Subgroups — #34295727

Order 20224.

898 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098691	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14579140	C₂	1	1	yes	maximal, characteristic
3	#23764340	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764123	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763964	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763964	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763578	C₂	1	1	yes	maximal, characteristic
8	#23763578	C₂	1	1	yes	maximal, characteristic
9	#23763380	C₂	1	1	yes	maximal, characteristic
10	#23763276	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763272	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763268	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763176	C₂	1	1	yes	maximal, characteristic
14	C₈×C₂²⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic
15	C₂²×#97×C₇₉	C₂	1	1	yes	maximal, characteristic
16	C₂×#14579140	C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
18	#19098691	—	2	4	no	—
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₇₉⋊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×#14579071	C₂²	1	1	yes	characteristic
28	C₂×#14579071	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
31	#19098469	C₄	1	1	yes	characteristic
32	#19098461	C₄	1	1	yes	characteristic
33	#19098447	C₄	1	1	yes	characteristic
34	#19098447	C₄	1	1	yes	characteristic
35	#19098436	C₄	1	1	yes	characteristic
36	#19098436	C₄	1	1	yes	characteristic
37	#19098423	C₄	1	1	yes	characteristic
38	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	#19098318	C₂²	1	1	yes	characteristic
45	#19098317	C₂²	1	1	yes	characteristic
46	#19098317	C₂²	1	1	yes	characteristic
47	#19098317	C₂²	1	1	yes	characteristic
48	#19098317	C₂²	1	1	yes	characteristic
49	#19098317	C₂²	1	1	yes	characteristic
50	#19098317	C₂²	1	1	yes	characteristic
51	#19098317	C₂²	1	1	yes	characteristic
52	#19098317	C₂²	1	1	yes	characteristic
53	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
54	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×#97×C₇₉	—	2	4	no	—
57	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
58	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
60	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
61	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
66	#14579140	—	2	4	no	—
67	C₄×Dic₁₅₈	—	2	2	no	—
68	C₄×Dic₁₅₈	—	2	2	no	—
69	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
72	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
84	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
86	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
87	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
88	Dic₇₉⋊C₈	—	2	2	no	—
89	Dic₇₉⋊C₈	—	2	2	no	—
90	Dic₇₉⋊C₈	—	2	2	no	—
91	Dic₇₉⋊C₈	—	2	2	no	—
92	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
