Subgroups — C₇₉×#3371 #23760993

Order 10112.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#559×C₇₉	C₂	1	1	yes	maximal, characteristic
2	#557×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#490×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#489×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#488×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#479×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#478×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#476×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#464×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#464×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#460×C₇₉	C₂	1	1	yes	maximal, characteristic
12	#446×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#441×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#440×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	C₄⋊Q₈×C₇₉	—	2	1	no	—
20	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	#127×C₇₉	C₂²	1	1	yes	characteristic
22	#125×C₇₉	—	2	1	no	—
23	#125×C₇₉	—	2	1	no	—
24	#125×C₇₉	C₂²	1	1	yes	characteristic
25	#125×C₇₉	C₂²	1	1	yes	characteristic
26	#124×C₇₉	—	2	1	no	—
27	#124×C₇₉	C₂²	1	1	yes	characteristic
28	#124×C₇₉	C₂²	1	1	yes	characteristic
29	#123×C₇₉	—	2	1	no	—
30	#123×C₇₉	—	2	1	no	—
31	C₄×Q₈×C₇₉	—	2	1	no	—
32	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₇₉	—	2	1	no	—
38	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	#107×C₇₉	C₂²	1	1	yes	characteristic
41	#106×C₇₉	C₂²	1	1	yes	characteristic
42	#106×C₇₉	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
44	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
45	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
46	#103×C₇₉	C₂²	1	1	yes	characteristic
47	#103×C₇₉	C₂²	1	1	yes	characteristic
48	#103×C₇₉	C₂²	1	1	yes	characteristic
49	#103×C₇₉	C₂²	1	1	yes	characteristic
50	#102×C₇₉	C₂²	1	1	yes	characteristic
51	#102×C₇₉	C₂²	1	1	yes	characteristic
52	#102×C₇₉	C₂²	1	1	yes	characteristic
53	#102×C₇₉	C₂²	1	1	yes	characteristic
54	#102×C₇₉	C₂²	1	1	yes	characteristic
55	#102×C₇₉	C₂²	1	1	yes	characteristic
56	#97×C₇₉	C₂²	1	1	yes	characteristic
57	#97×C₇₉	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₇₉	—	2	1	no	—
60	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
61	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₇₉	—	2	1	no	—
64	C₂×D₄×C₇₉	—	2	1	no	—
65	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	—	2	1	no	—
68	C₂²×C₄×C₇₉	—	2	1	no	—
69	Q₁₆×C₇₉	—	2	2	no	—
70	SD₁₆×C₇₉	—	2	2	no	—
71	SD₁₆×C₇₉	—	2	2	no	—
72	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
73	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
74	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₄⋊C₄×C₇₉	—	2	1	no	—
78	C₄⋊C₄×C₇₉	—	2	1	no	—
79	C₄⋊C₄×C₇₉	—	2	1	no	—
80	C₄⋊C₄×C₇₉	—	2	1	no	—
81	C₄⋊C₄×C₇₉	—	2	1	no	—
82	C₄⋊C₄×C₇₉	—	2	1	no	—
83	C₄⋊C₄×C₇₉	—	2	1	no	—
84	C₄⋊C₄×C₇₉	—	2	1	no	—
85	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
