Subgroups — C₇₉×#18905 #34130594

Order 20224.

926 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3501	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#474×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#1649	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1644	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1478	C₂	1	1	yes	maximal, characteristic
10	#554×C₇₉	—	2	1	no	—
11	#554×C₇₉	—	2	2	no	—
12	#554×C₇₉	—	2	2	no	—
13	#554×C₇₉	C₂²	1	2	yes	—
14	D₄×Q₈×C₇₉	—	2	1	no	—
15	D₄×Q₈×C₇₉	C₂²	1	2	yes	—
16	#544×C₇₉	—	2	1	no	—
17	#543×C₇₉	—	2	2	no	—
18	#533×C₇₉	C₂²	1	1	yes	characteristic
19	#533×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₇₉	—	2	2	no	—
22	#518×C₇₉	—	2	1	no	—
23	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
24	#500×C₇₉	C₂²	1	2	yes	complemented
25	#494×C₇₉	—	2	1	no	—
26	#487×C₇₉	—	2	1	no	—
27	#487×C₇₉	C₂²	1	2	yes	complemented
28	#484×C₇₉	—	2	2	no	—
29	#477×C₇₉	—	2	2	no	—
30	#474×C₇₉	—	2	2	no	—
31	#474×C₇₉	C₂²	1	4	yes	—
32	#462×C₇₉	C₂²	1	4	yes	complemented
33	#451×C₇₉	—	2	2	no	—
34	#431×C₇₉	C₂²	1	1	yes	characteristic
35	#431×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×#107×C₇₉	—	2	1	no	—
37	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#102×C₇₉	—	2	1	no	—
39	#333×C₇₉	C₂²	1	2	yes	complemented
40	#332×C₇₉	C₂²	1	2	yes	complemented
41	Q₈⋊C₈×C₇₉	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₇₉	C₂²	1	4	yes	—
43	C₂²×Q₈×C₇₉	—	2	2	no	—
44	C₂²×Q₈×C₇₉	—	2	1	no	—
45	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₇₉	—	2	1	no	—
47	C₂×Q₁₆×C₇₉	—	2	4	no	—
48	C₂²×C₈×C₇₉	—	2	1	no	—
49	C₄⋊Q₈×C₇₉	—	2	2	no	—
50	C₄⋊Q₈×C₇₉	—	2	2	no	—
51	C₄⋊Q₈×C₇₉	—	2	1	no	—
52	C₄⋊Q₈×C₇₉	—	2	1	no	—
53	C₄⋊Q₈×C₇₉	—	2	1	no	—
54	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
59	#125×C₇₉	—	2	2	no	—
60	#125×C₇₉	—	2	2	no	—
61	#125×C₇₉	—	2	1	no	—
62	#125×C₇₉	—	2	1	no	—
63	C₂²⋊Q₈×C₇₉	—	2	4	no	—
64	C₂²⋊Q₈×C₇₉	—	2	4	no	—
65	C₂²⋊Q₈×C₇₉	—	2	4	no	—
66	C₂²⋊Q₈×C₇₉	—	2	4	no	—
67	C₂²⋊Q₈×C₇₉	—	2	2	no	—
68	C₂²⋊Q₈×C₇₉	—	2	4	no	—
69	C₂²⋊Q₈×C₇₉	—	2	1	no	—
70	C₂²⋊Q₈×C₇₉	—	2	1	no	—
71	C₂²⋊Q₈×C₇₉	—	2	2	no	—
72	C₂²⋊Q₈×C₇₉	—	2	4	no	—
73	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
74	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
75	C₄×Q₈×C₇₉	—	2	1	no	—
76	C₄×Q₈×C₇₉	—	2	1	no	—
77	C₄×Q₈×C₇₉	D₄	1	2	yes	—
78	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
79	C₄×D₄×C₇₉	—	2	2	no	—
80	C₄×D₄×C₇₉	—	2	2	no	—
81	C₄×D₄×C₇₉	—	2	2	no	—
82	C₄×D₄×C₇₉	—	2	2	no	—
83	C₄×D₄×C₇₉	—	2	1	no	—
84	C₄×D₄×C₇₉	—	2	1	no	—
85	C₄×D₄×C₇₉	D₄	1	2	yes	—
86	C₄×D₄×C₇₉	C₂³	1	2	yes	—
87	#117×C₇₉	—	2	1	no	—
88	#117×C₇₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
90	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
96	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
97	#107×C₇₉	—	2	4	no	—
98	#107×C₇₉	—	2	4	no	—
99	C₄⋊C₈×C₇₉	—	2	1	no	—
100	C₄⋊C₈×C₇₉	—	2	1	no	—
101	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
102	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
103	#103×C₇₉	—	2	4	no	—
104	#103×C₇₉	—	2	4	no	—
105	#102×C₇₉	—	2	4	no	—
106	C₂²⋊C₈×C₇₉	—	2	1	no	—
