Subgroups — C₇₉×#26792 #34138481

Order 20224.

782 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#485×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#479×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2489	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2362	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2036	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#2001	C₂	1	1	yes	maximal, characteristic
9	C₇₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1923	C₂	1	1	yes	maximal, characteristic
13	C₇₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1854	C₂	1	1	yes	maximal, characteristic
15	C₄×#107×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
22	#485×C₇₉	—	2	4	no	—
23	#479×C₇₉	—	2	4	no	—
24	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×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×#103×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
39	#400×C₇₉	—	2	1	no	—
40	#397×C₇₉	—	2	1	no	—
41	#391×C₇₉	C₂²	1	1	yes	characteristic
42	#391×C₇₉	C₂²	1	1	yes	characteristic
43	#391×C₇₉	C₂²	1	1	yes	characteristic
44	#389×C₇₉	C₂²	1	1	yes	characteristic
45	#388×C₇₉	—	2	1	no	—
46	#388×C₇₉	—	2	1	no	—
47	#388×C₇₉	—	2	1	no	—
48	#387×C₇₉	—	2	1	no	—
49	#382×C₇₉	—	2	1	no	—
50	#380×C₇₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
52	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×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	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₇₉	—	2	2	no	—
65	C₂×Q₁₆×C₇₉	—	2	2	no	—
66	C₂×Q₁₆×C₇₉	—	4	1	no	—
67	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
71	#125×C₇₉	—	2	2	no	—
72	#125×C₇₉	—	4	1	no	—
73	C₂²⋊Q₈×C₇₉	—	2	2	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	C₂²⋊Q₈×C₇₉	—	2	2	no	—
76	C₂²⋊Q₈×C₇₉	—	4	1	no	—
77	C₄×Q₈×C₇₉	—	2	2	no	—
78	C₄×Q₈×C₇₉	—	4	1	no	—
79	#117×C₇₉	—	2	2	no	—
80	#117×C₇₉	—	4	1	no	—
81	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₇₉	—	2	1	no	—
100	C₂×C₄²×C₇₉	—	2	1	no	—
101	C₂×C₄²×C₇₉	—	2	1	no	—
102	C₂×C₄²×C₇₉	—	2	1	no	—
103	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
105	#107×C₇₉	—	2	2	no	—
106	#107×C₇₉	—	4	1	no	—
107	#107×C₇₉	D₄	1	4	yes	—
108	#106×C₇₉	—	2	2	no	—
109	#106×C₇₉	—	2	2	no	—
110	C₄⋊C₈×C₇₉	—	2	2	no	—
111	#103×C₇₉	—	2	2	no	—
112	#103×C₇₉	—	2	2	no	—
113	#103×C₇₉	—	2	2	no	—
114	#103×C₇₉	—	2	2	no	—
115	#103×C₇₉	—	2	2	no	—
116	#103×C₇₉	—	2	2	no	—
117	C₂²⋊C₈×C₇₉	—	2	2	no	—
118	C₂²⋊C₈×C₇₉	—	2	2	no	—
119	C₄×C₈×C₇₉	—	2	2	no	—
120	#95×C₇₉	—	2	1	no	—
121	#95×C₇₉	—	2	1	no	—
122	#95×C₇₉	—	2	1	no	—
123	#95×C₇₉	—	2	1	no	—
124	#95×C₇₉	—	2	1	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	D₄	1	1	yes	characteristic
131	#95×C₇₉	D₄	1	1	yes	characteristic
132	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₇₉	—	2	1	no	—
134	C₂×Q₈×C₇₉	—	2	1	no	—
135	C₂×Q₈×C₇₉	—	2	1	no	—
136	C₂×Q₈×C₇₉	—	2	1	no	—
137	C₂×Q₈×C₇₉	—	2	1	no	—
138	C₂×Q₈×C₇₉	—	2	1	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	—	2	1	no	—
141	C₂×Q₈×C₇₉	—	2	1	no	—
142	C₂×Q₈×C₇₉	—	2	1	no	—
143	C₂×Q₈×C₇₉	—	2	1	no	—
144	C₂×Q₈×C₇₉	#41	1	2	yes	—
145	C₂²×C₄×C₇₉	—	2	1	no	—
146	C₂²×C₄×C₇₉	—	2	1	no	—
147	C₂²×C₄×C₇₉	—	2	1	no	—
148	C₂²×C₄×C₇₉	—	2	1	no	—
149	C₂²×C₄×C₇₉	—	2	1	no	—
150	C₂²×C₄×C₇₉	—	2	1	no	—
151	C₂²×C₄×C₇₉	—	2	1	no	—
152	C₂²×C₄×C₇₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
