Subgroups — #34257074

Order 20224.

862 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772517	C₂	1	1	yes	maximal, characteristic
2	#23772066	C₂	1	1	yes	maximal, characteristic
3	#23762138	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762130	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762130	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762117	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762110	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762110	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762100	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762100	C₂	1	1	yes	maximal, characteristic, complemented
11	#23762090	C₂	1	1	yes	maximal, characteristic, complemented
12	#23762085	C₂	1	1	yes	maximal, characteristic, complemented
13	#23762065	C₂	1	1	yes	maximal, characteristic, complemented
14	#23762057	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3509	C₂	1	1	yes	maximal, characteristic
16	#19098694	—	2	1	no	—
17	#19098641	—	2	1	no	—
18	#19098635	—	2	1	no	—
19	#19098635	—	2	1	no	—
20	#19098624	—	2	1	no	—
21	#19098624	—	2	1	no	—
22	#19098620	C₂²	1	1	yes	characteristic
23	#19098620	C₂²	1	1	yes	characteristic
24	#19098620	C₂²	1	1	yes	characteristic
25	#19098620	C₂²	1	1	yes	characteristic
26	#19098616	C₂²	1	1	yes	characteristic
27	#19098616	C₂²	1	1	yes	characteristic
28	#19098616	C₂²	1	1	yes	characteristic
29	#19098587	C₂²	1	1	yes	characteristic
30	#19098587	C₂²	1	1	yes	characteristic
31	#19098587	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
34	#19098530	—	2	1	no	—
35	#19098519	—	2	1	no	—
36	#19098312	C₂²	1	1	yes	characteristic
37	#19098312	C₂²	1	1	yes	characteristic
38	#19098312	C₂²	1	1	yes	characteristic
39	#19098312	C₂²	1	1	yes	characteristic
40	#19098309	C₂²	1	1	yes	characteristic
41	#19098309	C₂²	1	1	yes	characteristic
42	#19098309	C₂²	1	1	yes	characteristic
43	#19098309	C₂²	1	1	yes	characteristic
44	#19098309	C₂²	1	1	yes	characteristic
45	#19098309	C₂²	1	1	yes	characteristic
46	#19098309	C₂²	1	1	yes	characteristic
47	#19098309	C₂²	1	1	yes	characteristic
48	#19098309	C₂²	1	1	yes	characteristic
49	#19098309	C₂²	1	1	yes	characteristic
50	#19098309	C₂²	1	1	yes	characteristic
51	#19098309	C₂²	1	1	yes	characteristic
52	#557×C₇₉	—	2	1	no	—
53	#557×C₇₉	C₄	1	2	yes	—
54	#556×C₇₉	—	2	1	no	—
55	#556×C₇₉	C₄	1	2	yes	—
56	#552×C₇₉	—	2	1	no	—
57	#552×C₇₉	—	2	1	no	—
58	#552×C₇₉	C₄	1	2	yes	—
59	#552×C₇₉	C₄	1	2	yes	—
60	#541×C₇₉	—	2	1	no	—
61	#541×C₇₉	—	2	1	no	—
62	#536×C₇₉	—	2	1	no	—
63	#533×C₇₉	C₂²	1	1	yes	characteristic
64	#533×C₇₉	C₂²	1	1	yes	characteristic
65	#533×C₇₉	C₂²	1	1	yes	characteristic
66	#533×C₇₉	C₂²	1	1	yes	characteristic
67	#533×C₇₉	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
69	#519×C₇₉	—	2	1	no	—
70	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
71	C₂×#11929608	—	2	1	no	—
72	C₂×#11929608	—	2	1	no	—
73	C₂×#11929608	—	2	1	no	—
74	C₂²×C₇₉⋊C₈	—	2	1	no	—
75	C₂²×C₇₉⋊C₈	—	2	1	no	—
76	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
79	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
80	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
81	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
82	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
83	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
84	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
85	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
86	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
