Subgroups — C₇₉×#17918 #34129607

Order 20224.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3105	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2972	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#1586	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1585	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#1582	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1581	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×SD₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	#529×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
18	#484×C₇₉	C₄	1	1	yes	characteristic
19	#481×C₇₉	C₄	1	1	yes	characteristic
20	#478×C₇₉	C₄	1	1	yes	characteristic
21	#478×C₇₉	C₄	1	1	yes	characteristic
22	#463×C₇₉	C₄	1	1	yes	characteristic
23	#463×C₇₉	C₄	1	1	yes	characteristic
24	#450×C₇₉	C₄	1	1	yes	characteristic
25	#447×C₇₉	C₄	1	1	yes	characteristic
26	#446×C₇₉	C₂²	1	1	yes	characteristic, complemented
27	C₈×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
28	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
29	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
30	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
32	#436×C₇₉	—	2	1	no	—
33	#436×C₇₉	C₂²	1	1	yes	characteristic, complemented
34	#435×C₇₉	—	2	1	no	—
35	C₈×D₄×C₇₉	—	2	1	no	—
36	C₈×D₄×C₇₉	—	2	1	no	—
37	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic
38	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	#433×C₇₉	—	2	1	no	—
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	#431×C₇₉	C₂²	1	1	yes	characteristic
45	#431×C₇₉	C₂²	1	1	yes	characteristic
46	#431×C₇₉	C₂²	1	1	yes	characteristic
47	#424×C₇₉	—	2	1	no	—
48	#423×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₇₉	—	2	1	no	—
50	C₂×C₂²⋊C₈×C₇₉	—	2	1	no	—
51	#335×C₇₉	C₂²	1	1	yes	characteristic, complemented
52	#335×C₇₉	C₂²	1	1	yes	characteristic, complemented
53	#334×C₇₉	C₂²	1	1	yes	characteristic, complemented
54	#334×C₇₉	C₂²	1	1	yes	characteristic, complemented
55	Q₈⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
56	Q₈⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
57	D₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
58	D₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
59	D₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
60	D₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
61	D₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
62	D₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
63	#322×C₇₉	C₂²	1	1	yes	characteristic, complemented
64	#322×C₇₉	C₂²	1	1	yes	characteristic, complemented
65	#322×C₇₉	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₇₉	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₇₉	—	2	1	no	—
69	C₂×SD₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
71	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
72	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
73	C₂×M₁₆×C₇₉	—	2	1	no	—
74	C₂×M₁₆×C₇₉	—	2	1	no	—
75	C₂²×C₈×C₇₉	—	2	1	no	—
76	C₂²×C₈×C₇₉	—	2	1	no	—
77	C₂²×C₈×C₇₉	—	2	1	no	—
78	C₂²×C₈×C₇₉	—	2	1	no	—
79	C₂²×C₈×C₇₉	—	2	1	no	—
80	#126×C₇₉	—	2	1	no	—
81	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
