Subgroups — C₇₉×#18972 #34130661

Order 20224.

818 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3555	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3239	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1653	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1652	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1645	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1644	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1482	C₂	1	1	yes	maximal, characteristic
12	#563×C₇₉	—	2	2	no	—
13	Q₈²×C₇₉	C₂²	1	1	yes	characteristic
14	#557×C₇₉	—	2	1	no	—
15	#557×C₇₉	C₂²	1	1	yes	characteristic
16	#556×C₇₉	—	2	1	no	—
17	#556×C₇₉	—	2	1	no	—
18	#556×C₇₉	C₂²	1	1	yes	characteristic
19	#554×C₇₉	C₂²	1	1	yes	characteristic
20	#552×C₇₉	—	2	1	no	—
21	#544×C₇₉	—	2	1	no	—
22	#542×C₇₉	—	2	1	no	—
23	#541×C₇₉	—	2	1	no	—
24	#541×C₇₉	—	2	1	no	—
25	#541×C₇₉	—	2	2	no	—
26	#533×C₇₉	C₂²	1	1	yes	characteristic
27	#533×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
29	#529×C₇₉	C₂²	1	1	yes	characteristic
30	#501×C₇₉	—	2	1	no	—
31	#498×C₇₉	C₂²	1	2	yes	—
32	#494×C₇₉	—	2	1	no	—
33	#489×C₇₉	—	2	1	no	—
34	#487×C₇₉	—	2	1	no	—
35	#487×C₇₉	C₂²	1	2	yes	—
36	#484×C₇₉	—	2	1	no	—
37	#483×C₇₉	—	2	2	no	—
38	#481×C₇₉	—	2	1	no	—
39	#475×C₇₉	—	2	2	no	—
40	#475×C₇₉	C₂²	1	2	yes	—
41	#474×C₇₉	C₂²	1	2	yes	—
42	#462×C₇₉	C₂²	1	2	yes	—
43	#462×C₇₉	C₂²	1	2	yes	—
44	#451×C₇₉	—	2	1	no	—
45	#451×C₇₉	—	2	1	no	—
46	#432×C₇₉	C₂²	1	1	yes	characteristic
47	#431×C₇₉	C₂²	1	1	yes	characteristic
48	#431×C₇₉	C₂²	1	1	yes	characteristic
49	#333×C₇₉	C₂²	1	2	yes	—
50	#332×C₇₉	C₂²	1	2	yes	—
51	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
52	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
53	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
54	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
55	C₂²×Q₈×C₇₉	—	2	1	no	—
56	C₂×Q₁₆×C₇₉	—	2	2	no	—
57	C₂×Q₁₆×C₇₉	—	2	2	no	—
58	C₄⋊Q₈×C₇₉	—	2	2	no	—
59	C₄⋊Q₈×C₇₉	—	2	1	no	—
60	C₄⋊Q₈×C₇₉	—	2	2	no	—
61	C₄⋊Q₈×C₇₉	—	2	1	no	—
62	C₄⋊Q₈×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	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
71	#126×C₇₉	—	2	2	no	—
72	#126×C₇₉	—	2	2	no	—
73	#126×C₇₉	—	2	2	no	—
74	#126×C₇₉	—	2	2	no	—
75	#126×C₇₉	—	2	2	no	—
76	#126×C₇₉	—	2	2	no	—
77	#126×C₇₉	—	2	1	no	—
78	#125×C₇₉	—	2	2	no	—
79	#125×C₇₉	—	2	2	no	—
80	#125×C₇₉	—	2	2	no	—
81	#125×C₇₉	—	2	2	no	—
82	#125×C₇₉	—	2	1	no	—
83	#125×C₇₉	—	2	2	no	—
84	#125×C₇₉	—	2	1	no	—
85	#125×C₇₉	—	2	1	no	—
86	#125×C₇₉	—	2	1	no	—
87	#125×C₇₉	D₄	1	1	yes	characteristic
88	#124×C₇₉	—	2	2	no	—
89	#124×C₇₉	—	2	1	no	—
90	#124×C₇₉	D₄	1	1	yes	characteristic
91	#123×C₇₉	—	2	2	no	—
92	#123×C₇₉	—	2	1	no	—
