Subgroups — #34306326

Order 20224.

980 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098641	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098635	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098590	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098587	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764124	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764119	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763585	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763585	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763585	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763580	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763554	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763384	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763380	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763257	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#2290	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂²×#11929608	C₂²	1	1	yes	characteristic
18	C₂²×#11929608	C₂²	1	1	yes	characteristic
19	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	#19098641	—	2	4	no	—
21	#19098635	—	2	4	no	—
22	#19098590	—	2	4	no	—
23	#19098587	—	2	4	no	—
24	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂×#14579072	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
42	#19098318	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	#19098318	C₂²	1	1	yes	characteristic
45	#19098318	C₂²	1	1	yes	characteristic
46	#19098318	C₂²	1	1	yes	characteristic
47	#19098318	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
51	#388×C₇₉	C₄	1	1	yes	characteristic
52	#388×C₇₉	C₄	1	1	yes	characteristic
53	#387×C₇₉	C₄	1	1	yes	characteristic
54	#387×C₇₉	C₄	1	1	yes	characteristic
55	#386×C₇₉	C₄	1	1	yes	characteristic
56	#386×C₇₉	C₄	1	1	yes	characteristic
57	#385×C₇₉	C₄	1	1	yes	characteristic
58	#385×C₇₉	C₄	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
62	#376×C₇₉	C₂²	1	1	yes	characteristic
63	C₂×#11929608	—	2	2	no	—
64	C₂×#11929608	—	2	2	no	—
65	C₂×#11929608	—	2	2	no	—
66	C₂×#11929608	—	2	2	no	—
67	C₂×#11929608	—	2	2	no	—
68	C₂×#11929608	—	2	2	no	—
69	C₂×#11929608	—	4	1	no	—
70	C₂×#11929608	—	4	1	no	—
71	C₂×#11929608	—	4	1	no	—
72	C₂²×C₇₉⋊C₈	—	2	2	no	—
73	C₂²×C₇₉⋊C₈	—	2	2	no	—
74	C₂²×C₇₉⋊C₈	—	4	1	no	—
75	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
84	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
85	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
86	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
87	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
88	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
89	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
90	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
91	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
92	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
93	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
94	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	complemented
95	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
96	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
