	C₂×#117	—	79	1	no	—
563	C₂×#117	—	79	4	no	—
564	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
565	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
566	C₂×#117	C₂×D₇₉	1	4	yes	complemented
567	C₂²×C₂²⋊C₄	—	79	4	no	—
568	C₂⁵	—	79	2	no	—
569	C₂×#41	—	2	8	no	—
570	C₂×#41	—	79	32	no	—
571	C₂×#41	—	79	2	no	—
572	C₂×#41	—	79	2	no	—
573	C₂×#41	—	79	2	no	—
574	C₂×#41	—	79	2	no	—
575	C₂×#41	—	158	8	no	—
576	C₂×#41	C₂²×D₇₉	1	2	yes	—
577	C₂×#41	C₂²×D₇₉	1	2	yes	—
578	C₂×#41	C₂²×D₇₉	1	2	yes	—
579	C₂×#41	C₂²×D₇₉	1	2	yes	—
580	C₂²×Q₈	—	79	1	no	—
581	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
582	C₂²×D₄	—	79	8	no	—
583	C₂²×D₄	—	79	2	no	—
584	C₂²×D₄	—	79	8	no	—
585	C₂²×D₄	—	79	2	no	—
586	C₂²×D₄	—	79	2	no	—
587	C₂²×D₄	—	79	2	no	—
588	C₂²×D₄	—	79	2	no	—
589	C₂²×D₄	—	79	2	no	—
590	C₂²×D₄	—	79	2	no	—
591	C₂²×D₄	—	79	1	no	—
592	C₂²×D₄	—	158	8	no	—
593	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
594	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
595	C₂³×C₄	—	79	8	no	—
596	C₂³×C₄	—	79	2	no	—
597	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
598	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
599	C₄⋊Q₈	—	79	4	no	—
600	C₄⋊Q₈	—	79	8	no	—
601	C₄⋊Q₈	—	79	8	no	—
602	C₄⋊Q₈	—	79	8	no	—
603	#127	—	79	8	no	—
604	#127	—	79	8	no	—
605	#127	—	79	4	no	—
606	#127	—	79	8	no	—
607	#127	—	79	8	no	—
608	#126	—	79	32	no	—
609	#126	—	79	32	no	—
610	#125	—	79	8	no	—
611	#125	—	79	8	no	—
612	#125	—	79	8	no	—
613	#124	—	79	8	no	—
614	#124	—	79	8	no	—
615	#124	—	79	4	no	—
616	#124	—	79	4	no	—
617	#124	—	79	32	no	—
618	#124	—	79	8	no	—
619	#124	—	79	8	no	—
620	#124	—	79	32	no	—
621	#123	—	79	8	no	—
622	#123	—	79	8	no	—
623	#123	—	79	32	no	—
624	#123	—	79	32	no	—
625	#123	—	79	32	no	—
626	#123	—	79	32	no	—
627	C₂²⋊Q₈	—	79	8	no	—
628	C₂²⋊Q₈	—	79	8	no	—
629	C₂²⋊Q₈	—	79	16	no	—
630	C₂²⋊Q₈	—	79	32	no	—
631	C₂²⋊Q₈	—	79	16	no	—
632	C₂²⋊Q₈	—	79	16	no	—
633	#121	—	79	16	no	—
634	#121	—	79	8	no	—
635	#121	—	79	16	no	—
636	#121	—	79	16	no	—
637	#121	—	79	8	no	—
638	#121	—	79	32	no	—
639	#121	—	79	16	no	—
640	#121	—	79	16	no	—
641	#121	—	79	32	no	—
642	#121	—	79	32	no	—
643	#120	—	79	8	no	—
644	#120	—	79	16	no	—
645	#120	—	79	16	no	—
646	#120	—	79	8	no	—
647	#120	—	79	16	no	—
648	#120	—	79	16	no	—
649	C₄×Q₈	—	79	8	no	—
650	C₄×Q₈	—	79	8	no	—
651	C₄×Q₈	—	79	16	no	—
652	C₄×Q₈	C₂²×D₇₉	1	8	yes	complemented
653	C₄×Q₈	C₂²×D₇₉	1	8	yes	complemented
654	C₄×D₄	—	79	16	no	—
655	C₄×D₄	—	79	16	no	—
656	C₄×D₄	—	79	32	no	—
657	C₄×D₄	—	79	16	no	—
658	C₄×D₄	—	79	16	no	—
659	C₄×D₄	—	79	8	no	—
660	C₄×D₄	—	79	16	no	—