107	C₂²⋊C₈×C₇₉	—	2	1	no	—
108	C₄×C₈×C₇₉	—	2	1	no	—
109	C₄×C₈×C₇₉	C₂³	1	2	yes	—
110	C₂⁴×C₇₉	—	2	1	no	—
111	C₂×Q₈×C₇₉	—	2	4	no	—
112	C₂×Q₈×C₇₉	—	2	1	no	—
113	C₂×Q₈×C₇₉	—	2	1	no	—
114	C₂×Q₈×C₇₉	—	2	2	no	—
115	C₂×Q₈×C₇₉	—	4	1	no	—
116	C₂×Q₈×C₇₉	—	8	2	no	—
117	C₂×Q₈×C₇₉	—	8	4	no	—
118	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₇₉	—	2	1	no	—
121	C₂×D₄×C₇₉	—	2	2	no	—
122	C₂×D₄×C₇₉	Q₁₆	1	4	yes	complemented
123	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇₉	—	2	4	no	—
125	C₂²×C₄×C₇₉	—	2	4	no	—
126	C₂²×C₄×C₇₉	—	2	1	no	—
127	C₂²×C₄×C₇₉	—	2	2	no	—
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	—	4	1	no	—
130	C₂²×C₄×C₇₉	—	8	2	no	—
131	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	Q₁₆×C₇₉	—	8	4	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	—	2	2	no	—
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	—	4	2	no	—
139	C₄⋊C₄×C₇₉	—	2	4	no	—
140	C₄⋊C₄×C₇₉	—	2	4	no	—
141	C₄⋊C₄×C₇₉	—	2	4	no	—
142	C₄⋊C₄×C₇₉	—	2	2	no	—
143	C₄⋊C₄×C₇₉	—	2	2	no	—
144	C₄⋊C₄×C₇₉	—	2	1	no	—
145	C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	—	2	1	no	—
148	C₄⋊C₄×C₇₉	—	2	2	no	—
149	C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₄⋊C₄×C₇₉	—	2	1	no	—
151	C₄⋊C₄×C₇₉	—	2	1	no	—
152	C₄⋊C₄×C₇₉	—	2	2	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	—	4	1	no	—
156	C₄⋊C₄×C₇₉	—	4	1	no	—
157	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₇₉	—	2	4	no	—
161	C₂²⋊C₄×C₇₉	—	2	4	no	—
162	C₂²⋊C₄×C₇₉	—	2	2	no	—
163	C₂²⋊C₄×C₇₉	—	2	2	no	—
164	C₂²⋊C₄×C₇₉	—	2	2	no	—
165	C₂²⋊C₄×C₇₉	—	2	2	no	—
166	C₄²×C₇₉	—	2	2	no	—
167	C₄²×C₇₉	—	2	2	no	—
168	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
172	C₂³×C₇₉	—	2	2	no	—
173	C₂³×C₇₉	—	2	4	no	—
174	C₂³×C₇₉	—	8	1	no	—
175	C₂³×C₇₉	—	8	1	no	—
176	C₂³×C₇₉	#120	1	1	yes	characteristic
177	Q₈×C₇₉	—	2	4	no	—
178	Q₈×C₇₉	—	4	2	no	—
179	Q₈×C₇₉	—	4	2	no	—
180	Q₈×C₇₉	—	4	4	no	—
181	Q₈×C₇₉	—	8	1	no	—
182	Q₈×C₇₉	—	8	2	no	—
183	Q₈×C₇₉	—	8	4	no	—
184	D₄×C₇₉	—	2	2	no	—
185	D₄×C₇₉	—	2	4	no	—
186	D₄×C₇₉	C₂×Q₁₆	1	4	yes	—
187	C₂×C₄×C₇₉	—	2	2	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	—	2	2	no	—
190	C₂×C₄×C₇₉	—	2	2	no	—
191	C₂×C₄×C₇₉	—	2	2	no	—
192	C₂×C₄×C₇₉	—	2	2	no	—
193	C₂×C₄×C₇₉	—	4	1	no	—
194	C₂×C₄×C₇₉	—	4	4	no	—
195	C₂×C₄×C₇₉	—	4	2	no	—
196	C₂×C₄×C₇₉	—	8	2	no	—
197	C₂×C₄×C₇₉	—	8	1	no	—
198	C₂×C₄×C₇₉	—	8	4	no	—
199	C₂×C₄×C₇₉	—	8	4	no	—
200	C₂×C₄×C₇₉	—	8	2	no	—
201	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
202	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
203	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
204	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
205	C₂×C₄×C₇₉	#137	1	2	yes	—
206	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
209	C₈×C₇₉	—	4	2	no	—
210	C₈×C₇₉	—	4	2	no	—
211	C₈×C₇₉	—	4	2	no	—
212	C₂²×C₇₉	—	2	1	no	—
213	C₂²×C₇₉	—	2	1	no	—
214	C₂²×C₇₉	—	2	4	no	—
215	C₂²×C₇₉	—	4	2	no	—
216	C₂²×C₇₉	—	4	2	no	—
217	C₂²×C₇₉	—	8	4	no	—
218	C₂²×C₇₉	#451	1	2	yes	—
219	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
220	C₄×C₇₉	—	2	1	no	—
221	C₄×C₇₉	—	2	1	no	—
222	C₄×C₇₉	—	2	1	no	—
223	C₄×C₇₉	—	4	2	no	—
224	C₄×C₇₉	—	4	2	no	—