87	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
88	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
89	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
92	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
93	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
94	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
95	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
96	#14579072	—	2	1	no	—
97	#14579072	—	2	1	no	—
98	#14579072	—	2	1	no	—
99	#14579072	—	2	1	no	—
100	C₄×C₇₉⋊C₈	—	2	1	no	—
101	C₄×C₇₉⋊C₈	—	2	1	no	—
102	C₄×C₇₉⋊C₈	—	2	1	no	—
103	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
104	C₂²×Q₈×C₇₉	—	2	1	no	—
105	C₄⋊Q₈×C₇₉	—	2	2	no	—
106	C₄⋊Q₈×C₇₉	—	2	1	no	—
107	C₄⋊Q₈×C₇₉	—	2	1	no	—
108	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
109	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
113	#126×C₇₉	—	2	2	no	—
114	#126×C₇₉	—	2	2	no	—
115	#126×C₇₉	—	2	2	no	—
116	#126×C₇₉	—	2	2	no	—
117	#125×C₇₉	—	2	2	no	—
118	#125×C₇₉	—	2	2	no	—
119	#125×C₇₉	—	2	2	no	—
120	#125×C₇₉	—	2	2	no	—
121	#125×C₇₉	—	2	1	no	—
122	#125×C₇₉	—	2	1	no	—
123	#125×C₇₉	—	2	1	no	—
124	#125×C₇₉	C₂×C₄	1	2	yes	—
125	#125×C₇₉	C₂×C₄	1	2	yes	—
126	#124×C₇₉	—	2	2	no	—
127	#123×C₇₉	—	2	2	no	—
128	#123×C₇₉	—	2	2	no	—
129	C₂²⋊Q₈×C₇₉	—	2	1	no	—
130	C₂²⋊Q₈×C₇₉	—	2	1	no	—
131	C₂²⋊Q₈×C₇₉	—	2	1	no	—
132	C₂²⋊Q₈×C₇₉	—	2	1	no	—
133	C₂²⋊Q₈×C₇₉	—	2	1	no	—
134	C₂²⋊Q₈×C₇₉	—	2	1	no	—
135	C₂²⋊Q₈×C₇₉	—	2	1	no	—
136	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
137	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
138	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
139	C₄×Q₈×C₇₉	—	2	2	no	—
140	C₄×Q₈×C₇₉	—	2	2	no	—
141	C₄×Q₈×C₇₉	—	2	1	no	—
142	C₄×Q₈×C₇₉	—	2	1	no	—
143	C₄×Q₈×C₇₉	—	2	1	no	—
144	C₄×Q₈×C₇₉	—	2	1	no	—
145	C₄×Q₈×C₇₉	—	2	1	no	—
146	C₄×Q₈×C₇₉	—	2	1	no	—
147	C₄×Q₈×C₇₉	—	2	1	no	—
148	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
149	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
150	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
151	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
152	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
153	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
154	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
155	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
156	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
157	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
158	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
159	#117×C₇₉	—	2	1	no	—
160	#117×C₇₉	—	2	1	no	—
161	#117×C₇₉	—	2	1	no	—
162	#117×C₇₉	—	2	2	no	—
163	#117×C₇₉	—	2	2	no	—
164	#117×C₇₉	C₂×C₄	1	2	yes	—
165	#117×C₇₉	C₂×C₄	1	2	yes	—
166	#117×C₇₉	D₄	1	1	yes	characteristic
167	#117×C₇₉	D₄	1	1	yes	characteristic
168	#117×C₇₉	D₄	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
170	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
171	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
174	#11929608	—	4	2	no	—
175	#11929608	—	8	1	no	—
176	#11929608	—	8	1	no	—
177	C₂×C₇₉⋊C₈	—	2	1	no	—
178	C₂×C₇₉⋊C₈	—	2	1	no	—
179	C₂×C₇₉⋊C₈	—	2	1	no	—
180	C₂×C₇₉⋊C₈	—	2	1	no	—
181	C₂×C₇₉⋊C₈	—	2	1	no	—
182	C₂×C₇₉⋊C₈	—	2	1	no	—
183	C₂×C₇₉⋊C₈	—	2	1	no	—
184	C₂×C₇₉⋊C₈	—	2	1	no	—
185	C₂×C₇₉⋊C₈	—	4	2	no	—
186	C₂×C₇₉⋊C₈	—	8	1	no	—
187	#41×C₇₉	—	4	1	no	—
188	#41×C₇₉	—	4	1	no	—
189	C₂×Q₈×C₇₉	—	2	2	no	—
190	C₂×Q₈×C₇₉	—	2	1	no	—
191	C₂×Q₈×C₇₉	—	2	1	no	—
192	C₂×Q₈×C₇₉	—	2	1	no	—
193	C₂×Q₈×C₇₉	—	4	2	no	—
