Subgroups — C₇₉×#18852 #34130541

Order 20224.

970 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1628	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1627	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1624	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1623	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1559	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₇₉	—	2	1	no	—
13	Q₈²×C₇₉	C₂²	1	1	yes	characteristic, complemented
14	#556×C₇₉	—	2	1	no	—
15	#556×C₇₉	—	2	2	no	—
16	#556×C₇₉	—	2	1	no	—
17	#556×C₇₉	C₂²	1	1	yes	characteristic, complemented
18	#555×C₇₉	—	2	1	no	—
19	#555×C₇₉	C₂²	1	1	yes	characteristic, complemented
20	D₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
21	#548×C₇₉	—	2	1	no	—
22	#542×C₇₉	—	2	2	no	—
23	#542×C₇₉	—	2	1	no	—
24	#533×C₇₉	—	2	1	no	—
25	#533×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
27	#529×C₇₉	—	2	1	no	—
28	#529×C₇₉	C₂²	1	1	yes	characteristic
29	#519×C₇₉	—	2	1	no	—
30	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
31	#496×C₇₉	—	2	1	no	—
32	#492×C₇₉	C₂²	1	2	yes	—
33	#490×C₇₉	—	2	1	no	—
34	#486×C₇₉	C₂²	1	2	yes	—
35	#460×C₇₉	—	2	1	no	—
36	#460×C₇₉	—	2	2	no	—
37	#460×C₇₉	C₂²	1	2	yes	—
38	#460×C₇₉	C₂²	1	2	yes	—
39	#459×C₇₉	—	2	1	no	—
40	#459×C₇₉	C₂²	1	2	yes	—
41	#459×C₇₉	C₂²	1	2	yes	—
42	#450×C₇₉	—	2	2	no	—
43	#450×C₇₉	—	2	1	no	—
44	#447×C₇₉	—	2	1	no	—
45	#432×C₇₉	C₂²	1	1	yes	characteristic
46	#431×C₇₉	C₂²	1	1	yes	characteristic
47	#423×C₇₉	C₂²	1	1	yes	characteristic
48	#418×C₇₉	—	2	1	no	—
49	#333×C₇₉	C₂²	1	2	yes	complemented
50	#332×C₇₉	C₂²	1	2	yes	complemented
51	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
52	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
53	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
54	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
55	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₇₉	—	2	1	no	—
57	C₂²×D₄×C₇₉	—	2	1	no	—
58	C₂²×D₄×C₇₉	—	2	1	no	—
59	C₂²×D₄×C₇₉	—	2	1	no	—
60	AGL(1,ℤ/8)×C₇₉	—	4	4	no	—
61	C₂×SD₁₆×C₇₉	—	2	2	no	—
62	C₂×SD₁₆×C₇₉	—	2	4	no	—
63	C₂×SD₁₆×C₇₉	—	2	2	no	—
64	C₂×D₈×C₇₉	—	2	2	no	—
65	C₂×D₈×C₇₉	—	2	2	no	—
66	C₂×M₁₆×C₇₉	—	2	1	no	—
67	C₄⋊Q₈×C₇₉	—	2	2	no	—
68	C₄⋊Q₈×C₇₉	—	2	1	no	—
69	C₄⋊Q₈×C₇₉	—	2	1	no	—
70	C₄⋊Q₈×C₇₉	—	2	1	no	—
71	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
73	#127×C₇₉	—	2	1	no	—
74	#127×C₇₉	—	2	1	no	—
75	#127×C₇₉	—	2	1	no	—
76	#127×C₇₉	C₂³	1	2	yes	—
77	#126×C₇₉	—	2	2	no	—
78	#126×C₇₉	—	2	2	no	—
79	#126×C₇₉	—	2	2	no	—
80	#126×C₇₉	—	2	2	no	—
81	#126×C₇₉	—	2	1	no	—
82	#125×C₇₉	—	2	1	no	—
