Subgroups — C₇₉×#3310 #23760932

Order 10112.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#552×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄²×C₇₉	C₂	1	1	yes	maximal, characteristic
3	#490×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#482×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#480×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#478×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#468×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#465×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#460×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#450×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#450×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#440×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#435×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#418×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#102×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₇₉	—	2	1	no	—
17	C₂²×D₄×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
24	#127×C₇₉	C₂²	1	1	yes	characteristic
25	#126×C₇₉	—	2	1	no	—
26	#125×C₇₉	—	2	1	no	—
27	#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
28	#123×C₇₉	—	2	1	no	—
29	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
31	#121×C₇₉	—	2	1	no	—
32	#121×C₇₉	C₂²	1	1	yes	characteristic
33	#121×C₇₉	C₂²	1	1	yes	characteristic
34	#120×C₇₉	—	2	1	no	—
35	#120×C₇₉	—	2	1	no	—
36	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
39	#117×C₇₉	—	2	1	no	—
40	#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	#107×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	#107×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	#106×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	#102×C₇₉	C₂²	1	1	yes	characteristic
48	#102×C₇₉	C₂²	1	1	yes	characteristic
49	#102×C₇₉	C₂²	1	1	yes	characteristic
50	#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
51	#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
52	#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
53	#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
54	#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
55	#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
57	C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
58	#97×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	C₂⁴×C₇₉	—	2	1	no	—
60	C₂⁴×C₇₉	—	2	1	no	—
61	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₇₉	—	2	2	no	—
63	C₂×D₄×C₇₉	—	2	2	no	—
64	C₂×D₄×C₇₉	—	2	1	no	—
65	C₂×D₄×C₇₉	—	2	1	no	—
66	C₂×D₄×C₇₉	—	2	1	no	—
67	C₂×D₄×C₇₉	—	2	1	no	—
68	C₂×D₄×C₇₉	—	2	1	no	—
69	C₂×D₄×C₇₉	—	2	1	no	—
70	C₂×D₄×C₇₉	—	4	1	no	—
71	C₂×D₄×C₇₉	—	4	1	no	—
72	C₂×D₄×C₇₉	—	4	4	no	—
73	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
74	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
76	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₇₉	—	2	1	no	—
78	C₂²×C₄×C₇₉	—	2	1	no	—
79	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
81	SD₁₆×C₇₉	—	2	2	no	—
82	SD₁₆×C₇₉	—	4	1	no	—
83	SD₁₆×C₇₉	—	4	1	no	—
84	M₁₆×C₇₉	—	4	1	no	—
85	C₂×C₈×C₇₉	—	4	1	no	—
86	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
89	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₄×C₇₉	—	2	1	no	—
91	C₄⋊C₄×C₇₉	—	2	1	no	—
92	C₄⋊C₄×C₇₉	—	2	1	no	—
93	C₄⋊C₄×C₇₉	—	2	1	no	—
94	C₄⋊C₄×C₇₉	—	2	1	no	—
95	C₄⋊C₄×C₇₉	—	2	1	no	—
96	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
97	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
101	C₂²⋊C₄×C₇₉	—	2	1	no	—