93	C₂²⋊Q₈×C₇₉	—	2	2	no	—
94	C₂²⋊Q₈×C₇₉	—	2	2	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	—	2	1	no	—
99	C₂²⋊Q₈×C₇₉	—	2	1	no	—
100	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
101	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
102	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
103	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
104	#121×C₇₉	D₄	1	1	yes	characteristic
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	D₄	1	2	yes	—
114	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
116	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₇₉	—	2	1	no	—
118	C₄×D₄×C₇₉	—	2	1	no	—
119	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
120	#117×C₇₉	—	2	2	no	—
121	#117×C₇₉	—	2	1	no	—
122	#117×C₇₉	—	2	1	no	—
123	#117×C₇₉	—	2	1	no	—
124	#117×C₇₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
128	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
129	#107×C₇₉	—	2	2	no	—
130	#106×C₇₉	—	2	4	no	—
131	#106×C₇₉	—	2	2	no	—
132	C₄⋊C₈×C₇₉	—	2	1	no	—
133	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
134	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
135	#103×C₇₉	—	2	4	no	—
136	#103×C₇₉	—	2	2	no	—
137	#103×C₇₉	—	2	2	no	—
138	#103×C₇₉	—	2	2	no	—
139	#102×C₇₉	—	2	2	no	—
140	C₂²⋊C₈×C₇₉	—	2	1	no	—
141	C₂²⋊C₈×C₇₉	—	2	1	no	—
142	C₂²⋊C₈×C₇₉	—	2	1	no	—
143	#97×C₇₉	—	2	1	no	—
144	C₄×C₈×C₇₉	—	2	1	no	—
145	C₄×C₈×C₇₉	C₂³	1	2	yes	—
146	C₂×Q₈×C₇₉	—	2	2	no	—
147	C₂×Q₈×C₇₉	—	2	1	no	—
148	C₂×Q₈×C₇₉	—	2	1	no	—
149	C₂×Q₈×C₇₉	—	2	2	no	—
150	C₂×Q₈×C₇₉	—	4	1	no	—
151	C₂×Q₈×C₇₉	—	8	2	no	—
152	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₇₉	—	2	1	no	—
157	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₉	—	2	2	no	—
159	C₂²×C₄×C₇₉	—	2	1	no	—
160	C₂²×C₄×C₇₉	—	4	1	no	—
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	Q₁₆×C₇₉	—	8	2	no	—
165	Q₁₆×C₇₉	—	8	2	no	—
166	C₂×C₈×C₇₉	—	2	2	no	—
167	C₂×C₈×C₇₉	—	2	2	no	—
168	C₂×C₈×C₇₉	—	2	2	no	—
169	C₄⋊C₄×C₇₉	—	2	2	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	1	no	—
180	C₄⋊C₄×C₇₉	—	2	1	no	—
181	C₄⋊C₄×C₇₉	—	2	1	no	—
182	C₄⋊C₄×C₇₉	—	2	1	no	—
183	C₄⋊C₄×C₇₉	—	2	1	no	—
184	C₄⋊C₄×C₇₉	—	2	2	no	—
185	C₄⋊C₄×C₇₉	—	2	1	no	—
186	C₄⋊C₄×C₇₉	—	2	2	no	—
187	C₄⋊C₄×C₇₉	—	2	1	no	—
188	C₄⋊C₄×C₇₉	—	2	1	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	2	no	—
194	C₄⋊C₄×C₇₉	—	2	2	no	—
195	C₄⋊C₄×C₇₉	—	4	1	no	—
196	C₄⋊C₄×C₇₉	—	4	1	no	—
197	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
202	C₂²⋊C₄×C₇₉	—	2	2	no	—
203	C₂²⋊C₄×C₇₉	—	2	2	no	—
204	C₂²⋊C₄×C₇₉	—	2	2	no	—
205	C₂²⋊C₄×C₇₉	—	2	1	no	—
206	C₂²⋊C₄×C₇₉	—	2	2	no	—
207	C₂²⋊C₄×C₇₉	—	2	1	no	—
208	C₂²⋊C₄×C₇₉	—	2	1	no	—
209	C₂²⋊C₄×C₇₉	—	2	1	no	—
