Subgroups — #35196929

Order 20224.

7382 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777613	C₂	1	8	yes	maximal, complemented
2	#23777594	C₂	1	8	yes	maximal, complemented
3	#23777571	C₂	1	8	yes	maximal, complemented
4	#23777332	C₂	1	16	yes	maximal, complemented
5	#23777109	C₂	1	4	yes	maximal, complemented
6	#23777096	C₂	1	4	yes	maximal, complemented
7	#23777089	C₂	1	2	yes	maximal, complemented
8	#23777089	C₂	1	4	yes	maximal, complemented
9	#23777038	C₂	1	4	yes	maximal, complemented
10	#23777035	C₂	1	2	yes	maximal, complemented
11	C₂×#19099074	C₂	1	2	yes	maximal, complemented
12	C₂²×#123×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14579206	C₂²	1	2	yes	complemented
14	C₂²×#11929624	C₂²	1	2	yes	complemented
15	#19099316	C₂²	1	8	yes	complemented
16	#19099310	C₂²	1	16	yes	complemented
17	#19099303	C₂²	1	8	yes	complemented
18	#19099297	C₂²	1	8	yes	complemented
19	#19099268	C₂²	1	16	yes	complemented
20	#19099261	C₂²	1	16	yes	complemented
21	#19099258	C₂²	1	16	yes	complemented
22	#19099250	C₂²	1	16	yes	complemented
23	#19099248	C₂²	1	16	yes	complemented
24	#19099241	C₂²	1	8	yes	complemented
25	#19099239	C₂²	1	16	yes	complemented
26	#19099239	C₂²	1	16	yes	complemented
27	#19099239	C₂²	1	16	yes	complemented
28	#19099236	C₂²	1	16	yes	complemented
29	#19099214	C₂²	1	16	yes	complemented
30	#19099211	C₂²	1	16	yes	complemented
31	#19099207	C₂²	1	16	yes	complemented
32	#19099205	C₂²	1	16	yes	complemented
33	#19099203	C₂²	1	16	yes	complemented
34	#19099203	C₂²	1	16	yes	complemented
35	#19099203	C₂²	1	16	yes	complemented
36	D₄×C₂²⋊D₇₉	C₂²	1	16	yes	complemented
37	#19099194	C₂²	1	4	yes	complemented
38	#19099189	C₂²	1	2	yes	complemented
39	#19099189	C₂²	1	4	yes	complemented
40	#19099181	C₂²	1	16	yes	complemented
41	#19099165	C₂²	1	16	yes	complemented
42	#19099160	C₂²	1	8	yes	complemented
43	#19099160	C₂²	1	8	yes	complemented
44	#19099157	C₂²	1	16	yes	complemented
45	#19099156	C₂²	1	16	yes	complemented
46	#19099151	C₂²	1	8	yes	complemented
47	#19099151	C₂²	1	8	yes	complemented
48	#19099151	C₂²	1	8	yes	complemented
49	#19099149	C₂²	1	16	yes	complemented
50	#19099144	C₂²	1	4	yes	complemented
51	#19099135	C₂²	1	8	yes	complemented
52	#19099130	C₂²	1	4	yes	complemented
53	#19099125	C₂²	1	2	yes	complemented
54	#19099125	C₂²	1	4	yes	complemented
55	#19099124	C₂²	1	8	yes	complemented
56	#19099122	C₂²	1	4	yes	—
57	#19099122	C₂²	1	4	yes	complemented
58	#19099090	C₂²	1	16	yes	complemented
59	#19099074	C₂²	1	4	yes	complemented
60	#19099074	C₂²	1	8	yes	complemented
61	#19099074	C₂²	1	8	yes	complemented
62	#19099074	C₂²	1	8	yes	complemented
63	#19099074	C₂²	1	8	yes	complemented
64	#19099074	C₂²	1	8	yes	complemented
65	#19099071	C₂²	1	8	yes	complemented
66	C₂×#14579144	C₂²	1	4	yes	complemented
67	#123×D₇₉	C₂²	1	8	yes	complemented
68	C₂×#14579140	C₂²	1	4	yes	complemented
69	C₂×#14579135	C₂²	1	4	yes	complemented
70	C₂×#14579130	C₂²	1	4	yes	complemented
71	C₂×#14579130	C₂²	1	4	yes	complemented
72	#19099044	C₂²	1	8	yes	complemented
73	#19099038	C₂²	1	2	yes	complemented
74	#19099036	C₂²	1	4	yes	complemented
75	#19099036	C₂²	1	8	yes	complemented
76	C₂×C₄×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
77	C₂×#14579120	C₂²	1	2	yes	complemented
78	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
79	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
80	C₂×#123×C₇₉	C₂²	1	4	yes	complemented
81	C₂×#123×C₇₉	C₂²	1	4	yes	complemented
82	C₂×#123×C₇₉	C₂²	1	8	yes	complemented
83	C₂×#123×C₇₉	C₂²	1	8	yes	complemented
84	C₂²×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
85	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
86	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
87	#14579206	—	4	8	no	—
88	C₂×#11929624	—	4	8	no	—
89	C₂×#11929624	C₂³	1	4	yes	—
90	C₂×#11929624	C₂³	1	8	yes	—
91	C₂×#11929624	C₂³	1	8	yes	—
92	C₂×#11929624	C₂³	1	8	yes	complemented
93	C₂×#11929623	C₂³	1	8	yes	—
94	C₂²×Dic₁₅₈	C₂³	1	2	yes	complemented
95	C₂²×D₃₁₆	C₂³	1	2	yes	complemented
96	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
97	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
98	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