83	#125×C₇₉	D₄	1	1	yes	characteristic
84	#124×C₇₉	—	2	2	no	—
85	#124×C₇₉	—	2	2	no	—
86	#124×C₇₉	—	2	2	no	—
87	#124×C₇₉	—	2	2	no	—
88	#124×C₇₉	—	2	1	no	—
89	#124×C₇₉	D₄	1	1	yes	characteristic
90	#123×C₇₉	—	2	2	no	—
91	#123×C₇₉	—	2	1	no	—
92	C₂²⋊Q₈×C₇₉	—	2	2	no	—
93	C₂²⋊Q₈×C₇₉	—	2	2	no	—
94	C₂²⋊Q₈×C₇₉	—	2	1	no	—
95	C₂²⋊Q₈×C₇₉	—	2	1	no	—
96	C₂²⋊Q₈×C₇₉	—	2	1	no	—
97	C₂²⋊Q₈×C₇₉	—	2	2	no	—
98	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
99	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
100	#121×C₇₉	—	2	2	no	—
101	#121×C₇₉	—	2	1	no	—
102	#121×C₇₉	—	2	1	no	—
103	#121×C₇₉	D₄	1	1	yes	characteristic
104	C₄×Q₈×C₇₉	—	2	2	no	—
105	C₄×Q₈×C₇₉	—	2	2	no	—
106	C₄×Q₈×C₇₉	—	2	2	no	—
107	C₄×Q₈×C₇₉	—	2	1	no	—
108	C₄×Q₈×C₇₉	—	2	1	no	—
109	C₄×Q₈×C₇₉	—	2	1	no	—
110	C₄×Q₈×C₇₉	—	2	1	no	—
111	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
112	C₄×Q₈×C₇₉	D₄	1	2	yes	—
113	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
114	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₇₉	—	2	2	no	—
116	C₄×D₄×C₇₉	—	2	1	no	—
117	C₄×D₄×C₇₉	—	2	1	no	—
118	C₄×D₄×C₇₉	—	2	1	no	—
119	C₄×D₄×C₇₉	—	2	1	no	—
120	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
121	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
123	#117×C₇₉	—	2	2	no	—
124	#117×C₇₉	—	2	2	no	—
125	#117×C₇₉	—	2	1	no	—
126	#117×C₇₉	—	2	1	no	—
127	#117×C₇₉	—	2	1	no	—
128	#117×C₇₉	—	2	1	no	—
129	#117×C₇₉	—	2	1	no	—
130	#117×C₇₉	—	2	1	no	—
131	#117×C₇₉	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₇₉	—	2	1	no	—
133	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₇₉	—	2	1	no	—
135	C₄⋊C₈×C₇₉	—	2	1	no	—
136	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
137	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
138	#102×C₇₉	—	2	2	no	—
139	#102×C₇₉	—	2	2	no	—
140	#102×C₇₉	—	2	2	no	—
141	#102×C₇₉	—	2	2	no	—
142	#102×C₇₉	—	2	4	no	—
143	C₂²⋊C₈×C₇₉	—	2	1	no	—
144	C₂²⋊C₈×C₇₉	—	2	1	no	—
145	#97×C₇₉	—	2	1	no	—
146	C₄×C₈×C₇₉	C₂³	1	2	yes	—
147	C₂⁴×C₇₉	—	4	1	no	—
148	#41×C₇₉	—	2	2	no	—
149	#41×C₇₉	—	4	1	no	—
150	C₂×Q₈×C₇₉	—	2	2	no	—
151	C₂×Q₈×C₇₉	—	2	2	no	—
152	C₂×Q₈×C₇₉	—	2	1	no	—
153	C₂×Q₈×C₇₉	—	4	2	no	—
154	C₂×Q₈×C₇₉	—	4	2	no	—
155	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₇₉	—	2	1	no	—
159	C₂×D₄×C₇₉	—	2	2	no	—
160	C₂×D₄×C₇₉	—	2	1	no	—
161	C₂×D₄×C₇₉	—	2	2	no	—
162	C₂×D₄×C₇₉	—	2	2	no	—
163	C₂×D₄×C₇₉	—	2	2	no	—
164	C₂×D₄×C₇₉	—	4	2	no	—
165	C₂×D₄×C₇₉	—	4	2	no	—
166	C₂×D₄×C₇₉	—	4	1	no	—
167	C₂×D₄×C₇₉	—	4	1	no	—
168	C₂×D₄×C₇₉	—	4	1	no	—
169	C₂×D₄×C₇₉	—	8	2	no	—
170	C₂×D₄×C₇₉	—	8	2	no	—