661	C₄×D₄	—	79	16	no	—
662	C₄×D₄	—	79	16	no	—
663	C₄×D₄	—	79	8	no	—
664	C₄×D₄	—	79	32	no	—
665	C₄×D₄	C₂²×D₇₉	1	16	yes	—
666	C₄×D₄	C₂²×D₇₉	1	16	yes	—
667	C₄×D₄	C₂²×D₇₉	1	8	yes	complemented
668	C₄×D₄	C₂²×D₇₉	1	8	yes	complemented
669	#117	—	79	2	no	—
670	#117	—	79	2	no	—
671	#117	—	79	2	no	—
672	#117	—	79	2	no	—
673	#117	—	79	2	no	—
674	#117	—	79	2	no	—
675	#117	—	79	2	no	—
676	#117	—	79	2	no	—
677	#117	—	79	8	no	—
678	#117	—	79	8	no	—
679	#117	—	79	8	no	—
680	#117	—	79	32	no	—
681	#117	C₂²×D₇₉	1	2	yes	—
682	#117	C₂²×D₇₉	1	2	yes	—
683	#117	C₂²×D₇₉	1	2	yes	—
684	#117	C₂²×D₇₉	1	2	yes	—
685	#117	C₂²×D₇₉	1	2	yes	—
686	#117	C₂²×D₇₉	1	2	yes	—
687	#117	C₂²×D₇₉	1	2	yes	—
688	#117	C₂²×D₇₉	1	2	yes	—
689	#117	C₂²×D₇₉	1	8	yes	—
690	#117	C₂²×D₇₉	1	8	yes	complemented
691	#117	C₂²×D₇₉	1	8	yes	complemented
692	C₂×C₄⋊C₄	—	79	2	no	—
693	C₂×C₄⋊C₄	—	79	2	no	—
694	C₂×C₄⋊C₄	—	79	8	no	—
695	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
696	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
697	C₂×C₄⋊C₄	C₂²×D₇₉	1	8	yes	complemented
698	C₂×C₂²⋊C₄	—	79	2	no	—
699	C₂×C₂²⋊C₄	—	79	2	no	—
700	C₂×C₂²⋊C₄	—	79	8	no	—
701	C₂×C₂²⋊C₄	—	79	8	no	—
702	C₂×C₂²⋊C₄	—	79	8	no	—
703	C₂×C₂²⋊C₄	—	79	16	no	—
704	C₂×C₂²⋊C₄	—	79	16	no	—
705	C₂×C₂²⋊C₄	—	79	8	no	—
706	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
709	C₂×C₄²	—	79	2	no	—
710	C₂×C₄²	—	79	2	no	—
711	C₂×C₄²	—	79	8	no	—
712	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
713	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
714	C₂×C₄²	C₂²×D₇₉	1	8	yes	complemented
715	C₂⁴	—	79	4	no	—
716	C₂⁴	—	79	4	no	—
717	C₂⁴	—	79	2	no	—
718	C₂⁴	—	79	4	no	—
719	C₂⁴	—	632	4	no	—
720	C₂⁴	—	158	8	no	—
721	C₂⁴	C₂³×D₇₉	1	2	yes	—
722	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
723	#41	—	2	8	no	—
724	#41	—	2	8	no	—
725	#41	—	2	8	no	—
726	#41	—	2	8	no	—
727	#41	—	632	32	no	—
728	#41	—	158	8	no	—
729	#41	—	158	8	no	—
730	#41	—	158	8	no	—
731	#41	—	158	8	no	—
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	79	16	no	—
734	C₂×Q₈	—	79	2	no	—
735	C₂×Q₈	—	79	2	no	—
736	C₂×Q₈	—	158	4	no	—
737	C₂×Q₈	C₂³×D₇₉	1	2	yes	—
738	C₂×Q₈	C₂³×D₇₉	1	2	yes	—
739	C₂×D₄	—	2	8	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	79	16	no	—
742	C₂×D₄	—	79	32	no	—
743	C₂×D₄	—	79	4	no	—
744	C₂×D₄	—	79	4	no	—
745	C₂×D₄	—	79	32	no	—
746	C₂×D₄	—	79	4	no	—
747	C₂×D₄	—	79	4	no	—
748	C₂×D₄	—	79	4	no	—
749	C₂×D₄	—	79	2	no	—
750	C₂×D₄	—	79	4	no	—
751	C₂×D₄	—	79	2	no	—
752	C₂×D₄	—	632	8	no	—
753	C₂×D₄	—	632	8	no	—
754	C₂×D₄	—	158	8	no	—
755	C₂×D₄	—	158	8	no	—
756	C₂×D₄	—	158	8	no	—
757	C₂×D₄	—	158	8	no	—