82	#124×C₇₉	C₂×C₄	1	1	yes	characteristic
83	#123×C₇₉	—	2	1	no	—
84	C₂²⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
85	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₇₉	—	2	1	no	—
88	C₄×D₄×C₇₉	—	2	1	no	—
89	C₄×D₄×C₇₉	—	2	1	no	—
90	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
95	#117×C₇₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
98	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
99	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
100	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
101	#106×C₇₉	C₂×C₄	1	1	yes	characteristic
102	#106×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₄⋊C₈×C₇₉	—	2	1	no	—
104	C₄⋊C₈×C₇₉	—	2	1	no	—
105	C₄⋊C₈×C₇₉	—	2	1	no	—
106	C₄⋊C₈×C₇₉	—	2	1	no	—
107	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
109	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
110	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
111	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
115	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
116	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
117	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
118	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
119	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
120	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
121	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
122	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
123	C₂²⋊C₈×C₇₉	—	2	1	no	—
124	C₂²⋊C₈×C₇₉	—	2	1	no	—
125	C₂²⋊C₈×C₇₉	—	2	1	no	—
126	C₂²⋊C₈×C₇₉	—	2	1	no	—
127	C₂²⋊C₈×C₇₉	—	2	1	no	—
128	C₂²⋊C₈×C₇₉	—	2	1	no	—
129	C₂²⋊C₈×C₇₉	—	2	1	no	—
130	C₂²⋊C₈×C₇₉	—	2	1	no	—
131	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
132	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
133	C₂²⋊C₈×C₇₉	D₄	1	1	yes	characteristic
134	C₂²⋊C₈×C₇₉	D₄	1	1	yes	characteristic
135	#97×C₇₉	—	2	1	no	—
136	C₄×C₈×C₇₉	—	2	1	no	—
137	C₄×C₈×C₇₉	—	2	1	no	—
138	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
144	C₂⁴×C₇₉	—	2	1	no	—
145	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₇₉	—	2	2	no	—
147	C₂×D₄×C₇₉	—	2	2	no	—
148	C₂×D₄×C₇₉	—	2	1	no	—
149	C₂×D₄×C₇₉	—	2	1	no	—
150	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	—	2	1	no	—
154	C₂²×C₄×C₇₉	—	2	1	no	—
155	C₂²×C₄×C₇₉	—	2	1	no	—
156	C₂²×C₄×C₇₉	—	2	1	no	—
157	C₂²×C₄×C₇₉	—	2	1	no	—
158	C₂²×C₄×C₇₉	—	2	1	no	—
159	C₂²×C₄×C₇₉	—	8	1	no	—
160	C₂²×C₄×C₇₉	—	8	1	no	—
161	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
164	SD₁₆×C₇₉	—	2	2	no	—
165	SD₁₆×C₇₉	—	2	2	no	—
166	D₈×C₇₉	—	2	2	no	—
167	D₈×C₇₉	—	2	2	no	—
168	M₁₆×C₇₉	—	8	1	no	—
169	M₁₆×C₇₉	—	8	1	no	—
170	C₂×C₈×C₇₉	—	2	1	no	—
171	C₂×C₈×C₇₉	—	2	1	no	—
172	C₂×C₈×C₇₉	—	2	1	no	—
173	C₂×C₈×C₇₉	—	2	1	no	—
174	C₂×C₈×C₇₉	—	2	1	no	—
175	C₂×C₈×C₇₉	—	2	1	no	—
176	C₂×C₈×C₇₉	—	8	1	no	—
177	C₂×C₈×C₇₉	—	8	1	no	—
178	C₂×C₈×C₇₉	—	8	1	no	—
179	C₂×C₈×C₇₉	—	8	1	no	—
180	C₂×C₈×C₇₉	—	8	1	no	—
181	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₇₉	—	2	1	no	—
190	C₄⋊C₄×C₇₉	—	2	1	no	—
191	C₄⋊C₄×C₇₉	—	2	1	no	—
192	C₄⋊C₄×C₇₉	—	2	1	no	—
193	C₄⋊C₄×C₇₉	—	2	1	no	—
