Subgroups — C₇₉×#24536 #34136225

Order 20224.

1006 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#452×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#416×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2339	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
24	#452×C₇₉	—	2	4	no	—
25	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	#416×C₇₉	—	2	4	no	—
28	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
37	#397×C₇₉	—	2	1	no	—
38	#397×C₇₉	—	2	1	no	—
39	#391×C₇₉	C₂²	1	1	yes	characteristic
40	#391×C₇₉	C₂²	1	1	yes	characteristic
41	#391×C₇₉	C₂²	1	1	yes	characteristic
42	#391×C₇₉	C₂²	1	1	yes	characteristic
43	#387×C₇₉	—	2	1	no	—
44	#387×C₇₉	—	2	1	no	—
45	#386×C₇₉	—	2	1	no	—
46	#386×C₇₉	—	2	1	no	—
47	#384×C₇₉	C₂²	1	1	yes	characteristic
48	#382×C₇₉	C₂²	1	1	yes	characteristic
49	#381×C₇₉	—	2	1	no	—
50	#380×C₇₉	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×#95×C₇₉	—	2	1	no	—
53	#340×C₇₉	C₂²	1	1	yes	characteristic
54	#340×C₇₉	C₂²	1	1	yes	characteristic
55	#340×C₇₉	C₂²	1	1	yes	characteristic
56	#340×C₇₉	C₂²	1	1	yes	characteristic
57	#340×C₇₉	C₂²	1	1	yes	characteristic
58	#340×C₇₉	C₂²	1	1	yes	characteristic
59	#336×C₇₉	C₂²	1	1	yes	characteristic
60	#336×C₇₉	C₂²	1	1	yes	characteristic
61	C₂×#41×C₇₉	—	2	2	no	—
62	C₂×#41×C₇₉	—	2	2	no	—
63	C₂×#41×C₇₉	—	2	2	no	—
64	C₂×#41×C₇₉	—	4	1	no	—
65	C₂×#41×C₇₉	—	4	1	no	—
66	C₂×#41×C₇₉	D₄	1	4	yes	—
67	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₇₉	—	2	1	no	—
70	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇₉	—	2	1	no	—
72	C₂³×C₄×C₇₉	—	2	1	no	—
73	C₂³×C₄×C₇₉	—	2	1	no	—
74	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×Q₁₆×C₇₉	—	2	2	no	—
76	C₂×Q₁₆×C₇₉	—	4	1	no	—
77	C₂×Q₁₆×C₇₉	—	4	1	no	—
78	C₂×SD₁₆×C₇₉	—	2	2	no	—
79	C₂×SD₁₆×C₇₉	—	2	2	no	—
80	C₂×SD₁₆×C₇₉	—	2	2	no	—
81	C₂²×C₈×C₇₉	—	2	2	no	—
82	C₂²×C₈×C₇₉	—	4	1	no	—
83	C₂²×C₈×C₇₉	—	4	1	no	—
84	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₂²⋊Q₈×C₇₉	—	2	2	no	—
89	C₂²⋊Q₈×C₇₉	—	2	2	no	—
90	C₄×D₄×C₇₉	—	2	2	no	—
91	C₄×D₄×C₇₉	—	2	2	no	—
92	C₄×D₄×C₇₉	—	4	1	no	—
93	C₄×D₄×C₇₉	—	4	1	no	—
94	#117×C₇₉	—	2	2	no	—
95	#117×C₇₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₇₉	—	2	1	no	—
112	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₇₉	—	4	1	no	—
115	C₄⋊C₈×C₇₉	—	4	1	no	—
116	#103×C₇₉	—	2	2	no	—
117	#103×C₇₉	—	2	2	no	—
118	#103×C₇₉	—	2	2	no	—
119	#103×C₇₉	—	4	1	no	—
120	#103×C₇₉	—	4	1	no	—
121	#102×C₇₉	—	2	2	no	—
122	#102×C₇₉	—	2	2	no	—
123	#102×C₇₉	—	2	2	no	—
124	C₂²⋊C₈×C₇₉	—	2	2	no	—
125	#95×C₇₉	—	2	1	no	—
126	#95×C₇₉	—	2	1	no	—
127	#95×C₇₉	—	2	1	no	—
128	#95×C₇₉	—	2	1	no	—
129	#95×C₇₉	—	2	1	no	—
130	#95×C₇₉	—	2	1	no	—