171	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₉	—	2	2	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	2	1	no	—
178	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
181	SD₁₆×C₇₉	—	4	4	no	—
182	SD₁₆×C₇₉	—	8	2	no	—
183	SD₁₆×C₇₉	—	8	4	no	—
184	D₈×C₇₉	—	4	4	no	—
185	D₈×C₇₉	—	8	2	no	—
186	M₁₆×C₇₉	—	4	2	no	—
187	C₂×C₈×C₇₉	—	2	2	no	—
188	C₂×C₈×C₇₉	—	2	2	no	—
189	C₂×C₈×C₇₉	—	2	2	no	—
190	C₄⋊C₄×C₇₉	—	2	2	no	—
191	C₄⋊C₄×C₇₉	—	2	2	no	—
192	C₄⋊C₄×C₇₉	—	2	2	no	—
193	C₄⋊C₄×C₇₉	—	2	2	no	—
194	C₄⋊C₄×C₇₉	—	2	1	no	—
195	C₄⋊C₄×C₇₉	—	2	1	no	—
196	C₄⋊C₄×C₇₉	—	2	2	no	—
197	C₄⋊C₄×C₇₉	—	2	1	no	—
198	C₄⋊C₄×C₇₉	—	2	1	no	—
199	C₄⋊C₄×C₇₉	—	2	2	no	—
200	C₄⋊C₄×C₇₉	—	2	1	no	—
201	C₄⋊C₄×C₇₉	—	2	1	no	—
202	C₄⋊C₄×C₇₉	—	2	1	no	—
203	C₄⋊C₄×C₇₉	—	2	1	no	—
204	C₄⋊C₄×C₇₉	—	2	1	no	—
205	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
210	C₂²⋊C₄×C₇₉	—	2	2	no	—
211	C₂²⋊C₄×C₇₉	—	2	2	no	—
212	C₂²⋊C₄×C₇₉	—	2	2	no	—
213	C₂²⋊C₄×C₇₉	—	2	2	no	—
214	C₂²⋊C₄×C₇₉	—	2	2	no	—
215	C₂²⋊C₄×C₇₉	—	2	2	no	—
216	C₂²⋊C₄×C₇₉	—	2	1	no	—
217	C₂²⋊C₄×C₇₉	—	2	1	no	—
218	C₂²⋊C₄×C₇₉	—	2	1	no	—
219	C₂²⋊C₄×C₇₉	—	2	1	no	—
220	C₂²⋊C₄×C₇₉	—	2	1	no	—
221	C₂²⋊C₄×C₇₉	—	2	1	no	—
222	C₂²⋊C₄×C₇₉	—	2	1	no	—
223	C₂²⋊C₄×C₇₉	—	2	1	no	—
224	C₄²×C₇₉	—	2	2	no	—
225	C₄²×C₇₉	—	2	2	no	—
226	C₄²×C₇₉	—	2	2	no	—
227	C₄²×C₇₉	—	2	1	no	—
228	C₄²×C₇₉	—	2	1	no	—
229	C₄²×C₇₉	—	2	2	no	—
230	C₄²×C₇₉	—	2	1	no	—
231	C₄²×C₇₉	—	2	1	no	—
232	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
236	C₂³×C₇₉	—	2	1	no	—
237	C₂³×C₇₉	—	2	1	no	—
238	C₂³×C₇₉	—	4	2	no	—
239	C₂³×C₇₉	—	8	2	no	—
240	C₂³×C₇₉	—	8	2	no	—
241	C₂³×C₇₉	—	8	2	no	—
242	C₂³×C₇₉	#120	1	1	yes	characteristic
243	Q₈×C₇₉	—	2	1	no	—
244	Q₈×C₇₉	—	2	2	no	—
245	Q₈×C₇₉	—	4	2	no	—
246	Q₈×C₇₉	—	4	4	no	—
247	Q₈×C₇₉	—	4	1	no	—
248	Q₈×C₇₉	—	4	1	no	—
249	Q₈×C₇₉	—	8	2	no	—
250	Q₈×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
251	D₄×C₇₉	—	2	1	no	—
252	D₄×C₇₉	—	2	1	no	—
253	D₄×C₇₉	—	2	2	no	—
254	D₄×C₇₉	—	4	2	no	—
255	D₄×C₇₉	—	4	4	no	—
256	D₄×C₇₉	—	4	2	no	—
257	D₄×C₇₉	—	4	2	no	—
258	D₄×C₇₉	—	4	2	no	—
259	D₄×C₇₉	—	4	2	no	—
260	D₄×C₇₉	—	8	2	no	—
261	D₄×C₇₉	—	8	2	no	—
262	D₄×C₇₉	—	8	2	no	—
263	D₄×C₇₉	—	8	1	no	—
264	D₄×C₇₉	—	8	2	no	—
265	C₂×C₄×C₇₉	—	2	1	no	—
266	C₂×C₄×C₇₉	—	2	1	no	—
267	C₂×C₄×C₇₉	—	2	1	no	—
268	C₂×C₄×C₇₉	—	2	2	no	—
269	C₂×C₄×C₇₉	—	2	1	no	—
270	C₂×C₄×C₇₉	—	2	1	no	—
271	C₂×C₄×C₇₉	—	2	2	no	—
272	C₂×C₄×C₇₉	—	2	1	no	—
273	C₂×C₄×C₇₉	—	2	1	no	—
274	C₂×C₄×C₇₉	—	2	2	no	—
275	C₂×C₄×C₇₉	—	2	1	no	—
276	C₂×C₄×C₇₉	—	4	1	no	—
277	C₂×C₄×C₇₉	—	4	2	no	—
278	C₂×C₄×C₇₉	—	4	4	no	—
279	C₂×C₄×C₇₉	—	4	1	no	—
280	C₂×C₄×C₇₉	—	4	1	no	—