194	C₂×Q₈×C₇₉	—	4	2	no	—
195	C₂×Q₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
196	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
197	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
199	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄×C₇₉	—	2	2	no	—
201	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₇₉	—	2	2	no	—
211	C₄⋊C₄×C₇₉	—	2	2	no	—
212	C₄⋊C₄×C₇₉	—	2	2	no	—
213	C₄⋊C₄×C₇₉	—	2	2	no	—
214	C₄⋊C₄×C₇₉	—	2	2	no	—
215	C₄⋊C₄×C₇₉	—	2	2	no	—
216	C₄⋊C₄×C₇₉	—	2	2	no	—
217	C₄⋊C₄×C₇₉	—	2	2	no	—
218	C₄⋊C₄×C₇₉	—	2	2	no	—
219	C₄⋊C₄×C₇₉	—	2	2	no	—
220	C₄⋊C₄×C₇₉	—	2	2	no	—
221	C₄⋊C₄×C₇₉	—	2	2	no	—
222	C₄⋊C₄×C₇₉	—	2	1	no	—
223	C₄⋊C₄×C₇₉	—	2	1	no	—
224	C₄⋊C₄×C₇₉	—	2	1	no	—
225	C₄⋊C₄×C₇₉	—	2	1	no	—
226	C₄⋊C₄×C₇₉	—	2	1	no	—
227	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
228	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
229	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
230	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
231	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
232	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
233	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
234	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
235	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
236	C₂²⋊C₄×C₇₉	—	2	2	no	—
237	C₂²⋊C₄×C₇₉	—	2	2	no	—
238	C₂²⋊C₄×C₇₉	—	2	2	no	—
239	C₂²⋊C₄×C₇₉	—	2	2	no	—
240	C₂²⋊C₄×C₇₉	—	2	2	no	—
241	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
242	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
243	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
244	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
245	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
246	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
247	C₄²×C₇₉	—	2	2	no	—
248	C₄²×C₇₉	—	2	2	no	—
249	C₄²×C₇₉	—	2	2	no	—
250	C₄²×C₇₉	—	2	2	no	—
251	C₄²×C₇₉	—	2	2	no	—
252	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
253	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
254	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
255	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
262	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	Q₈×C₇₉	—	4	1	no	—
266	Q₈×C₇₉	—	4	2	no	—
267	Q₈×C₇₉	—	4	4	no	—
268	Q₈×C₇₉	—	4	1	no	—
269	Q₈×C₇₉	—	4	1	no	—
270	Q₈×C₇₉	—	4	1	no	—
271	Q₈×C₇₉	—	4	1	no	—
272	Q₈×C₇₉	—	4	1	no	—
273	Q₈×C₇₉	—	4	1	no	—
274	D₄×C₇₉	—	4	1	no	—
275	D₄×C₇₉	—	4	1	no	—
276	D₄×C₇₉	—	4	1	no	—
277	C₂×C₄×C₇₉	—	2	1	no	—
278	C₂×C₄×C₇₉	—	2	1	no	—
279	C₂×C₄×C₇₉	—	2	1	no	—
280	C₂×C₄×C₇₉	—	2	1	no	—
281	C₂×C₄×C₇₉	—	2	1	no	—
282	C₂×C₄×C₇₉	—	2	1	no	—
283	C₂×C₄×C₇₉	—	2	1	no	—
284	C₂×C₄×C₇₉	—	2	1	no	—
285	C₂×C₄×C₇₉	—	2	1	no	—
286	C₂×C₄×C₇₉	—	2	1	no	—
287	C₂×C₄×C₇₉	—	2	1	no	—
288	C₂×C₄×C₇₉	—	2	1	no	—
289	C₂×C₄×C₇₉	—	2	2	no	—
290	C₂×C₄×C₇₉	—	2	2	no	—
291	C₂×C₄×C₇₉	—	2	2	no	—
292	C₂×C₄×C₇₉	—	2	2	no	—
293	C₂×C₄×C₇₉	—	4	1	no	—
294	C₂×C₄×C₇₉	—	4	1	no	—
295	C₂×C₄×C₇₉	—	4	1	no	—
296	C₂×C₄×C₇₉	—	4	4	no	—
297	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
309	C₇₉⋊C₈	—	4	1	no	—
310	C₇₉⋊C₈	—	4	1	no	—
311	C₇₉⋊C₈	—	4	1	no	—
312	C₇₉⋊C₈	—	4	1	no	—
313	C₇₉⋊C₈	—	4	1	no	—
314	C₇₉⋊C₈	—	4	1	no	—
315	C₇₉⋊C₈	—	4	1	no	—
316	C₇₉⋊C₈	—	4	1	no	—
317	C₂²×C₇₉	—	2	1	no	—
318	C₂²×C₇₉	—	2	1	no	—
319	C₂²×C₇₉	—	2	1	no	—
320	C₂²×C₇₉	—	2	1	no	—
321	C₂²×C₇₉	—	2	1	no	—
322	C₂²×C₇₉	—	2	1	no	—
323	C₂²×C₇₉	—	2	1	no	—
324	C₂²×C₇₉	—	2	1	no	—
325	C₂²×C₇₉	—	2	1	no	—
326	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
