Subgroups — C₇₉×#18580 #34130269

Order 20224.

962 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3217	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#460×C₇₉	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×#1626	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1626	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1552	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₉	—	2	1	no	—
13	#557×C₇₉	—	2	1	no	—
14	#557×C₇₉	C₂²	1	1	yes	characteristic, complemented
15	#557×C₇₉	C₂²	1	1	yes	characteristic, complemented
16	#556×C₇₉	—	2	1	no	—
17	#556×C₇₉	C₂²	1	1	yes	characteristic, complemented
18	#552×C₇₉	—	2	2	no	—
19	#552×C₇₉	—	2	1	no	—
20	D₄×Q₈×C₇₉	—	2	1	no	—
21	D₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
22	#541×C₇₉	—	2	2	no	—
23	#541×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	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
31	#496×C₇₉	—	2	1	no	—
32	#490×C₇₉	—	2	2	no	—
33	#490×C₇₉	—	2	1	no	—
34	#486×C₇₉	C₂²	1	2	yes	—
35	#486×C₇₉	C₂²	1	2	yes	—
36	#460×C₇₉	—	2	1	no	—
37	#460×C₇₉	—	2	1	no	—
38	#460×C₇₉	C₂²	1	2	yes	—
39	#460×C₇₉	C₂²	1	2	yes	—
40	#460×C₇₉	C₂²	1	2	yes	—
41	#459×C₇₉	C₂²	1	2	yes	—
42	#450×C₇₉	—	2	1	no	—
43	#447×C₇₉	—	2	1	no	—
44	#432×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
46	#418×C₇₉	—	2	2	no	—
47	C₂×#102×C₇₉	—	2	1	no	—
48	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
49	#332×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	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	complemented
54	D₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
55	C₂²×Q₈×C₇₉	—	2	1	no	—
56	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₇₉	—	2	1	no	—
58	C₂²×D₄×C₇₉	—	2	1	no	—
59	C₂²×D₄×C₇₉	—	2	1	no	—
60	C₂×SD₁₆×C₇₉	—	2	2	no	—
61	C₂×SD₁₆×C₇₉	—	2	2	no	—
62	C₂×SD₁₆×C₇₉	—	2	2	no	—
63	C₂×SD₁₆×C₇₉	—	4	4	no	—
64	C₂×D₈×C₇₉	—	2	2	no	—
65	C₂×M₁₆×C₇₉	—	2	1	no	—
66	C₂²×C₈×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	2	no	—
83	#125×C₇₉	—	2	2	no	—
84	#125×C₇₉	—	2	2	no	—
85	#125×C₇₉	—	2	1	no	—
86	#125×C₇₉	—	2	2	no	—
87	#125×C₇₉	—	2	2	no	—
88	#125×C₇₉	—	2	1	no	—
89	#125×C₇₉	D₄	1	1	yes	characteristic
90	#125×C₇₉	D₄	1	2	yes	—
91	#124×C₇₉	—	2	1	no	—
92	#124×C₇₉	D₄	1	1	yes	characteristic
93	#123×C₇₉	—	2	2	no	—
94	#123×C₇₉	—	2	1	no	—
95	C₂²⋊Q₈×C₇₉	—	2	2	no	—
96	C₂²⋊Q₈×C₇₉	—	2	2	no	—
97	C₂²⋊Q₈×C₇₉	—	2	1	no	—
98	C₂²⋊Q₈×C₇₉	—	2	1	no	—
99	C₂²⋊Q₈×C₇₉	—	2	1	no	—
100	C₂²⋊Q₈×C₇₉	—	2	1	no	—
101	C₂²⋊Q₈×C₇₉	—	2	2	no	—
102	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
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	1	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	—	2	1	no	—
112	C₄×Q₈×C₇₉	—	2	1	no	—
113	C₄×Q₈×C₇₉	—	2	1	no	—
114	C₄×Q₈×C₇₉	—	2	1	no	—