281	C₂×C₄×C₇₉	—	4	2	no	—
282	C₂×C₄×C₇₉	—	8	1	no	—
283	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
284	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
285	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
286	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
289	C₈×C₇₉	—	4	2	no	—
290	C₈×C₇₉	—	4	2	no	—
291	C₈×C₇₉	—	4	2	no	—
292	C₂²×C₇₉	—	2	1	no	—
293	C₂²×C₇₉	—	2	1	no	—
294	C₂²×C₇₉	—	2	1	no	—
295	C₂²×C₇₉	—	4	1	no	—
296	C₂²×C₇₉	—	4	1	no	—
297	C₂²×C₇₉	—	4	1	no	—
298	C₂²×C₇₉	—	4	1	no	—
299	C₂²×C₇₉	—	4	1	no	—
300	C₂²×C₇₉	—	4	1	no	—
301	C₂²×C₇₉	—	8	2	no	—
302	C₂²×C₇₉	—	8	2	no	—
303	C₂²×C₇₉	—	8	2	no	—
304	C₂²×C₇₉	—	16	4	no	—
305	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
306	C₄×C₇₉	—	2	1	no	—
307	C₄×C₇₉	—	2	2	no	—
308	C₄×C₇₉	—	2	1	no	—
309	C₄×C₇₉	—	2	1	no	—
310	C₄×C₇₉	—	2	1	no	—
311	C₄×C₇₉	—	4	2	no	—
312	C₄×C₇₉	—	4	1	no	—
313	C₄×C₇₉	—	4	1	no	—
314	C₄×C₇₉	—	4	1	no	—
315	C₄×C₇₉	—	4	1	no	—
316	C₄×C₇₉	—	4	2	no	—
317	C₄×C₇₉	—	4	1	no	—
318	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₄×C₇₉	#575	1	1	yes	characteristic
320	C₄×C₇₉	#577	1	2	yes	—
321	#18852	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂×C₇₉	—	4	1	no	—
323	C₂×C₇₉	—	8	1	no	—
324	C₂×C₇₉	—	8	1	no	—
325	C₂×C₇₉	—	16	2	no	—
326	C₂×C₇₉	#3006	1	1	yes	characteristic
327	C₂×C₇₉	#3010	1	1	yes	characteristic
328	C₂×C₇₉	#3021	1	1	yes	characteristic
329	#3518	C₂×C₇₉	1	1	yes	characteristic, complemented
330	#3217	C₂×C₇₉	1	1	yes	characteristic, complemented
331	#3208	C₂×C₇₉	1	1	yes	characteristic, complemented
332	#3038	C₂×C₇₉	1	1	yes	characteristic, complemented
333	#1628	C₂×C₇₉	1	2	yes	complemented
334	#1627	C₂×C₇₉	1	2	yes	complemented
335	#1624	C₂×C₇₉	1	2	yes	complemented
336	#1623	C₂×C₇₉	1	2	yes	complemented
337	#1559	C₂×C₇₉	1	1	yes	characteristic, complemented
338	#1495	C₂×C₇₉	1	1	yes	characteristic, complemented
339	#1488	C₂×C₇₉	1	1	yes	characteristic, complemented
340	C₇₉	#18852	1	1	yes	characteristic, direct product factor, Sylow
341	C₂×AGL(1,ℤ/8)	—	2	1	no	—
342	Q₈²	C₂²×C₇₉	1	1	yes	characteristic, complemented
343	#556	—	2	1	no	—
344	#556	—	2	2	no	—
345	#556	—	2	1	no	—
346	#556	C₂²×C₇₉	1	1	yes	characteristic, complemented
347	#555	—	2	1	no	—
348	#555	C₂²×C₇₉	1	1	yes	characteristic, complemented
349	D₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
350	#548	—	2	1	no	—
351	#542	—	2	2	no	—
352	#542	—	2	1	no	—
353	#533	—	2	1	no	—
354	#533	C₂²×C₇₉	1	1	yes	characteristic
355	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
356	#529	—	2	1	no	—
357	#529	C₂²×C₇₉	1	1	yes	characteristic