102	C₂²⋊C₄×C₇₉	—	2	1	no	—
103	C₂²⋊C₄×C₇₉	—	2	1	no	—
104	C₂²⋊C₄×C₇₉	—	2	1	no	—
105	C₂²⋊C₄×C₇₉	—	2	1	no	—
106	C₂²⋊C₄×C₇₉	—	2	1	no	—
107	C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
108	C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
109	C₄²×C₇₉	—	2	1	no	—
110	C₄²×C₇₉	—	2	1	no	—
111	C₄²×C₇₉	C₂³	1	1	yes	characteristic
112	C₂³×C₇₉	—	2	1	no	—
113	C₂³×C₇₉	—	2	1	no	—
114	C₂³×C₇₉	—	2	1	no	—
115	C₂³×C₇₉	—	4	2	no	—
116	C₂³×C₇₉	—	4	2	no	—
117	C₂³×C₇₉	—	4	2	no	—
118	C₂³×C₇₉	—	4	2	no	—
119	C₂³×C₇₉	—	8	1	no	—
120	C₂³×C₇₉	—	8	1	no	—
121	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
123	Q₈×C₇₉	—	2	1	no	—
124	Q₈×C₇₉	—	2	1	no	—
125	D₄×C₇₉	—	2	2	no	—
126	D₄×C₇₉	—	2	1	no	—
127	D₄×C₇₉	—	2	1	no	—
128	D₄×C₇₉	—	2	1	no	—
129	D₄×C₇₉	—	2	1	no	—
130	D₄×C₇₉	—	2	1	no	—
131	D₄×C₇₉	—	4	2	no	—
132	D₄×C₇₉	—	4	2	no	—
133	D₄×C₇₉	—	4	2	no	—
134	D₄×C₇₉	—	4	2	no	—
135	D₄×C₇₉	—	4	2	no	—
136	D₄×C₇₉	—	8	1	no	—
137	D₄×C₇₉	#41	1	2	yes	—
138	C₂×C₄×C₇₉	—	2	1	no	—
139	C₂×C₄×C₇₉	—	2	1	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	1	no	—
142	C₂×C₄×C₇₉	—	2	1	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	4	2	no	—
148	C₂×C₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
154	C₈×C₇₉	—	2	1	no	—
155	C₈×C₇₉	—	2	1	no	—
156	C₈×C₇₉	—	2	1	no	—
157	C₈×C₇₉	—	2	1	no	—
158	C₂²×C₇₉	—	2	1	no	—
159	C₂²×C₇₉	—	2	1	no	—
160	C₂²×C₇₉	—	2	1	no	—
161	C₂²×C₇₉	—	2	2	no	—
162	C₂²×C₇₉	—	2	1	no	—
163	C₂²×C₇₉	—	2	1	no	—
164	C₂²×C₇₉	—	4	1	no	—
165	C₂²×C₇₉	—	4	1	no	—
166	C₂²×C₇₉	—	4	1	no	—
167	C₂²×C₇₉	—	4	1	no	—
168	C₂²×C₇₉	—	4	1	no	—
169	C₂²×C₇₉	—	4	1	no	—
170	C₂²×C₇₉	—	4	1	no	—
171	C₂²×C₇₉	—	4	1	no	—
172	C₂²×C₇₉	—	8	4	no	—
173	C₂²×C₇₉	—	8	4	no	—
174	C₂²×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	C₄×C₇₉	—	2	1	no	—
177	C₄×C₇₉	—	2	1	no	—
178	C₄×C₇₉	—	2	1	no	—
179	C₄×C₇₉	—	2	1	no	—
180	C₄×C₇₉	—	4	1	no	—
181	C₄×C₇₉	—	4	1	no	—
182	C₄×C₇₉	—	4	1	no	—
183	C₄×C₇₉	—	4	1	no	—
184	C₄×C₇₉	—	4	1	no	—
185	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
186	C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₇₉	—	2	2	no	—
188	C₂×C₇₉	—	4	1	no	—
189	C₂×C₇₉	—	4	2	no	—
190	C₂×C₇₉	—	8	1	no	—
191	C₂×C₇₉	—	8	1	no	—
192	C₂×C₇₉	#546	1	1	yes	characteristic
193	C₂×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂×C₇₉	#577	1	1	yes	characteristic
195	#3310	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₇₉	#3310	1	1	yes	characteristic, direct product factor, Sylow
197	#552	C₂×C₇₉	1	1	yes	characteristic, complemented
198	D₄²	C₂×C₇₉	1	1	yes	characteristic
199	#490	C₂×C₇₉	1	1	yes	characteristic, complemented
200	#482	C₂×C₇₉	1	1	yes	characteristic, complemented
201	#480	C₂×C₇₉	1	1	yes	characteristic, complemented
202	#478	C₂×C₇₉	1	1	yes	characteristic, complemented
203	#468	C₂×C₇₉	1	1	yes	characteristic, complemented
204	#465	C₂×C₇₉	1	1	yes	characteristic, complemented
205	#460	C₂×C₇₉	1	1	yes	characteristic, complemented
206	#450	C₂×C₇₉	1	1	yes	characteristic, complemented
207	#450	C₂×C₇₉	1	1	yes	characteristic, complemented
208	#440	C₂×C₇₉	1	1	yes	characteristic, complemented
209	#435	C₂×C₇₉	1	1	yes	characteristic, complemented
210	#418	C₂×C₇₉	1	1	yes	characteristic, complemented
211	C₂×#102	C₂×C₇₉	1	1	yes	characteristic, complemented
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	C₂²×C₇₉	1	1	yes	characteristic
214	C₂²×D₄	C₂²×C₇₉	1	1	yes	characteristic
215	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
216	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
217	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
