Subgroups — C₇₉×#18835 #34130524

Order 20224.

940 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3514	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1638	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1637	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1630	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1629	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1557	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	#559×C₇₉	C₂²	1	1	yes	characteristic
13	#556×C₇₉	C₂²	1	1	yes	characteristic
14	#555×C₇₉	—	2	1	no	—
15	#551×C₇₉	—	2	2	no	—
16	D₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
17	#548×C₇₉	—	2	1	no	—
18	#546×C₇₉	—	2	1	no	—
19	#546×C₇₉	—	2	1	no	—
20	D₄²×C₇₉	C₂²	1	1	yes	characteristic
21	#542×C₇₉	—	2	1	no	—
22	#538×C₇₉	—	2	2	no	—
23	#532×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
25	#529×C₇₉	—	2	1	no	—
26	#529×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₇₉	—	2	1	no	—
28	#518×C₇₉	—	2	1	no	—
29	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
30	#501×C₇₉	—	2	1	no	—
31	#492×C₇₉	C₂²	1	2	yes	—
32	#489×C₇₉	—	2	1	no	—
33	#487×C₇₉	C₂²	1	2	yes	complemented
34	#483×C₇₉	—	2	1	no	—
35	#480×C₇₉	—	2	1	no	—
36	#477×C₇₉	C₂²	1	2	yes	complemented
37	#477×C₇₉	C₂²	1	2	yes	complemented
38	#476×C₇₉	C₂²	1	2	yes	—
39	#476×C₇₉	C₂²	1	2	yes	—
40	#475×C₇₉	—	2	1	no	—
41	#474×C₇₉	—	2	1	no	—
42	#461×C₇₉	—	2	2	no	—
43	#448×C₇₉	—	2	2	no	—
44	#432×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	#431×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	#428×C₇₉	—	2	1	no	—
47	#423×C₇₉	C₂²	1	1	yes	characteristic, complemented
48	#417×C₇₉	—	2	1	no	—
49	#332×C₇₉	C₂²	1	2	yes	complemented
50	#331×C₇₉	C₂²	1	2	yes	—
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	—
54	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
55	C₂×#41×C₇₉	—	2	1	no	—
56	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₇₉	—	2	1	no	—
58	C₂²×Q₈×C₇₉	—	2	1	no	—
59	C₂²×D₄×C₇₉	—	2	1	no	—
60	C₂²×D₄×C₇₉	—	2	1	no	—
61	C₂×SD₁₆×C₇₉	—	2	4	no	—
62	C₂×M₁₆×C₇₉	—	2	1	no	—
63	C₄⋊Q₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	—	2	1	no	—
66	C₄⋊Q₈×C₇₉	—	2	1	no	—
67	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
69	#127×C₇₉	C₂³	1	1	yes	characteristic
70	#126×C₇₉	—	2	2	no	—
71	#126×C₇₉	—	2	2	no	—
72	#126×C₇₉	—	2	1	no	—
73	#125×C₇₉	D₄	1	1	yes	characteristic
74	#124×C₇₉	—	2	2	no	—
75	#124×C₇₉	—	2	2	no	—
76	#124×C₇₉	—	2	2	no	—
77	#124×C₇₉	—	2	1	no	—
78	#124×C₇₉	—	2	1	no	—
79	#124×C₇₉	—	2	1	no	—
80	#124×C₇₉	—	2	1	no	—
81	#124×C₇₉	D₄	1	1	yes	characteristic
82	#123×C₇₉	—	2	2	no	—
83	#123×C₇₉	—	2	2	no	—
84	#123×C₇₉	—	2	2	no	—
85	#123×C₇₉	—	2	1	no	—
86	C₂²⋊Q₈×C₇₉	—	2	2	no	—
87	C₂²⋊Q₈×C₇₉	—	2	1	no	—
88	C₂²⋊Q₈×C₇₉	—	2	1	no	—