131	#95×C₇₉	—	2	1	no	—
132	#95×C₇₉	—	2	1	no	—
133	#95×C₇₉	—	2	1	no	—
134	#95×C₇₉	—	2	1	no	—
135	#95×C₇₉	—	2	1	no	—
136	#95×C₇₉	D₄	1	1	yes	characteristic
137	#95×C₇₉	D₄	1	1	yes	characteristic
138	C₂⁴×C₇₉	—	2	1	no	—
139	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
140	#41×C₇₉	—	2	8	no	—
141	#41×C₇₉	—	4	4	no	—
142	#41×C₇₉	—	4	4	no	—
143	#41×C₇₉	—	4	4	no	—
144	C₂×Q₈×C₇₉	—	2	1	no	—
145	C₂×Q₈×C₇₉	—	2	1	no	—
146	C₂×Q₈×C₇₉	—	2	1	no	—
147	C₂×Q₈×C₇₉	—	2	1	no	—
148	C₂×Q₈×C₇₉	—	2	1	no	—
149	C₂×Q₈×C₇₉	—	2	1	no	—
150	C₂×Q₈×C₇₉	—	2	1	no	—
151	C₂×Q₈×C₇₉	—	2	1	no	—
152	C₂×Q₈×C₇₉	—	2	1	no	—
153	C₂×Q₈×C₇₉	—	2	1	no	—
154	C₂×Q₈×C₇₉	—	2	1	no	—
155	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₇₉	—	2	4	no	—
157	C₂×D₄×C₇₉	—	2	1	no	—
158	C₂×D₄×C₇₉	—	2	1	no	—
159	C₂×D₄×C₇₉	—	2	1	no	—
160	C₂×D₄×C₇₉	—	4	2	no	—
161	C₂×D₄×C₇₉	—	4	2	no	—
162	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₇₉	#41	1	2	yes	—
164	C₂×D₄×C₇₉	#41	1	2	yes	—
165	C₂²×C₄×C₇₉	—	2	1	no	—
166	C₂²×C₄×C₇₉	—	2	1	no	—
167	C₂²×C₄×C₇₉	—	2	1	no	—
168	C₂²×C₄×C₇₉	—	2	1	no	—
169	C₂²×C₄×C₇₉	—	2	1	no	—
170	C₂²×C₄×C₇₉	—	2	4	no	—
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	1	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	—	4	2	no	—
178	C₂²×C₄×C₇₉	—	4	2	no	—
179	C₂²×C₄×C₇₉	—	4	2	no	—
180	C₂²×C₄×C₇₉	—	4	2	no	—
181	C₂²×C₄×C₇₉	—	4	2	no	—
182	C₂²×C₄×C₇₉	—	4	2	no	—
183	C₂²×C₄×C₇₉	—	8	1	no	—
184	C₂²×C₄×C₇₉	—	8	1	no	—
185	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₉	#41	1	2	yes	—
192	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
193	Q₁₆×C₇₉	—	4	4	no	—
194	SD₁₆×C₇₉	—	4	4	no	—
195	C₂×C₈×C₇₉	—	2	1	no	—
196	C₂×C₈×C₇₉	—	2	1	no	—
197	C₂×C₈×C₇₉	—	2	1	no	—
198	C₂×C₈×C₇₉	—	2	1	no	—
199	C₂×C₈×C₇₉	—	2	1	no	—
200	C₂×C₈×C₇₉	—	2	1	no	—
201	C₂×C₈×C₇₉	—	2	1	no	—
202	C₂×C₈×C₇₉	—	2	1	no	—
203	C₂×C₈×C₇₉	—	2	1	no	—
204	C₂×C₈×C₇₉	—	2	1	no	—
205	C₂×C₈×C₇₉	—	2	1	no	—
206	C₂×C₈×C₇₉	—	2	1	no	—
207	C₂×C₈×C₇₉	—	4	4	no	—
208	C₄⋊C₄×C₇₉	—	2	1	no	—
209	C₄⋊C₄×C₇₉	—	2	1	no	—
210	C₄⋊C₄×C₇₉	—	2	1	no	—
211	C₄⋊C₄×C₇₉	—	2	1	no	—
212	C₄⋊C₄×C₇₉	—	2	1	no	—
213	C₄⋊C₄×C₇₉	—	2	1	no	—
214	C₄⋊C₄×C₇₉	—	2	1	no	—
215	C₄⋊C₄×C₇₉	—	2	1	no	—
216	C₄⋊C₄×C₇₉	—	2	1	no	—
217	C₄⋊C₄×C₇₉	—	2	1	no	—
218	C₄⋊C₄×C₇₉	—	4	2	no	—
219	C₄⋊C₄×C₇₉	—	4	2	no	—
220	C₄⋊C₄×C₇₉	—	4	2	no	—
221	C₂²⋊C₄×C₇₉	—	2	2	no	—
222	C₂²⋊C₄×C₇₉	—	4	1	no	—
223	C₂²⋊C₄×C₇₉	—	4	2	no	—
224	C₂²⋊C₄×C₇₉	—	4	2	no	—
225	C₂²⋊C₄×C₇₉	—	4	2	no	—
226	C₂²⋊C₄×C₇₉	—	4	2	no	—
227	C₂²⋊C₄×C₇₉	—	8	1	no	—
228	C₄²×C₇₉	—	2	1	no	—
229	C₄²×C₇₉	—	2	1	no	—
230	C₄²×C₇₉	—	2	1	no	—
231	C₄²×C₇₉	—	2	1	no	—
232	C₄²×C₇₉	—	4	2	no	—
233	C₂³×C₇₉	—	2	2	no	—
234	C₂³×C₇₉	—	2	2	no	—
235	C₂³×C₇₉	—	2	2	no	—
236	C₂³×C₇₉	—	2	1	no	—