97	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
98	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
99	#14579072	—	2	2	no	—
100	C₄×C₇₉⋊C₈	—	2	2	no	—
101	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₇₉	D₄	1	4	yes	—
107	C₄×D₄×C₇₉	Q₈	1	4	yes	—
108	#117×C₇₉	—	2	2	no	—
109	#117×C₇₉	—	2	2	no	—
110	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄²×C₇₉	—	2	2	no	—
124	C₂×C₄²×C₇₉	—	2	2	no	—
125	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
132	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
133	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
134	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
135	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
136	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
137	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
138	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
139	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
140	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
141	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
142	#11929608	—	4	4	no	—
143	#11929608	—	4	4	no	—
144	#11929608	—	4	4	no	—
145	C₂×C₇₉⋊C₈	—	2	1	no	—
146	C₂×C₇₉⋊C₈	—	2	1	no	—
147	C₂×C₇₉⋊C₈	—	2	1	no	—
148	C₂×C₇₉⋊C₈	—	2	1	no	—
149	C₂×C₇₉⋊C₈	—	2	1	no	—
150	C₂×C₇₉⋊C₈	—	2	1	no	—
151	C₂×C₇₉⋊C₈	—	2	1	no	—
152	C₂×C₇₉⋊C₈	—	2	1	no	—
153	C₂×C₇₉⋊C₈	—	2	1	no	—
154	C₂×C₇₉⋊C₈	—	2	1	no	—
155	C₂×C₇₉⋊C₈	—	2	1	no	—
156	C₂×C₇₉⋊C₈	—	2	1	no	—
157	C₂×C₇₉⋊C₈	—	2	1	no	—
158	C₂×C₇₉⋊C₈	—	2	1	no	—
159	C₂×C₇₉⋊C₈	—	2	1	no	—
160	C₂×C₇₉⋊C₈	—	2	1	no	—
161	C₂×C₇₉⋊C₈	—	2	1	no	—
162	C₂×C₇₉⋊C₈	—	2	1	no	—
163	C₂×C₇₉⋊C₈	—	2	1	no	—
164	C₂×C₇₉⋊C₈	—	2	1	no	—
165	C₂×C₇₉⋊C₈	—	2	1	no	—
166	C₂×C₇₉⋊C₈	—	2	1	no	—
167	C₂×C₇₉⋊C₈	—	4	4	no	—
168	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
169	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
170	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
171	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
172	C₂×D₄×C₇₉	—	4	1	no	—
173	C₂×D₄×C₇₉	—	4	1	no	—
174	C₂×D₄×C₇₉	C₄⋊C₄	1	4	yes	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	2	1	no	—
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	1	no	—
180	C₂²×C₄×C₇₉	—	2	1	no	—
181	C₂²×C₄×C₇₉	—	2	1	no	—
182	C₂²×C₄×C₇₉	—	2	1	no	—
183	C₂²×C₄×C₇₉	—	2	2	no	—
184	C₂²×C₄×C₇₉	—	2	2	no	—
185	C₂²×C₄×C₇₉	—	2	2	no	—
186	C₂²×C₄×C₇₉	—	4	1	no	—
187	C₂²×C₄×C₇₉	—	4	1	no	—
188	C₂²×C₄×C₇₉	—	4	1	no	—
189	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
204	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
205	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
206	C₄⋊C₄×C₇₉	—	2	2	no	—
207	C₄⋊C₄×C₇₉	—	2	2	no	—
208	C₄⋊C₄×C₇₉	—	2	2	no	—
209	C₄⋊C₄×C₇₉	—	4	1	no	—
210	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
211	C₂²⋊C₄×C₇₉	—	2	2	no	—
212	C₂²⋊C₄×C₇₉	—	2	2	no	—
213	C₂²⋊C₄×C₇₉	—	2	2	no	—
214	C₂²⋊C₄×C₇₉	—	4	1	no	—
215	C₂²⋊C₄×C₇₉	—	4	1	no	—
216	C₂²⋊C₄×C₇₉	—	4	1	no	—
217	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
218	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
219	C₄²×C₇₉	—	2	2	no	—
220	C₄²×C₇₉	—	2	2	no	—
221	C₄²×C₇₉	—	2	1	no	—
222	C₄²×C₇₉	—	2	1	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	2	yes	—
228	C₄²×C₇₉	C₂×D₄	1	2	yes	—