358	#519	—	2	1	no	—
359	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
360	#496	—	2	1	no	—
361	#492	C₂²×C₇₉	1	2	yes	—
362	#490	—	2	1	no	—
363	#486	C₂²×C₇₉	1	2	yes	—
364	#460	—	2	2	no	—
365	#460	—	2	1	no	—
366	#460	C₂²×C₇₉	1	2	yes	—
367	#460	C₂²×C₇₉	1	2	yes	—
368	#459	—	2	1	no	—
369	#459	C₂²×C₇₉	1	2	yes	—
370	#459	C₂²×C₇₉	1	2	yes	—
371	#450	—	2	2	no	—
372	#450	—	2	1	no	—
373	#447	—	2	1	no	—
374	#432	C₂²×C₇₉	1	1	yes	characteristic
375	#431	C₂²×C₇₉	1	1	yes	characteristic
376	#423	C₂²×C₇₉	1	1	yes	characteristic
377	#418	—	2	1	no	—
378	#333	C₂²×C₇₉	1	2	yes	complemented
379	#332	C₂²×C₇₉	1	2	yes	complemented
380	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
381	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
382	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
383	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
384	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
385	C₂²×Q₈	—	2	1	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	AGL(1,ℤ/8)	—	4	4	no	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×SD₁₆	—	2	4	no	—
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×D₈	—	2	2	no	—
394	C₂×D₈	—	2	2	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₄⋊Q₈	—	2	2	no	—
397	C₄⋊Q₈	—	2	1	no	—
398	C₄⋊Q₈	—	2	1	no	—
399	C₄⋊Q₈	—	2	1	no	—
400	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
401	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
402	#127	—	2	1	no	—
403	#127	—	2	1	no	—
404	#127	—	2	1	no	—
405	#127	C₂³×C₇₉	1	2	yes	—
406	#126	—	2	2	no	—
407	#126	—	2	2	no	—
408	#126	—	2	2	no	—
409	#126	—	2	2	no	—
410	#126	—	2	1	no	—
411	#125	—	2	1	no	—
412	#125	D₄×C₇₉	1	1	yes	characteristic
413	#124	—	2	2	no	—
414	#124	—	2	2	no	—
415	#124	—	2	2	no	—
416	#124	—	2	2	no	—
417	#124	—	2	1	no	—
418	#124	D₄×C₇₉	1	1	yes	characteristic
419	#123	—	2	2	no	—
420	#123	—	2	1	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	1	no	—
424	C₂²⋊Q₈	—	2	1	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
428	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
429	#121	—	2	2	no	—
430	#121	—	2	1	no	—
431	#121	—	2	1	no	—
432	#121	D₄×C₇₉	1	1	yes	characteristic
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	2	1	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	—	2	1	no	—
439	C₄×Q₈	—	2	1	no	—
440	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
441	C₄×Q₈	D₄×C₇₉	1	2	yes	—
442	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
443	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	—	2	1	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