225	C₄×C₇₉	—	4	2	no	—
226	C₄×C₇₉	—	4	2	no	—
227	C₄×C₇₉	—	4	2	no	—
228	C₄×C₇₉	—	8	2	no	—
229	C₄×C₇₉	#451	1	2	yes	—
230	C₄×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
231	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
232	C₄×C₇₉	#576	1	2	yes	—
233	#18905	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂×C₇₉	—	2	2	no	—
235	C₂×C₇₉	—	4	4	no	—
236	C₂×C₇₉	C₂×#451	1	1	yes	characteristic
237	C₂×C₇₉	#3008	1	1	yes	characteristic
238	C₂×C₇₉	#3022	1	1	yes	characteristic
239	#3501	C₂×C₇₉	1	1	yes	characteristic
240	#3230	C₂×C₇₉	1	1	yes	characteristic, complemented
241	#3209	C₂×C₇₉	1	1	yes	characteristic, complemented
242	C₂×#474	C₂×C₇₉	1	1	yes	characteristic
243	#1649	C₂×C₇₉	1	4	yes	complemented
244	#1644	C₂×C₇₉	1	4	yes	complemented
245	#1542	C₂×C₇₉	1	1	yes	characteristic, complemented
246	#1481	C₂×C₇₉	1	1	yes	characteristic, complemented
247	#1478	C₂×C₇₉	1	1	yes	characteristic
248	C₇₉	#18905	1	1	yes	characteristic, direct product factor, Sylow
249	#554	—	2	1	no	—
250	#554	—	2	2	no	—
251	#554	—	2	2	no	—
252	#554	C₂²×C₇₉	1	2	yes	—
253	D₄×Q₈	—	2	1	no	—
254	D₄×Q₈	C₂²×C₇₉	1	2	yes	—
255	#544	—	2	1	no	—
256	#543	—	2	2	no	—
257	#533	C₂²×C₇₉	1	1	yes	characteristic
258	#533	C₂²×C₇₉	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
260	C₂×C₂²⋊Q₈	—	2	2	no	—
261	#518	—	2	1	no	—
262	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
263	#500	C₂²×C₇₉	1	2	yes	complemented
264	#494	—	2	1	no	—
265	#487	—	2	1	no	—
266	#487	C₂²×C₇₉	1	2	yes	complemented
267	#484	—	2	2	no	—
268	#477	—	2	2	no	—
269	#474	—	2	2	no	—
270	#474	C₂²×C₇₉	1	4	yes	—
271	#462	C₂²×C₇₉	1	4	yes	complemented
272	#451	—	2	2	no	—
273	#431	C₂²×C₇₉	1	1	yes	characteristic
274	#431	C₂²×C₇₉	1	1	yes	characteristic
275	C₂×#107	—	2	1	no	—
276	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
277	C₂×#102	—	2	1	no	—
278	#333	C₂²×C₇₉	1	2	yes	complemented
279	#332	C₂²×C₇₉	1	2	yes	complemented
280	Q₈⋊C₈	C₂²×C₇₉	1	4	yes	complemented
281	D₄⋊C₈	C₂²×C₇₉	1	4	yes	—
282	C₂²×Q₈	—	2	2	no	—
283	C₂²×Q₈	—	2	1	no	—
284	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂×Q₁₆	—	2	4	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
294	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
295	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
296	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
297	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
298	#125	—	2	2	no	—
299	#125	—	2	2	no	—
300	#125	—	2	1	no	—
301	#125	—	2	1	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	—	2	2	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
313	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	D₄×C₇₉	1	2	yes	—
317	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	D₄×C₇₉	1	2	yes	—
325	C₄×D₄	C₂³×C₇₉	1	2	yes	—
326	#117	—	2	1	no	—
327	#117	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	—	2	4	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
336	#107	—	2	4	no	—
337	#107	—	2	4	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
341	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
342	#103	—	2	4	no	—
343	#103	—	2	4	no	—