99	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
100	C₂×D₄×D₇₉	C₂³	1	8	yes	—
101	C₂²×C₄×D₇₉	C₂³	1	4	yes	complemented
102	#14579160	C₂³	1	16	yes	complemented
103	#14579157	C₂³	1	8	yes	—
104	#14579156	C₂³	1	16	yes	complemented
105	#14579156	C₂³	1	16	yes	complemented
106	#14579154	C₂³	1	16	yes	complemented
107	#14579154	C₂³	1	16	yes	complemented
108	#14579154	C₂³	1	16	yes	complemented
109	#14579152	C₂³	1	16	yes	complemented
110	#14579151	C₂³	1	16	yes	complemented
111	#14579151	C₂³	1	16	yes	complemented
112	#14579148	C₂³	1	8	yes	—
113	#14579147	C₂³	1	16	yes	complemented
114	#14579147	C₂³	1	16	yes	complemented
115	#14579147	C₂³	1	16	yes	complemented
116	#14579146	C₂³	1	16	yes	complemented
117	#14579146	C₂³	1	16	yes	complemented
118	#14579145	C₂³	1	16	yes	complemented
119	#14579145	C₂³	1	8	yes	complemented
120	#14579144	C₂³	1	16	yes	—
121	#14579144	C₂³	1	16	yes	—
122	#14579144	C₂³	1	8	yes	—
123	#14579144	C₂³	1	8	yes	complemented
124	#14579144	C₂³	1	8	yes	complemented
125	#14579143	C₂³	1	16	yes	complemented
126	#14579143	C₂³	1	16	yes	complemented
127	#14579143	C₂³	1	16	yes	complemented
128	#14579142	C₂³	1	8	yes	—
129	#14579142	C₂³	1	8	yes	—
130	#14579141	C₂³	1	16	yes	complemented
131	#14579140	C₂³	1	8	yes	—
132	#14579140	C₂³	1	8	yes	—
133	#14579140	C₂³	1	8	yes	—
134	#14579140	C₂³	1	8	yes	—
135	#14579140	C₂³	1	8	yes	—
136	#14579140	C₂³	1	8	yes	complemented
137	#14579140	C₂³	1	8	yes	complemented
138	#14579139	C₂³	1	16	yes	complemented
139	#14579139	C₂³	1	16	yes	complemented
140	#14579138	C₂³	1	16	yes	complemented
141	#14579138	C₂³	1	16	yes	complemented
142	#14579138	C₂³	1	16	yes	complemented
143	#14579136	C₂³	1	16	yes	complemented
144	#14579135	C₂³	1	8	yes	—
145	#14579135	C₂³	1	8	yes	—
146	#14579135	C₂³	1	8	yes	—
147	#14579135	C₂³	1	8	yes	—
148	#14579135	C₂³	1	8	yes	—
149	#14579135	C₂³	1	8	yes	complemented
150	#14579135	C₂³	1	8	yes	complemented
151	#14579134	C₂³	1	16	yes	complemented
152	#14579134	C₂³	1	16	yes	complemented
153	#14579134	C₂³	1	16	yes	complemented
154	#14579133	C₂³	1	16	yes	—
155	#14579133	C₂³	1	16	yes	—
156	#14579132	C₂³	1	16	yes	—
157	#14579131	C₂³	1	16	yes	complemented
158	#14579131	C₂³	1	8	yes	complemented
159	#14579130	C₂³	1	16	yes	—
160	#14579130	C₂³	1	8	yes	—
161	#14579130	C₂³	1	16	yes	—
162	#14579130	C₂³	1	8	yes	—
163	#14579130	C₂³	1	8	yes	—
164	#14579129	C₂³	1	8	yes	—
165	#14579129	C₂³	1	8	yes	—
166	#14579126	C₂³	1	16	yes	complemented
167	D₄×Dic₇₉	C₂³	1	16	yes	—
168	#14579123	C₂³	1	16	yes	complemented
169	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
170	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
171	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
172	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
173	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
174	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
175	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
176	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
177	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
178	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
179	#14579120	C₂³	1	8	yes	—
180	#14579120	C₂³	1	8	yes	—
181	#14579120	C₂³	1	4	yes	—
182	#14579120	C₂³	1	8	yes	complemented
183	#14579119	C₂³	1	16	yes	complemented
184	#14579117	C₂³	1	16	yes	complemented
185	#14579117	C₂³	1	8	yes	complemented
186	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	complemented
187	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	complemented
188	C₄⋊C₄×D₇₉	C₂³	1	16	yes	complemented
189	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
190	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
191	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
192	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
193	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
194	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	complemented
195	C₂²⋊C₄×D₇₉	C₂³	1	8	yes	complemented
196	C₂×C₄×Dic₇₉	C₂³	1	4	yes	complemented
197	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
198	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₇₉	—	4	4	no	—
200	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