89	C₂²⋊Q₈×C₇₉	—	2	2	no	—
90	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
91	#121×C₇₉	—	2	2	no	—
92	#121×C₇₉	—	2	2	no	—
93	#121×C₇₉	—	2	1	no	—
94	#121×C₇₉	—	2	1	no	—
95	#121×C₇₉	—	2	1	no	—
96	#121×C₇₉	D₄	1	2	yes	—
97	#121×C₇₉	D₄	1	1	yes	characteristic
98	#120×C₇₉	—	2	2	no	—
99	#120×C₇₉	—	2	2	no	—
100	C₄×Q₈×C₇₉	—	2	1	no	—
101	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
102	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₇₉	—	2	2	no	—
105	C₄×D₄×C₇₉	—	2	2	no	—
106	C₄×D₄×C₇₉	—	2	1	no	—
107	C₄×D₄×C₇₉	—	2	1	no	—
108	C₄×D₄×C₇₉	—	2	1	no	—
109	C₄×D₄×C₇₉	—	2	1	no	—
110	C₄×D₄×C₇₉	—	2	1	no	—
111	C₄×D₄×C₇₉	—	2	1	no	—
112	C₄×D₄×C₇₉	—	2	1	no	—
113	C₄×D₄×C₇₉	D₄	1	2	yes	—
114	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
115	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
116	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
117	#117×C₇₉	—	2	2	no	—
118	#117×C₇₉	—	2	1	no	—
119	#117×C₇₉	—	2	1	no	—
120	#117×C₇₉	—	2	1	no	—
121	#117×C₇₉	D₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
126	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
127	C₂×C₄²×C₇₉	—	2	1	no	—
128	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
129	#107×C₇₉	—	2	2	no	—
130	#107×C₇₉	—	2	2	no	—
131	#106×C₇₉	—	2	2	no	—
132	#106×C₇₉	—	2	2	no	—
133	C₄⋊C₈×C₇₉	—	2	1	no	—
134	C₄⋊C₈×C₇₉	—	2	1	no	—
135	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
136	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
137	#103×C₇₉	—	2	2	no	—
138	#103×C₇₉	—	2	2	no	—
139	#103×C₇₉	—	2	4	no	—
140	#102×C₇₉	—	2	2	no	—
141	#102×C₇₉	—	2	2	no	—
142	C₂²⋊C₈×C₇₉	—	2	1	no	—
143	C₂²⋊C₈×C₇₉	—	2	1	no	—
144	#97×C₇₉	—	2	1	no	—
145	C₄×C₈×C₇₉	C₂³	1	2	yes	—
146	C₂⁴×C₇₉	—	2	2	no	—
147	#41×C₇₉	—	2	2	no	—
148	#41×C₇₉	—	4	1	no	—
149	#41×C₇₉	—	8	2	no	—
150	C₂×Q₈×C₇₉	—	2	2	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	—	8	2	no	—
155	C₂×Q₈×C₇₉	—	8	2	no	—
156	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₇₉	—	2	2	no	—
159	C₂×D₄×C₇₉	—	2	1	no	—
160	C₂×D₄×C₇₉	—	2	2	no	—
161	C₂×D₄×C₇₉	—	2	1	no	—
162	C₂×D₄×C₇₉	—	2	2	no	—
163	C₂×D₄×C₇₉	—	2	1	no	—
164	C₂×D₄×C₇₉	—	2	1	no	—
165	C₂×D₄×C₇₉	—	4	2	no	—
166	C₂×D₄×C₇₉	—	4	2	no	—
167	C₂×D₄×C₇₉	—	8	2	no	—
168	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₇₉	—	2	2	no	—
172	C₂²×C₄×C₇₉	—	2	2	no	—
173	C₂²×C₄×C₇₉	—	2	1	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	2	no	—
178	C₂²×C₄×C₇₉	—	4	1	no	—
179	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
182	SD₁₆×C₇₉	—	8	4	no	—
183	M₁₆×C₇₉	—	4	2	no	—
184	C₂×C₈×C₇₉	—	2	2	no	—
185	C₂×C₈×C₇₉	—	2	2	no	—
186	C₂×C₈×C₇₉	—	2	2	no	—
187	C₄⋊C₄×C₇₉	—	2	2	no	—
188	C₄⋊C₄×C₇₉	—	2	2	no	—
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	—	2	1	no	—
195	C₄⋊C₄×C₇₉	—	2	1	no	—
196	C₄⋊C₄×C₇₉	—	2	2	no	—