758	C₂×D₄	—	158	8	no	—
759	C₂×D₄	—	158	8	no	—
760	C₂×D₄	—	158	8	no	—
761	C₂×D₄	—	158	4	no	—
762	C₂×D₄	C₂³×D₇₉	1	4	yes	—
763	C₂×D₄	C₂³×D₇₉	1	4	yes	—
764	C₂×D₄	C₂³×D₇₉	1	2	yes	—
765	C₂×D₄	C₂³×D₇₉	1	2	yes	—
766	C₂²×C₄	—	2	8	no	—
767	C₂²×C₄	—	79	4	no	—
768	C₂²×C₄	—	79	4	no	—
769	C₂²×C₄	—	79	16	no	—
770	C₂²×C₄	—	79	32	no	—
771	C₂²×C₄	—	79	2	no	—
772	C₂²×C₄	—	79	4	no	—
773	C₂²×C₄	—	79	4	no	—
774	C₂²×C₄	—	632	8	no	—
775	C₂²×C₄	—	158	8	no	—
776	C₂²×C₄	#11929624	1	8	yes	complemented
777	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
778	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
779	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
780	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
781	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
782	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
783	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
784	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
785	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
786	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
787	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
788	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
789	C₄⋊C₄	—	79	16	no	—
790	C₄⋊C₄	—	79	16	no	—
791	C₄⋊C₄	—	79	16	no	—
792	C₄⋊C₄	—	79	16	no	—
793	C₄⋊C₄	—	79	4	no	—
794	C₄⋊C₄	—	79	4	no	—
795	C₄⋊C₄	—	79	4	no	—
796	C₄⋊C₄	—	79	4	no	—
797	C₄⋊C₄	—	79	16	no	—
798	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
799	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
800	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
801	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
802	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
803	C₂²⋊C₄	—	79	4	no	—
804	C₂²⋊C₄	—	79	4	no	—
805	C₂²⋊C₄	—	79	4	no	—
806	C₂²⋊C₄	—	79	4	no	—
807	C₂²⋊C₄	—	79	16	no	—
808	C₂²⋊C₄	—	79	32	no	—
809	C₂²⋊C₄	—	79	16	no	—
810	C₂²⋊C₄	—	79	32	no	—
811	C₂²⋊C₄	—	79	32	no	—
812	C₂²⋊C₄	—	79	16	no	—
813	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
814	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
815	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
816	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
817	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
818	C₄²	—	79	4	no	—
819	C₄²	—	79	16	no	—
820	C₄²	—	79	4	no	—
821	C₄²	—	79	4	no	—
822	C₄²	—	79	4	no	—
823	C₄²	C₂³×D₇₉	1	4	yes	—
824	C₄²	C₂³×D₇₉	1	4	yes	—
825	C₄²	C₂³×D₇₉	1	4	yes	—
826	C₄²	C₂³×D₇₉	1	4	yes	—
827	C₄²	C₂³×D₇₉	1	16	yes	—
828	C₂³	—	2	4	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	316	8	no	—
832	C₂³	—	316	4	no	—