201	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
202	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
203	C₂³×C₄×C₇₉	—	4	4	no	—
204	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
205	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
206	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
207	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
209	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
210	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
211	#123×C₇₉	C₂³	1	16	yes	—
212	#123×C₇₉	C₂³	1	8	yes	—
213	#123×C₇₉	C₂³	1	16	yes	—
214	#123×C₇₉	C₂³	1	8	yes	—
215	#123×C₇₉	C₂³	1	8	yes	—
216	#123×C₇₉	C₂³	1	8	yes	—
217	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
218	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
219	C₂×C₄⋊C₄×C₇₉	C₂³	1	8	yes	—
220	C₂×C₄⋊C₄×C₇₉	C₂³	1	8	yes	—
221	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
223	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
226	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
227	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
228	C₂³×D₇₉	C₂⁴	1	4	yes	—
229	C₂³×D₇₉	C₂⁴	1	4	yes	—
230	#11929624	—	4	16	no	—
231	#11929624	—	4	16	no	—
232	#11929624	—	4	16	no	—
233	#11929624	—	4	8	no	—
234	#11929623	—	4	16	no	—
235	C₂×Dic₁₅₈	—	4	4	no	—
236	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
237	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
238	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
239	C₂×D₃₁₆	—	4	4	no	—
240	C₂×D₃₁₆	C₂⁴	1	8	yes	—
241	C₂×D₃₁₆	C₂⁴	1	8	yes	—
242	C₂×D₃₁₆	C₂⁴	1	4	yes	—
243	C₂×C₂²⋊D₇₉	—	2	16	no	—
244	C₂×C₂²⋊D₇₉	—	4	8	no	—
245	C₂×C₂²⋊D₇₉	—	4	16	no	—
246	C₂×C₂²⋊D₇₉	—	4	16	no	—
247	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
248	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
249	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
250	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
251	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
252	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
253	D₄×D₇₉	—	4	16	no	—
254	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
255	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
256	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
257	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
258	C₂×C₄×D₇₉	—	4	8	no	—
259	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
260	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
261	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
262	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
263	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
264	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
265	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
266	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
267	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
268	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
269	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
270	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
271	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
272	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
273	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
274	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
275	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
276	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
277	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
278	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
279	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
280	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
281	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
282	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
283	C₄×Dic₇₉	C₂⁴	1	16	yes	—
284	C₄×Dic₇₉	C₂⁴	1	16	yes	—
285	C₄×Dic₇₉	C₂⁴	1	8	yes	—
286	C₂⁴×C₇₉	—	2	4	no	—
287	C₂⁴×C₇₉	—	4	4	no	—
288	C₂⁴×C₇₉	—	4	2	no	—
289	C₂⁴×C₇₉	—	4	4	no	—
290	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
291	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
292	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
293	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
