Subgroups — #34314766

Order 20224.

758 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23764341	C₂	1	1	yes	maximal, characteristic, complemented
2	#23764337	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764015	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764015	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764008	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764008	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763698	C₂	1	1	yes	maximal, characteristic
8	#23763693	C₂	1	1	yes	maximal, characteristic
9	#23763585	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763585	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763580	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763580	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763517	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763517	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#124×C₇₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×#14579072	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
32	#19098318	C₂²	1	1	yes	characteristic
33	#19098318	C₂²	1	1	yes	characteristic
34	#19098318	C₂²	1	1	yes	characteristic
35	#19098318	C₂²	1	1	yes	characteristic
36	#19098318	C₂²	1	1	yes	characteristic
37	#19098318	C₂²	1	1	yes	characteristic
38	#19098318	C₂²	1	1	yes	characteristic
39	#19098318	C₂²	1	1	yes	characteristic
40	#19098318	C₂²	1	1	yes	characteristic
41	#19098318	C₂²	1	1	yes	characteristic
42	#19098318	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	C₂×#124×C₇₉	C₄	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
47	#391×C₇₉	C₄	1	1	yes	characteristic
48	#390×C₇₉	C₄	1	1	yes	characteristic
49	#388×C₇₉	C₄	1	1	yes	characteristic
50	#388×C₇₉	C₄	1	1	yes	characteristic
51	#388×C₇₉	C₄	1	1	yes	characteristic
52	#388×C₇₉	C₄	1	1	yes	characteristic
53	#382×C₇₉	C₄	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
58	C₄³×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×#11929608	—	4	1	no	—
60	C₂×#11929608	—	4	1	no	—
61	C₂×#11929608	—	4	1	no	—
62	C₂²×C₇₉⋊C₈	—	4	1	no	—
63	C₂²×C₇₉⋊C₈	—	4	1	no	—
64	C₂²×C₇₉⋊C₈	—	4	1	no	—
65	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
73	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
74	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
75	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
76	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
77	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
78	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
79	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
80	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
81	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
82	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
83	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
84	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
85	#14579072	—	4	1	no	—
86	C₄×C₇₉⋊C₈	—	4	1	no	—
87	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
89	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
91	#124×C₇₉	—	2	4	no	—
92	C₄×Q₈×C₇₉	—	4	1	no	—
93	C₄×Q₈×C₇₉	—	4	1	no	—
94	C₄×D₄×C₇₉	—	4	1	no	—
95	C₄×D₄×C₇₉	—	4	1	no	—
96	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