197	C₄⋊C₄×C₇₉	—	2	2	no	—
198	C₄⋊C₄×C₇₉	—	4	1	no	—
199	C₄⋊C₄×C₇₉	—	4	1	no	—
200	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₇₉	—	2	2	no	—
206	C₂²⋊C₄×C₇₉	—	2	2	no	—
207	C₂²⋊C₄×C₇₉	—	2	2	no	—
208	C₂²⋊C₄×C₇₉	—	2	2	no	—
209	C₂²⋊C₄×C₇₉	—	2	2	no	—
210	C₂²⋊C₄×C₇₉	—	2	2	no	—
211	C₂²⋊C₄×C₇₉	—	2	2	no	—
212	C₂²⋊C₄×C₇₉	—	2	1	no	—
213	C₂²⋊C₄×C₇₉	—	2	1	no	—
214	C₂²⋊C₄×C₇₉	—	2	1	no	—
215	C₂²⋊C₄×C₇₉	—	2	1	no	—
216	C₂²⋊C₄×C₇₉	—	2	1	no	—
217	C₂²⋊C₄×C₇₉	—	2	1	no	—
218	C₂²⋊C₄×C₇₉	—	2	2	no	—
219	C₂²⋊C₄×C₇₉	—	2	2	no	—
220	C₂²⋊C₄×C₇₉	—	2	1	no	—
221	C₂²⋊C₄×C₇₉	—	2	1	no	—
222	C₄²×C₇₉	—	2	2	no	—
223	C₄²×C₇₉	—	2	1	no	—
224	C₄²×C₇₉	—	2	1	no	—
225	C₄²×C₇₉	—	2	1	no	—
226	C₄²×C₇₉	—	2	1	no	—
227	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
231	C₂³×C₇₉	—	2	1	no	—
232	C₂³×C₇₉	—	2	1	no	—
233	C₂³×C₇₉	—	2	2	no	—
234	C₂³×C₇₉	—	4	4	no	—
235	C₂³×C₇₉	—	8	2	no	—
236	C₂³×C₇₉	—	8	2	no	—
237	C₂³×C₇₉	#120	1	1	yes	characteristic
238	Q₈×C₇₉	—	2	1	no	—
239	Q₈×C₇₉	—	2	1	no	—
240	Q₈×C₇₉	—	2	2	no	—
241	Q₈×C₇₉	—	4	4	no	—
242	Q₈×C₇₉	—	4	2	no	—
243	Q₈×C₇₉	—	8	2	no	—
244	Q₈×C₇₉	—	8	2	no	—
245	D₄×C₇₉	—	2	1	no	—
246	D₄×C₇₉	—	2	2	no	—
247	D₄×C₇₉	—	4	2	no	—
248	D₄×C₇₉	—	4	2	no	—
249	D₄×C₇₉	—	4	4	no	—
250	D₄×C₇₉	—	4	1	no	—
251	D₄×C₇₉	—	4	1	no	—
252	D₄×C₇₉	—	4	2	no	—
253	D₄×C₇₉	—	8	1	no	—
254	D₄×C₇₉	—	8	2	no	—
255	D₄×C₇₉	—	8	2	no	—
256	D₄×C₇₉	#137	1	2	yes	—
257	C₂×C₄×C₇₉	—	2	1	no	—
258	C₂×C₄×C₇₉	—	2	1	no	—
259	C₂×C₄×C₇₉	—	2	2	no	—
260	C₂×C₄×C₇₉	—	2	1	no	—
261	C₂×C₄×C₇₉	—	2	1	no	—
262	C₂×C₄×C₇₉	—	2	1	no	—
263	C₂×C₄×C₇₉	—	2	1	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	—	4	1	no	—
268	C₂×C₄×C₇₉	—	4	2	no	—
269	C₂×C₄×C₇₉	—	4	1	no	—
270	C₂×C₄×C₇₉	—	4	1	no	—
271	C₂×C₄×C₇₉	—	4	2	no	—
272	C₂×C₄×C₇₉	—	4	2	no	—
273	C₂×C₄×C₇₉	—	8	1	no	—
274	C₂×C₄×C₇₉	—	8	2	no	—
275	C₂×C₄×C₇₉	—	8	2	no	—
276	C₂×C₄×C₇₉	—	8	2	no	—
277	C₂×C₄×C₇₉	—	8	2	no	—
278	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
279	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
280	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
281	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
284	C₈×C₇₉	—	4	2	no	—
285	C₈×C₇₉	—	4	2	no	—
286	C₈×C₇₉	—	4	2	no	—
287	C₂²×C₇₉	—	2	1	no	—
288	C₂²×C₇₉	—	2	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	—	4	2	no	—
295	C₂²×C₇₉	—	4	2	no	—
296	C₂²×C₇₉	—	4	1	no	—
297	C₂²×C₇₉	—	4	2	no	—
298	C₂²×C₇₉	—	4	1	no	—
299	C₂²×C₇₉	—	16	4	no	—
300	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
301	C₄×C₇₉	—	2	1	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	1	no	—
307	C₄×C₇₉	—	4	1	no	—
308	C₄×C₇₉	—	4	2	no	—
309	C₄×C₇₉	—	4	1	no	—
310	C₄×C₇₉	—	4	1	no	—
311	C₄×C₇₉	—	4	1	no	—
312	C₄×C₇₉	—	8	2	no	—
313	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
314	C₄×C₇₉	#575	1	1	yes	characteristic