93	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
94	#14579071	—	2	2	no	—
95	#14579071	—	2	2	no	—
96	C₈×Dic₇₉	—	2	2	no	—
97	C₈×Dic₇₉	—	2	2	no	—
98	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
109	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
110	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₉	—	2	2	no	—
112	C₂²×C₈×C₇₉	—	2	2	no	—
113	C₂²×C₈×C₇₉	—	2	2	no	—
114	C₂²×C₈×C₇₉	—	2	2	no	—
115	C₂²×C₈×C₇₉	—	2	2	no	—
116	C₂²×C₈×C₇₉	Q₈	1	4	yes	complemented
117	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇₉	—	2	2	no	—
122	C₂×C₄²×C₇₉	—	2	2	no	—
123	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
127	#97×C₇₉	—	2	2	no	—
128	#97×C₇₉	—	2	2	no	—
129	#97×C₇₉	—	2	2	no	—
130	#97×C₇₉	D₄	1	4	yes	—
131	C₂×Dic₁₅₈	—	2	2	no	—
132	C₂×Dic₁₅₈	—	2	2	no	—
133	C₂×Dic₁₅₈	—	4	1	no	—
134	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
153	C₂×C₇₉⋊C₈	—	2	1	no	—
154	C₄⋊Dic₇₉	—	2	2	no	—
155	C₄⋊Dic₇₉	—	2	2	no	—
156	C₄⋊Dic₇₉	—	4	1	no	—
157	Dic₇₉⋊C₄	—	2	2	no	—
158	Dic₇₉⋊C₄	—	2	2	no	—
159	Dic₇₉⋊C₄	—	2	2	no	—
160	Dic₇₉⋊C₄	—	2	2	no	—
161	Dic₇₉⋊C₄	—	4	1	no	—
162	Dic₇₉⋊C₄	—	4	1	no	—
163	C₂²⋊Dic₇₉	—	2	2	no	—
164	C₂²⋊Dic₇₉	—	2	2	no	—
165	C₂²⋊Dic₇₉	—	2	2	no	—
166	C₂²⋊Dic₇₉	M₁₆	1	4	yes	—
167	C₄×Dic₇₉	—	2	1	no	—
168	C₄×Dic₇₉	—	2	1	no	—
169	C₄×Dic₇₉	—	2	1	no	—
170	C₄×Dic₇₉	—	2	1	no	—
171	C₄×Dic₇₉	—	2	1	no	—
172	C₄×Dic₇₉	—	2	1	no	—
173	C₄×Dic₇₉	—	2	1	no	—
174	C₄×Dic₇₉	—	2	1	no	—
175	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
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	2	no	—
181	C₂²×C₄×C₇₉	—	2	2	no	—
182	C₂²×C₄×C₇₉	—	2	2	no	—
183	C₂²×C₄×C₇₉	—	2	2	no	—
184	C₂²×C₄×C₇₉	—	4	1	no	—
185	C₂²×C₄×C₇₉	—	4	1	no	—
186	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
192	C₂²×C₄×C₇₉	#41	1	2	yes	—
193	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₈×C₇₉	—	2	8	no	—
195	C₂×C₈×C₇₉	—	2	8	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	C₂×D₄	1	2	yes	—
203	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
204	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
205	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
206	C₂×C₈×C₇₉	#41	1	2	yes	—
207	C₂×C₈×C₇₉	#41	1	2	yes	—
208	C₄²×C₇₉	—	2	2	no	—
209	C₄²×C₇₉	—	2	2	no	—
210	C₄²×C₇₉	—	2	1	no	—
211	C₄²×C₇₉	—	2	1	no	—
212	C₄²×C₇₉	C₂×D₄	1	2	yes	—
213	C₄²×C₇₉	#41	1	2	yes	—
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	C₄×Q₈	1	2	yes	—
219	C₂³×C₇₉	C₂×M₁₆	1	2	yes	—
220	C₂³×C₇₉	#131	1	2	yes	—
221	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₇₉	—	2	1	no	—
223	C₂×C₄×C₇₉	—	2	1	no	—
224	C₂×C₄×C₇₉	—	2	1	no	—
225	C₂×C₄×C₇₉	—	2	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	2	no	—
231	C₂×C₄×C₇₉	—	2	2	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	—	4	4	no	—
239	C₂×C₄×C₇₉	—	4	4	no	—
240	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