237	C₂³×C₇₉	—	2	1	no	—
238	C₂³×C₇₉	—	2	1	no	—
239	C₂³×C₇₉	—	2	1	no	—
240	C₂³×C₇₉	—	2	1	no	—
241	C₂³×C₇₉	—	2	1	no	—
242	C₂³×C₇₉	—	4	1	no	—
243	C₂³×C₇₉	—	4	1	no	—
244	C₂³×C₇₉	—	4	1	no	—
245	C₂³×C₇₉	—	4	1	no	—
246	C₂³×C₇₉	#121	1	2	yes	—
247	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
248	Q₈×C₇₉	—	2	2	no	—
249	Q₈×C₇₉	—	2	2	no	—
250	Q₈×C₇₉	—	4	1	no	—
251	Q₈×C₇₉	—	4	1	no	—
252	Q₈×C₇₉	—	4	1	no	—
253	Q₈×C₇₉	—	4	1	no	—
254	Q₈×C₇₉	—	4	1	no	—
255	Q₈×C₇₉	—	4	1	no	—
256	D₄×C₇₉	—	2	2	no	—
257	D₄×C₇₉	—	2	2	no	—
258	D₄×C₇₉	—	2	2	no	—
259	D₄×C₇₉	—	4	8	no	—
260	D₄×C₇₉	#123	1	4	yes	—
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	2	no	—
266	C₂×C₄×C₇₉	—	2	2	no	—
267	C₂×C₄×C₇₉	—	2	2	no	—
268	C₂×C₄×C₇₉	—	2	2	no	—
269	C₂×C₄×C₇₉	—	2	2	no	—
270	C₂×C₄×C₇₉	—	2	1	no	—
271	C₂×C₄×C₇₉	—	2	1	no	—
272	C₂×C₄×C₇₉	—	2	1	no	—
273	C₂×C₄×C₇₉	—	2	1	no	—
274	C₂×C₄×C₇₉	—	2	1	no	—
275	C₂×C₄×C₇₉	—	2	1	no	—
276	C₂×C₄×C₇₉	—	2	1	no	—
277	C₂×C₄×C₇₉	—	2	1	no	—
278	C₂×C₄×C₇₉	—	2	1	no	—
279	C₂×C₄×C₇₉	—	4	8	no	—
280	C₂×C₄×C₇₉	—	4	1	no	—
281	C₂×C₄×C₇₉	—	4	1	no	—
282	C₂×C₄×C₇₉	—	4	1	no	—
283	C₂×C₄×C₇₉	—	4	1	no	—
284	C₂×C₄×C₇₉	—	4	1	no	—
285	C₂×C₄×C₇₉	—	4	1	no	—
286	C₂×C₄×C₇₉	—	4	1	no	—
287	C₂×C₄×C₇₉	—	4	1	no	—
288	C₂×C₄×C₇₉	—	4	1	no	—
289	C₂×C₄×C₇₉	—	4	1	no	—
290	C₂×C₄×C₇₉	—	4	1	no	—
291	C₂×C₄×C₇₉	—	4	1	no	—
292	C₂×C₄×C₇₉	—	4	1	no	—
293	C₂×C₄×C₇₉	—	4	1	no	—
294	C₂×C₄×C₇₉	—	4	1	no	—
295	C₂×C₄×C₇₉	—	4	1	no	—
296	C₂×C₄×C₇₉	—	4	1	no	—
297	C₂×C₄×C₇₉	—	4	1	no	—
298	C₂×C₄×C₇₉	—	4	1	no	—
299	C₂×C₄×C₇₉	—	4	1	no	—
300	C₂×C₄×C₇₉	—	8	4	no	—
301	C₂×C₄×C₇₉	—	8	4	no	—
302	C₂×C₄×C₇₉	#121	1	2	yes	—
303	C₂×C₄×C₇₉	#135	1	2	yes	—
304	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
310	C₈×C₇₉	—	4	1	no	—
311	C₈×C₇₉	—	4	1	no	—
312	C₈×C₇₉	—	4	1	no	—
313	C₈×C₇₉	—	4	1	no	—
314	C₂²×C₇₉	—	2	2	no	—
315	C₂²×C₇₉	—	2	4	no	—
316	C₂²×C₇₉	—	2	2	no	—
317	C₂²×C₇₉	—	2	2	no	—
318	C₂²×C₇₉	—	4	2	no	—
319	C₂²×C₇₉	—	4	2	no	—
320	C₂²×C₇₉	—	4	1	no	—
321	C₂²×C₇₉	—	4	2	no	—
322	C₂²×C₇₉	—	4	1	no	—
323	C₂²×C₇₉	—	4	2	no	—
324	C₂²×C₇₉	—	4	2	no	—
325	C₂²×C₇₉	—	4	1	no	—
326	C₂²×C₇₉	—	4	1	no	—
327	C₂²×C₇₉	—	4	2	no	—
328	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
329	C₂²×C₇₉	#546	1	1	yes	characteristic
330	C₂²×C₇₉	#546	1	1	yes	characteristic
331	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
332	C₂²×C₇₉	#575	1	1	yes	characteristic
333	C₂²×C₇₉	#577	1	1	yes	characteristic
334	C₂²×C₇₉	#578	1	1	yes	characteristic
335	C₄×C₇₉	—	2	2	no	—
336	C₄×C₇₉	—	2	2	no	—
337	C₄×C₇₉	—	4	2	no	—
338	C₄×C₇₉	—	4	1	no	—
339	C₄×C₇₉	—	4	1	no	—
340	C₄×C₇₉	—	4	1	no	—
341	C₄×C₇₉	—	8	1	no	—
342	C₄×C₇₉	—	8	1	no	—
343	C₄×C₇₉	—	8	1	no	—
344	C₄×C₇₉	—	8	1	no	—