315	C₄×C₇₉	#577	1	2	yes	—
316	#18835	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂×C₇₉	—	4	1	no	—
318	C₂×C₇₉	—	4	2	no	—
319	C₂×C₇₉	—	8	2	no	—
320	C₂×C₇₉	—	8	1	no	—
321	C₂×C₇₉	#3007	1	1	yes	characteristic
322	C₂×C₇₉	#3009	1	1	yes	characteristic
323	C₂×C₇₉	#3021	1	1	yes	characteristic
324	#3514	C₂×C₇₉	1	1	yes	characteristic
325	#3238	C₂×C₇₉	1	1	yes	characteristic, complemented
326	#3206	C₂×C₇₉	1	1	yes	characteristic, complemented
327	#3079	C₂×C₇₉	1	1	yes	characteristic, complemented
328	#1638	C₂×C₇₉	1	2	yes	complemented
329	#1637	C₂×C₇₉	1	2	yes	complemented
330	#1630	C₂×C₇₉	1	2	yes	complemented
331	#1629	C₂×C₇₉	1	2	yes	complemented
332	#1557	C₂×C₇₉	1	1	yes	characteristic, complemented
333	#1495	C₂×C₇₉	1	1	yes	characteristic, complemented
334	#1488	C₂×C₇₉	1	1	yes	characteristic, complemented
335	C₇₉	#18835	1	1	yes	characteristic, direct product factor, Sylow
336	#559	C₂²×C₇₉	1	1	yes	characteristic
337	#556	C₂²×C₇₉	1	1	yes	characteristic
338	#555	—	2	1	no	—
339	#551	—	2	2	no	—
340	D₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
341	#548	—	2	1	no	—
342	#546	—	2	1	no	—
343	#546	—	2	1	no	—
344	D₄²	C₂²×C₇₉	1	1	yes	characteristic
345	#542	—	2	1	no	—
346	#538	—	2	2	no	—
347	#532	C₂²×C₇₉	1	1	yes	characteristic
348	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
349	#529	—	2	1	no	—
350	#529	C₂²×C₇₉	1	1	yes	characteristic
351	C₂×#124	—	2	1	no	—
352	#518	—	2	1	no	—
353	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
354	#501	—	2	1	no	—
355	#492	C₂²×C₇₉	1	2	yes	—
356	#489	—	2	1	no	—
357	#487	C₂²×C₇₉	1	2	yes	complemented
358	#483	—	2	1	no	—
359	#480	—	2	1	no	—
360	#477	C₂²×C₇₉	1	2	yes	complemented
361	#477	C₂²×C₇₉	1	2	yes	complemented
362	#476	C₂²×C₇₉	1	2	yes	—
363	#476	C₂²×C₇₉	1	2	yes	—
364	#475	—	2	1	no	—
365	#474	—	2	1	no	—
366	#461	—	2	2	no	—
367	#448	—	2	2	no	—
368	#432	C₂²×C₇₉	1	1	yes	characteristic, complemented
369	#431	C₂²×C₇₉	1	1	yes	characteristic, complemented
370	#428	—	2	1	no	—
371	#423	C₂²×C₇₉	1	1	yes	characteristic, complemented
372	#417	—	2	1	no	—
373	#332	C₂²×C₇₉	1	2	yes	complemented
374	#331	C₂²×C₇₉	1	2	yes	—
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	—
378	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
379	C₂×#41	—	2	1	no	—
380	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
381	C₂²×Q₈	—	2	1	no	—
382	C₂²×Q₈	—	2	1	no	—
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	—	2	1	no	—
385	C₂×SD₁₆	—	2	4	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₄⋊Q₈	—	2	1	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	—	2	1	no	—
390	C₄⋊Q₈	—	2	1	no	—
391	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
392	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