115	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
116	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
117	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
118	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
119	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₇₉	—	2	2	no	—
121	C₄×D₄×C₇₉	—	2	1	no	—
122	C₄×D₄×C₇₉	—	2	1	no	—
123	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
124	#117×C₇₉	—	2	2	no	—
125	#117×C₇₉	—	2	2	no	—
126	#117×C₇₉	—	2	2	no	—
127	#117×C₇₉	—	2	1	no	—
128	#117×C₇₉	—	2	1	no	—
129	#117×C₇₉	D₄	1	2	yes	—
130	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
131	C₂×C₄⋊C₄×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	C₂³	1	2	yes	—
136	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
137	#102×C₇₉	—	2	4	no	—
138	#102×C₇₉	—	2	4	no	—
139	#102×C₇₉	—	2	2	no	—
140	#102×C₇₉	—	2	2	no	—
141	#102×C₇₉	—	2	2	no	—
142	#102×C₇₉	—	2	2	no	—
143	C₂²⋊C₈×C₇₉	—	2	1	no	—
144	#97×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	C₂×Q₈×C₇₉	—	2	2	no	—
149	C₂×Q₈×C₇₉	—	2	1	no	—
150	C₂×Q₈×C₇₉	—	2	1	no	—
151	C₂×Q₈×C₇₉	—	2	1	no	—
152	C₂×Q₈×C₇₉	—	2	2	no	—
153	C₂×Q₈×C₇₉	—	4	1	no	—
154	C₂×Q₈×C₇₉	—	4	2	no	—
155	C₂×Q₈×C₇₉	—	4	2	no	—
156	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₇₉	—	2	1	no	—
160	C₂×D₄×C₇₉	—	2	2	no	—
161	C₂×D₄×C₇₉	—	2	2	no	—
162	C₂×D₄×C₇₉	—	2	2	no	—
163	C₂×D₄×C₇₉	—	4	2	no	—
164	C₂×D₄×C₇₉	—	4	4	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	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₉	—	2	2	no	—
172	C₂²×C₄×C₇₉	—	2	1	no	—
173	C₂²×C₄×C₇₉	—	2	1	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
178	SD₁₆×C₇₉	—	4	4	no	—
179	SD₁₆×C₇₉	—	4	4	no	—
180	SD₁₆×C₇₉	—	8	2	no	—
181	D₈×C₇₉	—	8	2	no	—
182	M₁₆×C₇₉	—	4	2	no	—
183	C₂×C₈×C₇₉	—	2	2	no	—
184	C₂×C₈×C₇₉	—	2	2	no	—
185	C₂×C₈×C₇₉	—	2	2	no	—
186	C₂×C₈×C₇₉	—	4	2	no	—
187	C₄⋊C₄×C₇₉	—	2	2	no	—
188	C₄⋊C₄×C₇₉	—	2	2	no	—
189	C₄⋊C₄×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	2	no	—
195	C₄⋊C₄×C₇₉	—	2	1	no	—
196	C₄⋊C₄×C₇₉	—	2	1	no	—
197	C₄⋊C₄×C₇₉	—	2	1	no	—
198	C₄⋊C₄×C₇₉	—	2	2	no	—
199	C₄⋊C₄×C₇₉	—	2	1	no	—
200	C₄⋊C₄×C₇₉	—	2	1	no	—
201	C₄⋊C₄×C₇₉	—	2	1	no	—
202	C₄⋊C₄×C₇₉	—	2	2	no	—
203	C₄⋊C₄×C₇₉	—	2	1	no	—
204	C₄⋊C₄×C₇₉	—	2	1	no	—
205	C₄⋊C₄×C₇₉	—	2	1	no	—
206	C₄⋊C₄×C₇₉	—	2	1	no	—
207	C₄⋊C₄×C₇₉	—	2	1	no	—
208	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
211	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
213	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
214	C₂²⋊C₄×C₇₉	—	2	2	no	—
215	C₂²⋊C₄×C₇₉	—	2	2	no	—
216	C₂²⋊C₄×C₇₉	—	2	2	no	—
217	C₂²⋊C₄×C₇₉	—	2	1	no	—
218	C₂²⋊C₄×C₇₉	—	2	2	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	C₄²×C₇₉	—	2	2	no	—
224	C₄²×C₇₉	—	2	2	no	—
225	C₄²×C₇₉	—	2	2	no	—