218	C₂×M₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
219	C₂²×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
220	#127	C₂²×C₇₉	1	1	yes	characteristic
221	#126	—	2	1	no	—
222	#125	—	2	1	no	—
223	#125	C₂²×C₇₉	1	1	yes	characteristic, complemented
224	#123	—	2	1	no	—
225	C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
226	C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
227	#121	—	2	1	no	—
228	#121	C₂²×C₇₉	1	1	yes	characteristic
229	#121	C₂²×C₇₉	1	1	yes	characteristic
230	#120	—	2	1	no	—
231	#120	—	2	1	no	—
232	C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
233	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
234	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
235	#117	—	2	1	no	—
236	#117	C₂²×C₇₉	1	1	yes	characteristic, complemented
237	C₂×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
238	#107	C₂²×C₇₉	1	1	yes	characteristic, complemented
239	#107	C₂²×C₇₉	1	1	yes	characteristic, complemented
240	#106	C₂²×C₇₉	1	1	yes	characteristic, complemented
241	C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
242	#103	C₂²×C₇₉	1	1	yes	characteristic, complemented
243	#102	C₂²×C₇₉	1	1	yes	characteristic
244	#102	C₂²×C₇₉	1	1	yes	characteristic
245	#102	C₂²×C₇₉	1	1	yes	characteristic
246	#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
247	#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
248	#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
249	#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
250	#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
251	#102	C₂²×C₇₉	1	1	yes	characteristic, complemented
252	C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
253	C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
254	#97	C₂²×C₇₉	1	1	yes	characteristic, complemented
255	C₂⁴	—	2	1	no	—
256	C₂⁴	—	2	1	no	—
257	C₂×Q₈	C₂³×C₇₉	1	1	yes	characteristic
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	2	1	no	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	—	4	4	no	—
269	C₂×D₄	D₄×C₇₉	1	1	yes	characteristic
270	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
271	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
272	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	C₂³×C₇₉	1	1	yes	characteristic
276	C₂²×C₄	C₂³×C₇₉	1	1	yes	characteristic
277	SD₁₆	—	2	2	no	—
278	SD₁₆	—	4	1	no	—
279	SD₁₆	—	4	1	no	—
280	M₁₆	—	4	1	no	—
281	C₂×C₈	—	4	1	no	—
282	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
283	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
284	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
285	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
293	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
294	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
295	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
296	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
297	C₂²⋊C₄	—	2	1	no	—
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	2	1	no	—
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
304	C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	C₂³×C₇₉	1	1	yes	characteristic
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	8	1	no	—
316	C₂³	—	8	1	no	—
317	C₂³	C₂×D₄×C₇₉	1	1	yes	characteristic
318	C₂³	C₂×D₄×C₇₉	1	1	yes	characteristic
319	Q₈	—	2	1	no	—
320	Q₈	—	2	1	no	—
321	D₄	—	2	2	no	—
322	D₄	—	2	1	no	—
323	D₄	—	2	1	no	—
324	D₄	—	2	1	no	—
325	D₄	—	2	1	no	—
326	D₄	—	2	1	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	8	1	no	—