194	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²⋊C₄×C₇₉	—	2	1	no	—
199	C₂²⋊C₄×C₇₉	—	2	1	no	—
200	C₂²⋊C₄×C₇₉	—	2	1	no	—
201	C₂²⋊C₄×C₇₉	—	2	1	no	—
202	C₂²⋊C₄×C₇₉	—	2	1	no	—
203	C₂²⋊C₄×C₇₉	—	2	1	no	—
204	C₂²⋊C₄×C₇₉	—	2	1	no	—
205	C₂²⋊C₄×C₇₉	—	2	1	no	—
206	C₂²⋊C₄×C₇₉	—	2	1	no	—
207	C₄²×C₇₉	—	2	1	no	—
208	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₇₉	#41	1	1	yes	characteristic
211	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
212	C₂³×C₇₉	—	2	4	no	—
213	C₂³×C₇₉	—	2	1	no	—
214	C₂³×C₇₉	—	2	1	no	—
215	C₂³×C₇₉	—	2	1	no	—
216	C₂³×C₇₉	—	8	1	no	—
217	C₂³×C₇₉	—	8	1	no	—
218	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
219	Q₈×C₇₉	—	2	1	no	—
220	Q₈×C₇₉	—	2	1	no	—
221	D₄×C₇₉	—	2	4	no	—
222	D₄×C₇₉	—	2	1	no	—
223	D₄×C₇₉	—	2	1	no	—
224	D₄×C₇₉	—	2	1	no	—
225	D₄×C₇₉	—	2	1	no	—
226	D₄×C₇₉	—	8	1	no	—
227	D₄×C₇₉	#131	1	2	yes	—
228	D₄×C₇₉	#131	1	2	yes	—
229	C₂×C₄×C₇₉	—	2	1	no	—
230	C₂×C₄×C₇₉	—	2	1	no	—
231	C₂×C₄×C₇₉	—	2	1	no	—
232	C₂×C₄×C₇₉	—	2	1	no	—
233	C₂×C₄×C₇₉	—	2	1	no	—
234	C₂×C₄×C₇₉	—	2	1	no	—
235	C₂×C₄×C₇₉	—	2	1	no	—
236	C₂×C₄×C₇₉	—	2	1	no	—
237	C₂×C₄×C₇₉	—	2	1	no	—
238	C₂×C₄×C₇₉	—	4	1	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	—	8	1	no	—
246	C₂×C₄×C₇₉	—	8	1	no	—
247	C₂×C₄×C₇₉	—	8	1	no	—
248	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
254	C₈×C₇₉	—	2	1	no	—
255	C₈×C₇₉	—	2	1	no	—
256	C₈×C₇₉	—	2	1	no	—
257	C₈×C₇₉	—	2	1	no	—
258	C₈×C₇₉	—	2	1	no	—
259	C₈×C₇₉	—	2	1	no	—
260	C₈×C₇₉	—	2	1	no	—
261	C₈×C₇₉	—	2	1	no	—
262	C₈×C₇₉	—	4	1	no	—
263	C₈×C₇₉	—	4	1	no	—
264	C₈×C₇₉	—	4	1	no	—
265	C₈×C₇₉	—	4	1	no	—
266	C₈×C₇₉	—	4	1	no	—
267	C₈×C₇₉	—	4	1	no	—
268	C₂²×C₇₉	—	2	1	no	—
269	C₂²×C₇₉	—	2	2	no	—
270	C₂²×C₇₉	—	2	2	no	—
271	C₂²×C₇₉	—	2	1	no	—
272	C₂²×C₇₉	—	2	1	no	—
273	C₂²×C₇₉	—	4	1	no	—
274	C₂²×C₇₉	—	4	1	no	—
275	C₂²×C₇₉	—	4	1	no	—
276	C₂²×C₇₉	—	4	1	no	—
277	C₂²×C₇₉	—	4	1	no	—
278	C₂²×C₇₉	—	4	1	no	—
279	C₂²×C₇₉	—	4	1	no	—
280	C₂²×C₇₉	—	8	4	no	—
281	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
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	—	4	1	no	—
287	C₄×C₇₉	—	4	1	no	—
288	C₄×C₇₉	—	4	1	no	—
289	C₄×C₇₉	—	4	1	no	—
290	C₄×C₇₉	—	4	1	no	—
291	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
292	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
293	C₄×C₇₉	#576	1	1	yes	characteristic
294	C₄×C₇₉	#577	1	1	yes	characteristic
295	#17918	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂×C₇₉	—	4	1	no	—
297	C₂×C₇₉	—	4	2	no	—
298	C₂×C₇₉	—	4	2	no	—
299	C₂×C₇₉	—	8	1	no	—
300	C₂×C₇₉	#2929	1	1	yes	characteristic
301	C₂×C₇₉	#2946	1	1	yes	characteristic
302	C₂×C₇₉	#2957	1	1	yes	characteristic
303	#3105	C₂×C₇₉	1	1	yes	characteristic
304	#2993	C₂×C₇₉	1	1	yes	characteristic, complemented
305	#2972	C₂×C₇₉	1	1	yes	characteristic, complemented
306	#1586	C₂×C₇₉	1	1	yes	characteristic, complemented
307	#1585	C₂×C₇₉	1	1	yes	characteristic, complemented
308	#1582	C₂×C₇₉	1	1	yes	characteristic, complemented
309	#1581	C₂×C₇₉	1	1	yes	characteristic, complemented
310	#1580	C₂×C₇₉	1	1	yes	characteristic, complemented
311	SD₁₆⋊C₈	C₂×C₇₉	1	1	yes	characteristic, complemented