229	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
230	C₄²×C₇₉	#41	1	2	yes	—
231	C₂³×C₇₉	—	2	1	no	—
232	C₂³×C₇₉	—	2	1	no	—
233	C₂³×C₇₉	—	2	1	no	—
234	C₂³×C₇₉	—	2	1	no	—
235	C₂³×C₇₉	—	2	1	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	—	2	1	no	—
243	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
244	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
245	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
246	D₄×C₇₉	—	4	4	no	—
247	C₂×C₄×C₇₉	—	2	1	no	—
248	C₂×C₄×C₇₉	—	2	1	no	—
249	C₂×C₄×C₇₉	—	2	1	no	—
250	C₂×C₄×C₇₉	—	2	1	no	—
251	C₂×C₄×C₇₉	—	2	1	no	—
252	C₂×C₄×C₇₉	—	2	1	no	—
253	C₂×C₄×C₇₉	—	2	1	no	—
254	C₂×C₄×C₇₉	—	2	1	no	—
255	C₂×C₄×C₇₉	—	2	1	no	—
256	C₂×C₄×C₇₉	—	2	1	no	—
257	C₂×C₄×C₇₉	—	2	1	no	—
258	C₂×C₄×C₇₉	—	2	1	no	—
259	C₂×C₄×C₇₉	—	2	1	no	—
260	C₂×C₄×C₇₉	—	2	1	no	—
261	C₂×C₄×C₇₉	—	2	2	no	—
262	C₂×C₄×C₇₉	—	2	2	no	—
263	C₂×C₄×C₇₉	—	2	2	no	—
264	C₂×C₄×C₇₉	—	2	2	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	1	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	—	2	1	no	—
280	C₂×C₄×C₇₉	—	2	1	no	—
281	C₂×C₄×C₇₉	—	2	1	no	—
282	C₂×C₄×C₇₉	—	2	1	no	—
283	C₂×C₄×C₇₉	—	2	1	no	—
284	C₂×C₄×C₇₉	—	4	4	no	—
285	C₂×C₄×C₇₉	—	4	4	no	—
286	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
287	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
288	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
289	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
290	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
291	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
292	C₂×C₄×C₇₉	#131	1	2	yes	—
293	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
296	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
299	C₇₉⋊C₈	—	2	2	no	—
300	C₇₉⋊C₈	—	2	2	no	—
301	C₇₉⋊C₈	—	4	1	no	—
302	C₇₉⋊C₈	—	4	1	no	—
303	C₇₉⋊C₈	—	4	1	no	—
304	C₇₉⋊C₈	—	4	1	no	—
305	C₇₉⋊C₈	—	4	1	no	—
306	C₇₉⋊C₈	—	4	1	no	—
307	C₂²×C₇₉	—	2	2	no	—
308	C₂²×C₇₉	—	2	2	no	—
309	C₂²×C₇₉	—	2	2	no	—
310	C₂²×C₇₉	—	2	2	no	—
311	C₂²×C₇₉	—	2	2	no	—
312	C₂²×C₇₉	—	2	2	no	—
313	C₂²×C₇₉	—	4	1	no	—
314	C₂²×C₇₉	—	4	1	no	—
315	C₂²×C₇₉	—	4	1	no	—
316	C₂²×C₇₉	—	4	1	no	—
317	C₂²×C₇₉	—	4	1	no	—
318	C₂²×C₇₉	—	4	1	no	—
319	C₂²×C₇₉	—	4	1	no	—
320	C₂²×C₇₉	—	4	1	no	—
321	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
322	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
323	C₂²×C₇₉	#520	1	1	yes	characteristic
324	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
325	C₂²×C₇₉	#568	1	1	yes	characteristic
326	C₂²×C₇₉	#568	1	1	yes	characteristic
327	C₂²×C₇₉	#568	1	1	yes	characteristic
328	C₄×C₇₉	—	2	2	no	—
329	C₄×C₇₉	—	2	2	no	—
330	C₄×C₇₉	—	2	2	no	—
331	C₄×C₇₉	—	2	2	no	—
332	C₄×C₇₉	—	2	2	no	—
333	C₄×C₇₉	—	2	2	no	—
334	C₄×C₇₉	—	2	2	no	—
335	C₄×C₇₉	—	4	1	no	—
336	C₄×C₇₉	—	4	1	no	—
337	C₄×C₇₉	—	4	1	no	—
338	C₄×C₇₉	—	4	1	no	—
339	C₄×C₇₉	—	4	1	no	—
340	C₄×C₇₉	D₄²	1	1	yes	characteristic
341	C₄×C₇₉	#547	1	1	yes	characteristic
342	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
343	C₄×C₇₉	#554	1	1	yes	characteristic
344	#22649	—	79	1	no	maximal, Sylow
345	C₂×C₇₉	—	4	2	no	—
346	C₂×C₇₉	—	4	2	no	—
347	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
348	C₂×C₇₉	#2905	1	1	yes	characteristic