119	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
120	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
121	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
122	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
123	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
124	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
125	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
126	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
127	#11929608	—	4	4	no	—
128	C₂×C₇₉⋊C₈	—	2	1	no	—
129	C₂×C₇₉⋊C₈	—	2	1	no	—
130	C₂×C₇₉⋊C₈	—	2	1	no	—
131	C₂×C₇₉⋊C₈	—	2	1	no	—
132	C₂×C₇₉⋊C₈	—	2	1	no	—
133	C₂×C₇₉⋊C₈	—	2	1	no	—
134	C₂×C₇₉⋊C₈	—	2	1	no	—
135	C₂×C₇₉⋊C₈	—	2	1	no	—
136	C₂×C₇₉⋊C₈	—	2	1	no	—
137	C₂×C₇₉⋊C₈	—	2	1	no	—
138	C₂×C₇₉⋊C₈	—	2	1	no	—
139	C₂×C₇₉⋊C₈	—	2	1	no	—
140	C₂×C₇₉⋊C₈	—	2	1	no	—
141	C₂×C₇₉⋊C₈	—	2	1	no	—
142	C₂×C₇₉⋊C₈	—	2	1	no	—
143	C₂×C₇₉⋊C₈	—	2	1	no	—
144	C₂×C₇₉⋊C₈	—	2	1	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	—	4	4	no	—
153	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
154	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×Q₈×C₇₉	—	2	2	no	—
156	C₂×Q₈×C₇₉	—	2	2	no	—
157	C₂×Q₈×C₇₉	—	4	1	no	—
158	C₂×D₄×C₇₉	—	2	2	no	—
159	C₂×D₄×C₇₉	—	2	2	no	—
160	C₂×D₄×C₇₉	—	4	1	no	—
161	C₂²×C₄×C₇₉	—	2	1	no	—
162	C₂²×C₄×C₇₉	—	2	1	no	—
163	C₂²×C₄×C₇₉	—	2	1	no	—
164	C₂²×C₄×C₇₉	—	2	1	no	—
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	1	no	—
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	1	no	—
173	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₇₉	—	4	1	no	—
187	C₄⋊C₄×C₇₉	—	4	1	no	—
188	C₄⋊C₄×C₇₉	—	4	1	no	—
189	C₄⋊C₄×C₇₉	—	4	1	no	—
190	C₂²⋊C₄×C₇₉	—	2	2	no	—
191	C₂²⋊C₄×C₇₉	—	2	2	no	—
192	C₂²⋊C₄×C₇₉	—	2	2	no	—
193	C₂²⋊C₄×C₇₉	—	2	2	no	—
194	C₂²⋊C₄×C₇₉	—	2	2	no	—
195	C₂²⋊C₄×C₇₉	—	4	1	no	—
196	C₂²⋊C₄×C₇₉	—	4	1	no	—
197	C₂²⋊C₄×C₇₉	—	4	1	no	—
198	C₂²⋊C₄×C₇₉	—	4	1	no	—
199	C₂²⋊C₄×C₇₉	M₁₆	1	4	yes	complemented
200	C₄²×C₇₉	—	2	2	no	—
201	C₄²×C₇₉	—	2	2	no	—
202	C₄²×C₇₉	—	2	2	no	—
203	C₄²×C₇₉	—	2	1	no	—
204	C₄²×C₇₉	—	2	1	no	—
205	C₄²×C₇₉	—	2	1	no	—
206	C₄²×C₇₉	—	2	1	no	—
207	C₄²×C₇₉	—	2	1	no	—
208	C₄²×C₇₉	—	2	1	no	—
209	C₄²×C₇₉	—	2	1	no	—
210	C₄²×C₇₉	—	2	1	no	—
211	C₄²×C₇₉	—	2	1	no	—
212	C₄²×C₇₉	—	2	1	no	—
213	C₄²×C₇₉	—	4	1	no	—
214	C₂³×C₇₉	—	2	1	no	—
215	C₂³×C₇₉	—	2	1	no	—
216	C₂³×C₇₉	—	2	1	no	—
217	C₂³×C₇₉	—	2	1	no	—
218	C₂³×C₇₉	—	2	1	no	—
219	C₂³×C₇₉	—	2	1	no	—
220	C₂³×C₇₉	—	2	1	no	—
221	C₂³×C₇₉	—	2	1	no	—
222	C₂³×C₇₉	—	2	1	no	—
223	C₂³×C₇₉	—	2	1	no	—
224	C₂³×C₇₉	—	2	1	no	—
225	C₂³×C₇₉	—	2	1	no	—
226	C₂³×C₇₉	—	2	1	no	—
227	C₂³×C₇₉	C₂×M₁₆	1	2	yes	—
228	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
229	Q₈×C₇₉	—	4	4	no	—
230	D₄×C₇₉	—	4	4	no	—
231	C₂×C₄×C₇₉	—	2	1	no	—
232	C₂×C₄×C₇₉	—	2	1	no	—
233	C₂×C₄×C₇₉	—	2	1	no	—
234	C₂×C₄×C₇₉	—	2	1	no	—
235	C₂×C₄×C₇₉	—	2	1	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	—	2	1	no	—
245	C₂×C₄×C₇₉	—	2	1	no	—
246	C₂×C₄×C₇₉	—	2	1	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	1	no	—
262	C₂×C₄×C₇₉	—	2	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	—	4	1	no	—
269	C₂×C₄×C₇₉	—	4	1	no	—
270	C₂×C₄×C₇₉	—	4	1	no	—
271	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