450	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
451	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
452	#117	—	2	2	no	—
453	#117	—	2	2	no	—
454	#117	—	2	1	no	—
455	#117	—	2	1	no	—
456	#117	—	2	1	no	—
457	#117	—	2	1	no	—
458	#117	—	2	1	no	—
459	#117	—	2	1	no	—
460	#117	D₄×C₇₉	1	1	yes	characteristic
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
463	C₄⋊C₈	—	2	1	no	—
464	C₄⋊C₈	—	2	1	no	—
465	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
466	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
467	#102	—	2	2	no	—
468	#102	—	2	2	no	—
469	#102	—	2	2	no	—
470	#102	—	2	2	no	—
471	#102	—	2	4	no	—
472	C₂²⋊C₈	—	2	1	no	—
473	C₂²⋊C₈	—	2	1	no	—
474	#97	—	2	1	no	—
475	C₄×C₈	C₂³×C₇₉	1	2	yes	—
476	C₂⁴	—	4	1	no	—
477	#41	—	2	2	no	—
478	#41	—	4	1	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	—	2	2	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	4	2	no	—
483	C₂×Q₈	—	4	2	no	—
484	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
485	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
486	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	1	no	—
496	C₂×D₄	—	4	1	no	—
497	C₂×D₄	—	4	1	no	—
498	C₂×D₄	—	8	2	no	—
499	C₂×D₄	—	8	2	no	—
500	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
501	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
510	SD₁₆	—	4	4	no	—
511	SD₁₆	—	8	2	no	—
512	SD₁₆	—	8	4	no	—
513	D₈	—	4	4	no	—
514	D₈	—	8	2	no	—
515	M₁₆	—	4	2	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
537	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
538	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	2	1	no	—
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	1	no	—
550	C₂²⋊C₄	—	2	1	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
562	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
563	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
564	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	4	2	no	—
568	C₂³	—	8	2	no	—
569	C₂³	—	8	2	no	—
570	C₂³	—	8	2	no	—
571	C₂³	#120×C₇₉	1	1	yes	characteristic
572	Q₈	—	2	1	no	—
573	Q₈	—	2	2	no	—
574	Q₈	—	4	2	no	—
575	Q₈	—	4	4	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	8	2	no	—
579	Q₈	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
580	D₄	—	2	1	no	—
581	D₄	—	2	1	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	4	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	8	2	no	—
590	D₄	—	8	2	no	—
591	D₄	—	8	2	no	—
592	D₄	—	8	1	no	—
593	D₄	—	8	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	4	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	8	1	no	—