210	C₂²⋊C₄×C₇₉	—	2	1	no	—
211	C₂²⋊C₄×C₇₉	—	2	1	no	—
212	C₂²⋊C₄×C₇₉	—	2	1	no	—
213	C₄²×C₇₉	—	2	2	no	—
214	C₄²×C₇₉	—	2	2	no	—
215	C₄²×C₇₉	—	2	2	no	—
216	C₄²×C₇₉	—	2	2	no	—
217	C₄²×C₇₉	—	2	1	no	—
218	C₄²×C₇₉	—	2	1	no	—
219	C₄²×C₇₉	—	2	1	no	—
220	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
224	C₂³×C₇₉	—	2	1	no	—
225	C₂³×C₇₉	#120	1	1	yes	characteristic
226	Q₈×C₇₉	—	2	2	no	—
227	Q₈×C₇₉	—	2	2	no	—
228	Q₈×C₇₉	—	2	2	no	—
229	Q₈×C₇₉	—	4	2	no	—
230	Q₈×C₇₉	—	4	2	no	—
231	Q₈×C₇₉	—	4	2	no	—
232	Q₈×C₇₉	—	4	2	no	—
233	Q₈×C₇₉	—	8	1	no	—
234	Q₈×C₇₉	—	8	2	no	—
235	Q₈×C₇₉	—	8	2	no	—
236	D₄×C₇₉	—	2	2	no	—
237	D₄×C₇₉	—	8	1	no	—
238	C₂×C₄×C₇₉	—	2	2	no	—
239	C₂×C₄×C₇₉	—	2	2	no	—
240	C₂×C₄×C₇₉	—	2	1	no	—
241	C₂×C₄×C₇₉	—	2	1	no	—
242	C₂×C₄×C₇₉	—	2	1	no	—
243	C₂×C₄×C₇₉	—	2	2	no	—
244	C₂×C₄×C₇₉	—	2	1	no	—
245	C₂×C₄×C₇₉	—	2	1	no	—
246	C₂×C₄×C₇₉	—	2	1	no	—
247	C₂×C₄×C₇₉	—	2	2	no	—
248	C₂×C₄×C₇₉	—	2	1	no	—
249	C₂×C₄×C₇₉	—	4	1	no	—
250	C₂×C₄×C₇₉	—	4	2	no	—
251	C₂×C₄×C₇₉	—	4	2	no	—
252	C₂×C₄×C₇₉	—	8	2	no	—
253	C₂×C₄×C₇₉	—	8	2	no	—
254	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
255	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
260	C₈×C₇₉	—	4	2	no	—
261	C₈×C₇₉	—	4	2	no	—
262	C₈×C₇₉	—	4	2	no	—
263	C₂²×C₇₉	—	2	1	no	—
264	C₂²×C₇₉	—	2	1	no	—
265	C₂²×C₇₉	—	2	1	no	—
266	C₂²×C₇₉	—	4	1	no	—
267	C₂²×C₇₉	—	4	1	no	—
268	C₂²×C₇₉	—	4	1	no	—
269	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
270	C₄×C₇₉	—	2	1	no	—
271	C₄×C₇₉	—	2	1	no	—
272	C₄×C₇₉	—	2	1	no	—
273	C₄×C₇₉	—	2	1	no	—
274	C₄×C₇₉	—	4	1	no	—
275	C₄×C₇₉	—	4	1	no	—
276	C₄×C₇₉	—	4	1	no	—
277	C₄×C₇₉	—	4	1	no	—
278	C₄×C₇₉	—	4	2	no	—
279	C₄×C₇₉	—	4	1	no	—
280	C₄×C₇₉	—	4	2	no	—
281	C₄×C₇₉	—	4	1	no	—
282	C₄×C₇₉	—	4	1	no	—
283	C₄×C₇₉	—	8	2	no	—
284	C₄×C₇₉	#577	1	2	yes	—
285	C₄×C₇₉	#578	1	2	yes	—
286	#18972	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₇₉	—	4	1	no	—
288	C₂×C₇₉	—	8	1	no	—
289	C₂×C₇₉	#3010	1	1	yes	characteristic
290	C₂×C₇₉	#3011	1	1	yes	characteristic
291	C₂×C₇₉	#3022	1	1	yes	characteristic
292	#3555	C₂×C₇₉	1	1	yes	characteristic
293	#3239	C₂×C₇₉	1	1	yes	characteristic
294	#3229	C₂×C₇₉	1	1	yes	characteristic, complemented
295	#3209	C₂×C₇₉	1	1	yes	characteristic, complemented
296	#1653	C₂×C₇₉	1	2	yes	complemented
297	#1652	C₂×C₇₉	1	2	yes	complemented
298	#1645	C₂×C₇₉	1	2	yes	complemented
299	#1644	C₂×C₇₉	1	2	yes	complemented
300	#1554	C₂×C₇₉	1	1	yes	characteristic, complemented
301	#1497	C₂×C₇₉	1	1	yes	characteristic, complemented
302	#1482	C₂×C₇₉	1	1	yes	characteristic
303	C₇₉	#18972	1	1	yes	characteristic, direct product factor, Sylow
304	#563	—	2	2	no	—
305	Q₈²	C₂²×C₇₉	1	1	yes	characteristic
306	#557	—	2	1	no	—