345	C₄×C₇₉	—	8	1	no	—
346	C₄×C₇₉	—	8	1	no	—
347	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
348	C₄×C₇₉	#534	1	1	yes	characteristic
349	C₄×C₇₉	#551	1	1	yes	characteristic
350	C₄×C₇₉	#551	1	1	yes	characteristic
351	#24536	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂×C₇₉	—	4	2	no	—
353	C₂×C₇₉	—	4	4	no	—
354	C₂×C₇₉	#2412	1	1	yes	characteristic
355	C₂×C₇₉	#3035	1	1	yes	characteristic
356	C₂×C₇₉	#3046	1	1	yes	characteristic
357	C₂×C₇₉	#3296	1	1	yes	characteristic
358	C₂×C₇₉	#3302	1	1	yes	characteristic
359	C₂×C₇₉	#3311	1	1	yes	characteristic
360	C₂×C₇₉	#3315	1	1	yes	characteristic
361	C₂×#452	C₂×C₇₉	1	1	yes	characteristic
362	C₂×#416	C₂×C₇₉	1	1	yes	characteristic
363	#2499	C₂×C₇₉	1	1	yes	characteristic, complemented
364	#2339	C₂×C₇₉	1	1	yes	characteristic
365	#2074	C₂×C₇₉	1	1	yes	characteristic, complemented
366	#2072	C₂×C₇₉	1	1	yes	characteristic, complemented
367	#2056	C₂×C₇₉	1	1	yes	characteristic, complemented
368	#2056	C₂×C₇₉	1	1	yes	characteristic, complemented
369	#1892	C₂×C₇₉	1	1	yes	characteristic, complemented
370	#1877	C₂×C₇₉	1	1	yes	characteristic, complemented
371	#1877	C₂×C₇₉	1	1	yes	characteristic, complemented
372	#1850	C₂×C₇₉	1	1	yes	characteristic, complemented
373	#1825	C₂×C₇₉	1	1	yes	characteristic, complemented
374	#1804	C₂×C₇₉	1	1	yes	characteristic, complemented
375	#1802	C₂×C₇₉	1	1	yes	characteristic, complemented
376	C₇₉	#24536	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
378	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
379	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
380	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
384	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
385	#452	—	2	4	no	—
386	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
387	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
388	#416	—	2	4	no	—
389	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
390	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
391	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
392	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
393	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
394	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
395	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
396	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
398	#397	—	2	1	no	—
399	#397	—	2	1	no	—
400	#391	C₂²×C₇₉	1	1	yes	characteristic
401	#391	C₂²×C₇₉	1	1	yes	characteristic
402	#391	C₂²×C₇₉	1	1	yes	characteristic
403	#391	C₂²×C₇₉	1	1	yes	characteristic
404	#387	—	2	1	no	—
405	#387	—	2	1	no	—
406	#386	—	2	1	no	—
407	#386	—	2	1	no	—
408	#384	C₂²×C₇₉	1	1	yes	characteristic