612	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
613	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
614	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
615	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
616	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
617	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
618	C₈	—	4	2	no	—
619	C₈	—	4	2	no	—
620	C₈	—	4	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	8	2	no	—
631	C₂²	—	8	2	no	—
632	C₂²	—	8	2	no	—
633	C₂²	—	16	4	no	—
634	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	1	no	—
647	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
648	C₄	#575×C₇₉	1	1	yes	characteristic
649	C₄	#577×C₇₉	1	2	yes	—
650	C₂	—	4	1	no	—
651	C₂	—	8	1	no	—
652	C₂	—	8	1	no	—
653	C₂	—	16	2	no	—
654	C₂	C₇₉×#3006	1	1	yes	characteristic
655	C₂	C₇₉×#3010	1	1	yes	characteristic
656	C₂	C₇₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
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
1. C₇₉×#3518	C₂	semidirect
2. C₇₉×#3217	C₂	semidirect
3. C₇₉×#3208	C₂	semidirect
4. C₇₉×#3038	C₂	semidirect
5. C₇₉×#1628	C₂	semidirect
6. C₇₉×#1627	C₂	semidirect
7. C₇₉×#1624	C₂	semidirect
8. C₇₉×#1623	C₂	semidirect
9. C₇₉×#1559	C₂	semidirect
10. C₇₉×#1495	C₂	semidirect
11. C₇₉×#1488	C₂	semidirect
13. Q₈²×C₇₉	C₂²	semidirect
17. #556×C₇₉	C₂²	semidirect
19. #555×C₇₉	C₂²	semidirect
20. D₄×Q₈×C₇₉	C₂²	semidirect
49. #333×C₇₉	C₂²	semidirect
50. #332×C₇₉	C₂²	semidirect
51. Q₈⋊C₈×C₇₉	C₂²	semidirect
52. Q₈⋊C₈×C₇₉	C₂²	semidirect
53. D₄⋊C₈×C₇₉	C₂²	semidirect
54. D₄⋊C₈×C₇₉	C₂²	semidirect
321. #18852	C₇₉	direct (N × H)
329. #3518	C₂×C₇₉	semidirect
330. #3217	C₂×C₇₉	semidirect
331. #3208	C₂×C₇₉	semidirect
332. #3038	C₂×C₇₉	semidirect
333. #1628	C₂×C₇₉	semidirect
334. #1627	C₂×C₇₉	semidirect
335. #1624	C₂×C₇₉	semidirect
336. #1623	C₂×C₇₉	semidirect
337. #1559	C₂×C₇₉	semidirect
338. #1495	C₂×C₇₉	semidirect
339. #1488	C₂×C₇₉	semidirect
340. C₇₉	#18852	direct (N × H)
342. Q₈²	C₂²×C₇₉	semidirect
346. #556	C₂²×C₇₉	semidirect
348. #555	C₂²×C₇₉	semidirect
349. D₄×Q₈	C₂²×C₇₉	semidirect
378. #333	C₂²×C₇₉	semidirect
379. #332	C₂²×C₇₉	semidirect
380. Q₈⋊C₈	C₂²×C₇₉	semidirect
381. Q₈⋊C₈	C₂²×C₇₉	semidirect
382. D₄⋊C₈	C₂²×C₇₉	semidirect
383. D₄⋊C₈	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3518	2
C₇₉×#3217	2
C₇₉×#3208	2
C₇₉×#3038	2
C₇₉×#1628	2
C₇₉×#1627	2
C₇₉×#1624	2
C₇₉×#1623	2
C₇₉×#1559	2
C₇₉×#1495	2
C₇₉×#1488	2
#18852	79

Subgroups — C79×#18852 #34130541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18852 #34130541