344	#102	—	2	4	no	—
345	C₂²⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	C₄×C₈	—	2	1	no	—
348	C₄×C₈	C₂³×C₇₉	1	2	yes	—
349	C₂⁴	—	2	1	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	4	1	no	—
355	C₂×Q₈	—	8	2	no	—
356	C₂×Q₈	—	8	4	no	—
357	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
358	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	Q₁₆×C₇₉	1	4	yes	complemented
362	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	8	2	no	—
370	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
373	Q₁₆	—	8	4	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
398	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
409	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
410	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	8	1	no	—
414	C₂³	—	8	1	no	—
415	C₂³	#120×C₇₉	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	8	1	no	—
421	Q₈	—	8	2	no	—
422	Q₈	—	8	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	2	no	—
425	D₄	C₂×Q₁₆×C₇₉	1	4	yes	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	8	2	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	—	8	4	no	—
438	C₂×C₄	—	8	4	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
441	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
442	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
443	C₂×C₄	C₂×Q₁₆×C₇₉	1	2	yes	—
444	C₂×C₄	#137×C₇₉	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
448	C₈	—	4	2	no	—
449	C₈	—	4	2	no	—
450	C₈	—	4	2	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	4	no	—
457	C₂²	#451×C₇₉	1	2	yes	—
458	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	2	no	—
468	C₄	#451×C₇₉	1	2	yes	—
469	C₄	C₂²×Q₁₆×C₇₉	1	1	yes	characteristic
470	C₄	C₂×#137×C₇₉	1	1	yes	characteristic
471	C₄	#576×C₇₉	1	2	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	4	4	no	—
474	C₂	C₂×#451×C₇₉	1	1	yes	characteristic
475	C₂	C₇₉×#3008	1	1	yes	characteristic
476	C₂	C₇₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₂²×D₄×C₇₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#3230	C₂	semidirect
3. C₇₉×#3209	C₂	semidirect
5. C₇₉×#1649	C₂	semidirect
6. C₇₉×#1644	C₂	semidirect
7. C₇₉×#1542	C₂	semidirect
8. C₇₉×#1481	C₂	semidirect
24. #500×C₇₉	C₂²	semidirect
27. #487×C₇₉	C₂²	semidirect
32. #462×C₇₉	C₂²	semidirect
39. #333×C₇₉	C₂²	semidirect
40. #332×C₇₉	C₂²	semidirect
41. Q₈⋊C₈×C₇₉	C₂²	semidirect
122. C₂×D₄×C₇₉	Q₁₆	semidirect
233. #18905	C₇₉	direct (N × H)
240. #3230	C₂×C₇₉	semidirect
241. #3209	C₂×C₇₉	semidirect
243. #1649	C₂×C₇₉	semidirect
244. #1644	C₂×C₇₉	semidirect
245. #1542	C₂×C₇₉	semidirect
246. #1481	C₂×C₇₉	semidirect
248. C₇₉	#18905	direct (N × H)
263. #500	C₂²×C₇₉	semidirect
266. #487	C₂²×C₇₉	semidirect
271. #462	C₂²×C₇₉	semidirect
278. #333	C₂²×C₇₉	semidirect
279. #332	C₂²×C₇₉	semidirect
280. Q₈⋊C₈	C₂²×C₇₉	semidirect
361. C₂×D₄	Q₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3501	2
C₇₉×#3230	2
C₇₉×#3209	2
C₂×#474×C₇₉	2
C₇₉×#1649	2
C₇₉×#1644	2
C₇₉×#1542	2
C₇₉×#1481	2
C₇₉×#1478	2
#18905	79

Subgroups — C79×#18905 #34130594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18905 #34130594