409	#382	C₂²×C₇₉	1	1	yes	characteristic
410	#381	—	2	1	no	—
411	#380	C₂²×C₇₉	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
413	C₂×#95	—	2	1	no	—
414	#340	C₂²×C₇₉	1	1	yes	characteristic
415	#340	C₂²×C₇₉	1	1	yes	characteristic
416	#340	C₂²×C₇₉	1	1	yes	characteristic
417	#340	C₂²×C₇₉	1	1	yes	characteristic
418	#340	C₂²×C₇₉	1	1	yes	characteristic
419	#340	C₂²×C₇₉	1	1	yes	characteristic
420	#336	C₂²×C₇₉	1	1	yes	characteristic
421	#336	C₂²×C₇₉	1	1	yes	characteristic
422	C₂×#41	—	2	2	no	—
423	C₂×#41	—	2	2	no	—
424	C₂×#41	—	2	2	no	—
425	C₂×#41	—	4	1	no	—
426	C₂×#41	—	4	1	no	—
427	C₂×#41	D₄×C₇₉	1	4	yes	—
428	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
432	C₂³×C₄	—	2	1	no	—
433	C₂³×C₄	—	2	1	no	—
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
436	C₂×Q₁₆	—	2	2	no	—
437	C₂×Q₁₆	—	4	1	no	—
438	C₂×Q₁₆	—	4	1	no	—
439	C₂×SD₁₆	—	2	2	no	—
440	C₂×SD₁₆	—	2	2	no	—
441	C₂×SD₁₆	—	2	2	no	—
442	C₂²×C₈	—	2	2	no	—
443	C₂²×C₈	—	4	1	no	—
444	C₂²×C₈	—	4	1	no	—
445	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	4	1	no	—
454	C₄×D₄	—	4	1	no	—
455	#117	—	2	2	no	—
456	#117	—	2	2	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
472	C₂×C₄²	—	2	1	no	—
473	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
475	C₄⋊C₈	—	4	1	no	—
476	C₄⋊C₈	—	4	1	no	—
477	#103	—	2	2	no	—
478	#103	—	2	2	no	—
479	#103	—	2	2	no	—
480	#103	—	4	1	no	—
481	#103	—	4	1	no	—
482	#102	—	2	2	no	—
483	#102	—	2	2	no	—
484	#102	—	2	2	no	—
485	C₂²⋊C₈	—	2	2	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	D₄×C₇₉	1	1	yes	characteristic
498	#95	D₄×C₇₉	1	1	yes	characteristic
499	C₂⁴	—	2	1	no	—
500	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
501	#41	—	2	8	no	—
502	#41	—	4	4	no	—
503	#41	—	4	4	no	—
504	#41	—	4	4	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
524	C₂×D₄	#41×C₇₉	1	2	yes	—
525	C₂×D₄	#41×C₇₉	1	2	yes	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	8	1	no	—
545	C₂²×C₄	—	8	1	no	—
546	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
551	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
552	C₂²×C₄	#41×C₇₉	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
554	Q₁₆	—	4	4	no	—
555	SD₁₆	—	4	4	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	4	4	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	4	1	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	8	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	4	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	#121×C₇₉	1	2	yes	—
608	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	2	2	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	2	no	—
619	D₄	—	2	2	no	—
620	D₄	—	4	8	no	—