833	C₂³	—	316	8	no	—
834	C₂³	—	316	8	no	—
835	C₂³	—	79	8	no	—
836	C₂³	—	79	4	no	—
837	C₂³	—	632	16	no	—
838	C₂³	—	158	8	no	—
839	C₂³	—	158	4	no	—
840	C₂³	—	158	8	no	—
841	C₂³	—	158	8	no	—
842	C₂³	C₂×#11929624	1	4	yes	—
843	C₂³	C₂⁴×D₇₉	1	4	yes	—
844	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
845	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
846	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
847	Q₈	—	2	4	no	—
848	Q₈	—	2	4	no	—
849	Q₈	—	316	16	no	—
850	Q₈	—	158	4	no	—
851	Q₈	—	158	4	no	—
852	D₄	—	2	8	no	—
853	D₄	—	2	8	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	4	no	—
856	D₄	—	316	32	no	—
857	D₄	—	316	32	no	—
858	D₄	—	316	16	no	—
859	D₄	—	158	8	no	—
860	D₄	—	158	8	no	—
861	D₄	—	158	8	no	—
862	D₄	—	158	8	no	—
863	D₄	—	158	8	no	—
864	D₄	—	158	8	no	—
865	D₄	—	158	4	no	—
866	D₄	—	158	4	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	2	8	no	—
869	C₂×C₄	—	2	8	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	4	no	—
872	C₂×C₄	—	4	16	no	—
873	C₂×C₄	—	316	32	no	—
874	C₂×C₄	—	316	16	no	—
875	C₂×C₄	—	316	4	no	—
876	C₂×C₄	—	316	4	no	—
877	C₂×C₄	—	79	4	no	—
878	C₂×C₄	—	79	8	no	—
879	C₂×C₄	—	79	8	no	—
880	C₂×C₄	—	158	4	no	—
881	C₂×C₄	—	158	8	no	—
882	C₂×C₄	—	158	8	no	—
883	C₂×C₄	C₂×#11929624	1	4	yes	—
884	C₂×C₄	C₂×#11929624	1	4	yes	—
885	C₂×C₄	C₂×#11929624	1	4	yes	—
886	C₂×C₄	C₂×#11929624	1	4	yes	—
887	C₂×C₄	C₂×#11929624	1	4	yes	—
888	C₂×C₄	C₂×#11929624	1	4	yes	—
889	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
890	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
891	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
892	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
893	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
894	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
895	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	2	8	no	—
901	C₂²	—	4	4	no	—
902	C₂²	—	8	4	no	—
903	C₂²	—	316	16	no	—
904	C₂²	—	632	8	no	—
905	C₂²	—	632	8	no	—
906	C₂²	—	632	4	no	—
907	C₂²	—	158	4	no	—
908	C₂²	—	158	8	no	—
909	C₂²	—	158	8	no	—
910	C₂²	—	158	16	no	—
911	C₂²	C₂²×#11929624	1	2	yes	—
912	C₂²	C₂²×#11929624	1	2	yes	—
913	C₂²	C₂²×#11929624	1	2	yes	—
914	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
915	C₄	—	2	4	no	—
916	C₄	—	2	8	no	—
917	C₄	—	2	8	no	—
918	C₄	—	158	4	no	—
919	C₄	—	158	8	no	—
920	C₄	—	158	8	no	—
921	C₄	C₂²×#11929624	1	2	yes	—
922	C₄	C₂²×#11929624	1	2	yes	—
923	C₄	C₂²×#11929624	1	2	yes	—
924	C₄	C₂²×#11929624	1	2	yes	—
925	C₂	—	2	2	no	—
926	C₂	—	2	2	no	—
927	C₂	—	2	2	no	—
928	C₂	—	4	4	no	—
929	C₂	—	316	8	no	—