165	Q₁₆×C₇₉	—	4	4	no	—
166	C₂×C₈×C₇₉	—	2	1	no	—
167	C₂×C₈×C₇₉	—	2	1	no	—
168	C₂×C₈×C₇₉	—	2	1	no	—
169	C₂×C₈×C₇₉	—	2	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	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₇₉	#41	1	2	yes	—
178	C₄⋊C₄×C₇₉	—	2	4	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	1	no	—
185	C₄⋊C₄×C₇₉	—	2	1	no	—
186	C₄⋊C₄×C₇₉	—	2	1	no	—
187	C₄⋊C₄×C₇₉	—	2	1	no	—
188	C₄⋊C₄×C₇₉	—	4	2	no	—
189	C₄⋊C₄×C₇₉	—	4	2	no	—
190	C₄⋊C₄×C₇₉	—	4	2	no	—
191	C₄⋊C₄×C₇₉	—	4	2	no	—
192	C₄⋊C₄×C₇₉	—	4	2	no	—
193	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
195	C₄⋊C₄×C₇₉	#41	1	2	yes	—
196	C₂²⋊C₄×C₇₉	—	2	4	no	—
197	C₂²⋊C₄×C₇₉	—	2	2	no	—
198	C₂²⋊C₄×C₇₉	—	4	1	no	—
199	C₂²⋊C₄×C₇₉	—	4	2	no	—
200	C₂²⋊C₄×C₇₉	—	4	2	no	—
201	C₂²⋊C₄×C₇₉	—	4	2	no	—
202	C₄²×C₇₉	—	2	1	no	—
203	C₄²×C₇₉	—	2	1	no	—
204	C₄²×C₇₉	—	2	1	no	—
205	C₄²×C₇₉	—	2	1	no	—
206	C₄²×C₇₉	—	4	2	no	—
207	C₄²×C₇₉	—	4	2	no	—
208	C₄²×C₇₉	—	4	2	no	—
209	C₄²×C₇₉	—	4	2	no	—
210	C₂³×C₇₉	—	2	1	no	—
211	C₂³×C₇₉	—	2	1	no	—
212	C₂³×C₇₉	—	2	1	no	—
213	C₂³×C₇₉	—	2	1	no	—
214	C₂³×C₇₉	—	2	1	no	—
215	C₂³×C₇₉	—	2	1	no	—
216	C₂³×C₇₉	—	2	1	no	—
217	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₇₉	—	2	2	no	—
219	Q₈×C₇₉	—	2	2	no	—
220	Q₈×C₇₉	—	4	1	no	—
221	Q₈×C₇₉	—	4	1	no	—
222	Q₈×C₇₉	—	4	1	no	—
223	Q₈×C₇₉	—	4	1	no	—
224	Q₈×C₇₉	—	4	1	no	—
225	Q₈×C₇₉	—	4	1	no	—
226	C₂×C₄×C₇₉	—	2	1	no	—
227	C₂×C₄×C₇₉	—	2	1	no	—
228	C₂×C₄×C₇₉	—	2	2	no	—
229	C₂×C₄×C₇₉	—	2	2	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	2	no	—
234	C₂×C₄×C₇₉	—	2	1	no	—
235	C₂×C₄×C₇₉	—	2	2	no	—
236	C₂×C₄×C₇₉	—	2	1	no	—
237	C₂×C₄×C₇₉	—	2	1	no	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	1	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	1	no	—
244	C₂×C₄×C₇₉	—	4	1	no	—
245	C₂×C₄×C₇₉	—	4	1	no	—
246	C₂×C₄×C₇₉	—	4	1	no	—
247	C₂×C₄×C₇₉	—	4	1	no	—
248	C₂×C₄×C₇₉	—	4	1	no	—
249	C₂×C₄×C₇₉	—	4	1	no	—
250	C₂×C₄×C₇₉	—	4	1	no	—
251	C₂×C₄×C₇₉	—	4	1	no	—
252	C₂×C₄×C₇₉	—	4	1	no	—
253	C₂×C₄×C₇₉	—	4	1	no	—
254	C₂×C₄×C₇₉	—	4	1	no	—
255	C₂×C₄×C₇₉	—	4	1	no	—
256	C₂×C₄×C₇₉	—	4	1	no	—
257	C₂×C₄×C₇₉	—	4	1	no	—
258	C₂×C₄×C₇₉	—	4	1	no	—
259	C₂×C₄×C₇₉	—	4	1	no	—
260	C₂×C₄×C₇₉	—	4	1	no	—
261	C₂×C₄×C₇₉	—	4	1	no	—
262	C₂×C₄×C₇₉	—	4	1	no	—
263	C₂×C₄×C₇₉	—	4	1	no	—
264	C₂×C₄×C₇₉	—	4	1	no	—
265	C₂×C₄×C₇₉	—	4	1	no	—
266	C₂×C₄×C₇₉	—	4	1	no	—
267	C₂×C₄×C₇₉	—	4	1	no	—
268	C₂×C₄×C₇₉	#135	1	2	yes	—
269	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
275	C₈×C₇₉	—	2	2	no	—
276	C₈×C₇₉	—	2	2	no	—
277	C₈×C₇₉	—	4	1	no	—
278	C₈×C₇₉	—	4	1	no	—
279	C₂²×C₇₉	—	4	1	no	—
280	C₂²×C₇₉	—	4	1	no	—
281	C₂²×C₇₉	—	4	1	no	—
282	C₂²×C₇₉	—	4	1	no	—
283	C₂²×C₇₉	—	4	1	no	—
284	C₂²×C₇₉	—	4	1	no	—
285	C₂²×C₇₉	—	4	1	no	—
286	C₂²×C₇₉	#525	1	1	yes	characteristic
287	C₂²×C₇₉	D₄²	1	1	yes	characteristic
288	C₂²×C₇₉	#547	1	1	yes	characteristic
289	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
290	C₂²×C₇₉	#575	1	1	yes	characteristic
291	C₂²×C₇₉	#578	1	1	yes	characteristic
292	C₂²×C₇₉	#578	1	1	yes	characteristic
293	C₄×C₇₉	—	2	2	no	—
294	C₄×C₇₉	—	4	1	no	—
295	C₄×C₇₉	—	4	2	no	—
296	C₄×C₇₉	—	4	1	no	—
297	C₄×C₇₉	—	4	2	no	—
298	C₄×C₇₉	—	4	1	no	—
299	C₄×C₇₉	—	4	1	no	—
300	C₄×C₇₉	—	4	2	no	—
301	C₄×C₇₉	—	4	2	no	—
302	C₄×C₇₉	—	8	1	no	—
303	C₄×C₇₉	—	8	1	no	—
304	C₄×C₇₉	—	8	1	no	—
305	C₄×C₇₉	—	8	1	no	—
306	C₄×C₇₉	#532	1	1	yes	characteristic