86	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
87	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
88	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂²⋊C₄×C₇₉	—	2	1	no	—
93	C₂²⋊C₄×C₇₉	—	2	1	no	—
94	C₂²⋊C₄×C₇₉	—	2	1	no	—
95	C₂²⋊C₄×C₇₉	—	2	1	no	—
96	C₂²⋊C₄×C₇₉	—	2	1	no	—
97	C₂²⋊C₄×C₇₉	—	2	1	no	—
98	C₄²×C₇₉	—	2	1	no	—
99	C₄²×C₇₉	—	2	1	no	—
100	C₄²×C₇₉	—	2	1	no	—
101	C₄²×C₇₉	—	2	1	no	—
102	C₄²×C₇₉	C₂³	1	1	yes	characteristic
103	C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	C₄²×C₇₉	C₂³	1	1	yes	characteristic
105	C₂³×C₇₉	—	2	1	no	—
106	C₂³×C₇₉	—	2	1	no	—
107	Q₈×C₇₉	—	2	1	no	—
108	Q₈×C₇₉	—	2	1	no	—
109	Q₈×C₇₉	—	2	1	no	—
110	Q₈×C₇₉	—	4	1	no	—
111	Q₈×C₇₉	—	4	2	no	—
112	Q₈×C₇₉	#41	1	2	yes	—
113	D₄×C₇₉	—	2	1	no	—
114	D₄×C₇₉	—	2	1	no	—
115	D₄×C₇₉	—	2	1	no	—
116	D₄×C₇₉	—	2	1	no	—
117	D₄×C₇₉	—	4	2	no	—
118	D₄×C₇₉	—	8	1	no	—
119	C₂×C₄×C₇₉	—	2	1	no	—
120	C₂×C₄×C₇₉	—	2	1	no	—
121	C₂×C₄×C₇₉	—	2	1	no	—
122	C₂×C₄×C₇₉	—	2	1	no	—
123	C₂×C₄×C₇₉	—	2	1	no	—
124	C₂×C₄×C₇₉	—	2	1	no	—
125	C₂×C₄×C₇₉	—	8	1	no	—
126	C₂×C₄×C₇₉	—	8	1	no	—
127	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
134	C₈×C₇₉	—	2	1	no	—
135	C₈×C₇₉	—	2	1	no	—
136	C₈×C₇₉	—	2	1	no	—
137	C₈×C₇₉	—	2	1	no	—
138	C₂²×C₇₉	—	4	1	no	—
139	C₂²×C₇₉	—	4	1	no	—
140	C₂²×C₇₉	—	4	1	no	—
141	C₂²×C₇₉	—	4	1	no	—
142	C₂²×C₇₉	—	4	1	no	—
143	C₂²×C₇₉	—	4	1	no	—
144	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
145	C₄×C₇₉	—	2	2	no	—
146	C₄×C₇₉	—	2	1	no	—
147	C₄×C₇₉	—	2	1	no	—
148	C₄×C₇₉	—	2	1	no	—
149	C₄×C₇₉	—	2	1	no	—
150	C₄×C₇₉	—	2	1	no	—
151	C₄×C₇₉	—	2	1	no	—
152	C₄×C₇₉	—	4	1	no	—
153	C₄×C₇₉	—	4	1	no	—
154	C₄×C₇₉	—	4	1	no	—
155	C₄×C₇₉	—	4	1	no	—
156	C₄×C₇₉	—	4	1	no	—
157	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
158	C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
159	C₂×C₇₉	—	8	1	no	—
160	C₂×C₇₉	—	8	1	no	—
161	C₂×C₇₉	#548	1	1	yes	characteristic
162	C₂×C₇₉	#575	1	1	yes	characteristic
163	C₂×C₇₉	#577	1	1	yes	characteristic
164	#3371	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₇₉	#3371	1	1	yes	characteristic, direct product factor, Sylow
166	#559	C₂×C₇₉	1	1	yes	characteristic
167	#557	C₂×C₇₉	1	1	yes	characteristic, complemented
168	#490	C₂×C₇₉	1	1	yes	characteristic
169	#489	C₂×C₇₉	1	1	yes	characteristic, complemented
170	#488	C₂×C₇₉	1	1	yes	characteristic, complemented
171	#479	C₂×C₇₉	1	1	yes	characteristic, complemented
172	#478	C₂×C₇₉	1	1	yes	characteristic, complemented
173	#476	C₂×C₇₉	1	1	yes	characteristic, complemented
174	#464	C₂×C₇₉	1	1	yes	characteristic, complemented
175	#464	C₂×C₇₉	1	1	yes	characteristic, complemented
176	#460	C₂×C₇₉	1	1	yes	characteristic
177	#446	C₂×C₇₉	1	1	yes	characteristic, complemented
178	#441	C₂×C₇₉	1	1	yes	characteristic, complemented
179	#440	C₂×C₇₉	1	1	yes	characteristic, complemented
180	C₄×SD₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
181	C₂×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
182	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