349	C₂×C₇₉	#2906	1	1	yes	characteristic
350	C₂×C₇₉	#2930	1	1	yes	characteristic
351	C₂×C₇₉	#2933	1	1	yes	characteristic
352	C₂×C₇₉	#2993	1	1	yes	characteristic
353	C₂×C₇₉	#2995	1	1	yes	characteristic
354	C₂×#436	—	79	1	no	—
355	C₂×#435	—	79	1	no	—
356	C₂×#424	—	79	1	no	—
357	C₂×#423	—	79	1	no	—
358	#2290	D₇₉	1	1	yes	characteristic
359	#1940	—	79	1	no	—
360	#1939	—	79	1	no	—
361	#1851	—	79	1	no	—
362	#1851	—	79	1	no	—
363	#1851	—	79	1	no	—
364	#1850	—	79	1	no	—
365	#1843	—	79	1	no	—
366	#1798	—	79	1	no	—
367	#1797	—	79	1	no	—
368	#1768	—	79	1	no	—
369	C₇₉	#22649	1	1	yes	characteristic, complemented, Sylow
370	C₂²×M₁₆	—	79	1	no	—
371	C₂²×M₁₆	—	79	1	no	—
372	C₂²×M₁₆	—	79	1	no	—
373	C₂³×C₈	—	79	1	no	—
374	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
375	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
376	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
377	#436	—	158	4	no	—
378	#435	—	158	4	no	—
379	#424	—	158	4	no	—
380	#423	—	158	4	no	—
381	C₂×C₄⋊C₈	—	79	1	no	—
382	C₂×C₄⋊C₈	—	79	1	no	—
383	C₂×C₄⋊C₈	—	79	1	no	—
384	C₂×C₄⋊C₈	—	79	1	no	—
385	C₂×C₄⋊C₈	—	79	1	no	—
386	C₂×C₄⋊C₈	—	79	1	no	—
387	C₂×C₄⋊C₈	—	79	1	no	—
388	C₂×C₄⋊C₈	—	79	1	no	—
389	C₂×C₄⋊C₈	—	79	1	no	—
390	C₂×C₄⋊C₈	—	79	1	no	—
391	C₂×C₄⋊C₈	—	79	1	no	—
392	C₂×C₄⋊C₈	—	79	1	no	—
393	C₂×C₂²⋊C₈	—	79	1	no	—
394	C₂×C₂²⋊C₈	—	79	1	no	—
395	C₂×C₂²⋊C₈	—	79	1	no	—
396	C₂×C₂²⋊C₈	—	79	1	no	—
397	C₂×#97	—	79	1	no	—
398	C₂×C₄×C₈	—	79	1	no	—
399	#388	Dic₇₉	1	1	yes	characteristic
400	#388	Dic₇₉	1	1	yes	characteristic
401	#387	Dic₇₉	1	1	yes	characteristic
402	#387	Dic₇₉	1	1	yes	characteristic
403	#386	Dic₇₉	1	1	yes	characteristic
404	#386	Dic₇₉	1	1	yes	characteristic
405	#385	Dic₇₉	1	1	yes	characteristic
406	#385	Dic₇₉	1	1	yes	characteristic
407	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
408	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
409	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
410	#376	C₂×D₇₉	1	1	yes	characteristic
411	#336	—	79	1	no	—
412	#336	—	79	1	no	—
413	#336	—	79	1	no	—
414	#336	—	79	1	no	—
415	#336	—	79	1	no	—
416	#336	—	79	1	no	—
417	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
418	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
419	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
420	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
421	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
422	C₂×M₁₆	—	316	1	no	—
423	C₂×M₁₆	—	316	1	no	—
424	C₂×M₁₆	—	316	1	no	—
425	C₂×M₁₆	—	158	2	no	—
426	C₂×M₁₆	—	158	2	no	—
427	C₂×M₁₆	—	158	2	no	—
428	C₂×M₁₆	—	158	2	no	—
429	C₂×M₁₆	—	158	2	no	—
430	C₂×M₁₆	—	158	2	no	—
431	C₂²×C₈	—	316	1	no	—
432	C₂²×C₈	—	79	1	no	—
433	C₂²×C₈	—	79	1	no	—
434	C₂²×C₈	—	79	1	no	—
435	C₂²×C₈	—	79	1	no	—
436	C₂²×C₈	—	79	1	no	—
437	C₂²×C₈	—	79	1	no	—
438	C₂²×C₈	—	79	1	no	—
439	C₂²×C₈	—	79	1	no	—
440	C₂²×C₈	—	158	2	no	—
441	C₂²×C₈	—	158	2	no	—
442	C₄×D₄	Dic₁₅₈	1	4	yes	—
443	C₄×D₄	D₃₁₆	1	4	yes	—
444	#117	—	2	2	no	—
445	#117	—	2	2	no	—
446	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
459	C₂×C₄²	—	2	2	no	—
460	C₂×C₄²	—	2	2	no	—
461	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
462	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