226	C₄²×C₇₉	—	2	1	no	—
227	C₄²×C₇₉	—	2	1	no	—
228	C₄²×C₇₉	—	2	2	no	—
229	C₄²×C₇₉	—	2	1	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	—	4	2	no	—
238	C₂³×C₇₉	—	8	2	no	—
239	C₂³×C₇₉	—	8	2	no	—
240	C₂³×C₇₉	—	8	2	no	—
241	C₂³×C₇₉	#120	1	1	yes	characteristic
242	Q₈×C₇₉	—	2	1	no	—
243	Q₈×C₇₉	—	2	1	no	—
244	Q₈×C₇₉	—	2	1	no	—
245	Q₈×C₇₉	—	2	2	no	—
246	Q₈×C₇₉	—	4	2	no	—
247	Q₈×C₇₉	—	4	4	no	—
248	Q₈×C₇₉	—	4	1	no	—
249	Q₈×C₇₉	—	4	1	no	—
250	Q₈×C₇₉	—	4	2	no	—
251	Q₈×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
252	D₄×C₇₉	—	2	2	no	—
253	D₄×C₇₉	—	4	4	no	—
254	D₄×C₇₉	—	4	2	no	—
255	D₄×C₇₉	—	4	2	no	—
256	D₄×C₇₉	—	4	2	no	—
257	D₄×C₇₉	—	4	2	no	—
258	D₄×C₇₉	—	4	2	no	—
259	D₄×C₇₉	—	8	2	no	—
260	D₄×C₇₉	—	8	2	no	—
261	D₄×C₇₉	—	8	2	no	—
262	C₂×C₄×C₇₉	—	2	1	no	—
263	C₂×C₄×C₇₉	—	2	2	no	—
264	C₂×C₄×C₇₉	—	2	1	no	—
265	C₂×C₄×C₇₉	—	2	1	no	—
266	C₂×C₄×C₇₉	—	2	2	no	—
267	C₂×C₄×C₇₉	—	2	1	no	—
268	C₂×C₄×C₇₉	—	2	1	no	—
269	C₂×C₄×C₇₉	—	2	2	no	—
270	C₂×C₄×C₇₉	—	2	1	no	—
271	C₂×C₄×C₇₉	—	2	1	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	—	4	2	no	—
276	C₂×C₄×C₇₉	—	4	4	no	—
277	C₂×C₄×C₇₉	—	4	2	no	—
278	C₂×C₄×C₇₉	—	4	1	no	—
279	C₂×C₄×C₇₉	—	4	1	no	—
280	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
281	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
282	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
283	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
286	C₈×C₇₉	—	4	2	no	—
287	C₈×C₇₉	—	4	2	no	—
288	C₈×C₇₉	—	4	2	no	—
289	C₂²×C₇₉	—	2	1	no	—
290	C₂²×C₇₉	—	2	1	no	—
291	C₂²×C₇₉	—	4	1	no	—
292	C₂²×C₇₉	—	4	1	no	—
293	C₂²×C₇₉	—	4	1	no	—
294	C₂²×C₇₉	—	8	2	no	—
295	C₂²×C₇₉	—	8	2	no	—
296	C₂²×C₇₉	—	8	2	no	—
297	C₂²×C₇₉	—	16	4	no	—
298	C₂²×C₇₉	#454	1	2	yes	—
299	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
300	C₄×C₇₉	—	2	1	no	—
301	C₄×C₇₉	—	2	2	no	—
302	C₄×C₇₉	—	2	1	no	—
303	C₄×C₇₉	—	2	1	no	—
304	C₄×C₇₉	—	2	1	no	—
305	C₄×C₇₉	—	4	1	no	—
306	C₄×C₇₉	—	4	2	no	—
307	C₄×C₇₉	—	4	1	no	—
308	C₄×C₇₉	—	4	1	no	—
309	C₄×C₇₉	—	4	2	no	—
310	C₄×C₇₉	—	4	1	no	—
311	C₄×C₇₉	—	4	1	no	—
312	C₄×C₇₉	—	4	1	no	—
313	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
314	C₄×C₇₉	#575	1	1	yes	characteristic
315	C₄×C₇₉	#577	1	2	yes	—
316	#18580	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂×C₇₉	—	2	2	no	—
318	C₂×C₇₉	—	8	1	no	—
319	C₂×C₇₉	—	16	2	no	—
320	C₂×C₇₉	#3006	1	1	yes	characteristic
321	C₂×C₇₉	#3010	1	1	yes	characteristic
322	C₂×C₇₉	C₂×#454	1	1	yes	characteristic
323	#3523	C₂×C₇₉	1	1	yes	characteristic, complemented
324	#3217	C₂×C₇₉	1	1	yes	characteristic
325	#3138	C₂×C₇₉	1	1	yes	characteristic, complemented
326	C₂×#460	C₂×C₇₉	1	1	yes	characteristic, complemented
327	#1628	C₂×C₇₉	1	2	yes	complemented
328	#1627	C₂×C₇₉	1	2	yes	complemented