183	C₂×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
184	C₄⋊Q₈	—	2	1	no	—
185	C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
186	#127	C₂²×C₇₉	1	1	yes	characteristic
187	#125	—	2	1	no	—
188	#125	—	2	1	no	—
189	#125	C₂²×C₇₉	1	1	yes	characteristic
190	#125	C₂²×C₇₉	1	1	yes	characteristic
191	#124	—	2	1	no	—
192	#124	C₂²×C₇₉	1	1	yes	characteristic
193	#124	C₂²×C₇₉	1	1	yes	characteristic
194	#123	—	2	1	no	—
195	#123	—	2	1	no	—
196	C₄×Q₈	—	2	1	no	—
197	C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
198	C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
199	C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
200	C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
201	C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
202	C₄×D₄	—	2	1	no	—
203	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
204	C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
205	#107	C₂²×C₇₉	1	1	yes	characteristic
206	#106	C₂²×C₇₉	1	1	yes	characteristic
207	#106	C₂²×C₇₉	1	1	yes	characteristic
208	C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
209	C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
210	C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
211	#103	C₂²×C₇₉	1	1	yes	characteristic
212	#103	C₂²×C₇₉	1	1	yes	characteristic
213	#103	C₂²×C₇₉	1	1	yes	characteristic
214	#103	C₂²×C₇₉	1	1	yes	characteristic
215	#102	C₂²×C₇₉	1	1	yes	characteristic
216	#102	C₂²×C₇₉	1	1	yes	characteristic
217	#102	C₂²×C₇₉	1	1	yes	characteristic
218	#102	C₂²×C₇₉	1	1	yes	characteristic
219	#102	C₂²×C₇₉	1	1	yes	characteristic
220	#102	C₂²×C₇₉	1	1	yes	characteristic
221	#97	C₂²×C₇₉	1	1	yes	characteristic
222	#97	C₂²×C₇₉	1	1	yes	characteristic
223	C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
224	C₂×Q₈	—	2	1	no	—
225	C₂×Q₈	D₄×C₇₉	1	1	yes	characteristic
226	C₂×Q₈	C₂³×C₇₉	1	1	yes	characteristic
227	C₂×Q₈	C₂³×C₇₉	1	1	yes	characteristic
228	C₂×D₄	—	2	1	no	—
229	C₂×D₄	—	2	1	no	—
230	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
231	C₂×D₄	C₂³×C₇₉	1	1	yes	characteristic
232	C₂²×C₄	—	2	1	no	—
233	C₂²×C₄	—	2	1	no	—
234	Q₁₆	—	2	2	no	—
235	SD₁₆	—	2	2	no	—
236	SD₁₆	—	2	2	no	—
237	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
238	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
239	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
240	C₂×C₈	C₂³×C₇₉	1	1	yes	characteristic
241	C₄⋊C₄	—	2	1	no	—
242	C₄⋊C₄	—	2	1	no	—
243	C₄⋊C₄	—	2	1	no	—
244	C₄⋊C₄	—	2	1	no	—
245	C₄⋊C₄	—	2	1	no	—
246	C₄⋊C₄	—	2	1	no	—
247	C₄⋊C₄	—	2	1	no	—
248	C₄⋊C₄	—	2	1	no	—
249	C₄⋊C₄	—	2	1	no	—
250	C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
251	C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
252	C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
253	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
254	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
255	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
256	C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
257	C₂²⋊C₄	—	2	1	no	—
258	C₂²⋊C₄	—	2	1	no	—