327	C₄×C₇₉	—	2	1	no	—
328	C₄×C₇₉	—	2	1	no	—
329	C₄×C₇₉	—	2	1	no	—
330	C₄×C₇₉	—	2	1	no	—
331	C₄×C₇₉	—	2	1	no	—
332	C₄×C₇₉	—	2	1	no	—
333	C₄×C₇₉	—	2	1	no	—
334	C₄×C₇₉	—	2	1	no	—
335	C₄×C₇₉	—	2	1	no	—
336	C₄×C₇₉	—	2	1	no	—
337	C₄×C₇₉	—	4	2	no	—
338	C₄×C₇₉	—	4	2	no	—
339	C₄×C₇₉	—	4	2	no	—
340	C₄×C₇₉	—	4	2	no	—
341	C₄×C₇₉	#575	1	1	yes	characteristic
342	C₄×C₇₉	#575	1	1	yes	characteristic
343	C₄×C₇₉	#577	1	1	yes	characteristic
344	C₄×C₇₉	#578	1	1	yes	characteristic
345	#17767	—	79	1	no	maximal, Sylow
346	C₂×C₇₉	—	4	1	no	—
347	C₂×C₇₉	—	4	1	no	—
348	C₂×C₇₉	—	4	1	no	—
349	C₂×C₇₉	#2889	1	1	yes	characteristic
350	C₂×C₇₉	#2896	1	1	yes	characteristic
351	C₂×C₇₉	#2898	1	1	yes	characteristic
352	#3509	D₇₉	1	1	yes	characteristic
353	#2989	—	79	1	no	—
354	#2925	—	79	1	no	—
355	#1561	—	79	1	no	—
356	#1559	—	79	1	no	—
357	#1559	—	79	1	no	—
358	#1556	—	79	1	no	—
359	#1554	—	79	1	no	—
360	#1554	—	79	1	no	—
361	#1552	—	79	1	no	—
362	#1552	—	79	1	no	—
363	#1550	—	79	1	no	—
364	#1549	—	79	1	no	—
365	#1544	—	79	1	no	—
366	#1542	—	79	1	no	—
367	C₇₉	#17767	1	1	yes	characteristic, complemented, Sylow
368	#557	—	2	1	no	—
369	#557	Dic₇₉	1	2	yes	—
370	#556	—	2	1	no	—
371	#556	Dic₇₉	1	2	yes	—
372	#552	—	2	1	no	—
373	#552	—	2	1	no	—
374	#552	Dic₇₉	1	2	yes	—
375	#552	Dic₇₉	1	2	yes	—
376	#541	—	2	1	no	—
377	#541	—	2	1	no	—
378	#536	—	2	1	no	—
379	#533	C₂×D₇₉	1	1	yes	characteristic
380	#533	C₂×D₇₉	1	1	yes	characteristic
381	#533	C₂×D₇₉	1	1	yes	characteristic
382	#533	C₂×D₇₉	1	1	yes	characteristic
383	#533	C₂×D₇₉	1	1	yes	characteristic
384	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
385	#519	—	2	1	no	—
386	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
387	#446	—	158	1	no	—
388	#436	—	158	1	no	—
389	#435	—	158	1	no	—
390	#435	—	158	1	no	—
391	#433	—	158	1	no	—
392	#433	—	158	1	no	—
393	#432	—	79	1	no	—
394	#432	—	79	1	no	—
395	#432	—	79	1	no	—
396	#432	—	79	1	no	—
397	#431	—	79	1	no	—
398	#431	—	79	1	no	—
399	#431	—	79	1	no	—
400	#423	—	79	1	no	—
401	#423	—	79	1	no	—
402	#423	—	79	1	no	—
403	C₂×C₄⋊C₈	—	79	1	no	—
404	C₂×C₄⋊C₈	—	79	1	no	—
405	#408	—	158	1	no	—
406	#405	—	158	1	no	—
407	#333	—	79	1	no	—
408	#333	—	79	1	no	—
409	#333	—	79	1	no	—
410	#333	—	79	1	no	—
411	#332	—	79	1	no	—
412	#332	—	79	1	no	—
413	#332	—	79	1	no	—
414	#332	—	79	1	no	—
415	#332	—	79	1	no	—
416	#332	—	79	1	no	—
417	#332	—	79	1	no	—
418	#332	—	79	1	no	—
419	#332	—	79	1	no	—
420	#332	—	79	1	no	—
421	#332	—	79	1	no	—
422	#332	—	79	1	no	—
423	C₂×#41	C₂²⋊D₇₉	1	1	yes	characteristic
424	C₂²×Q₈	—	2	1	no	—
425	C₂×M₁₆	—	158	1	no	—
426	C₂×M₁₆	—	158	1	no	—
427	C₂×M₁₆	—	158	1	no	—
428	C₂²×C₈	—	158	1	no	—
429	C₂²×C₈	—	158	1	no	—
430	C₄⋊Q₈	—	2	2	no	—
431	C₄⋊Q₈	—	2	1	no	—
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
434	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
435	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
436	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
437	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
438	#126	—	2	2	no	—
439	#126	—	2	2	no	—
440	#126	—	2	2	no	—
441	#126	—	2	2	no	—
442	#125	—	2	2	no	—
443	#125	—	2	2	no	—
444	#125	—	2	2	no	—
445	#125	—	2	2	no	—
446	#125	—	2	1	no	—
447	#125	—	2	1	no	—
448	#125	—	2	1	no	—
449	#125	C₂×Dic₇₉	1	2	yes	—
450	#125	C₂×Dic₇₉	1	2	yes	—
451	#124	—	2	2	no	—
452	#123	—	2	2	no	—
453	#123	—	2	2	no	—
454	C₂²⋊Q₈	—	2	1	no	—
455	C₂²⋊Q₈	—	2	1	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	C₂²⋊Q₈	—	2	1	no	—