307	C₄×C₇₉	#542	1	1	yes	characteristic
308	C₄×C₇₉	#548	1	1	yes	characteristic
309	C₄×C₇₉	#551	1	1	yes	characteristic
310	#26792	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂×C₇₉	—	8	1	no	—
312	C₂×C₇₉	#2461	1	1	yes	characteristic
313	C₂×C₇₉	#3102	1	1	yes	characteristic
314	C₂×C₇₉	#3127	1	1	yes	characteristic
315	C₂×C₇₉	#3277	1	1	yes	characteristic
316	C₂×C₇₉	#3283	1	1	yes	characteristic
317	C₂×C₇₉	#3336	1	1	yes	characteristic
318	C₂×C₇₉	#3349	1	1	yes	characteristic
319	C₂×#485	C₂×C₇₉	1	1	yes	characteristic
320	C₂×#479	C₂×C₇₉	1	1	yes	characteristic, complemented
321	#2489	C₂×C₇₉	1	1	yes	characteristic
322	#2362	C₂×C₇₉	1	1	yes	characteristic
323	#2068	C₂×C₇₉	1	1	yes	characteristic, complemented
324	#2059	C₂×C₇₉	1	1	yes	characteristic, complemented
325	#2036	C₂×C₇₉	1	1	yes	characteristic
326	#2001	C₂×C₇₉	1	1	yes	characteristic
327	#1969	C₂×C₇₉	1	1	yes	characteristic, complemented
328	#1927	C₂×C₇₉	1	1	yes	characteristic, complemented
329	#1927	C₂×C₇₉	1	1	yes	characteristic, complemented
330	#1923	C₂×C₇₉	1	1	yes	characteristic
331	#1878	C₂×C₇₉	1	1	yes	characteristic, complemented
332	#1854	C₂×C₇₉	1	1	yes	characteristic
333	C₄×#107	C₂×C₇₉	1	1	yes	characteristic, complemented
334	C₇₉	#26792	1	1	yes	characteristic, direct product factor, Sylow
335	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
336	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
337	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
338	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
339	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
340	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
341	#485	—	2	4	no	—
342	#479	—	2	4	no	—
343	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
344	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
345	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
346	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
347	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
349	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
350	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
351	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
352	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
353	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
354	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
355	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
357	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
358	#400	—	2	1	no	—
359	#397	—	2	1	no	—
360	#391	C₂²×C₇₉	1	1	yes	characteristic
361	#391	C₂²×C₇₉	1	1	yes	characteristic
362	#391	C₂²×C₇₉	1	1	yes	characteristic
363	#389	C₂²×C₇₉	1	1	yes	characteristic
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#387	—	2	1	no	—
368	#382	—	2	1	no	—
369	#380	C₂²×C₇₉	1	1	yes	characteristic
370	C₄×C₄⋊C₄	—	2	1	no	—
371	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
373	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
374	#340	C₂²×C₇₉	1	1	yes	characteristic
375	#340	C₂²×C₇₉	1	1	yes	characteristic
376	#340	C₂²×C₇₉	1	1	yes	characteristic
377	#340	C₂²×C₇₉	1	1	yes	characteristic
378	#336	C₂²×C₇₉	1	1	yes	characteristic
379	#336	C₂²×C₇₉	1	1	yes	characteristic
380	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
383	C₂×Q₁₆	—	2	2	no	—
384	C₂×Q₁₆	—	2	2	no	—
385	C₂×Q₁₆	—	4	1	no	—
386	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