241	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
243	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
245	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
249	C₂×Dic₇₉	—	2	1	no	—
250	C₂×Dic₇₉	—	2	1	no	—
251	C₂×Dic₇₉	—	2	1	no	—
252	C₂×Dic₇₉	—	2	1	no	—
253	C₂×Dic₇₉	—	2	1	no	—
254	C₂×Dic₇₉	—	2	1	no	—
255	C₂×Dic₇₉	—	2	1	no	—
256	C₂×Dic₇₉	—	2	1	no	—
257	C₂×Dic₇₉	—	2	1	no	—
258	C₂×Dic₇₉	—	2	1	no	—
259	C₂×Dic₇₉	—	2	1	no	—
260	C₂×Dic₇₉	—	2	1	no	—
261	C₂×Dic₇₉	—	2	1	no	—
262	C₂×Dic₇₉	—	2	1	no	—
263	C₂×Dic₇₉	—	2	1	no	—
264	C₂×Dic₇₉	—	2	1	no	—
265	C₂×Dic₇₉	—	2	1	no	—
266	C₂×Dic₇₉	—	2	1	no	—
267	C₂×Dic₇₉	—	2	1	no	—
268	C₂×Dic₇₉	—	2	1	no	—
269	C₂×Dic₇₉	—	2	1	no	—
270	C₂×Dic₇₉	—	2	1	no	—
271	C₂×Dic₇₉	C₂×M₁₆	1	2	yes	—
272	C₂×Dic₇₉	C₂×M₁₆	1	2	yes	—
273	Dic₁₅₈	—	4	4	no	—
274	C₈×C₇₉	—	2	2	no	—
275	C₈×C₇₉	—	2	2	no	—
276	C₈×C₇₉	—	2	2	no	—
277	C₈×C₇₉	C₂²⋊Q₈	1	4	yes	complemented
278	C₇₉⋊C₈	—	4	1	no	—
279	C₇₉⋊C₈	—	4	1	no	—
280	C₇₉⋊C₈	—	4	1	no	—
281	C₇₉⋊C₈	—	4	1	no	—
282	C₂²×C₇₉	—	2	2	no	—
283	C₂²×C₇₉	—	2	2	no	—
284	C₂²×C₇₉	—	2	2	no	—
285	C₂²×C₇₉	—	2	2	no	—
286	C₂²×C₇₉	—	2	2	no	—
287	C₂²×C₇₉	—	2	2	no	—
288	C₂²×C₇₉	#446	1	4	yes	complemented
289	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
291	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
292	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
293	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
294	C₂²×C₇₉	#568	1	1	yes	characteristic
295	C₂²×C₇₉	#568	1	1	yes	characteristic
296	C₄×C₇₉	—	2	2	no	—
297	C₄×C₇₉	—	2	2	no	—
298	C₄×C₇₉	—	2	2	no	—
299	C₄×C₇₉	—	4	1	no	—
300	C₄×C₇₉	—	4	1	no	—
301	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
302	C₄×C₇₉	#525	1	1	yes	characteristic
303	C₄×C₇₉	#529	1	1	yes	characteristic
304	C₄×C₇₉	#533	1	1	yes	characteristic
305	Dic₇₉	—	2	2	no	—
306	Dic₇₉	—	2	2	no	—
307	Dic₇₉	—	4	1	no	—
308	Dic₇₉	—	4	1	no	—
309	Dic₇₉	—	4	1	no	—
310	Dic₇₉	—	4	1	no	—
311	Dic₇₉	—	4	1	no	—
312	Dic₇₉	—	4	1	no	—
313	#21599	—	79	1	no	maximal, Sylow
314	C₂×C₇₉	—	2	4	no	—
315	C₂×C₇₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
316	C₂×C₇₉	#2933	1	1	yes	characteristic
317	C₂×C₇₉	D₄×M₁₆	1	1	yes	characteristic
318	C₂×C₇₉	C₂×#446	1	1	yes	characteristic
319	C₂×C₇₉	#2961	1	1	yes	characteristic
320	C₂×C₇₉	#2968	1	1	yes	characteristic
321	C₂×C₇₉	#2970	1	1	yes	characteristic
322	C₂×#446	—	79	1	no	—
323	C₂²×#97	D₇₉	1	1	yes	characteristic
324	C₄×C₂²⋊Q₈	—	79	1	no	—
325	#1985	—	79	1	no	—
326	#1940	—	79	1	no	—
327	#1917	—	79	1	no	—
328	#1917	—	79	1	no	—
329	#1850	—	79	1	no	—
330	#1850	—	79	1	no	—
331	#1797	—	79	1	no	—
332	#1771	—	79	1	no	—
333	#1771	—	79	1	no	—
334	#1770	—	79	1	no	—
335	#1752	—	79	1	no	—
336	C₈×C₂²⋊C₄	—	79	1	no	—
337	C₇₉	#21599	1	1	yes	characteristic, complemented, Sylow
338	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
