Subgroups — C₇₉×#17465 #34129154

Order 20224.

1020 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#431×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#1483	C₂	1	4	yes	maximal, complemented
5	C₇₉×#1482	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1479	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1478	C₂	1	2	yes	maximal, complemented
8	#529×C₇₉	—	2	1	no	—
9	#529×C₇₉	—	2	1	no	—
10	#529×C₇₉	—	2	1	no	—
11	#529×C₇₉	—	2	1	no	—
12	#529×C₇₉	C₄	1	2	yes	—
13	#529×C₇₉	C₄	1	2	yes	—
14	#529×C₇₉	C₂²	1	2	yes	—
15	#529×C₇₉	C₂²	1	2	yes	—
16	C₂×#126×C₇₉	—	2	1	no	—
17	C₂×#125×C₇₉	C₄	1	1	yes	characteristic
18	C₂×#124×C₇₉	C₄	1	1	yes	characteristic
19	C₂×#123×C₇₉	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
21	C₂×#121×C₇₉	C₄	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₉	—	2	1	no	—
24	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₇₉	—	2	1	no	—
26	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
27	#432×C₇₉	—	2	1	no	—
28	#432×C₇₉	—	2	1	no	—
29	#431×C₇₉	—	2	1	no	—
30	#431×C₇₉	—	2	1	no	—
31	#431×C₇₉	C₂²	1	2	yes	—
32	#431×C₇₉	C₂²	1	2	yes	—
33	#431×C₇₉	C₂²	1	2	yes	complemented
34	#431×C₇₉	C₂²	1	2	yes	complemented
35	#423×C₇₉	—	2	1	no	—
36	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
37	#407×C₇₉	—	2	1	no	—
38	C₂×C₂²⋊C₈×C₇₉	—	2	1	no	—
39	C₄×M₁₆×C₇₉	C₂²	1	2	yes	complemented
40	C₂×C₄×C₈×C₇₉	—	2	1	no	—
41	Q₈⋊C₈×C₇₉	C₂²	1	8	yes	complemented
42	D₄⋊C₈×C₇₉	C₂²	1	8	yes	complemented
43	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₇₉	—	2	1	no	—
45	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₇₉	—	2	1	no	—
47	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
50	C₂×M₁₆×C₇₉	—	2	2	no	—
51	C₂²×C₈×C₇₉	—	2	2	no	—
52	#126×C₇₉	—	2	2	no	—
53	#126×C₇₉	—	2	2	no	—
54	#126×C₇₉	—	2	2	no	—
55	#126×C₇₉	—	2	2	no	—
56	#125×C₇₉	—	2	1	no	—
57	#125×C₇₉	—	2	1	no	—
58	#125×C₇₉	C₂×C₄	1	2	yes	—
59	#125×C₇₉	C₂×C₄	1	2	yes	—
60	#124×C₇₉	—	2	1	no	—
61	#124×C₇₉	—	2	1	no	—
62	#124×C₇₉	C₂×C₄	1	2	yes	—
63	#124×C₇₉	C₂×C₄	1	2	yes	—
64	#123×C₇₉	—	2	2	no	—
65	#123×C₇₉	—	2	2	no	—
66	#123×C₇₉	—	2	2	no	—
67	#123×C₇₉	—	2	2	no	—
68	C₂²⋊Q₈×C₇₉	—	2	1	no	—
69	C₂²⋊Q₈×C₇₉	—	2	1	no	—
70	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
71	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
72	#121×C₇₉	—	2	1	no	—
73	#121×C₇₉	—	2	1	no	—
74	#121×C₇₉	C₂×C₄	1	2	yes	—
75	#121×C₇₉	C₂×C₄	1	2	yes	—
76	C₄×Q₈×C₇₉	—	2	1	no	—
77	C₄×Q₈×C₇₉	—	2	1	no	—
78	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
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	2	no	—
84	C₄×D₄×C₇₉	—	2	1	no	—
85	C₄×D₄×C₇₉	—	2	1	no	—
86	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
87	C₄×D₄×C₇₉	C₂³	1	2	yes	—
88	#117×C₇₉	—	2	2	no	—
89	#117×C₇₉	—	2	2	no	—
90	#117×C₇₉	—	2	2	no	—
91	#117×C₇₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
103	C₂×C₄²×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₇₉	—	2	2	no	—
117	C₄⋊C₈×C₇₉	—	2	2	no	—
118	C₄⋊C₈×C₇₉	—	2	2	no	—