463	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
464	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
465	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
466	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
467	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
468	C₄⋊C₈	—	316	1	no	—
469	C₄⋊C₈	—	316	1	no	—
470	C₄⋊C₈	—	79	4	no	—
471	C₄⋊C₈	—	158	2	no	—
472	C₄⋊C₈	—	158	2	no	—
473	C₄⋊C₈	—	158	2	no	—
474	C₄⋊C₈	—	158	2	no	—
475	C₄⋊C₈	—	158	2	no	—
476	C₄⋊C₈	—	158	2	no	—
477	C₄⋊C₈	—	158	2	no	—
478	C₄⋊C₈	—	158	2	no	—
479	C₄⋊C₈	—	158	2	no	—
480	C₂²⋊C₈	—	158	2	no	—
481	C₂²⋊C₈	—	158	2	no	—
482	C₂²⋊C₈	—	158	2	no	—
483	C₂²⋊C₈	—	158	2	no	—
484	#97	—	158	2	no	—
485	C₄×C₈	—	158	2	no	—
486	#95	C₂×Dic₇₉	1	1	yes	characteristic
487	#95	C₂×Dic₇₉	1	1	yes	characteristic
488	#95	C₂×Dic₇₉	1	1	yes	characteristic
489	#95	C₂×Dic₇₉	1	1	yes	characteristic
490	#95	C₂×Dic₇₉	1	1	yes	characteristic
491	#95	C₂×Dic₇₉	1	1	yes	characteristic
492	#95	C₂×Dic₇₉	1	1	yes	characteristic
493	#95	C₂×Dic₇₉	1	1	yes	characteristic
494	#95	C₂×Dic₇₉	1	1	yes	characteristic
495	#95	C₂×Dic₇₉	1	1	yes	characteristic
496	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
497	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
498	C₂×D₄	—	4	1	no	—
499	C₂×D₄	—	4	1	no	—
500	C₂×D₄	C₄⋊Dic₇₉	1	4	yes	—
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	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	4	1	no	—
513	C₂²×C₄	—	4	1	no	—
514	C₂²×C₄	—	4	1	no	—
515	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
516	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
517	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
518	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
519	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
520	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
521	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
522	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
523	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
524	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
525	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
526	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
528	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
529	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
530	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
531	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
532	M₁₆	—	316	4	no	—
533	M₁₆	—	316	4	no	—
534	M₁₆	—	316	4	no	—
535	C₂×C₈	—	316	4	no	—
536	C₂×C₈	—	79	2	no	—
537	C₂×C₈	—	79	2	no	—
538	C₂×C₈	—	158	1	no	—
539	C₂×C₈	—	158	1	no	—
540	C₂×C₈	—	158	1	no	—
541	C₂×C₈	—	158	1	no	—
542	C₂×C₈	—	158	1	no	—
543	C₂×C₈	—	158	1	no	—
544	C₂×C₈	—	158	1	no	—
545	C₂×C₈	—	158	1	no	—
546	C₂×C₈	—	158	1	no	—
547	C₂×C₈	—	158	1	no	—
548	C₂×C₈	—	158	1	no	—
549	C₂×C₈	—	158	1	no	—
550	C₂×C₈	—	158	1	no	—
551	C₂×C₈	—	158	1	no	—
552	C₂×C₈	—	158	1	no	—
553	C₂×C₈	—	158	1	no	—
554	C₂×C₈	—	158	1	no	—
555	C₂×C₈	—	158	1	no	—
556	C₂×C₈	—	158	1	no	—
557	C₂×C₈	—	158	1	no	—
558	C₂×C₈	—	158	1	no	—
559	C₂×C₈	—	158	1	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	4	1	no	—