333	D₄	#41×C₇₉	1	2	yes	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
347	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
348	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
349	C₂×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	8	4	no	—
369	C₂²	—	8	4	no	—
370	C₂²	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
371	C₂²	C₂²×D₄×C₇₉	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	C₂×#41×C₇₉	1	1	yes	characteristic
382	C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
383	C₂	—	2	2	no	—
384	C₂	—	4	1	no	—
385	C₂	—	4	2	no	—
386	C₂	—	8	1	no	—
387	C₂	—	8	1	no	—
388	C₂	#546×C₇₉	1	1	yes	characteristic
389	C₂	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
390	C₂	#577×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇₉
prime radical	D₄²×C₇₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₄×D₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #552×C₇₉	C₂	semidirect
3. #490×C₇₉	C₂	semidirect
4. #482×C₇₉	C₂	semidirect
5. #480×C₇₉	C₂	semidirect
6. #478×C₇₉	C₂	semidirect
7. #468×C₇₉	C₂	semidirect
8. #465×C₇₉	C₂	semidirect
9. #460×C₇₉	C₂	semidirect
10. #450×C₇₉	C₂	semidirect
11. #450×C₇₉	C₂	semidirect
12. #440×C₇₉	C₂	semidirect
13. #435×C₇₉	C₂	semidirect
14. #418×C₇₉	C₂	semidirect
15. C₂×#102×C₇₉	C₂	semidirect
20. C₂×SD₁₆×C₇₉	C₂²	semidirect
21. C₂×SD₁₆×C₇₉	C₂²	semidirect
22. C₂×M₁₆×C₇₉	C₂²	semidirect
23. C₂²×C₈×C₇₉	C₂²	semidirect
27. #125×C₇₉	C₂²	semidirect
29. C₂²⋊Q₈×C₇₉	C₂²	semidirect
30. C₂²⋊Q₈×C₇₉	C₂²	semidirect
36. C₄×Q₈×C₇₉	C₂²	semidirect
40. #117×C₇₉	C₂²	semidirect
41. C₂×C₄⋊C₄×C₇₉	C₂²	semidirect
42. #107×C₇₉	C₂²	semidirect
43. #107×C₇₉	C₂²	semidirect
44. #106×C₇₉	C₂²	semidirect
45. C₄⋊C₈×C₇₉	C₂²	semidirect
46. #103×C₇₉	C₂²	semidirect
50. #102×C₇₉	C₂²	semidirect
51. #102×C₇₉	C₂²	semidirect
52. #102×C₇₉	C₂²	semidirect
53. #102×C₇₉	C₂²	semidirect
54. #102×C₇₉	C₂²	semidirect
55. #102×C₇₉	C₂²	semidirect
56. C₂²⋊C₈×C₇₉	C₂²	semidirect
57. C₂²⋊C₈×C₇₉	C₂²	semidirect
58. #97×C₇₉	C₂²	semidirect
195. #3310	C₇₉	direct (N × H)
196. C₇₉	#3310	direct (N × H)
197. #552	C₂×C₇₉	semidirect
199. #490	C₂×C₇₉	semidirect
200. #482	C₂×C₇₉	semidirect
201. #480	C₂×C₇₉	semidirect
202. #478	C₂×C₇₉	semidirect
203. #468	C₂×C₇₉	semidirect
204. #465	C₂×C₇₉	semidirect
205. #460	C₂×C₇₉	semidirect
206. #450	C₂×C₇₉	semidirect
207. #450	C₂×C₇₉	semidirect
208. #440	C₂×C₇₉	semidirect
209. #435	C₂×C₇₉	semidirect
210. #418	C₂×C₇₉	semidirect
211. C₂×#102	C₂×C₇₉	semidirect
216. C₂×SD₁₆	C₂²×C₇₉	semidirect
217. C₂×SD₁₆	C₂²×C₇₉	semidirect
218. C₂×M₁₆	C₂²×C₇₉	semidirect
219. C₂²×C₈	C₂²×C₇₉	semidirect
223. #125	C₂²×C₇₉	semidirect
225. C₂²⋊Q₈	C₂²×C₇₉	semidirect
226. C₂²⋊Q₈	C₂²×C₇₉	semidirect
232. C₄×Q₈	C₂²×C₇₉	semidirect
236. #117	C₂²×C₇₉	semidirect
237. C₂×C₄⋊C₄	C₂²×C₇₉	semidirect
238. #107	C₂²×C₇₉	semidirect
239. #107	C₂²×C₇₉	semidirect
240. #106	C₂²×C₇₉	semidirect
241. C₄⋊C₈	C₂²×C₇₉	semidirect
242. #103	C₂²×C₇₉	semidirect
246. #102	C₂²×C₇₉	semidirect
247. #102	C₂²×C₇₉	semidirect
248. #102	C₂²×C₇₉	semidirect
249. #102	C₂²×C₇₉	semidirect
250. #102	C₂²×C₇₉	semidirect
251. #102	C₂²×C₇₉	semidirect
252. C₂²⋊C₈	C₂²×C₇₉	semidirect
253. C₂²⋊C₈	C₂²×C₇₉	semidirect
254. #97	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
#552×C₇₉	2
D₄²×C₇₉	2
#490×C₇₉	2
#482×C₇₉	2
#480×C₇₉	2
#478×C₇₉	2
#468×C₇₉	2
#465×C₇₉	2
#460×C₇₉	2
#450×C₇₉	2
#440×C₇₉	2
#435×C₇₉	2
#418×C₇₉	2
C₂×#102×C₇₉	2
#3310	79

Subgroups — C79×#3310 #23760932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#3310 #23760932