329	#1626	C₂×C₇₉	1	2	yes	complemented
330	#1626	C₂×C₇₉	1	2	yes	complemented
331	#1552	C₂×C₇₉	1	1	yes	characteristic, complemented
332	#1491	C₂×C₇₉	1	1	yes	characteristic, complemented
333	#1483	C₂×C₇₉	1	1	yes	characteristic, complemented
334	C₇₉	#18580	1	1	yes	characteristic, direct product factor, Sylow
335	C₂²×SD₁₆	—	2	1	no	—
336	#557	—	2	1	no	—
337	#557	C₂²×C₇₉	1	1	yes	characteristic, complemented
338	#557	C₂²×C₇₉	1	1	yes	characteristic, complemented
339	#556	—	2	1	no	—
340	#556	C₂²×C₇₉	1	1	yes	characteristic, complemented
341	#552	—	2	2	no	—
342	#552	—	2	1	no	—
343	D₄×Q₈	—	2	1	no	—
344	D₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
345	#541	—	2	2	no	—
346	#541	—	2	1	no	—
347	#533	—	2	1	no	—
348	#533	C₂²×C₇₉	1	1	yes	characteristic
349	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
350	#529	—	2	1	no	—
351	#529	C₂²×C₇₉	1	1	yes	characteristic
352	#519	—	2	1	no	—
353	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
354	#496	—	2	1	no	—
355	#490	—	2	2	no	—
356	#490	—	2	1	no	—
357	#486	C₂²×C₇₉	1	2	yes	—
358	#486	C₂²×C₇₉	1	2	yes	—
359	#460	—	2	1	no	—
360	#460	—	2	1	no	—
361	#460	C₂²×C₇₉	1	2	yes	—
362	#460	C₂²×C₇₉	1	2	yes	—
363	#460	C₂²×C₇₉	1	2	yes	—
364	#459	C₂²×C₇₉	1	2	yes	—
365	#450	—	2	1	no	—
366	#447	—	2	1	no	—
367	#432	C₂²×C₇₉	1	1	yes	characteristic
368	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
369	#418	—	2	2	no	—
370	C₂×#102	—	2	1	no	—
371	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
372	#332	C₂²×C₇₉	1	2	yes	complemented
373	#332	C₂²×C₇₉	1	2	yes	complemented
374	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
375	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
376	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	complemented
377	D₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
378	C₂²×Q₈	—	2	1	no	—
379	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	2	1	no	—
382	C₂²×D₄	—	2	1	no	—
383	C₂×SD₁₆	—	2	2	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	4	4	no	—
387	C₂×D₈	—	2	2	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂²×C₈	—	2	1	no	—
390	C₄⋊Q₈	—	2	2	no	—
391	C₄⋊Q₈	—	2	1	no	—
392	C₄⋊Q₈	—	2	1	no	—
393	C₄⋊Q₈	—	2	1	no	—
394	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
395	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
396	#127	—	2	1	no	—
397	#127	—	2	1	no	—
398	#127	—	2	1	no	—
399	#127	C₂³×C₇₉	1	2	yes	—
400	#126	—	2	2	no	—
401	#126	—	2	2	no	—
402	#126	—	2	2	no	—
403	#126	—	2	2	no	—
404	#126	—	2	1	no	—
405	#125	—	2	2	no	—
406	#125	—	2	2	no	—
407	#125	—	2	2	no	—
408	#125	—	2	1	no	—
409	#125	—	2	2	no	—
410	#125	—	2	2	no	—
411	#125	—	2	1	no	—
412	#125	D₄×C₇₉	1	1	yes	characteristic
413	#125	D₄×C₇₉	1	2	yes	—
414	#124	—	2	1	no	—