393	#127	C₂³×C₇₉	1	1	yes	characteristic
394	#126	—	2	2	no	—
395	#126	—	2	2	no	—
396	#126	—	2	1	no	—
397	#125	D₄×C₇₉	1	1	yes	characteristic
398	#124	—	2	2	no	—
399	#124	—	2	2	no	—
400	#124	—	2	2	no	—
401	#124	—	2	1	no	—
402	#124	—	2	1	no	—
403	#124	—	2	1	no	—
404	#124	—	2	1	no	—
405	#124	D₄×C₇₉	1	1	yes	characteristic
406	#123	—	2	2	no	—
407	#123	—	2	2	no	—
408	#123	—	2	2	no	—
409	#123	—	2	1	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	1	no	—
418	#121	—	2	1	no	—
419	#121	—	2	1	no	—
420	#121	D₄×C₇₉	1	1	yes	characteristic
421	#121	D₄×C₇₉	1	2	yes	—
422	#120	—	2	2	no	—
423	#120	—	2	2	no	—
424	C₄×Q₈	—	2	1	no	—
425	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
426	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
427	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
438	C₄×D₄	D₄×C₇₉	1	2	yes	—
439	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
440	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
441	#117	—	2	2	no	—
442	#117	—	2	1	no	—
443	#117	—	2	1	no	—
444	#117	—	2	1	no	—
445	#117	D₄×C₇₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	2	no	—
449	C₂×C₂²⋊C₄	—	2	2	no	—
450	C₂×C₂²⋊C₄	—	2	2	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
453	#107	—	2	2	no	—
454	#107	—	2	2	no	—
455	#106	—	2	2	no	—
456	#106	—	2	2	no	—
457	C₄⋊C₈	—	2	1	no	—
458	C₄⋊C₈	—	2	1	no	—
459	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
460	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
461	#103	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	4	no	—
464	#102	—	2	2	no	—
465	#102	—	2	2	no	—
466	C₂²⋊C₈	—	2	1	no	—
467	C₂²⋊C₈	—	2	1	no	—
468	#97	—	2	1	no	—
469	C₄×C₈	C₂³×C₇₉	1	2	yes	—
470	C₂⁴	—	2	2	no	—
471	#41	—	2	2	no	—
472	#41	—	4	1	no	—
473	#41	—	8	2	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	4	1	no	—
478	C₂×Q₈	—	8	2	no	—
479	C₂×Q₈	—	8	2	no	—
480	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
481	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	4	2	no	—
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	—	8	2	no	—
492	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
493	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
494	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
506	SD₁₆	—	8	4	no	—
507	M₁₆	—	4	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
525	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
552	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
553	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
554	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	4	4	no	—
559	C₂³	—	8	2	no	—
560	C₂³	—	8	2	no	—
561	C₂³	#120×C₇₉	1	1	yes	characteristic
562	Q₈	—	2	1	no	—
563	Q₈	—	2	1	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	4	4	no	—
566	Q₈	—	4	2	no	—