930	C₂	—	316	4	no	—
931	C₂	C₂³×#11929624	1	1	yes	characteristic
932	C₂	#23778211	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₇₉×#3428	C₂
hypercenter	#3428	D₇₉
hypocenter	C₇₉	#62855
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #3428

Complements

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

N	H ≅ G/N	type
1. #23777297	C₂	semidirect
2. #23777296	C₂	semidirect
3. #23777276	C₂	semidirect
4. #23777271	C₂	semidirect
5. #23777245	C₂	semidirect
6. #23777136	C₂	semidirect
7. #23777135	C₂	semidirect
8. #23777085	C₂	semidirect
9. #23776816	C₂	semidirect
10. #23776805	C₂	semidirect
11. #23776729	C₂	semidirect
12. C₂×#19099132	C₂	semidirect
13. C₂×#19099127	C₂	semidirect
14. #23776601	C₂	semidirect
15. C₂×#19099037	C₂	semidirect
16. C₇₉×#3428	C₂	semidirect
19. #19099298	C₂²	semidirect
20. #19099296	C₂²	semidirect
21. #19099285	C₂²	semidirect
22. #19099276	C₂²	semidirect
23. #19099261	C₂²	semidirect
24. #19099257	C₂²	semidirect
25. #19099242	C₂²	semidirect
26. #19099237	C₂²	semidirect
27. #19099234	C₂²	semidirect
28. #19099214	C₂²	semidirect
29. #19099209	C₂²	semidirect
30. #19099203	C₂²	semidirect
31. #19099194	C₂²	semidirect
32. #19099191	C₂²	semidirect
33. #19099191	C₂²	semidirect
35. #19099185	C₂²	semidirect
36. #19099184	C₂²	semidirect
37. #19099168	C₂²	semidirect
38. #19099164	C₂²	semidirect
39. #19099146	C₂²	semidirect
40. #19099141	C₂²	semidirect
41. #19099137	C₂²	semidirect
42. #19099134	C₂²	semidirect
45. #19099132	C₂²	semidirect
46. #19099132	C₂²	semidirect
47. #19099130	C₂²	semidirect
50. #19099127	C₂²	semidirect
51. #19099127	C₂²	semidirect
52. #19099127	C₂²	semidirect
54. #19099120	C₂²	semidirect
55. #19099116	C₂²	semidirect
56. #19099116	C₂²	semidirect
57. #19099113	C₂²	semidirect
58. #19099110	C₂²	semidirect
59. #19099109	C₂²	semidirect
60. C₂×#14579158	C₂²	semidirect
61. C₂×#14579157	C₂²	semidirect
62. #19099100	C₂²	semidirect
63. #19099097	C₂²	semidirect
64. C₂×#14579150	C₂²	semidirect
65. C₂×#14579149	C₂²	semidirect
66. #19099074	C₂²	semidirect
67. #19099072	C₂²	semidirect
68. #19099070	C₂²	semidirect
69. C₂×#14579136	C₂²	semidirect
70. C₂×#14579135	C₂²	semidirect
73. #19099044	C₂²	semidirect
74. #19099043	C₂²	semidirect
75. #19099040	C₂²	semidirect
76. #19099037	C₂²	semidirect
77. #19099037	C₂²	semidirect
78. #19099037	C₂²	semidirect
79. #19099037	C₂²	semidirect
80. #19099037	C₂²	semidirect
82. C₄×#11929624	C₂²	semidirect
83. #19099031	C₂²	semidirect
84. C₂×C₄×D₃₁₆	C₂²	semidirect
85. C₂×#14579123	C₂²	semidirect
88. #117×D₇₉	C₂²	semidirect
91. #520×C₇₉	C₂²	semidirect