307	#557	C₂²×C₇₉	1	1	yes	characteristic
308	#556	—	2	1	no	—
309	#556	—	2	1	no	—
310	#556	C₂²×C₇₉	1	1	yes	characteristic
311	#554	C₂²×C₇₉	1	1	yes	characteristic
312	#552	—	2	1	no	—
313	#544	—	2	1	no	—
314	#542	—	2	1	no	—
315	#541	—	2	1	no	—
316	#541	—	2	1	no	—
317	#541	—	2	2	no	—
318	#533	C₂²×C₇₉	1	1	yes	characteristic
319	#533	C₂²×C₇₉	1	1	yes	characteristic
320	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
321	#529	C₂²×C₇₉	1	1	yes	characteristic
322	#501	—	2	1	no	—
323	#498	C₂²×C₇₉	1	2	yes	—
324	#494	—	2	1	no	—
325	#489	—	2	1	no	—
326	#487	—	2	1	no	—
327	#487	C₂²×C₇₉	1	2	yes	—
328	#484	—	2	1	no	—
329	#483	—	2	2	no	—
330	#481	—	2	1	no	—
331	#475	—	2	2	no	—
332	#475	C₂²×C₇₉	1	2	yes	—
333	#474	C₂²×C₇₉	1	2	yes	—
334	#462	C₂²×C₇₉	1	2	yes	—
335	#462	C₂²×C₇₉	1	2	yes	—
336	#451	—	2	1	no	—
337	#451	—	2	1	no	—
338	#432	C₂²×C₇₉	1	1	yes	characteristic
339	#431	C₂²×C₇₉	1	1	yes	characteristic
340	#431	C₂²×C₇₉	1	1	yes	characteristic
341	#333	C₂²×C₇₉	1	2	yes	—
342	#332	C₂²×C₇₉	1	2	yes	—
343	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
344	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
345	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
346	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
347	C₂²×Q₈	—	2	1	no	—
348	C₂×Q₁₆	—	2	2	no	—
349	C₂×Q₁₆	—	2	2	no	—
350	C₄⋊Q₈	—	2	2	no	—
351	C₄⋊Q₈	—	2	1	no	—
352	C₄⋊Q₈	—	2	2	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
359	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
361	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
363	#126	—	2	2	no	—
364	#126	—	2	2	no	—
365	#126	—	2	2	no	—
366	#126	—	2	2	no	—
367	#126	—	2	2	no	—
368	#126	—	2	2	no	—
369	#126	—	2	1	no	—
370	#125	—	2	2	no	—
371	#125	—	2	2	no	—
372	#125	—	2	2	no	—
373	#125	—	2	2	no	—
374	#125	—	2	1	no	—
375	#125	—	2	2	no	—
376	#125	—	2	1	no	—
377	#125	—	2	1	no	—
378	#125	—	2	1	no	—
379	#125	D₄×C₇₉	1	1	yes	characteristic
380	#124	—	2	2	no	—
381	#124	—	2	1	no	—
382	#124	D₄×C₇₉	1	1	yes	characteristic
383	#123	—	2	2	no	—
384	#123	—	2	1	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
393	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
394	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
395	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
396	#121	D₄×C₇₉	1	1	yes	characteristic
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	D₄×C₇₉	1	2	yes	—
406	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
407	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
408	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
412	#117	—	2	2	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	—	2	1	no	—
416	#117	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