119	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
120	C₂²⋊C₈×C₇₉	—	2	2	no	—
121	C₂²⋊C₈×C₇₉	—	2	2	no	—
122	C₂²⋊C₈×C₇₉	—	2	2	no	—
123	C₂²⋊C₈×C₇₉	—	2	2	no	—
124	#97×C₇₉	—	2	2	no	—
125	C₄×C₈×C₇₉	—	2	2	no	—
126	C₄×C₈×C₇₉	—	2	2	no	—
127	C₄×C₈×C₇₉	C₂³	1	4	yes	—
128	C₂⁴×C₇₉	—	2	1	no	—
129	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×Q₈×C₇₉	—	2	1	no	—
131	C₂×Q₈×C₇₉	—	2	4	no	—
132	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₇₉	—	2	2	no	—
134	C₂×D₄×C₇₉	—	2	2	no	—
135	C₂×D₄×C₇₉	—	2	1	no	—
136	C₂×D₄×C₇₉	—	2	4	no	—
137	C₂×D₄×C₇₉	—	4	4	no	—
138	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₇₉	—	2	4	no	—
140	C₂²×C₄×C₇₉	—	2	1	no	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	—	2	1	no	—
143	C₂²×C₄×C₇₉	—	2	2	no	—
144	C₂²×C₄×C₇₉	—	2	2	no	—
145	C₂²×C₄×C₇₉	—	4	2	no	—
146	C₂²×C₄×C₇₉	—	4	2	no	—
147	C₂²×C₄×C₇₉	—	4	4	no	—
148	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
166	M₁₆×C₇₉	—	4	4	no	—
167	C₂×C₈×C₇₉	—	2	4	no	—
168	C₂×C₈×C₇₉	—	2	4	no	—
169	C₂×C₈×C₇₉	—	4	4	no	—
170	C₄⋊C₄×C₇₉	—	2	2	no	—
171	C₄⋊C₄×C₇₉	—	2	2	no	—
172	C₄⋊C₄×C₇₉	—	2	2	no	—
173	C₄⋊C₄×C₇₉	—	2	2	no	—
174	C₄⋊C₄×C₇₉	—	2	2	no	—
175	C₄⋊C₄×C₇₉	—	2	2	no	—
176	C₄⋊C₄×C₇₉	—	2	2	no	—
177	C₄⋊C₄×C₇₉	—	2	1	no	—
178	C₄⋊C₄×C₇₉	—	2	1	no	—
179	C₄⋊C₄×C₇₉	—	2	2	no	—
180	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
181	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
182	C₂²⋊C₄×C₇₉	—	2	2	no	—
183	C₂²⋊C₄×C₇₉	—	2	2	no	—
184	C₂²⋊C₄×C₇₉	—	2	2	no	—
185	C₂²⋊C₄×C₇₉	—	2	2	no	—
186	C₂²⋊C₄×C₇₉	—	2	2	no	—
187	C₂²⋊C₄×C₇₉	—	2	2	no	—
188	C₂²⋊C₄×C₇₉	—	2	2	no	—
189	C₂²⋊C₄×C₇₉	—	2	2	no	—
190	C₂²⋊C₄×C₇₉	—	2	2	no	—
191	C₂²⋊C₄×C₇₉	—	2	2	no	—
192	C₄²×C₇₉	—	2	2	no	—
193	C₄²×C₇₉	—	2	2	no	—
194	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
195	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
196	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
197	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
198	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
199	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
200	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
210	C₂³×C₇₉	—	2	2	no	—
211	C₂³×C₇₉	—	2	2	no	—
212	C₂³×C₇₉	—	2	2	no	—
213	C₂³×C₇₉	—	4	1	no	—
214	C₂³×C₇₉	—	4	2	no	—
215	C₂³×C₇₉	—	4	2	no	—
216	C₂³×C₇₉	—	4	2	no	—
217	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	Q₈×C₇₉	—	2	4	no	—
221	Q₈×C₇₉	—	4	2	no	—
222	D₄×C₇₉	—	2	4	no	—
223	D₄×C₇₉	—	4	4	no	—
224	D₄×C₇₉	—	4	4	no	—
225	D₄×C₇₉	—	4	2	no	—
226	C₂×C₄×C₇₉	—	2	2	no	—
227	C₂×C₄×C₇₉	—	2	2	no	—
228	C₂×C₄×C₇₉	—	2	2	no	—
229	C₂×C₄×C₇₉	—	2	2	no	—
230	C₂×C₄×C₇₉	—	2	2	no	—
231	C₂×C₄×C₇₉	—	2	2	no	—
232	C₂×C₄×C₇₉	—	2	2	no	—
233	C₂×C₄×C₇₉	—	2	2	no	—
234	C₂×C₄×C₇₉	—	2	2	no	—
235	C₂×C₄×C₇₉	—	2	2	no	—
236	C₂×C₄×C₇₉	—	2	2	no	—
237	C₂×C₄×C₇₉	—	2	2	no	—
238	C₂×C₄×C₇₉	—	2	2	no	—
239	C₂×C₄×C₇₉	—	4	1	no	—
240	C₂×C₄×C₇₉	—	4	1	no	—
241	C₂×C₄×C₇₉	—	4	1	no	—
242	C₂×C₄×C₇₉	—	4	1	no	—
243	C₂×C₄×C₇₉	—	4	1	no	—
244	C₂×C₄×C₇₉	—	4	1	no	—
245	C₂×C₄×C₇₉	—	4	1	no	—