390	#125	—	2	2	no	—
391	#125	—	4	1	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	4	1	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	4	1	no	—
398	#117	—	2	2	no	—
399	#117	—	4	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
424	#107	—	2	2	no	—
425	#107	—	4	1	no	—
426	#107	D₄×C₇₉	1	4	yes	—
427	#106	—	2	2	no	—
428	#106	—	2	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	#103	—	2	2	no	—
431	#103	—	2	2	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	C₂²⋊C₈	—	2	2	no	—
437	C₂²⋊C₈	—	2	2	no	—
438	C₄×C₈	—	2	2	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	D₄×C₇₉	1	1	yes	characteristic
450	#95	D₄×C₇₉	1	1	yes	characteristic
451	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	#41×C₇₉	1	2	yes	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
484	Q₁₆	—	4	4	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
496	C₂×C₈	#41×C₇₉	1	2	yes	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
513	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
514	C₄⋊C₄	#41×C₇₉	1	2	yes	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	4	2	no	—
526	C₄²	—	4	2	no	—
527	C₄²	—	4	2	no	—
528	C₄²	—	4	2	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	#135×C₇₉	1	2	yes	—
588	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
590	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
592	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
593	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	2	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	#525×C₇₉	1	1	yes	characteristic
606	C₂²	D₄²×C₇₉	1	1	yes	characteristic
607	C₂²	#547×C₇₉	1	1	yes	characteristic
608	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
609	C₂²	#575×C₇₉	1	1	yes	characteristic
610	C₂²	#578×C₇₉	1	1	yes	characteristic
611	C₂²	#578×C₇₉	1	1	yes	characteristic
612	C₄	—	2	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	#532×C₇₉	1	1	yes	characteristic
626	C₄	#542×C₇₉	1	1	yes	characteristic
627	C₄	#548×C₇₉	1	1	yes	characteristic
628	C₄	#551×C₇₉	1	1	yes	characteristic
629	C₂	—	8	1	no	—
630	C₂	C₇₉×#2461	1	1	yes	characteristic
631	C₂	C₇₉×#3102	1	1	yes	characteristic
632	C₂	C₇₉×#3127	1	1	yes	characteristic
633	C₂	C₇₉×#3277	1	1	yes	characteristic
634	C₂	C₇₉×#3283	1	1	yes	characteristic
635	C₂	C₇₉×#3336	1	1	yes	characteristic
636	C₂	C₇₉×#3349	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂⁴×C₇₉	C₂×D₄
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
2. C₂×#479×C₇₉	C₂	semidirect
5. C₇₉×#2068	C₂	semidirect
6. C₇₉×#2059	C₂	semidirect
9. C₇₉×#1969	C₂	semidirect
10. C₇₉×#1927	C₂	semidirect
11. C₇₉×#1927	C₂	semidirect
13. C₇₉×#1878	C₂	semidirect
15. C₄×#107×C₇₉	C₂	semidirect
310. #26792	C₇₉	direct (N × H)
320. C₂×#479	C₂×C₇₉	semidirect
323. #2068	C₂×C₇₉	semidirect
324. #2059	C₂×C₇₉	semidirect
327. #1969	C₂×C₇₉	semidirect
328. #1927	C₂×C₇₉	semidirect
329. #1927	C₂×C₇₉	semidirect
331. #1878	C₂×C₇₉	semidirect
333. C₄×#107	C₂×C₇₉	semidirect
334. C₇₉	#26792	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×#485×C₇₉	2
C₂×#479×C₇₉	2
C₇₉×#2489	2
C₇₉×#2362	2
C₇₉×#2068	2
C₇₉×#2059	2
C₇₉×#2036	2
C₇₉×#2001	2
C₇₉×#1969	2
C₇₉×#1927	2
C₇₉×#1923	2
C₇₉×#1878	2
C₇₉×#1854	2
C₄×#107×C₇₉	2
#26792	79

Subgroups — C79×#26792 #34138481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#26792 #34138481