312	C₈×SD₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
313	C₈×D₈	C₂×C₇₉	1	1	yes	characteristic, complemented
314	#1574	C₂×C₇₉	1	1	yes	characteristic, complemented
315	#1486	C₂×C₇₉	1	1	yes	characteristic, complemented
316	#1482	C₂×C₇₉	1	1	yes	characteristic, complemented
317	#1454	C₂×C₇₉	1	1	yes	characteristic, complemented
318	C₇₉	#17918	1	1	yes	characteristic, direct product factor, Sylow
319	#529	C₂²×C₇₉	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
321	#484	C₄×C₇₉	1	1	yes	characteristic
322	#481	C₄×C₇₉	1	1	yes	characteristic
323	#478	C₄×C₇₉	1	1	yes	characteristic
324	#478	C₄×C₇₉	1	1	yes	characteristic
325	#463	C₄×C₇₉	1	1	yes	characteristic
326	#463	C₄×C₇₉	1	1	yes	characteristic
327	#450	C₄×C₇₉	1	1	yes	characteristic
328	#447	C₄×C₇₉	1	1	yes	characteristic
329	#446	C₂²×C₇₉	1	1	yes	characteristic, complemented
330	C₈×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
331	C₄×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
332	C₄×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
333	C₄×D₈	C₂²×C₇₉	1	1	yes	characteristic
334	C₄×D₈	C₂²×C₇₉	1	1	yes	characteristic
335	#436	—	2	1	no	—
336	#436	C₂²×C₇₉	1	1	yes	characteristic, complemented
337	#435	—	2	1	no	—
338	C₈×D₄	—	2	1	no	—
339	C₈×D₄	—	2	1	no	—
340	C₈×D₄	C₂²×C₇₉	1	1	yes	characteristic
341	C₈×D₄	C₂²×C₇₉	1	1	yes	characteristic
342	C₈×D₄	C₂²×C₇₉	1	1	yes	characteristic
343	C₈×D₄	C₂²×C₇₉	1	1	yes	characteristic
344	C₈×D₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
345	#433	—	2	1	no	—
346	#431	C₂²×C₇₉	1	1	yes	characteristic
347	#431	C₂²×C₇₉	1	1	yes	characteristic
348	#431	C₂²×C₇₉	1	1	yes	characteristic
349	#431	C₂²×C₇₉	1	1	yes	characteristic
350	#424	—	2	1	no	—
351	#423	C₂²×C₇₉	1	1	yes	characteristic
352	C₂×C₂²⋊C₈	—	2	1	no	—
353	C₂×C₂²⋊C₈	—	2	1	no	—
354	#335	C₂²×C₇₉	1	1	yes	characteristic, complemented
355	#335	C₂²×C₇₉	1	1	yes	characteristic, complemented
356	#334	C₂²×C₇₉	1	1	yes	characteristic, complemented
357	#334	C₂²×C₇₉	1	1	yes	characteristic, complemented
358	Q₈⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
359	Q₈⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
360	D₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
361	D₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
362	D₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
363	D₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
364	D₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
365	D₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
366	#322	C₂²×C₇₉	1	1	yes	characteristic, complemented
367	#322	C₂²×C₇₉	1	1	yes	characteristic, complemented
368	#322	C₂²×C₇₉	1	1	yes	characteristic, complemented
369	C₈²	C₂²×C₇₉	1	1	yes	characteristic, complemented
370	C₂²×D₄	C₂×C₄×C₇₉	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂×SD₁₆	C₂×C₄×C₇₉	1	1	yes	characteristic
373	C₂×SD₁₆	C₂×C₄×C₇₉	1	1	yes	characteristic
374	C₂×D₈	C₂×C₄×C₇₉	1	1	yes	characteristic
375	C₂×D₈	C₂×C₄×C₇₉	1	1	yes	characteristic
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	#126	—	2	1	no	—
384	#125	C₂×C₄×C₇₉	1	1	yes	characteristic
385	#124	C₂×C₄×C₇₉	1	1	yes	characteristic
386	#123	—	2	1	no	—