294	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
295	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
296	C₂×D₄×C₇₉	—	2	8	no	—
297	C₂×D₄×C₇₉	—	4	4	no	—
298	C₂×D₄×C₇₉	—	4	16	no	—
299	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
300	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
301	C₂²×C₄×C₇₉	—	2	8	no	—
302	C₂²×C₄×C₇₉	—	4	8	no	—
303	C₂²×C₄×C₇₉	—	4	8	no	—
304	C₂²×C₄×C₇₉	—	4	4	no	—
305	C₂²×C₄×C₇₉	—	4	4	no	—
306	C₂²×C₄×C₇₉	—	4	4	no	—
307	C₂²×C₄×C₇₉	—	4	2	no	—
308	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
310	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
311	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
313	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
315	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
316	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
320	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
322	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
323	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
324	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
325	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
326	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
328	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
329	C₂³×C₇₉	—	2	2	no	—
330	C₂³×C₇₉	—	2	4	no	—
331	C₂³×C₇₉	—	2	8	no	—
332	C₂³×C₇₉	—	2	2	no	—
333	C₂³×C₇₉	—	2	8	no	—
334	C₂³×C₇₉	—	2	4	no	—
335	C₂³×C₇₉	—	2	8	no	—
336	C₂³×C₇₉	—	4	2	no	—
337	C₂³×C₇₉	—	4	4	no	—
338	C₂³×C₇₉	—	4	2	no	—
339	C₂³×C₇₉	—	4	4	no	—
340	C₂³×C₇₉	—	4	4	no	—
341	C₂³×C₇₉	—	4	4	no	—
342	C₂³×C₇₉	—	4	16	no	—
343	C₂³×C₇₉	—	8	8	no	—
344	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
345	C₂³×C₇₉	C₂⁵	1	2	yes	—
346	C₂³×C₇₉	C₂⁵	1	4	yes	—
347	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
348	C₂³×C₇₉	C₂⁵	1	2	yes	—
349	C₂³×C₇₉	C₂⁵	1	2	yes	—
350	C₂²×D₇₉	—	2	8	no	—
351	C₂²×D₇₉	—	4	8	no	—
352	C₂²×D₇₉	—	4	4	no	—
353	C₂²×D₇₉	—	4	8	no	—
354	C₂²×D₇₉	C₂⁵	1	8	yes	—
355	D₄×C₇₉	—	2	16	no	—
356	D₄×C₇₉	—	4	8	no	—
357	C₂×C₄×C₇₉	—	2	4	no	—
358	C₂×C₄×C₇₉	—	2	4	no	—
359	C₂×C₄×C₇₉	—	2	8	no	—
360	C₂×C₄×C₇₉	—	2	8	no	—
361	C₂×C₄×C₇₉	—	2	4	no	—
362	C₂×C₄×C₇₉	—	2	8	no	—
363	C₂×C₄×C₇₉	—	4	2	no	—
364	C₂×C₄×C₇₉	—	4	2	no	—
365	C₂×C₄×C₇₉	—	4	4	no	—
366	C₂×C₄×C₇₉	—	4	4	no	—
367	C₂×C₄×C₇₉	—	4	2	no	—
368	C₂×C₄×C₇₉	—	4	2	no	—
369	C₂×C₄×C₇₉	—	4	4	no	—
370	C₂×C₄×C₇₉	—	4	4	no	—
371	C₂×C₄×C₇₉	—	4	4	no	—
372	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
373	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
374	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
375	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
376	C₂²⋊D₇₉	—	2	16	no	—
377	C₂²⋊D₇₉	—	2	16	no	—
378	C₂²⋊D₇₉	—	2	32	no	—
379	C₂²⋊D₇₉	—	4	8	no	—
380	C₂²⋊D₇₉	—	4	16	no	—
381	C₂²⋊D₇₉	—	4	16	no	—
382	C₂×Dic₇₉	—	2	8	no	—
383	C₂×Dic₇₉	—	4	8	no	—
384	C₂×Dic₇₉	—	4	8	no	—
385	C₂×Dic₇₉	—	4	4	no	—
386	C₂×Dic₇₉	C₂⁵	1	16	yes	—
387	C₂×Dic₇₉	C₂⁵	1	8	yes	—
388	D₃₁₆	—	4	4	no	—
389	D₃₁₆	—	4	8	no	—
390	D₃₁₆	—	4	8	no	—
391	C₄×D₇₉	—	4	16	no	—
392	C₄×D₇₉	—	4	8	no	—
393	C₄×D₇₉	—	4	16	no	—
394	Dic₁₅₈	—	4	8	no	—
395	Dic₁₅₈	—	4	4	no	—
396	Dic₁₅₈	—	4	8	no	—
397	C₂²×C₇₉	—	2	8	no	—
398	C₂²×C₇₉	—	2	2	no	—
399	C₂²×C₇₉	—	2	2	no	—
400	C₂²×C₇₉	—	2	2	no	—
401	C₂²×C₇₉	—	2	4	no	—
402	C₂²×C₇₉	—	2	4	no	—
403	C₂²×C₇₉	—	2	2	no	—
404	C₂²×C₇₉	—	2	4	no	—
405	C₂²×C₇₉	—	2	8	no	—
406	C₂²×C₇₉	—	4	4	no	—
407	C₂²×C₇₉	—	4	16	no	—
408	C₂²×C₇₉	—	4	4	no	—
409	C₂²×C₇₉	—	8	4	no	—
410	C₂²×C₇₉	—	8	8	no	—
411	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
412	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
413	C₂²×C₇₉	#585	1	4	yes	—
414	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
415	C₂×D₇₉	—	2	8	no	—
416	C₂×D₇₉	—	2	16	no	—
417	C₂×D₇₉	—	8	8	no	—
418	C₂×D₇₉	—	16	4	no	—
419	C₄×C₇₉	—	2	4	no	—
420	C₄×C₇₉	—	2	4	no	—
421	C₄×C₇₉	—	2	4	no	—
422	C₄×C₇₉	—	2	8	no	—
423	Dic₇₉	—	2	8	no	—
424	Dic₇₉	—	2	16	no	—
425	#62820	—	79	1	no	maximal, Sylow
426	C₂×C₇₉	—	2	4	no	—
427	C₂×C₇₉	—	2	2	no	—
428	C₂×C₇₉	—	2	4	no	—
429	C₂×C₇₉	—	4	4	no	—
430	C₂×C₇₉	—	4	2	no	—
431	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₇₉	C₂×#585	1	2	yes	—
433	D₇₉	—	4	8	no	—
434	#3535	—	79	8	no	—
435	#3534	—	79	8	no	—
436	#3533	—	79	8	no	—