421	#107	—	2	2	no	—
422	#106	—	2	4	no	—
423	#106	—	2	2	no	—
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
426	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
427	#103	—	2	4	no	—
428	#103	—	2	2	no	—
429	#103	—	2	2	no	—
430	#103	—	2	2	no	—
431	#102	—	2	2	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	#97	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	C₂³×C₇₉	1	2	yes	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	—	8	2	no	—
444	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
446	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
447	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
456	Q₁₆	—	8	2	no	—
457	Q₁₆	—	8	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
492	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
493	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
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	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
514	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
515	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	#120×C₇₉	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	8	1	no	—
526	Q₈	—	8	2	no	—
527	Q₈	—	8	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	8	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
547	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
548	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
552	C₈	—	4	2	no	—
553	C₈	—	4	2	no	—
554	C₈	—	4	2	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	8	2	no	—
576	C₄	#577×C₇₉	1	2	yes	—
577	C₄	#578×C₇₉	1	2	yes	—
578	C₂	—	4	1	no	—
579	C₂	—	8	1	no	—
580	C₂	C₇₉×#3010	1	1	yes	characteristic
581	C₂	C₇₉×#3011	1	1	yes	characteristic
582	C₂	C₇₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	#121×C₇₉	D₄
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
3. C₇₉×#3229	C₂	semidirect
4. C₇₉×#3209	C₂	semidirect
5. C₇₉×#1653	C₂	semidirect
6. C₇₉×#1652	C₂	semidirect
7. C₇₉×#1645	C₂	semidirect
8. C₇₉×#1644	C₂	semidirect
9. C₇₉×#1554	C₂	semidirect
10. C₇₉×#1497	C₂	semidirect
286. #18972	C₇₉	direct (N × H)
294. #3229	C₂×C₇₉	semidirect
295. #3209	C₂×C₇₉	semidirect
296. #1653	C₂×C₇₉	semidirect
297. #1652	C₂×C₇₉	semidirect
298. #1645	C₂×C₇₉	semidirect
299. #1644	C₂×C₇₉	semidirect
300. #1554	C₂×C₇₉	semidirect
301. #1497	C₂×C₇₉	semidirect
303. C₇₉	#18972	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₉×#3555	2
C₇₉×#3239	2
C₇₉×#3229	2
C₇₉×#3209	2
C₇₉×#1653	2
C₇₉×#1652	2
C₇₉×#1645	2
C₇₉×#1644	2
C₇₉×#1554	2
C₇₉×#1497	2
C₇₉×#1482	2
#18972	79

Subgroups — C79×#18972 #34130661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18972 #34130661