567	Q₈	—	8	2	no	—
568	Q₈	—	8	2	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	4	4	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	4	2	no	—
577	D₄	—	8	1	no	—
578	D₄	—	8	2	no	—
579	D₄	—	8	2	no	—
580	D₄	#137×C₇₉	1	2	yes	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	8	1	no	—
598	C₂×C₄	—	8	2	no	—
599	C₂×C₄	—	8	2	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	—	8	2	no	—
602	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
603	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
604	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×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	C₈	—	4	2	no	—
609	C₈	—	4	2	no	—
610	C₈	—	4	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	16	4	no	—
624	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	1	no	—
636	C₄	—	8	2	no	—
637	C₄	C₂×#137×C₇₉	1	1	yes	characteristic
638	C₄	#575×C₇₉	1	1	yes	characteristic
639	C₄	#577×C₇₉	1	2	yes	—
640	C₂	—	4	1	no	—
641	C₂	—	4	2	no	—
642	C₂	—	8	1	no	—
643	C₂	—	8	2	no	—
644	C₂	C₇₉×#3007	1	1	yes	characteristic
645	C₂	C₇₉×#3009	1	1	yes	characteristic
646	C₂	C₇₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3514	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
2. C₇₉×#3238	C₂	semidirect
3. C₇₉×#3206	C₂	semidirect
4. C₇₉×#3079	C₂	semidirect
5. C₇₉×#1638	C₂	semidirect
6. C₇₉×#1637	C₂	semidirect
7. C₇₉×#1630	C₂	semidirect
8. C₇₉×#1629	C₂	semidirect
9. C₇₉×#1557	C₂	semidirect
10. C₇₉×#1495	C₂	semidirect
11. C₇₉×#1488	C₂	semidirect
24. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
33. #487×C₇₉	C₂²	semidirect
36. #477×C₇₉	C₂²	semidirect
37. #477×C₇₉	C₂²	semidirect
44. #432×C₇₉	C₂²	semidirect
45. #431×C₇₉	C₂²	semidirect
47. #423×C₇₉	C₂²	semidirect
49. #332×C₇₉	C₂²	semidirect
51. Q₈⋊C₈×C₇₉	C₂²	semidirect
52. Q₈⋊C₈×C₇₉	C₂²	semidirect
316. #18835	C₇₉	direct (N × H)
325. #3238	C₂×C₇₉	semidirect
326. #3206	C₂×C₇₉	semidirect
327. #3079	C₂×C₇₉	semidirect
328. #1638	C₂×C₇₉	semidirect
329. #1637	C₂×C₇₉	semidirect
330. #1630	C₂×C₇₉	semidirect
331. #1629	C₂×C₇₉	semidirect
332. #1557	C₂×C₇₉	semidirect
333. #1495	C₂×C₇₉	semidirect
334. #1488	C₂×C₇₉	semidirect
335. C₇₉	#18835	direct (N × H)
348. C₂×C₄⋊Q₈	C₂²×C₇₉	semidirect
357. #487	C₂²×C₇₉	semidirect
360. #477	C₂²×C₇₉	semidirect
361. #477	C₂²×C₇₉	semidirect
368. #432	C₂²×C₇₉	semidirect
369. #431	C₂²×C₇₉	semidirect
371. #423	C₂²×C₇₉	semidirect
373. #332	C₂²×C₇₉	semidirect
375. Q₈⋊C₈	C₂²×C₇₉	semidirect
376. Q₈⋊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×#3514	2
C₇₉×#3238	2
C₇₉×#3206	2
C₇₉×#3079	2
C₇₉×#1638	2
C₇₉×#1637	2
C₇₉×#1630	2
C₇₉×#1629	2
C₇₉×#1557	2
C₇₉×#1495	2
C₇₉×#1488	2
#18835	79

Subgroups — C79×#18835 #34130524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18835 #34130524