461	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
462	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
463	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	1	no	—
467	C₄×Q₈	—	2	1	no	—
468	C₄×Q₈	—	2	1	no	—
469	C₄×Q₈	—	2	1	no	—
470	C₄×Q₈	—	2	1	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	—	2	1	no	—
473	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
474	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
475	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
476	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
477	C₄×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
478	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
479	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
480	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
481	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
482	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
483	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
484	#117	—	2	1	no	—
485	#117	—	2	1	no	—
486	#117	—	2	1	no	—
487	#117	—	2	2	no	—
488	#117	—	2	2	no	—
489	#117	C₂×Dic₇₉	1	2	yes	—
490	#117	C₂×Dic₇₉	1	2	yes	—
491	#117	C₂²⋊D₇₉	1	1	yes	characteristic
492	#117	C₂²⋊D₇₉	1	1	yes	characteristic
493	#117	C₂²⋊D₇₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
496	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
497	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
498	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
499	C₄⋊C₈	—	79	1	no	—
500	C₄⋊C₈	—	79	1	no	—
501	C₄⋊C₈	—	79	1	no	—
502	C₄⋊C₈	—	79	1	no	—
503	C₄⋊C₈	—	79	1	no	—
504	C₄⋊C₈	—	79	1	no	—
505	C₄⋊C₈	—	79	1	no	—
506	C₄⋊C₈	—	79	1	no	—
507	C₄⋊C₈	—	158	1	no	—
508	C₄⋊C₈	—	158	1	no	—
509	C₄⋊C₈	—	158	1	no	—
510	C₄⋊C₈	—	158	1	no	—
511	C₄⋊C₈	—	158	1	no	—
512	C₂²⋊C₈	—	158	1	no	—
513	C₂²⋊C₈	—	158	1	no	—
514	C₂²⋊C₈	—	158	1	no	—
515	C₂²⋊C₈	—	158	1	no	—
516	C₂²⋊C₈	—	158	1	no	—
517	C₂²⋊C₈	—	158	1	no	—
518	C₂²⋊C₈	—	158	1	no	—
519	#97	—	158	1	no	—
520	#97	—	158	1	no	—
521	#97	—	158	1	no	—
522	#97	—	158	1	no	—
523	C₄×C₈	—	158	1	no	—
524	C₄×C₈	—	158	1	no	—
525	C₄×C₈	—	158	1	no	—
526	#41	—	4	1	no	—
527	#41	—	4	1	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	4	2	no	—
533	C₂×Q₈	—	4	2	no	—
534	C₂×Q₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
535	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
536	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
537	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
538	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
541	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
542	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
543	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
544	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
546	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
549	M₁₆	—	316	2	no	—
550	M₁₆	—	632	1	no	—
551	M₁₆	—	632	1	no	—
552	C₂×C₈	—	316	2	no	—
553	C₂×C₈	—	632	1	no	—
554	C₂×C₈	—	158	1	no	—
555	C₂×C₈	—	158	1	no	—
556	C₂×C₈	—	158	1	no	—
557	C₂×C₈	—	158	1	no	—
558	C₂×C₈	—	158	1	no	—
559	C₂×C₈	—	158	1	no	—
560	C₂×C₈	—	158	1	no	—
561	C₂×C₈	—	158	1	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
580	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
581	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
582	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
583	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
584	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