339	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
340	C₂×C₂²⋊Q₈	—	79	1	no	—
341	C₂×C₄×Q₈	—	79	1	no	—
342	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
343	#446	—	158	4	no	—
344	C₂×C₄⋊C₈	—	79	1	no	—
345	C₂×C₄⋊C₈	—	79	1	no	—
346	C₂×C₄⋊C₈	—	79	1	no	—
347	C₂×C₄⋊C₈	—	79	1	no	—
348	C₂×C₄⋊C₈	—	79	1	no	—
349	C₂×C₄⋊C₈	—	79	1	no	—
350	C₂×C₂²⋊C₈	—	79	1	no	—
351	C₂×C₂²⋊C₈	—	79	1	no	—
352	C₂×#97	—	2	4	no	—
353	C₂×#97	—	79	1	no	—
354	C₂×#97	—	79	1	no	—
355	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
356	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
357	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
358	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
359	C₂×C₄×C₈	—	79	1	no	—
360	C₂×C₄×C₈	—	79	1	no	—
361	#391	—	79	1	no	—
362	#389	—	79	1	no	—
363	#387	—	79	1	no	—
364	#387	—	79	1	no	—
365	#385	—	79	1	no	—
366	#385	—	79	1	no	—
367	#380	—	79	1	no	—
368	C₄×C₄⋊C₄	—	79	1	no	—
369	C₄×C₄⋊C₄	—	79	1	no	—
370	C₄×C₄⋊C₄	—	79	1	no	—
371	C₄×C₂²⋊C₄	—	79	1	no	—
372	C₄×C₂²⋊C₄	—	79	1	no	—
373	#336	—	79	1	no	—
374	#336	—	79	1	no	—
375	#336	—	79	1	no	—
376	#336	—	79	1	no	—
377	#336	—	79	1	no	—
378	#336	—	79	1	no	—
379	#336	—	79	1	no	—
380	#336	—	79	1	no	—
381	#336	—	79	1	no	—
382	#336	—	79	1	no	—
383	C₂²×Q₈	—	79	1	no	—
384	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
385	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
386	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
387	C₂²×C₈	—	2	2	no	—
388	C₂²×C₈	—	2	2	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	—	2	2	no	—
391	C₂²×C₈	—	2	2	no	—
392	C₂²×C₈	—	79	1	no	—
393	C₂²×C₈	—	79	1	no	—
394	C₂²×C₈	—	79	1	no	—
395	C₂²×C₈	—	79	1	no	—
396	C₂²×C₈	Dic₁₅₈	1	4	yes	complemented
397	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
398	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
399	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
400	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
401	C₂²⋊Q₈	—	158	4	no	—
402	C₄×Q₈	—	158	2	no	—
403	C₄×Q₈	—	158	2	no	—
404	C₂×C₄⋊C₄	—	79	1	no	—
405	C₂×C₄⋊C₄	—	79	1	no	—
406	C₂×C₄⋊C₄	—	79	1	no	—
407	C₂×C₄⋊C₄	—	79	1	no	—
408	C₂×C₄⋊C₄	—	79	1	no	—
409	C₂×C₄⋊C₄	—	79	1	no	—
410	C₂×C₄⋊C₄	—	79	1	no	—
411	C₂×C₄⋊C₄	—	79	1	no	—
412	C₂×C₄⋊C₄	—	79	1	no	—
413	C₂×C₂²⋊C₄	—	79	1	no	—
414	C₂×C₂²⋊C₄	—	79	1	no	—
415	C₂×C₂²⋊C₄	—	79	1	no	—
416	C₂×C₂²⋊C₄	—	79	1	no	—
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	2	2	no	—
419	C₂×C₄²	—	79	1	no	—
420	C₂×C₄²	—	79	1	no	—
421	C₂×C₄²	—	79	1	no	—
422	C₂×C₄²	—	79	1	no	—
423	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
424	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
425	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
426	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
427	C₄⋊C₈	—	158	2	no	—
428	C₄⋊C₈	—	158	2	no	—
429	C₄⋊C₈	—	158	2	no	—