246	C₂×C₄×C₇₉	—	4	4	no	—
247	C₂×C₄×C₇₉	—	4	2	no	—
248	C₂×C₄×C₇₉	—	4	2	no	—
249	C₂×C₄×C₇₉	—	4	2	no	—
250	C₂×C₄×C₇₉	—	4	4	no	—
251	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₇₉	#131	1	4	yes	—
261	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
264	C₈×C₇₉	—	4	4	no	—
265	C₈×C₇₉	—	4	4	no	—
266	C₂²×C₇₉	—	2	1	no	—
267	C₂²×C₇₉	—	2	1	no	—
268	C₂²×C₇₉	—	2	1	no	—
269	C₂²×C₇₉	—	2	1	no	—
270	C₂²×C₇₉	—	2	1	no	—
271	C₂²×C₇₉	—	2	1	no	—
272	C₂²×C₇₉	—	2	1	no	—
273	C₂²×C₇₉	—	4	4	no	—
274	C₂²×C₇₉	—	4	2	no	—
275	C₂²×C₇₉	—	4	2	no	—
276	C₂²×C₇₉	—	4	2	no	—
277	C₂²×C₇₉	—	8	4	no	—
278	C₂²×C₇₉	#408	1	2	yes	—
279	C₂²×C₇₉	#421	1	2	yes	—
280	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
281	C₄×C₇₉	—	2	1	no	—
282	C₄×C₇₉	—	2	1	no	—
283	C₄×C₇₉	—	2	1	no	—
284	C₄×C₇₉	—	2	1	no	—
285	C₄×C₇₉	—	2	1	no	—
286	C₄×C₇₉	—	2	1	no	—
287	C₄×C₇₉	—	2	1	no	—
288	C₄×C₇₉	—	2	1	no	—
289	C₄×C₇₉	—	2	1	no	—
290	C₄×C₇₉	—	4	2	no	—
291	C₄×C₇₉	—	4	2	no	—
292	C₄×C₇₉	—	4	2	no	—
293	C₄×C₇₉	#408	1	2	yes	—
294	C₄×C₇₉	C₂×#131	1	2	yes	—
295	C₄×C₇₉	#575	1	2	yes	—
296	#17465	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂×C₇₉	—	2	2	no	—
298	C₂×C₇₉	—	2	2	no	—
299	C₂×C₇₉	—	4	1	no	—
300	C₂×C₇₉	—	8	2	no	—
301	C₂×C₇₉	C₂×#408	1	1	yes	characteristic
302	C₂×C₇₉	#2896	1	1	yes	characteristic
303	C₂×C₇₉	C₂×#421	1	1	yes	characteristic
304	C₂×#529	C₂×C₇₉	1	1	yes	characteristic
305	#2920	C₂×C₇₉	1	1	yes	characteristic, complemented
306	C₂×#431	C₂×C₇₉	1	1	yes	characteristic, complemented
307	#1483	C₂×C₇₉	1	4	yes	complemented
308	#1482	C₂×C₇₉	1	4	yes	complemented
309	#1479	C₂×C₇₉	1	2	yes	complemented
310	#1478	C₂×C₇₉	1	2	yes	complemented
311	C₇₉	#17465	1	1	yes	characteristic, direct product factor, Sylow
312	#529	—	2	1	no	—
313	#529	—	2	1	no	—
314	#529	—	2	1	no	—
315	#529	—	2	1	no	—
316	#529	C₄×C₇₉	1	2	yes	—
317	#529	C₄×C₇₉	1	2	yes	—
318	#529	C₂²×C₇₉	1	2	yes	—
319	#529	C₂²×C₇₉	1	2	yes	—
320	C₂×#126	—	2	1	no	—
321	C₂×#125	C₄×C₇₉	1	1	yes	characteristic
322	C₂×#124	C₄×C₇₉	1	1	yes	characteristic
323	C₂×#123	—	2	1	no	—
324	C₂×C₂²⋊Q₈	C₄×C₇₉	1	1	yes	characteristic
325	C₂×#121	C₄×C₇₉	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
327	C₂×C₄×D₄	—	2	1	no	—
328	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
329	C₂×#117	—	2	1	no	—
330	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
331	#432	—	2	1	no	—
332	#432	—	2	1	no	—
333	#431	—	2	1	no	—
334	#431	—	2	1	no	—
335	#431	C₂²×C₇₉	1	2	yes	—
336	#431	C₂²×C₇₉	1	2	yes	—
337	#431	C₂²×C₇₉	1	2	yes	complemented
338	#431	C₂²×C₇₉	1	2	yes	complemented
339	#423	—	2	1	no	—
340	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
341	#407	—	2	1	no	—
342	C₂×C₂²⋊C₈	—	2	1	no	—
343	C₄×M₁₆	C₂²×C₇₉	1	2	yes	complemented
344	C₂×C₄×C₈	—	2	1	no	—
345	Q₈⋊C₈	C₂²×C₇₉	1	8	yes	complemented
346	D₄⋊C₈	C₂²×C₇₉	1	8	yes	complemented
347	C₂²×Q₈	C₂×C₄×C₇₉	1	1	yes	characteristic
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	C₂×C₄×C₇₉	1	1	yes	characteristic
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