621	D₄	#123×C₇₉	1	4	yes	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	4	8	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	—	8	4	no	—
663	C₂×C₄	#121×C₇₉	1	2	yes	—
664	C₂×C₄	#135×C₇₉	1	2	yes	—
665	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
666	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
667	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
668	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
669	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
670	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	2	no	—
689	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
690	C₂²	#546×C₇₉	1	1	yes	characteristic
691	C₂²	#546×C₇₉	1	1	yes	characteristic
692	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
693	C₂²	#575×C₇₉	1	1	yes	characteristic
694	C₂²	#577×C₇₉	1	1	yes	characteristic
695	C₂²	#578×C₇₉	1	1	yes	characteristic
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	2	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
709	C₄	#534×C₇₉	1	1	yes	characteristic
710	C₄	#551×C₇₉	1	1	yes	characteristic
711	C₄	#551×C₇₉	1	1	yes	characteristic
712	C₂	—	4	2	no	—
713	C₂	—	4	4	no	—
714	C₂	C₇₉×#2412	1	1	yes	characteristic
715	C₂	C₇₉×#3035	1	1	yes	characteristic
716	C₂	C₇₉×#3046	1	1	yes	characteristic
717	C₂	C₇₉×#3296	1	1	yes	characteristic
718	C₂	C₇₉×#3302	1	1	yes	characteristic
719	C₂	C₇₉×#3311	1	1	yes	characteristic
720	C₂	C₇₉×#3315	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂²×#41×C₇₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₄×C₂²⋊C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇₉×#2499	C₂	semidirect
5. C₇₉×#2074	C₂	semidirect
6. C₇₉×#2072	C₂	semidirect
7. C₇₉×#2056	C₂	semidirect
8. C₇₉×#2056	C₂	semidirect
9. C₇₉×#1892	C₂	semidirect
10. C₇₉×#1877	C₂	semidirect
11. C₇₉×#1877	C₂	semidirect
12. C₇₉×#1850	C₂	semidirect
13. C₇₉×#1825	C₂	semidirect
14. C₇₉×#1804	C₂	semidirect
15. C₇₉×#1802	C₂	semidirect
351. #24536	C₇₉	direct (N × H)
363. #2499	C₂×C₇₉	semidirect
365. #2074	C₂×C₇₉	semidirect
366. #2072	C₂×C₇₉	semidirect
367. #2056	C₂×C₇₉	semidirect
368. #2056	C₂×C₇₉	semidirect
369. #1892	C₂×C₇₉	semidirect
370. #1877	C₂×C₇₉	semidirect
371. #1877	C₂×C₇₉	semidirect
372. #1850	C₂×C₇₉	semidirect
373. #1825	C₂×C₇₉	semidirect
374. #1804	C₂×C₇₉	semidirect
375. #1802	C₂×C₇₉	semidirect
376. C₇₉	#24536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#452×C₇₉	2
C₂×#416×C₇₉	2
C₇₉×#2499	2
C₇₉×#2339	2
C₇₉×#2074	2
C₇₉×#2072	2
C₇₉×#2056	2
C₇₉×#1892	2
C₇₉×#1877	2
C₇₉×#1850	2
C₇₉×#1825	2
C₇₉×#1804	2
C₇₉×#1802	2
#24536	79

Subgroups — C79×#24536 #34136225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24536 #34136225