430	C₄⋊C₈	—	158	2	no	—
431	C₄⋊C₈	—	158	2	no	—
432	C₄⋊C₈	—	158	2	no	—
433	C₂²⋊C₈	—	158	2	no	—
434	C₂²⋊C₈	—	158	2	no	—
435	#97	—	2	2	no	—
436	#97	—	2	2	no	—
437	#97	—	2	2	no	—
438	#97	—	158	2	no	—
439	#97	—	158	2	no	—
440	#97	C₂²⋊D₇₉	1	4	yes	—
441	C₄×C₈	—	158	2	no	—
442	C₄×C₈	—	158	2	no	—
443	#95	—	79	1	no	—
444	#95	—	79	1	no	—
445	#95	—	79	1	no	—
446	#95	—	79	1	no	—
447	#95	—	79	1	no	—
448	#95	—	79	1	no	—
449	#95	—	79	1	no	—
450	#95	—	79	1	no	—
451	#95	—	79	1	no	—
452	#95	—	79	1	no	—
453	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
454	C₂×Q₈	—	316	1	no	—
455	C₂×Q₈	—	158	2	no	—
456	C₂×Q₈	—	158	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	79	1	no	—
468	C₂²×C₄	—	79	1	no	—
469	C₂²×C₄	—	79	1	no	—
470	C₂²×C₄	—	79	1	no	—
471	C₂²×C₄	—	79	1	no	—
472	C₂²×C₄	—	79	1	no	—
473	C₂²×C₄	—	79	1	no	—
474	C₂²×C₄	—	79	1	no	—
475	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
481	C₂²×C₄	#11929624	1	2	yes	—
482	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
483	C₂×C₈	—	2	8	no	—
484	C₂×C₈	—	2	1	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	8	no	—
491	C₂×C₈	—	158	1	no	—
492	C₂×C₈	—	158	1	no	—
493	C₂×C₈	—	158	1	no	—
494	C₂×C₈	—	158	1	no	—
495	C₂×C₈	—	158	1	no	—
496	C₂×C₈	—	158	1	no	—
497	C₂×C₈	—	158	1	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	C₂×C₂²⋊D₇₉	1	2	yes	—
504	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
505	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
506	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
507	C₂×C₈	#11929624	1	2	yes	—
508	C₂×C₈	#11929624	1	2	yes	—
509	C₄⋊C₄	—	316	1	no	—
510	C₄⋊C₄	—	316	1	no	—
511	C₄⋊C₄	—	316	1	no	—
512	C₄⋊C₄	—	158	2	no	—
513	C₄⋊C₄	—	158	2	no	—
514	C₄⋊C₄	—	158	2	no	—
515	C₄⋊C₄	—	158	2	no	—
516	C₄⋊C₄	—	158	2	no	—
517	C₄⋊C₄	—	158	2	no	—
518	C₂²⋊C₄	—	79	4	no	—
519	C₂²⋊C₄	—	158	2	no	—
520	C₂²⋊C₄	—	158	2	no	—
521	C₂²⋊C₄	—	158	2	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	158	1	no	—
527	C₄²	—	158	1	no	—
528	C₄²	—	158	1	no	—
529	C₄²	—	158	1	no	—
530	C₄²	—	158	1	no	—
531	C₄²	—	158	1	no	—
532	C₄²	—	158	1	no	—
533	C₄²	—	158	1	no	—
534	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
535	C₄²	#11929624	1	2	yes	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	C₄×Dic₁₅₈	1	2	yes	—
541	C₂³	M₁₆×D₇₉	1	2	yes	—
542	C₂³	#14579169	1	2	yes	—
543	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
544	Q₈	—	316	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	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	—	4	4	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	79	2	no	—
564	C₂×C₄	—	79	2	no	—
565	C₂×C₄	—	158	1	no	—
566	C₂×C₄	—	158	1	no	—
567	C₂×C₄	—	158	1	no	—
568	C₂×C₄	—	158	1	no	—
569	C₂×C₄	—	158	1	no	—
570	C₂×C₄	—	158	1	no	—
571	C₂×C₄	—	158	1	no	—
572	C₂×C₄	—	158	1	no	—
573	C₂×C₄	—	158	1	no	—
574	C₂×C₄	—	158	1	no	—