415	#124	D₄×C₇₉	1	1	yes	characteristic
416	#123	—	2	2	no	—
417	#123	—	2	1	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	1	no	—
421	C₂²⋊Q₈	—	2	1	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	1	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
426	#121	D₄×C₇₉	1	1	yes	characteristic
427	C₄×Q₈	—	2	2	no	—
428	C₄×Q₈	—	2	2	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	—	2	1	no	—
432	C₄×Q₈	—	2	1	no	—
433	C₄×Q₈	—	2	1	no	—
434	C₄×Q₈	—	2	1	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×Q₈	—	2	1	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
439	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
440	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
441	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
442	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
447	#117	—	2	2	no	—
448	#117	—	2	2	no	—
449	#117	—	2	2	no	—
450	#117	—	2	1	no	—
451	#117	—	2	1	no	—
452	#117	D₄×C₇₉	1	2	yes	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
457	C₄⋊C₈	—	2	1	no	—
458	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
459	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
460	#102	—	2	2	no	—
461	#102	—	2	2	no	—
462	#102	—	2	4	no	—
463	#102	—	2	4	no	—
464	#102	—	2	2	no	—
465	#102	—	2	2	no	—
466	C₂²⋊C₈	—	2	1	no	—
467	#97	—	2	1	no	—
468	#97	—	2	1	no	—
469	C₄×C₈	C₂³×C₇₉	1	2	yes	—
470	C₂⁴	—	4	1	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	4	1	no	—
477	C₂×Q₈	—	4	2	no	—
478	C₂×Q₈	—	4	2	no	—
479	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
480	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
481	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	4	4	no	—
488	C₂×D₄	—	4	2	no	—
489	C₂×D₄	—	4	1	no	—
490	C₂×D₄	—	4	1	no	—
491	C₂×D₄	—	4	1	no	—
492	C₂×D₄	—	8	2	no	—
493	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
501	SD₁₆	—	4	4	no	—
502	SD₁₆	—	4	4	no	—
503	SD₁₆	—	8	2	no	—
504	D₈	—	8	2	no	—
505	M₁₆	—	4	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	4	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	1	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	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
532	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
533	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
534	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
535	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
556	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
557	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
558	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
559	C₂³	—	2	1	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	8	2	no	—
562	C₂³	—	8	2	no	—
563	C₂³	—	8	2	no	—
564	C₂³	#120×C₇₉	1	1	yes	characteristic
565	Q₈	—	2	1	no	—