352	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
353	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
354	C₂×M₁₆	—	2	2	no	—
355	C₂²×C₈	—	2	2	no	—
356	#126	—	2	2	no	—
357	#126	—	2	2	no	—
358	#126	—	2	2	no	—
359	#126	—	2	2	no	—
360	#125	—	2	1	no	—
361	#125	—	2	1	no	—
362	#125	C₂×C₄×C₇₉	1	2	yes	—
363	#125	C₂×C₄×C₇₉	1	2	yes	—
364	#124	—	2	1	no	—
365	#124	—	2	1	no	—
366	#124	C₂×C₄×C₇₉	1	2	yes	—
367	#124	C₂×C₄×C₇₉	1	2	yes	—
368	#123	—	2	2	no	—
369	#123	—	2	2	no	—
370	#123	—	2	2	no	—
371	#123	—	2	2	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	C₂×C₄×C₇₉	1	2	yes	—
375	C₂²⋊Q₈	C₂×C₄×C₇₉	1	2	yes	—
376	#121	—	2	1	no	—
377	#121	—	2	1	no	—
378	#121	C₂×C₄×C₇₉	1	2	yes	—
379	#121	C₂×C₄×C₇₉	1	2	yes	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	C₂×C₄×C₇₉	1	2	yes	—
383	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	C₂×C₄×C₇₉	1	2	yes	—
391	C₄×D₄	C₂³×C₇₉	1	2	yes	—
392	#117	—	2	2	no	—
393	#117	—	2	2	no	—
394	#117	—	2	2	no	—
395	#117	—	2	2	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
409	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
410	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
411	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
412	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
413	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
414	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
415	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
416	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
420	C₄⋊C₈	—	2	2	no	—
421	C₄⋊C₈	—	2	2	no	—
422	C₄⋊C₈	—	2	2	no	—
423	C₄⋊C₈	C₂³×C₇₉	1	4	yes	—
424	C₂²⋊C₈	—	2	2	no	—
425	C₂²⋊C₈	—	2	2	no	—
426	C₂²⋊C₈	—	2	2	no	—
427	C₂²⋊C₈	—	2	2	no	—
428	#97	—	2	2	no	—
429	C₄×C₈	—	2	2	no	—
430	C₄×C₈	—	2	2	no	—
431	C₄×C₈	C₂³×C₇₉	1	4	yes	—
432	C₂⁴	—	2	1	no	—
433	C₂⁴	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	C₂²×C₄×C₇₉	1	2	yes	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	C₂²×C₄×C₇₉	1	2	yes	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
453	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
454	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
455	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
456	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
457	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
458	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
459	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
460	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
461	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
462	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
463	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
470	M₁₆	—	4	4	no	—
471	C₂×C₈	—	2	4	no	—
472	C₂×C₈	—	2	4	no	—
473	C₂×C₈	—	4	4	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	C₂²×C₄×C₇₉	1	2	yes	—
485	C₄⋊C₄	C₂²×C₄×C₇₉	1	2	yes	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
499	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