437	#3513	—	79	16	no	—
438	#3492	—	79	4	no	—
439	#3491	—	79	4	no	—
440	#3490	—	79	2	no	—
441	#3490	—	79	4	no	—
442	#3485	—	79	4	no	—
443	#3484	—	79	2	no	—
444	C₂×#525	—	79	2	no	—
445	C₂²×#123	D₇₉	1	1	yes	characteristic, complemented
446	C₇₉	#62820	1	1	yes	characteristic, complemented, Sylow
447	C₂×H(5,𝔽₂)	—	79	2	no	—
448	C₂²×#41	—	79	2	no	—
449	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
450	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
451	#563	—	79	8	no	—
452	#562	—	79	16	no	—
453	#560	—	79	8	no	—
454	#559	—	79	8	no	—
455	#554	—	79	16	no	—
456	#553	—	79	16	no	—
457	#553	—	79	16	no	—
458	#552	—	79	16	no	—
459	#552	—	79	16	no	—
460	#551	—	79	16	no	—
461	#551	—	79	8	no	—
462	#551	—	79	16	no	—
463	#551	—	79	16	no	—
464	#551	—	79	16	no	—
465	#547	—	79	16	no	—
466	#547	—	79	16	no	—
467	#546	—	79	16	no	—
468	#546	—	79	16	no	—
469	#546	—	79	16	no	—
470	#546	—	79	16	no	—
471	#546	—	79	16	no	—
472	D₄²	—	79	16	no	—
473	#544	—	79	4	no	—
474	#543	—	79	2	no	—
475	#543	—	79	4	no	—
476	#542	—	79	16	no	—
477	#540	—	79	16	no	—
478	#539	—	79	16	no	—
479	#539	—	79	16	no	—
480	#539	—	79	8	no	—
481	#539	—	79	8	no	—
482	#538	—	79	16	no	—
483	#538	—	79	8	no	—
484	#538	—	79	8	no	—
485	#538	—	79	8	no	—
486	#537	—	79	4	no	—
487	#536	—	79	8	no	—
488	#535	—	79	4	no	—
489	#534	—	79	4	no	—
490	#534	—	79	4	no	—
491	#534	—	79	8	no	—
492	#534	—	79	2	no	—
493	#534	—	79	4	no	—
494	#529	—	79	16	no	—
495	#525	—	79	8	no	—
496	#525	—	79	8	no	—
497	#525	—	79	8	no	—
498	#525	—	79	8	no	—
499	#525	—	79	4	no	—
500	#525	—	79	8	no	—
501	#525	—	79	8	no	—
502	C₂×#123	—	79	4	no	—
503	C₂×#123	—	79	8	no	—
504	C₂×#123	C₂×D₇₉	1	4	yes	complemented
505	C₂×#123	C₂×D₇₉	1	8	yes	complemented
506	C₂×#123	C₂×D₇₉	1	4	yes	complemented
507	C₂×#123	C₂×D₇₉	1	8	yes	complemented
508	C₂×C₂²⋊Q₈	—	79	4	no	—
509	C₂×#121	—	79	4	no	—
510	C₂×#120	—	79	4	no	—
511	C₂×#120	—	79	4	no	—
512	#520	—	79	8	no	—
513	#518	—	79	2	no	—
514	#518	—	79	4	no	—
515	#518	—	79	8	no	—
516	C₂×C₄×D₄	—	79	8	no	—
517	C₂×#117	—	79	2	no	—
518	C₂²×C₄⋊C₄	C₂×D₇₉	1	2	yes	complemented
519	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
520	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
521	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
522	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
523	H(5,𝔽₂)	—	316	8	no	—
524	C₂×#41	—	316	8	no	—
525	C₂×#41	—	79	8	no	—
526	C₂×#41	—	79	8	no	—
527	C₂×#41	—	79	8	no	—
528	C₂×#41	—	79	4	no	—
529	C₂×#41	—	79	8	no	—
530	C₂²×Q₈	—	79	2	no	—
531	C₂²×D₄	—	4	4	no	—
532	C₂²×D₄	—	79	8	no	—
533	C₂²×D₄	—	79	8	no	—
534	C₂²×D₄	—	79	4	no	—
535	C₂²×D₄	—	79	8	no	—
536	C₂²×D₄	—	79	4	no	—
537	C₂²×D₄	—	79	2	no	—
538	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
539	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
540	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
541	C₂³×C₄	—	4	4	no	—
542	C₂³×C₄	—	79	4	no	—
543	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
544	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
545	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
546	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
547	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
548	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
549	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
550	C₄⋊Q₈	—	79	16	no	—
551	#127	—	79	8	no	—
552	#126	—	79	16	no	—
553	#126	—	79	16	no	—
554	#126	—	79	16	no	—
555	#126	—	79	16	no	—
556	#126	—	79	16	no	—
557	#125	—	79	16	no	—
558	#125	—	79	16	no	—
559	#125	—	79	16	no	—
560	#124	—	79	8	no	—
561	#124	—	79	16	no	—
562	#124	—	79	16	no	—
563	#124	—	79	16	no	—
564	#123	—	79	8	no	—
565	#123	—	79	8	no	—
566	#123	—	79	8	no	—
567	#123	—	79	8	no	—
568	#123	—	79	16	no	—
569	#123	—	79	8	no	—
570	#123	—	79	16	no	—
571	#123	—	79	16	no	—
572	#123	—	79	16	no	—
573	#123	—	79	8	no	—
574	#123	—	79	16	no	—
575	#123	—	79	16	no	—
576	#123	—	79	16	no	—
577	#123	—	79	16	no	—
578	#123	C₂²×D₇₉	1	8	yes	—
579	#123	C₂²×D₇₉	1	8	yes	—
580	#123	C₂²×D₇₉	1	16	yes	—
581	#123	C₂²×D₇₉	1	16	yes	—
582	#123	C₂²×D₇₉	1	8	yes	—
583	#123	C₂²×D₇₉	1	8	yes	—
584	C₂²⋊Q₈	—	79	8	no	—
585	C₂²⋊Q₈	—	79	8	no	—
586	C₂²⋊Q₈	—	79	8	no	—
587	C₂²⋊Q₈	—	79	8	no	—