259	C₂²⋊C₄	—	2	1	no	—
260	C₂²⋊C₄	—	2	1	no	—
261	C₂²⋊C₄	—	2	1	no	—
262	C₂²⋊C₄	—	2	1	no	—
263	C₄²	—	2	1	no	—
264	C₄²	—	2	1	no	—
265	C₄²	—	2	1	no	—
266	C₄²	—	2	1	no	—
267	C₄²	C₂³×C₇₉	1	1	yes	characteristic
268	C₄²	C₂³×C₇₉	1	1	yes	characteristic
269	C₄²	C₂³×C₇₉	1	1	yes	characteristic
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	Q₈	—	2	1	no	—
273	Q₈	—	2	1	no	—
274	Q₈	—	2	1	no	—
275	Q₈	—	4	1	no	—
276	Q₈	—	4	2	no	—
277	Q₈	#41×C₇₉	1	2	yes	—
278	D₄	—	2	1	no	—
279	D₄	—	2	1	no	—
280	D₄	—	2	1	no	—
281	D₄	—	2	1	no	—
282	D₄	—	4	2	no	—
283	D₄	—	8	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	8	1	no	—
291	C₂×C₄	—	8	1	no	—
292	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
293	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
294	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
295	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
296	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
297	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
298	C₂×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
299	C₈	—	2	1	no	—
300	C₈	—	2	1	no	—
301	C₈	—	2	1	no	—
302	C₈	—	2	1	no	—
303	C₂²	—	4	1	no	—
304	C₂²	—	4	1	no	—
305	C₂²	—	4	1	no	—
306	C₂²	—	4	1	no	—
307	C₂²	—	4	1	no	—
308	C₂²	—	4	1	no	—
309	C₂²	C₂²×D₄×C₇₉	1	1	yes	characteristic
310	C₄	—	2	2	no	—
311	C₄	—	2	1	no	—
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	2	1	no	—
315	C₄	—	2	1	no	—
316	C₄	—	2	1	no	—
317	C₄	—	4	1	no	—
318	C₄	—	4	1	no	—
319	C₄	—	4	1	no	—
320	C₄	—	4	1	no	—
321	C₄	—	4	1	no	—
322	C₄	C₂×#41×C₇₉	1	1	yes	characteristic
323	C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
324	C₂	—	8	1	no	—
325	C₂	—	8	1	no	—
326	C₂	#548×C₇₉	1	1	yes	characteristic
327	C₂	#575×C₇₉	1	1	yes	characteristic
328	C₂	#577×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇₉
prime radical	#127×C₇₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₄×Q₈×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #557×C₇₉	C₂	semidirect
4. #489×C₇₉	C₂	semidirect
5. #488×C₇₉	C₂	semidirect
6. #479×C₇₉	C₂	semidirect
7. #478×C₇₉	C₂	semidirect
8. #476×C₇₉	C₂	semidirect
9. #464×C₇₉	C₂	semidirect
10. #464×C₇₉	C₂	semidirect
12. #446×C₇₉	C₂	semidirect
13. #441×C₇₉	C₂	semidirect
14. #440×C₇₉	C₂	semidirect
15. C₄×SD₁₆×C₇₉	C₂	semidirect
164. #3371	C₇₉	direct (N × H)
165. C₇₉	#3371	direct (N × H)
167. #557	C₂×C₇₉	semidirect
169. #489	C₂×C₇₉	semidirect
170. #488	C₂×C₇₉	semidirect
171. #479	C₂×C₇₉	semidirect
172. #478	C₂×C₇₉	semidirect
173. #476	C₂×C₇₉	semidirect
174. #464	C₂×C₇₉	semidirect
175. #464	C₂×C₇₉	semidirect
177. #446	C₂×C₇₉	semidirect
178. #441	C₂×C₇₉	semidirect
179. #440	C₂×C₇₉	semidirect
180. C₄×SD₁₆	C₂×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
#559×C₇₉	2
#557×C₇₉	2
#490×C₇₉	2
#489×C₇₉	2
#488×C₇₉	2
#479×C₇₉	2
#478×C₇₉	2
#476×C₇₉	2
#464×C₇₉	2
#460×C₇₉	2
#446×C₇₉	2
#441×C₇₉	2
#440×C₇₉	2
C₄×SD₁₆×C₇₉	2
#3371	79

Subgroups — C79×#3371 #23760993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#3371 #23760993