500	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
501	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
502	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
503	C₄²	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
504	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
505	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
506	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
508	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
513	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
522	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
523	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
524	Q₈	—	2	4	no	—
525	Q₈	—	4	2	no	—
526	D₄	—	2	4	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
556	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
557	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
558	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
559	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
560	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
561	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
562	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
563	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
564	C₂×C₄	#131×C₇₉	1	4	yes	—
565	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
568	C₈	—	4	4	no	—
569	C₈	—	4	4	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	8	4	no	—
582	C₂²	#408×C₇₉	1	2	yes	—
583	C₂²	#421×C₇₉	1	2	yes	—
584	C₂²	C₂²×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	#408×C₇₉	1	2	yes	—
598	C₄	C₂×#131×C₇₉	1	2	yes	—
599	C₄	#575×C₇₉	1	2	yes	—
600	C₂	—	2	2	no	—
601	C₂	—	2	2	no	—
602	C₂	—	4	1	no	—
603	C₂	—	8	2	no	—
604	C₂	C₂×#408×C₇₉	1	1	yes	characteristic
605	C₂	C₇₉×#2896	1	1	yes	characteristic
606	C₂	C₂×#421×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₄²	C₂⁴×C₇₉
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂×#121×C₇₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#2920	C₂	semidirect
3. C₂×#431×C₇₉	C₂	semidirect
4. C₇₉×#1483	C₂	semidirect
5. C₇₉×#1482	C₂	semidirect
6. C₇₉×#1479	C₂	semidirect
7. C₇₉×#1478	C₂	semidirect
33. #431×C₇₉	C₂²	semidirect
34. #431×C₇₉	C₂²	semidirect
36. C₂×C₄⋊C₈×C₇₉	C₂²	semidirect
39. C₄×M₁₆×C₇₉	C₂²	semidirect
41. Q₈⋊C₈×C₇₉	C₂²	semidirect
42. D₄⋊C₈×C₇₉	C₂²	semidirect
296. #17465	C₇₉	direct (N × H)
305. #2920	C₂×C₇₉	semidirect
306. C₂×#431	C₂×C₇₉	semidirect
307. #1483	C₂×C₇₉	semidirect
308. #1482	C₂×C₇₉	semidirect
309. #1479	C₂×C₇₉	semidirect
310. #1478	C₂×C₇₉	semidirect
311. C₇₉	#17465	direct (N × H)
337. #431	C₂²×C₇₉	semidirect
338. #431	C₂²×C₇₉	semidirect
340. C₂×C₄⋊C₈	C₂²×C₇₉	semidirect
343. C₄×M₁₆	C₂²×C₇₉	semidirect
345. Q₈⋊C₈	C₂²×C₇₉	semidirect
346. 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
C₂×#529×C₇₉	2
C₇₉×#2920	2
C₂×#431×C₇₉	2
C₇₉×#1483	2
C₇₉×#1482	2
C₇₉×#1479	2
C₇₉×#1478	2
#17465	79

Subgroups — C79×#17465 #34129154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#17465 #34129154