272	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
273	C₂×C₄×C₇₉	#131	1	2	yes	—
274	C₂×C₄×C₇₉	#131	1	2	yes	—
275	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
276	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
278	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
280	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
281	C₇₉⋊C₈	—	4	1	no	—
282	C₇₉⋊C₈	—	4	1	no	—
283	C₇₉⋊C₈	—	4	1	no	—
284	C₇₉⋊C₈	—	4	1	no	—
285	C₇₉⋊C₈	—	4	1	no	—
286	C₇₉⋊C₈	—	4	1	no	—
287	C₇₉⋊C₈	—	4	1	no	—
288	C₇₉⋊C₈	—	4	1	no	—
289	C₂²×C₇₉	—	2	2	no	—
290	C₂²×C₇₉	—	2	2	no	—
291	C₂²×C₇₉	—	2	2	no	—
292	C₂²×C₇₉	—	4	1	no	—
293	C₂²×C₇₉	—	4	1	no	—
294	C₂²×C₇₉	—	4	1	no	—
295	C₂²×C₇₉	—	4	1	no	—
296	C₂²×C₇₉	—	4	1	no	—
297	C₂²×C₇₉	—	4	1	no	—
298	C₂²×C₇₉	—	4	1	no	—
299	C₂²×C₇₉	—	4	1	no	—
300	C₂²×C₇₉	—	4	1	no	—
301	C₂²×C₇₉	—	4	1	no	—
302	C₂²×C₇₉	—	4	1	no	—
303	C₂²×C₇₉	#518	1	1	yes	characteristic
304	C₂²×C₇₉	#520	1	1	yes	characteristic
305	C₂²×C₇₉	#520	1	1	yes	characteristic
306	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
307	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
308	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
309	C₂²×C₇₉	#568	1	1	yes	characteristic
310	C₄×C₇₉	—	2	2	no	—
311	C₄×C₇₉	—	2	2	no	—
312	C₄×C₇₉	—	2	2	no	—
313	C₄×C₇₉	—	2	2	no	—
314	C₄×C₇₉	—	4	1	no	—
315	C₄×C₇₉	—	4	1	no	—
316	C₄×C₇₉	—	4	1	no	—
317	C₄×C₇₉	—	4	1	no	—
318	C₄×C₇₉	—	4	1	no	—
319	C₄×C₇₉	—	4	1	no	—
320	C₄×C₇₉	—	4	1	no	—
321	C₄×C₇₉	—	4	1	no	—
322	C₄×C₇₉	H(3,𝔽₄)	1	1	yes	characteristic
323	C₄×C₇₉	#562	1	1	yes	characteristic
324	C₄×C₇₉	#562	1	1	yes	characteristic
325	C₄×C₇₉	#563	1	1	yes	characteristic
326	#23349	—	79	1	no	maximal, Sylow
327	C₂×C₇₉	—	4	2	no	—
328	C₂×C₇₉	—	8	1	no	—
329	C₂×C₇₉	#2379	1	1	yes	characteristic
330	C₂×C₇₉	#2974	1	1	yes	characteristic
331	C₂×C₇₉	#2981	1	1	yes	characteristic
332	C₂×C₇₉	#2989	1	1	yes	characteristic
333	C₂×C₇₉	#2990	1	1	yes	characteristic
334	C₂×C₇₉	#2993	1	1	yes	characteristic
335	C₂×C₇₉	#2994	1	1	yes	characteristic
336	C₄×#124	D₇₉	1	1	yes	characteristic
337	#1985	—	79	1	no	—
338	#1984	—	79	1	no	—
339	#1924	—	79	1	no	—
340	#1924	—	79	1	no	—
341	#1923	—	79	1	no	—
342	#1923	—	79	1	no	—
343	#1870	—	79	1	no	—
344	#1869	—	79	1	no	—
345	#1851	—	79	1	no	—
346	#1851	—	79	1	no	—
347	#1850	—	79	1	no	—
348	#1850	—	79	1	no	—
349	#1831	—	79	1	no	—
350	#1831	—	79	1	no	—
351	C₇₉	#23349	1	1	yes	characteristic, complemented, Sylow
352	C₂²×M₁₆	—	79	1	no	—
353	C₂³×C₈	—	79	1	no	—
354	C₂×#124	Dic₇₉	1	1	yes	characteristic
355	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
357	C₂×C₄⋊C₈	—	79	1	no	—
358	C₂×C₄⋊C₈	—	79	1	no	—
359	C₂×C₄⋊C₈	—	79	1	no	—
360	C₂×C₄⋊C₈	—	79	1	no	—
361	C₂×C₄⋊C₈	—	79	1	no	—
362	C₂×C₄⋊C₈	—	79	1	no	—
363	C₂×C₂²⋊C₈	—	79	1	no	—
364	C₂×C₂²⋊C₈	—	79	1	no	—
365	C₂×C₂²⋊C₈	—	79	1	no	—
366	C₂×C₂²⋊C₈	—	79	1	no	—
367	C₂×C₂²⋊C₈	—	79	1	no	—
368	C₂×C₂²⋊C₈	—	79	1	no	—
369	C₂×#97	—	79	1	no	—
370	C₂×C₄×C₈	—	79	1	no	—
371	#391	Dic₇₉	1	1	yes	characteristic
372	#390	Dic₇₉	1	1	yes	characteristic
373	#388	Dic₇₉	1	1	yes	characteristic
374	#388	Dic₇₉	1	1	yes	characteristic
375	#388	Dic₇₉	1	1	yes	characteristic
376	#388	Dic₇₉	1	1	yes	characteristic
377	#382	Dic₇₉	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