588	C₂²⋊Q₈	—	79	8	no	—
589	C₂²⋊Q₈	—	79	8	no	—
590	C₂²⋊Q₈	—	79	8	no	—
591	C₂²⋊Q₈	—	79	16	no	—
592	C₂²⋊Q₈	—	79	16	no	—
593	C₂²⋊Q₈	—	79	16	no	—
594	C₂²⋊Q₈	—	79	16	no	—
595	C₂²⋊Q₈	—	79	16	no	—
596	C₂²⋊Q₈	—	79	16	no	—
597	#121	—	79	16	no	—
598	#121	—	79	16	no	—
599	#121	—	79	16	no	—
600	#121	—	79	8	no	—
601	#121	—	79	8	no	—
602	#121	—	79	8	no	—
603	#121	—	79	8	no	—
604	#121	—	79	8	no	—
605	#121	—	79	8	no	—
606	#121	—	79	8	no	—
607	#121	—	79	16	no	—
608	#121	—	79	16	no	—
609	#121	—	79	16	no	—
610	#121	—	79	16	no	—
611	#120	—	79	8	no	—
612	#120	—	79	8	no	—
613	#120	—	79	16	no	—
614	#120	—	79	8	no	—
615	#120	—	79	16	no	—
616	#120	—	79	8	no	—
617	#120	—	79	8	no	—
618	#120	—	79	8	no	—
619	#120	—	79	16	no	—
620	C₄×Q₈	—	79	16	no	—
621	C₄×D₄	—	79	16	no	—
622	C₄×D₄	—	79	16	no	—
623	C₄×D₄	—	79	16	no	—
624	C₄×D₄	—	79	16	no	—
625	C₄×D₄	—	79	16	no	—
626	C₄×D₄	—	79	16	no	—
627	C₄×D₄	—	79	16	no	—
628	C₄×D₄	—	79	16	no	—
629	C₄×D₄	—	79	16	no	—
630	C₄×D₄	—	79	16	no	—
631	C₄×D₄	—	79	16	no	—
632	C₄×D₄	—	79	16	no	—
633	#117	—	79	8	no	—
634	#117	—	79	8	no	—
635	#117	—	79	4	no	—
636	#117	—	79	8	no	—
637	#117	—	79	16	no	—
638	#117	—	79	8	no	—
639	#117	—	79	16	no	—
640	C₂×C₄⋊C₄	—	79	4	no	—
641	C₂×C₄⋊C₄	—	79	8	no	—
642	C₂×C₄⋊C₄	—	79	16	no	—
643	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
644	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
645	C₂×C₄⋊C₄	C₂²×D₇₉	1	8	yes	—
646	C₂×C₄⋊C₄	C₂²×D₇₉	1	8	yes	—
647	C₂×C₂²⋊C₄	—	79	4	no	—
648	C₂×C₂²⋊C₄	—	79	8	no	—
649	C₂×C₂²⋊C₄	—	79	4	no	—
650	C₂×C₂²⋊C₄	—	79	8	no	—
651	C₂×C₂²⋊C₄	—	79	8	no	—
652	C₂×C₂²⋊C₄	—	79	8	no	—
653	C₂×C₂²⋊C₄	—	79	16	no	—
654	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
657	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
659	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
660	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
661	C₂×C₄²	—	79	4	no	—
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	4	4	no	—
664	C₂⁴	—	4	2	no	—
665	C₂⁴	—	4	4	no	—
666	C₂⁴	—	79	4	no	—
667	C₂⁴	—	79	4	no	—
668	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
669	C₂⁴	C₂³×D₇₉	1	4	yes	—
670	C₂⁴	C₂³×D₇₉	1	2	yes	—
671	C₂⁴	C₂³×D₇₉	1	4	yes	—
672	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
673	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
674	#41	—	316	16	no	—
675	#41	—	316	16	no	—
676	#41	—	316	16	no	—
677	#41	—	316	8	no	—
678	#41	—	316	16	no	—
679	C₂×Q₈	—	316	4	no	—
680	C₂×Q₈	—	79	8	no	—
681	C₂×Q₈	—	79	8	no	—
682	C₂×Q₈	—	79	4	no	—
683	C₂×D₄	—	2	8	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	4	16	no	—
686	C₂×D₄	—	316	4	no	—
687	C₂×D₄	—	316	16	no	—
688	C₂×D₄	—	316	16	no	—
689	C₂×D₄	—	316	16	no	—
690	C₂×D₄	—	316	8	no	—
691	C₂×D₄	—	79	16	no	—
692	C₂×D₄	—	79	16	no	—
693	C₂×D₄	—	79	8	no	—
694	C₂×D₄	—	79	16	no	—
695	C₂×D₄	—	79	8	no	—
696	C₂×D₄	—	79	8	no	—
697	C₂×D₄	—	79	8	no	—
698	C₂×D₄	—	79	8	no	—
699	C₂×D₄	—	79	4	no	—
700	C₂×D₄	—	158	16	no	—
701	C₂×D₄	C₂³×D₇₉	1	8	yes	—
702	C₂×D₄	C₂³×D₇₉	1	8	yes	—
703	C₂²×C₄	—	2	8	no	—
704	C₂²×C₄	—	4	8	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	—	4	4	no	—
707	C₂²×C₄	—	4	4	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	4	no	—
710	C₂²×C₄	—	316	8	no	—
711	C₂²×C₄	—	79	8	no	—
712	C₂²×C₄	—	79	8	no	—
713	C₂²×C₄	—	79	4	no	—
714	C₂²×C₄	—	79	16	no	—
715	C₂²×C₄	—	79	16	no	—
716	C₂²×C₄	—	79	8	no	—
717	C₂²×C₄	—	79	4	no	—
718	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
719	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
720	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
721	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
722	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
723	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
724	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
725	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
726	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
727	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
728	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
729	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
730	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
731	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