564	C₄⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₂²⋊C₄	—	4	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
572	C₂²⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	2	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	D₄×D₇₉	1	2	yes	—
582	C₄²	C₂×D₃₁₆	1	2	yes	—
583	C₄²	C₂×Dic₁₅₈	1	2	yes	—
584	C₄²	#11929623	1	2	yes	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	C₂×C₄⋊Dic₇₉	1	2	yes	—
598	C₂³	C₂×C₄⋊Dic₇₉	1	2	yes	—
599	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
600	D₄	—	4	4	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	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	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
641	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
642	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
643	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
644	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
645	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
646	C₂×C₄	#14579168	1	2	yes	—
647	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
648	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
649	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
650	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
651	C₂×C₄	#14579207	1	1	yes	characteristic
652	C₂×C₄	#14579208	1	1	yes	characteristic
653	C₈	—	316	1	no	—
654	C₈	—	316	1	no	—
655	C₈	—	316	1	no	—
656	C₈	—	316	1	no	—
657	C₈	—	316	1	no	—
658	C₈	—	316	1	no	—
659	C₈	—	158	2	no	—
660	C₈	—	158	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
676	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
677	C₂²	#19099046	1	1	yes	characteristic
678	C₂²	C₂×#14579168	1	1	yes	characteristic
679	C₂²	#19099330	1	1	yes	characteristic
680	C₂²	#19099330	1	1	yes	characteristic
681	C₂²	#19099330	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	D₄×D₃₁₆	1	1	yes	characteristic
695	C₄	#19099217	1	1	yes	characteristic
696	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
697	C₄	#19099270	1	1	yes	characteristic
698	C₂	—	4	2	no	—
699	C₂	—	4	2	no	—
700	C₂	D₄×C₄⋊Dic₇₉	1	1	yes	characteristic
701	C₂	#23771964	1	1	yes	characteristic
702	C₂	#23771968	1	1	yes	characteristic
703	C₂	#23772104	1	1	yes	characteristic
704	C₂	#23772127	1	1	yes	characteristic
705	C₂	#23772549	1	1	yes	characteristic
706	C₂	#23772570	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#2290	C₂
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2290	D₇₉
hypocenter	C₇₉	#22649
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2290

Complements

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

N	H ≅ G/N	type
3. C₂×#19098590	C₂	semidirect
4. C₂×#19098587	C₂	semidirect
5. #23764124	C₂	semidirect
6. #23764119	C₂	semidirect
7. #23763585	C₂	semidirect
8. #23763585	C₂	semidirect
9. #23763585	C₂	semidirect
10. #23763580	C₂	semidirect
11. #23763554	C₂	semidirect
12. #23763384	C₂	semidirect
13. #23763380	C₂	semidirect
14. #23763257	C₂	semidirect
94. C₄⋊(C₇₉⋊C₈)	D₄	semidirect
369. C₇₉	#22649	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098641	2
C₂×#19098635	2
C₂×#19098590	2
C₂×#19098587	2
#23764124	2
#23764119	2
#23763585	2
#23763580	2
#23763554	2
#23763384	2
#23763380	2
#23763257	2
C₇₉×#2290	2
#22649	79