575	C₂×C₄	—	158	1	no	—
576	C₂×C₄	—	158	1	no	—
577	C₂×C₄	—	158	1	no	—
578	C₂×C₄	—	158	1	no	—
579	C₂×C₄	—	158	1	no	—
580	C₂×C₄	—	158	1	no	—
581	C₂×C₄	—	158	1	no	—
582	C₂×C₄	—	158	1	no	—
583	C₂×C₄	—	158	1	no	—
584	C₂×C₄	—	158	1	no	—
585	C₂×C₄	—	158	1	no	—
586	C₂×C₄	—	158	1	no	—
587	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
588	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
589	C₂×C₄	C₄×Dic₁₅₈	1	2	yes	—
590	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
591	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
592	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
593	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
594	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
595	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	—	2	2	no	—
599	C₈	—	316	1	no	—
600	C₈	—	316	1	no	—
601	C₈	—	316	1	no	—
602	C₈	—	316	1	no	—
603	C₈	#14579140	1	4	yes	complemented
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	#19098691	1	4	yes	complemented
611	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
612	C₂²	C₂×C₄×Dic₁₅₈	1	1	yes	characteristic
613	C₂²	C₄×#11929624	1	1	yes	characteristic
614	C₂²	C₂×M₁₆×D₇₉	1	1	yes	characteristic
615	C₂²	C₂×#14579169	1	1	yes	characteristic
616	C₂²	#19099329	1	1	yes	characteristic
617	C₂²	#19099329	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	316	1	no	—
624	C₄	—	316	1	no	—
625	C₄	—	316	1	no	—
626	C₄	—	316	1	no	—
627	C₄	—	316	1	no	—
628	C₄	—	316	1	no	—
629	C₄	—	158	2	no	—
630	C₄	—	158	2	no	—
631	C₄	C₂×#14579140	1	1	yes	characteristic
632	C₄	#19099074	1	1	yes	characteristic
633	C₄	#19099097	1	1	yes	characteristic
634	C₄	#19099120	1	1	yes	characteristic
635	C₂	—	2	4	no	—
636	C₂	C₄×#14579140	1	1	yes	characteristic
637	C₂	#23772125	1	1	yes	characteristic
638	C₂	M₁₆×C₂²⋊D₇₉	1	1	yes	characteristic
639	C₂	C₂×#19098691	1	1	yes	characteristic
640	C₂	#23772340	1	1	yes	characteristic
641	C₂	#23772394	1	1	yes	characteristic
642	C₂	#23772411	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₂²×#97×C₇₉	C₂
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂²×#97	D₇₉
hypocenter	C₇₉	#21599
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
1. C₂×#19098691	C₂	semidirect
3. #23764340	C₂	semidirect
4. #23764123	C₂	semidirect
5. #23763964	C₂	semidirect
6. #23763964	C₂	semidirect
10. #23763276	C₂	semidirect
11. #23763272	C₂	semidirect
12. #23763268	C₂	semidirect
116. C₂²×C₈×C₇₉	Q₈	semidirect
277. C₈×C₇₉	C₂²⋊Q₈	semidirect
288. C₂²×C₇₉	#446	semidirect
337. C₇₉	#21599	semidirect
396. C₂²×C₈	Dic₁₅₈	semidirect
603. C₈	#14579140	semidirect
610. C₂²	#19098691	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098691	2
C₄×#14579140	2
#23764340	2
#23764123	2
#23763964	2
#23763578	2
#23763380	2
#23763276	2
#23763272	2
#23763268	2
#23763176	2
C₈×C₂²⋊Dic₇₉	2
C₂²×#97×C₇₉	2
#21599	79