92. #520×C₇₉	C₂²	semidirect
93. #519×C₇₉	C₂²	semidirect
95. #518×C₇₉	C₂²	semidirect
96. C₄×#41×C₇₉	C₂²	semidirect
97. C₄×#41×C₇₉	C₂²	semidirect
100. C₂×#117×C₇₉	C₂²	semidirect
107. C₂×#11929624	C₂³	semidirect
122. #14579161	C₂³	semidirect
123. #14579160	C₂³	semidirect
124. #14579160	C₂³	semidirect
125. #14579159	C₂³	semidirect
130. #14579157	C₂³	semidirect
131. #14579156	C₂³	semidirect
132. #14579155	C₂³	semidirect
133. #14579153	C₂³	semidirect
134. #14579152	C₂³	semidirect
135. #14579152	C₂³	semidirect
138. #14579150	C₂³	semidirect
141. #14579149	C₂³	semidirect
142. #14579148	C₂³	semidirect
143. #14579147	C₂³	semidirect
144. #14579146	C₂³	semidirect
145. #14579146	C₂³	semidirect
147. #14579144	C₂³	semidirect
148. #14579143	C₂³	semidirect
151. #14579140	C₂³	semidirect
152. #14579139	C₂³	semidirect
155. #14579137	C₂³	semidirect
160. #14579135	C₂³	semidirect
161. #14579135	C₂³	semidirect
162. #14579134	C₂³	semidirect
163. #14579134	C₂³	semidirect
165. #14579132	C₂³	semidirect
172. C₄×Dic₁₅₈	C₂³	semidirect
173. C₄×Dic₁₅₈	C₂³	semidirect
174. #14579126	C₂³	semidirect
177. C₄×D₃₁₆	C₂³	semidirect
178. C₄×D₃₁₆	C₂³	semidirect
181. #14579123	C₂³	semidirect
183. C₄×C₂²⋊D₇₉	C₂³	semidirect
184. C₄×C₂²⋊D₇₉	C₂³	semidirect
194. #14579119	C₂³	semidirect
195. #14579118	C₂³	semidirect
196. #14579118	C₂³	semidirect
200. C₄⋊C₄×D₇₉	C₂³	semidirect
211. C₄²×D₇₉	C₂³	semidirect
222. C₄×Q₈×C₇₉	C₂³	semidirect
223. C₄×Q₈×C₇₉	C₂³	semidirect
226. C₄×D₄×C₇₉	C₂³	semidirect
227. C₄×D₄×C₇₉	C₂³	semidirect
237. #117×C₇₉	C₂³	semidirect
238. #117×C₇₉	C₂³	semidirect
241. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
247. C₂×C₄²×C₇₉	C₂³	semidirect
333. C₂²×C₄×C₇₉	#41	semidirect
481. #3428	D₇₉	semidirect
483. C₇₉	#62855	semidirect
543. #520	C₂×D₇₉	semidirect
544. #520	C₂×D₇₉	semidirect
546. #519	C₂×D₇₉	semidirect
554. #518	C₂×D₇₉	semidirect
557. C₄×#41	C₂×D₇₉	semidirect
558. C₄×#41	C₂×D₇₉	semidirect
566. C₂×#117	C₂×D₇₉	semidirect
652. C₄×Q₈	C₂²×D₇₉	semidirect
653. C₄×Q₈	C₂²×D₇₉	semidirect
667. C₄×D₄	C₂²×D₇₉	semidirect
668. C₄×D₄	C₂²×D₇₉	semidirect
690. #117	C₂²×D₇₉	semidirect
691. #117	C₂²×D₇₉	semidirect
697. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
714. C₂×C₄²	C₂²×D₇₉	semidirect
776. C₂²×C₄	#11929624	semidirect

Maximal subgroups

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

subgroup	index
#23777297	2
#23777296	2
#23777276	2
#23777271	2
#23777245	2
#23777136	2
#23777135	2
#23777085	2
#23776816	2
#23776805	2
#23776729	2
C₂×#19099132	2
C₂×#19099127	2
#23776601	2
C₂×#19099037	2
C₇₉×#3428	2
#62855	79