379	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
380	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
381	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
382	C₄³	C₂×D₇₉	1	1	yes	characteristic
383	#336	—	79	1	no	—
384	#336	—	79	1	no	—
385	#336	—	79	1	no	—
386	#336	—	79	1	no	—
387	#336	—	79	1	no	—
388	#336	—	79	1	no	—
389	#336	—	79	1	no	—
390	#336	—	79	1	no	—
391	#336	—	79	1	no	—
392	#336	—	79	1	no	—
393	#336	—	79	1	no	—
394	#336	—	79	1	no	—
395	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
396	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
397	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
398	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
399	C₂×M₁₆	—	316	1	no	—
400	C₂×M₁₆	—	316	1	no	—
401	C₂×M₁₆	—	316	1	no	—
402	C₂²×C₈	—	316	1	no	—
403	C₂²×C₈	—	316	1	no	—
404	C₂²×C₈	—	316	1	no	—
405	C₂²×C₈	—	79	1	no	—
406	C₂²×C₈	—	79	1	no	—
407	C₂²×C₈	—	79	1	no	—
408	C₂²×C₈	—	79	1	no	—
409	C₂²×C₈	—	79	1	no	—
410	C₂²×C₈	—	79	1	no	—
411	C₂²×C₈	—	79	1	no	—
412	C₂²×C₈	—	79	1	no	—
413	#124	—	2	4	no	—
414	C₄×Q₈	—	4	1	no	—
415	C₄×Q₈	—	4	1	no	—
416	C₄×D₄	—	4	1	no	—
417	C₄×D₄	—	4	1	no	—
418	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
432	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
433	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
434	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
435	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
436	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
437	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
438	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
439	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
440	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
441	C₄⋊C₈	—	316	1	no	—
442	C₄⋊C₈	—	316	1	no	—
443	C₄⋊C₈	—	316	1	no	—
444	C₄⋊C₈	—	316	1	no	—
445	C₄⋊C₈	—	316	1	no	—
446	C₄⋊C₈	—	316	1	no	—
447	C₂²⋊C₈	—	316	1	no	—
448	C₂²⋊C₈	—	316	1	no	—
449	C₂²⋊C₈	—	316	1	no	—
450	C₂²⋊C₈	—	316	1	no	—
451	C₂²⋊C₈	—	316	1	no	—
452	C₂²⋊C₈	—	316	1	no	—
453	#97	—	316	1	no	—
454	C₄×C₈	—	316	1	no	—
455	#95	C₂×Dic₇₉	1	1	yes	characteristic
456	#95	C₂×Dic₇₉	1	1	yes	characteristic
457	#95	C₂×Dic₇₉	1	1	yes	characteristic
458	#95	C₂×Dic₇₉	1	1	yes	characteristic
459	#95	C₂×Dic₇₉	1	1	yes	characteristic
460	#95	C₂×Dic₇₉	1	1	yes	characteristic
461	#95	C₂×Dic₇₉	1	1	yes	characteristic
462	#95	C₂×Dic₇₉	1	1	yes	characteristic
463	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
464	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
465	C₂×Q₈	—	2	2	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	4	1	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	4	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	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
484	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
485	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
492	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
493	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
494	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
495	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
496	M₁₆	—	316	4	no	—
497	C₂×C₈	—	316	4	no	—
498	C₂×C₈	—	158	1	no	—
499	C₂×C₈	—	158	1	no	—