585	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
586	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
587	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
594	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
595	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
596	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
597	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
598	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
599	C₄²	—	2	2	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
605	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
606	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
607	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
608	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
609	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
610	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
611	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
612	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
613	C₄²	C₂³×D₇₉	1	1	yes	characteristic
614	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
615	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
616	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
617	Q₈	—	4	1	no	—
618	Q₈	—	4	2	no	—
619	Q₈	—	4	4	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
650	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
651	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
652	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
653	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
654	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
655	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
656	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
657	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
658	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
659	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
660	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
661	C₈	—	316	1	no	—
662	C₈	—	316	1	no	—
663	C₈	—	316	1	no	—
664	C₈	—	316	1	no	—
665	C₈	—	316	1	no	—
666	C₈	—	316	1	no	—
667	C₈	—	316	1	no	—
668	C₈	—	316	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	#19099361	1	1	yes	characteristic
694	C₄	#19099361	1	1	yes	characteristic
695	C₄	#19099371	1	1	yes	characteristic
696	C₄	#19099378	1	1	yes	characteristic
697	C₂	—	4	1	no	—
698	C₂	—	4	1	no	—
699	C₂	—	4	1	no	—
700	C₂	#23771883	1	1	yes	characteristic
701	C₂	#23771919	1	1	yes	characteristic
702	C₂	#23771933	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3509	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂×#41×C₇₉	D₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#3509	D₇₉
hypocenter	C₇₉	#17767
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3509

Complements

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

N	H ≅ G/N	type
3. #23762138	C₂	semidirect
4. #23762130	C₂	semidirect
5. #23762130	C₂	semidirect
6. #23762117	C₂	semidirect
7. #23762110	C₂	semidirect
8. #23762110	C₂	semidirect
9. #23762100	C₂	semidirect
10. #23762100	C₂	semidirect
11. #23762090	C₂	semidirect
12. #23762085	C₂	semidirect
13. #23762065	C₂	semidirect
14. #23762057	C₂	semidirect
367. C₇₉	#17767	semidirect

Maximal subgroups

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

subgroup	index
#23772517	2
#23772066	2
#23762138	2
#23762130	2
#23762117	2
#23762110	2
#23762100	2
#23762090	2
#23762085	2
#23762065	2
#23762057	2
C₇₉×#3509	2
#17767	79