387	C₂²⋊Q₈	C₂×C₄×C₇₉	1	1	yes	characteristic
388	#121	C₂×C₄×C₇₉	1	1	yes	characteristic
389	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂×C₄×C₇₉	1	1	yes	characteristic
394	C₄×D₄	C₂×C₄×C₇₉	1	1	yes	characteristic
395	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
396	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
397	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
398	#117	—	2	1	no	—
399	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
402	#107	C₂×C₄×C₇₉	1	1	yes	characteristic
403	#107	C₂×C₄×C₇₉	1	1	yes	characteristic
404	#106	C₂×C₄×C₇₉	1	1	yes	characteristic
405	#106	C₂×C₄×C₇₉	1	1	yes	characteristic
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂×C₄×C₇₉	1	1	yes	characteristic
411	C₄⋊C₈	C₂×C₄×C₇₉	1	1	yes	characteristic
412	C₄⋊C₈	D₄×C₇₉	1	1	yes	characteristic
413	C₄⋊C₈	D₄×C₇₉	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
418	#103	C₂×C₄×C₇₉	1	1	yes	characteristic
419	#103	C₂×C₄×C₇₉	1	1	yes	characteristic
420	#102	C₂×C₄×C₇₉	1	1	yes	characteristic
421	#102	C₂×C₄×C₇₉	1	1	yes	characteristic
422	#102	C₂×C₄×C₇₉	1	1	yes	characteristic
423	#102	C₂×C₄×C₇₉	1	1	yes	characteristic
424	#102	C₂×C₄×C₇₉	1	1	yes	characteristic
425	#102	C₂×C₄×C₇₉	1	1	yes	characteristic
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	C₂×C₄×C₇₉	1	1	yes	characteristic
435	C₂²⋊C₈	C₂×C₄×C₇₉	1	1	yes	characteristic
436	C₂²⋊C₈	D₄×C₇₉	1	1	yes	characteristic
437	C₂²⋊C₈	D₄×C₇₉	1	1	yes	characteristic
438	#97	—	2	1	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	2	1	no	—
441	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
442	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
443	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
444	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
445	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
447	C₂⁴	—	2	1	no	—
448	C₂×Q₈	C₂²×C₄×C₇₉	1	1	yes	characteristic
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
454	C₂×D₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
455	C₂×D₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	8	1	no	—
463	C₂²×C₄	—	8	1	no	—
464	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
466	C₂²×C₄	#41×C₇₉	1	1	yes	characteristic
467	SD₁₆	—	2	2	no	—
468	SD₁₆	—	2	2	no	—
469	D₈	—	2	2	no	—
470	D₈	—	2	2	no	—
471	M₁₆	—	8	1	no	—
472	M₁₆	—	8	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	8	1	no	—
480	C₂×C₈	—	8	1	no	—
481	C₂×C₈	—	8	1	no	—
482	C₂×C₈	—	8	1	no	—
483	C₂×C₈	—	8	1	no	—
484	C₂×C₈	C₂²×C₄×C₇₉	1	1	yes	characteristic
485	C₂×C₈	C₂²×C₄×C₇₉	1	1	yes	characteristic
486	C₂×C₈	C₂²×C₄×C₇₉	1	1	yes	characteristic
487	C₂×C₈	C₂²×C₄×C₇₉	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
513	C₄²	#41×C₇₉	1	1	yes	characteristic
514	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
515	C₂³	—	2	4	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	8	1	no	—
520	C₂³	—	8	1	no	—
521	C₂³	C₄×D₄×C₇₉	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	8	1	no	—
530	D₄	#131×C₇₉	1	2	yes	—
531	D₄	#131×C₇₉	1	2	yes	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	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	—	8	1	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	—	8	1	no	—