732	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
733	C₄⋊C₄	—	79	16	no	—
734	C₄⋊C₄	—	79	16	no	—
735	C₄⋊C₄	—	79	16	no	—
736	C₄⋊C₄	—	79	16	no	—
737	C₄⋊C₄	—	79	16	no	—
738	C₄⋊C₄	—	79	8	no	—
739	C₄⋊C₄	—	79	8	no	—
740	C₄⋊C₄	—	79	8	no	—
741	C₄⋊C₄	—	79	8	no	—
742	C₄⋊C₄	—	79	8	no	—
743	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
744	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
745	C₂²⋊C₄	—	79	8	no	—
746	C₂²⋊C₄	—	79	8	no	—
747	C₂²⋊C₄	—	79	16	no	—
748	C₂²⋊C₄	—	79	16	no	—
749	C₂²⋊C₄	—	79	8	no	—
750	C₂²⋊C₄	—	79	16	no	—
751	C₂²⋊C₄	—	79	16	no	—
752	C₂²⋊C₄	—	79	16	no	—
753	C₂²⋊C₄	—	79	16	no	—
754	C₂²⋊C₄	—	79	16	no	—
755	C₂²⋊C₄	—	79	16	no	—
756	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
757	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
758	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
759	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
760	C₄²	—	79	16	no	—
761	C₄²	—	79	16	no	—
762	C₄²	—	79	8	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	4	no	—
765	C₂³	—	2	8	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	8	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	4	4	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	4	16	no	—
777	C₂³	—	8	8	no	—
778	C₂³	—	316	8	no	—
779	C₂³	—	316	4	no	—
780	C₂³	—	316	8	no	—
781	C₂³	—	79	8	no	—
782	C₂³	—	158	8	no	—
783	C₂³	#14579206	1	4	yes	—
784	C₂³	C₂⁴×D₇₉	1	2	yes	—
785	C₂³	C₂⁴×D₇₉	1	4	yes	—
786	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
787	C₂³	C₂⁴×D₇₉	1	2	yes	—
788	C₂³	C₂⁴×D₇₉	1	2	yes	—
789	Q₈	—	316	8	no	—
790	Q₈	—	316	4	no	—
791	Q₈	—	316	8	no	—
792	D₄	—	2	16	no	—
793	D₄	—	4	8	no	—
794	D₄	—	316	4	no	—
795	D₄	—	316	8	no	—
796	D₄	—	316	8	no	—
797	D₄	—	316	8	no	—
798	D₄	—	316	16	no	—
799	D₄	—	316	16	no	—
800	D₄	—	158	16	no	—
801	D₄	—	158	16	no	—
802	D₄	—	158	32	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	8	no	—
806	C₂×C₄	—	2	8	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	8	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	316	16	no	—
819	C₂×C₄	—	316	8	no	—
820	C₂×C₄	—	316	16	no	—
821	C₂×C₄	—	316	4	no	—
822	C₂×C₄	—	316	8	no	—
823	C₂×C₄	—	316	8	no	—
824	C₂×C₄	—	79	16	no	—
825	C₂×C₄	—	79	8	no	—
826	C₂×C₄	—	158	8	no	—
827	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
828	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
829	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
830	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
831	C₂²	—	2	8	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	16	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	8	4	no	—
844	C₂²	—	8	8	no	—
845	C₂²	—	632	8	no	—
846	C₂²	—	158	8	no	—
847	C₂²	—	158	16	no	—
848	C₂²	—	1264	4	no	—
849	C₂²	C₂×#14579206	1	2	yes	—
850	C₂²	C₂×#14579206	1	4	yes	—
851	C₂²	#19099399	1	4	yes	—
852	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	158	8	no	—
858	C₄	—	158	16	no	—
859	C₂	—	2	2	no	—
860	C₂	—	2	4	no	—
861	C₂	—	2	4	no	—
862	C₂	—	4	2	no	—
863	C₂	—	4	4	no	—
864	C₂	—	316	8	no	—
865	C₂	C₂²×#14579206	1	1	yes	characteristic
866	C₂	C₂×#19099399	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₂²×#123×C₇₉	C₂
hypercenter	C₂²×#123	D₇₉
hypocenter	C₇₉	#62820
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×#123

Complements

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

N	H ≅ G/N	type
1. #23777613	C₂	semidirect
2. #23777594	C₂	semidirect
3. #23777571	C₂	semidirect
4. #23777332	C₂	semidirect
5. #23777109	C₂	semidirect
6. #23777096	C₂	semidirect
7. #23777089	C₂	semidirect
8. #23777089	C₂	semidirect
9. #23777038	C₂	semidirect
10. #23777035	C₂	semidirect
11. C₂×#19099074	C₂	semidirect
12. C₂²×#123×C₇₉	C₂	semidirect
13. C₂×#14579206	C₂²	semidirect
14. C₂²×#11929624	C₂²	semidirect
15. #19099316	C₂²	semidirect
16. #19099310	C₂²	semidirect
17. #19099303	C₂²	semidirect
18. #19099297	C₂²	semidirect
19. #19099268	C₂²	semidirect
20. #19099261	C₂²	semidirect
21. #19099258	C₂²	semidirect
22. #19099250	C₂²	semidirect
23. #19099248	C₂²	semidirect
24. #19099241	C₂²	semidirect
25. #19099239	C₂²	semidirect
26. #19099239	C₂²	semidirect
27. #19099239	C₂²	semidirect
28. #19099236	C₂²	semidirect
29. #19099214	C₂²	semidirect