566	Q₈	—	2	1	no	—
567	Q₈	—	2	1	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	4	2	no	—
570	Q₈	—	4	4	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	2	no	—
574	Q₈	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
575	D₄	—	2	2	no	—
576	D₄	—	4	4	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	8	2	no	—
583	D₄	—	8	2	no	—
584	D₄	—	8	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	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	—	4	2	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
604	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
605	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
609	C₈	—	4	2	no	—
610	C₈	—	4	2	no	—
611	C₈	—	4	2	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	8	2	no	—
618	C₂²	—	8	2	no	—
619	C₂²	—	8	2	no	—
620	C₂²	—	16	4	no	—
621	C₂²	#454×C₇₉	1	2	yes	—
622	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
637	C₄	#575×C₇₉	1	1	yes	characteristic
638	C₄	#577×C₇₉	1	2	yes	—
639	C₂	—	2	2	no	—
640	C₂	—	8	1	no	—
641	C₂	—	16	2	no	—
642	C₂	C₇₉×#3006	1	1	yes	characteristic
643	C₂	C₇₉×#3010	1	1	yes	characteristic
644	C₂	C₂×#454×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3217	C₂
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×#3523	C₂	semidirect
3. C₇₉×#3138	C₂	semidirect
4. C₂×#460×C₇₉	C₂	semidirect
5. C₇₉×#1628	C₂	semidirect
6. C₇₉×#1627	C₂	semidirect
7. C₇₉×#1626	C₂	semidirect
8. C₇₉×#1626	C₂	semidirect
9. C₇₉×#1552	C₂	semidirect
10. C₇₉×#1491	C₂	semidirect
11. C₇₉×#1483	C₂	semidirect
14. #557×C₇₉	C₂²	semidirect
15. #557×C₇₉	C₂²	semidirect
17. #556×C₇₉	C₂²	semidirect
21. D₄×Q₈×C₇₉	C₂²	semidirect
49. #332×C₇₉	C₂²	semidirect
50. #332×C₇₉	C₂²	semidirect
51. Q₈⋊C₈×C₇₉	C₂²	semidirect
52. Q₈⋊C₈×C₇₉	C₂²	semidirect
53. Q₈⋊C₈×C₇₉	C₂²	semidirect
54. D₄⋊C₈×C₇₉	C₂²	semidirect
316. #18580	C₇₉	direct (N × H)
323. #3523	C₂×C₇₉	semidirect
325. #3138	C₂×C₇₉	semidirect
326. C₂×#460	C₂×C₇₉	semidirect
327. #1628	C₂×C₇₉	semidirect
328. #1627	C₂×C₇₉	semidirect
329. #1626	C₂×C₇₉	semidirect
330. #1626	C₂×C₇₉	semidirect
331. #1552	C₂×C₇₉	semidirect
332. #1491	C₂×C₇₉	semidirect
333. #1483	C₂×C₇₉	semidirect
334. C₇₉	#18580	direct (N × H)
337. #557	C₂²×C₇₉	semidirect
338. #557	C₂²×C₇₉	semidirect
340. #556	C₂²×C₇₉	semidirect
344. D₄×Q₈	C₂²×C₇₉	semidirect
372. #332	C₂²×C₇₉	semidirect
373. #332	C₂²×C₇₉	semidirect
374. Q₈⋊C₈	C₂²×C₇₉	semidirect
375. Q₈⋊C₈	C₂²×C₇₉	semidirect
376. Q₈⋊C₈	C₂²×C₇₉	semidirect
377. 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×#3523	2
C₇₉×#3217	2
C₇₉×#3138	2
C₂×#460×C₇₉	2
C₇₉×#1628	2
C₇₉×#1627	2
C₇₉×#1626	2
C₇₉×#1552	2
C₇₉×#1491	2
C₇₉×#1483	2
#18580	79

Subgroups — C79×#18580 #34130269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18580 #34130269