551	C₂×C₄	C₄×D₄×C₇₉	1	1	yes	characteristic
552	C₂×C₄	C₄×D₄×C₇₉	1	1	yes	characteristic
553	C₂×C₄	C₄×D₄×C₇₉	1	1	yes	characteristic
554	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
556	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	4	no	—
584	C₂²	C₂×C₄×D₄×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	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	C₂×#131×C₇₉	1	1	yes	characteristic
595	C₄	C₂×#131×C₇₉	1	1	yes	characteristic
596	C₄	#576×C₇₉	1	1	yes	characteristic
597	C₄	#577×C₇₉	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	4	2	no	—
601	C₂	—	8	1	no	—
602	C₂	C₇₉×#2929	1	1	yes	characteristic
603	C₂	C₇₉×#2946	1	1	yes	characteristic
604	C₂	C₇₉×#2957	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	C₂×C₄×D₄
prime radical	#447×C₇₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₉ ◁ #431×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#2993	C₂	semidirect
3. C₇₉×#2972	C₂	semidirect
4. C₇₉×#1586	C₂	semidirect
5. C₇₉×#1585	C₂	semidirect
6. C₇₉×#1582	C₂	semidirect
7. C₇₉×#1581	C₂	semidirect
8. C₇₉×#1580	C₂	semidirect
9. C₇₉×SD₁₆⋊C₈	C₂	semidirect
10. C₈×SD₁₆×C₇₉	C₂	semidirect
11. C₈×D₈×C₇₉	C₂	semidirect
12. C₇₉×#1574	C₂	semidirect
13. C₇₉×#1486	C₂	semidirect
14. C₇₉×#1482	C₂	semidirect
15. C₇₉×#1454	C₂	semidirect
26. #446×C₇₉	C₂²	semidirect
27. C₈×Q₈×C₇₉	C₂²	semidirect
33. #436×C₇₉	C₂²	semidirect
41. C₈×D₄×C₇₉	C₂²	semidirect
51. #335×C₇₉	C₂²	semidirect
52. #335×C₇₉	C₂²	semidirect
53. #334×C₇₉	C₂²	semidirect
54. #334×C₇₉	C₂²	semidirect
55. Q₈⋊C₈×C₇₉	C₂²	semidirect
56. Q₈⋊C₈×C₇₉	C₂²	semidirect
61. D₄⋊C₈×C₇₉	C₂²	semidirect
62. D₄⋊C₈×C₇₉	C₂²	semidirect
63. #322×C₇₉	C₂²	semidirect
64. #322×C₇₉	C₂²	semidirect
65. #322×C₇₉	C₂²	semidirect
66. C₈²×C₇₉	C₂²	semidirect
295. #17918	C₇₉	direct (N × H)
304. #2993	C₂×C₇₉	semidirect
305. #2972	C₂×C₇₉	semidirect
306. #1586	C₂×C₇₉	semidirect
307. #1585	C₂×C₇₉	semidirect
308. #1582	C₂×C₇₉	semidirect
309. #1581	C₂×C₇₉	semidirect
310. #1580	C₂×C₇₉	semidirect
311. SD₁₆⋊C₈	C₂×C₇₉	semidirect
312. C₈×SD₁₆	C₂×C₇₉	semidirect
313. C₈×D₈	C₂×C₇₉	semidirect
314. #1574	C₂×C₇₉	semidirect
315. #1486	C₂×C₇₉	semidirect
316. #1482	C₂×C₇₉	semidirect
317. #1454	C₂×C₇₉	semidirect
318. C₇₉	#17918	direct (N × H)
329. #446	C₂²×C₇₉	semidirect
330. C₈×Q₈	C₂²×C₇₉	semidirect
336. #436	C₂²×C₇₉	semidirect
344. C₈×D₄	C₂²×C₇₉	semidirect
354. #335	C₂²×C₇₉	semidirect
355. #335	C₂²×C₇₉	semidirect
356. #334	C₂²×C₇₉	semidirect
357. #334	C₂²×C₇₉	semidirect
358. Q₈⋊C₈	C₂²×C₇₉	semidirect
359. Q₈⋊C₈	C₂²×C₇₉	semidirect
364. D₄⋊C₈	C₂²×C₇₉	semidirect
365. D₄⋊C₈	C₂²×C₇₉	semidirect
366. #322	C₂²×C₇₉	semidirect
367. #322	C₂²×C₇₉	semidirect
368. #322	C₂²×C₇₉	semidirect
369. C₈²	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×#3105	2
C₇₉×#2993	2
C₇₉×#2972	2
C₇₉×#1586	2
C₇₉×#1585	2
C₇₉×#1582	2
C₇₉×#1581	2
C₇₉×#1580	2
C₇₉×SD₁₆⋊C₈	2
C₈×SD₁₆×C₇₉	2
C₈×D₈×C₇₉	2
C₇₉×#1574	2
C₇₉×#1486	2
C₇₉×#1482	2
C₇₉×#1454	2
#17918	79

Subgroups — C79×#17918 #34129607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#17918 #34129607