30. #19099211	C₂²	semidirect
31. #19099207	C₂²	semidirect
32. #19099205	C₂²	semidirect
33. #19099203	C₂²	semidirect
34. #19099203	C₂²	semidirect
35. #19099203	C₂²	semidirect
36. D₄×C₂²⋊D₇₉	C₂²	semidirect
37. #19099194	C₂²	semidirect
38. #19099189	C₂²	semidirect
39. #19099189	C₂²	semidirect
40. #19099181	C₂²	semidirect
41. #19099165	C₂²	semidirect
42. #19099160	C₂²	semidirect
43. #19099160	C₂²	semidirect
44. #19099157	C₂²	semidirect
45. #19099156	C₂²	semidirect
46. #19099151	C₂²	semidirect
47. #19099151	C₂²	semidirect
48. #19099151	C₂²	semidirect
49. #19099149	C₂²	semidirect
50. #19099144	C₂²	semidirect
51. #19099135	C₂²	semidirect
52. #19099130	C₂²	semidirect
53. #19099125	C₂²	semidirect
54. #19099125	C₂²	semidirect
55. #19099124	C₂²	semidirect
57. #19099122	C₂²	semidirect
58. #19099090	C₂²	semidirect
59. #19099074	C₂²	semidirect
60. #19099074	C₂²	semidirect
61. #19099074	C₂²	semidirect
62. #19099074	C₂²	semidirect
63. #19099074	C₂²	semidirect
64. #19099074	C₂²	semidirect
65. #19099071	C₂²	semidirect
66. C₂×#14579144	C₂²	semidirect
67. #123×D₇₉	C₂²	semidirect
68. C₂×#14579140	C₂²	semidirect
69. C₂×#14579135	C₂²	semidirect
70. C₂×#14579130	C₂²	semidirect
71. C₂×#14579130	C₂²	semidirect
72. #19099044	C₂²	semidirect
73. #19099038	C₂²	semidirect
74. #19099036	C₂²	semidirect
75. #19099036	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
77. C₂×#14579120	C₂²	semidirect
79. C₂⁴×C₄×C₇₉	C₂²	semidirect
80. C₂×#123×C₇₉	C₂²	semidirect
81. C₂×#123×C₇₉	C₂²	semidirect
82. C₂×#123×C₇₉	C₂²	semidirect
83. C₂×#123×C₇₉	C₂²	semidirect
84. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
85. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
86. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
92. C₂×#11929624	C₂³	semidirect
94. C₂²×Dic₁₅₈	C₂³	semidirect
95. C₂²×D₃₁₆	C₂³	semidirect
101. C₂²×C₄×D₇₉	C₂³	semidirect
102. #14579160	C₂³	semidirect
104. #14579156	C₂³	semidirect
105. #14579156	C₂³	semidirect
106. #14579154	C₂³	semidirect
107. #14579154	C₂³	semidirect
108. #14579154	C₂³	semidirect
109. #14579152	C₂³	semidirect
110. #14579151	C₂³	semidirect
111. #14579151	C₂³	semidirect
113. #14579147	C₂³	semidirect
114. #14579147	C₂³	semidirect
115. #14579147	C₂³	semidirect
116. #14579146	C₂³	semidirect
117. #14579146	C₂³	semidirect
118. #14579145	C₂³	semidirect
119. #14579145	C₂³	semidirect
123. #14579144	C₂³	semidirect
124. #14579144	C₂³	semidirect
125. #14579143	C₂³	semidirect
126. #14579143	C₂³	semidirect
127. #14579143	C₂³	semidirect
130. #14579141	C₂³	semidirect
136. #14579140	C₂³	semidirect
137. #14579140	C₂³	semidirect
138. #14579139	C₂³	semidirect
139. #14579139	C₂³	semidirect
140. #14579138	C₂³	semidirect
141. #14579138	C₂³	semidirect
142. #14579138	C₂³	semidirect
143. #14579136	C₂³	semidirect
149. #14579135	C₂³	semidirect
150. #14579135	C₂³	semidirect
151. #14579134	C₂³	semidirect
152. #14579134	C₂³	semidirect
153. #14579134	C₂³	semidirect
157. #14579131	C₂³	semidirect
158. #14579131	C₂³	semidirect
166. #14579126	C₂³	semidirect
168. #14579123	C₂³	semidirect
174. C₄×C₂²⋊D₇₉	C₂³	semidirect
175. C₄×C₂²⋊D₇₉	C₂³	semidirect
176. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
177. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
178. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
182. #14579120	C₂³	semidirect
183. #14579119	C₂³	semidirect
184. #14579117	C₂³	semidirect
185. #14579117	C₂³	semidirect
186. C₂×C₄⋊Dic₇₉	C₂³	semidirect
187. C₂×Dic₇₉⋊C₄	C₂³	semidirect
188. C₄⋊C₄×D₇₉	C₂³	semidirect
193. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
194. C₂²⋊C₄×D₇₉	C₂³	semidirect
195. C₂²⋊C₄×D₇₉	C₂³	semidirect
196. C₂×C₄×Dic₇₉	C₂³	semidirect
445. C₂²×#123	D₇₉	semidirect
446. C₇₉	#62820	semidirect
450. C₂⁴×C₄	C₂×D₇₉	semidirect
504. C₂×#123	C₂×D₇₉	semidirect
505. C₂×#123	C₂×D₇₉	semidirect
506. C₂×#123	C₂×D₇₉	semidirect
507. C₂×#123	C₂×D₇₉	semidirect
518. C₂²×C₄⋊C₄	C₂×D₇₉	semidirect
519. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
520. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23777613	2
#23777594	2
#23777571	2
#23777332	2
#23777109	2
#23777096	2
#23777089	2
#23777038	2
#23777035	2
C₂×#19099074	2
C₂²×#123×C₇₉	2
#62820	79