500	C₂×C₈	—	158	1	no	—
501	C₂×C₈	—	158	1	no	—
502	C₂×C₈	—	158	1	no	—
503	C₂×C₈	—	158	1	no	—
504	C₂×C₈	—	158	1	no	—
505	C₂×C₈	—	158	1	no	—
506	C₂×C₈	—	158	1	no	—
507	C₂×C₈	—	158	1	no	—
508	C₂×C₈	—	158	1	no	—
509	C₂×C₈	—	158	1	no	—
510	C₂×C₈	—	158	1	no	—
511	C₂×C₈	—	158	1	no	—
512	C₂×C₈	—	158	1	no	—
513	C₂×C₈	—	158	1	no	—
514	C₂×C₈	—	158	1	no	—
515	C₂×C₈	—	158	1	no	—
516	C₂×C₈	—	158	1	no	—
517	C₂×C₈	—	158	1	no	—
518	C₂×C₈	—	158	1	no	—
519	C₂×C₈	—	158	1	no	—
520	C₂×C₈	—	158	1	no	—
521	C₂×C₈	—	158	1	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	#11929608	1	4	yes	complemented
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	4	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	C₂×#11929608	1	2	yes	—
564	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
565	Q₈	—	4	4	no	—
566	D₄	—	4	4	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	C₂×#11929608	1	2	yes	—
608	C₂×C₄	C₂×#11929608	1	2	yes	—
609	C₂×C₄	#14579168	1	2	yes	—
610	C₂×C₄	#14579168	1	2	yes	—
611	C₂×C₄	#14579206	1	1	yes	characteristic
612	C₂×C₄	#14579206	1	1	yes	characteristic
613	C₂×C₄	#14579207	1	1	yes	characteristic
614	C₂×C₄	#14579207	1	1	yes	characteristic
615	C₂×C₄	#14579208	1	1	yes	characteristic
616	C₂×C₄	#14579208	1	1	yes	characteristic
617	C₈	—	316	1	no	—
618	C₈	—	316	1	no	—
619	C₈	—	316	1	no	—
620	C₈	—	316	1	no	—
621	C₈	—	316	1	no	—
622	C₈	—	316	1	no	—
623	C₈	—	316	1	no	—
624	C₈	—	316	1	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	#19099038	1	1	yes	characteristic
640	C₂²	#19099046	1	1	yes	characteristic
641	C₂²	#19099046	1	1	yes	characteristic
642	C₂²	C₂²×#11929608	1	1	yes	characteristic
643	C₂²	C₂×#14579168	1	1	yes	characteristic
644	C₂²	C₂×#14579168	1	1	yes	characteristic
645	C₂²	#19099330	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	#19099305	1	1	yes	characteristic
659	C₄	#19099307	1	1	yes	characteristic
660	C₄	#19099307	1	1	yes	characteristic
661	C₄	#19099313	1	1	yes	characteristic
662	C₂	—	4	2	no	—
663	C₂	—	8	1	no	—
664	C₂	#23766574	1	1	yes	characteristic
665	C₂	#23772435	1	1	yes	characteristic
666	C₂	#23772476	1	1	yes	characteristic
667	C₂	#23772517	1	1	yes	characteristic
668	C₂	#23772525	1	1	yes	characteristic
669	C₂	#23772549	1	1	yes	characteristic
670	C₂	#23772560	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₄×#124×C₇₉	C₂
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×#124	D₇₉
hypocenter	C₇₉	#23349
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#124

Complements

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

N	H ≅ G/N	type
1. #23764341	C₂	semidirect
2. #23764337	C₂	semidirect
3. #23764015	C₂	semidirect
4. #23764015	C₂	semidirect
5. #23764008	C₂	semidirect
6. #23764008	C₂	semidirect
9. #23763585	C₂	semidirect
10. #23763585	C₂	semidirect
11. #23763580	C₂	semidirect
12. #23763580	C₂	semidirect
13. #23763517	C₂	semidirect
14. #23763517	C₂	semidirect
199. C₂²⋊C₄×C₇₉	M₁₆	semidirect
351. C₇₉	#23349	semidirect
535. C₂²⋊C₄	#11929608	semidirect

Maximal subgroups

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

subgroup	index
#23764341	2
#23764337	2
#23764015	2
#23764008	2
#23763698	2
#23763693	2
#23763585	2
#23763580	2
#23763517	2
C₄×#124×C₇₉	2
#23349	79