Subgroups — C₂×#23761276 #34178232

Order 20224.

906 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098527	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#23761276	C₂	1	4	yes	maximal, direct product factor
4	C₂×#407×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11929608	—	2	1	no	—
6	C₂³×C₇₉⋊C₈	C₄	1	2	yes	—
7	#19098527	—	2	1	no	—
8	#19098527	—	2	1	no	—
9	#19098527	C₄	1	2	yes	—
10	#19098527	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
12	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
13	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
14	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
15	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
16	C₂×C₂²⋊(C₇₉⋊C₈)	C₄	1	2	yes	—
17	C₂×C₂²⋊(C₇₉⋊C₈)	C₄	1	2	yes	—
18	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₇₉	—	2	1	no	—
21	#407×C₇₉	—	2	1	no	—
22	#407×C₇₉	—	2	1	no	—
23	#407×C₇₉	C₄	1	2	yes	—
24	#407×C₇₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₇₉	—	2	1	no	—
26	C₂×C₂²⋊C₈×C₇₉	C₄	1	2	yes	—
27	C₂×#11929608	—	2	2	no	—
28	C₂×#11929608	—	2	2	no	—
29	C₂×#11929608	—	4	4	no	—
30	C₂²×C₇₉⋊C₈	—	2	2	no	—
31	C₂²×C₇₉⋊C₈	—	2	2	no	—
32	C₂²×C₇₉⋊C₈	—	2	2	no	—
33	C₂²×C₇₉⋊C₈	—	4	4	no	—
34	C₂²×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
35	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
37	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
38	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
39	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
43	C₂⁵×C₇₉	Q₈	1	1	yes	characteristic
44	C₂³×C₄×C₇₉	—	4	4	no	—
45	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	Q₈	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₇₉	—	2	2	no	—
60	C₂×M₁₆×C₇₉	—	2	2	no	—
61	C₂×M₁₆×C₇₉	—	4	4	no	—
62	C₂²×C₈×C₇₉	—	2	2	no	—
63	C₂²⋊C₈×C₇₉	—	2	2	no	—
64	C₂²⋊C₈×C₇₉	—	2	2	no	—
65	C₂²⋊C₈×C₇₉	—	2	2	no	—
66	C₂²⋊C₈×C₇₉	C₂×C₄	1	4	yes	—
67	#11929608	—	4	4	no	—
68	#11929608	—	4	4	no	—
69	C₂×C₇₉⋊C₈	—	2	4	no	—
70	C₂×C₇₉⋊C₈	—	2	4	no	—
71	C₂×C₇₉⋊C₈	—	4	4	no	—
72	C₂×C₇₉⋊C₈	—	4	4	no	—
73	C₂×C₇₉⋊C₈	—	4	4	no	—
74	C₂×C₇₉⋊C₈	—	4	4	no	—
75	C₂⁴×C₇₉	—	2	4	no	—
76	C₂⁴×C₇₉	—	4	2	no	—
77	C₂⁴×C₇₉	—	4	2	no	—
78	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂⁴×C₇₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂⁴×C₇₉	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₇₉	—	2	4	no	—
86	C₂²×C₄×C₇₉	—	2	4	no	—
87	C₂²×C₄×C₇₉	—	2	4	no	—
88	C₂²×C₄×C₇₉	—	4	2	no	—
89	C₂²×C₄×C₇₉	—	4	2	no	—
90	C₂²×C₄×C₇₉	—	4	2	no	—
91	C₂²×C₄×C₇₉	—	4	2	no	—
92	C₂²×C₄×C₇₉	—	4	2	no	—
93	C₂²×C₄×C₇₉	—	4	2	no	—
94	C₂²×C₄×C₇₉	—	4	2	no	—
95	C₂²×C₄×C₇₉	—	4	2	no	—
96	C₂²×C₄×C₇₉	—	4	2	no	—
97	C₂²×C₄×C₇₉	—	4	2	no	—
98	C₂²×C₄×C₇₉	—	4	2	no	—
99	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₇₉	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
127	M₁₆×C₇₉	—	4	4	no	—
128	M₁₆×C₇₉	—	4	4	no	—
129	C₂×C₈×C₇₉	—	2	4	no	—
130	C₂×C₈×C₇₉	—	4	4	no	—
131	C₂³×C₇₉	—	2	2	no	—
132	C₂³×C₇₉	—	2	2	no	—
133	C₂³×C₇₉	—	2	2	no	—
134	C₂³×C₇₉	—	2	2	no	—
135	C₂³×C₇₉	—	2	2	no	—
136	C₂³×C₇₉	—	2	2	no	—
137	C₂³×C₇₉	—	2	2	no	—
138	C₂³×C₇₉	—	2	2	no	—
139	C₂³×C₇₉	—	2	2	no	—
140	C₂³×C₇₉	—	2	2	no	—
141	C₂³×C₇₉	—	2	2	no	—
142	C₂³×C₇₉	—	2	2	no	—
143	C₂³×C₇₉	—	4	1	no	—
144	C₂³×C₇₉	—	4	1	no	—
145	C₂³×C₇₉	—	4	1	no	—
146	C₂³×C₇₉	—	4	1	no	—
147	C₂³×C₇₉	—	4	1	no	—
148	C₂³×C₇₉	—	4	1	no	—
149	C₂³×C₇₉	—	4	1	no	—
150	C₂³×C₇₉	—	4	1	no	—
151	C₂³×C₇₉	—	4	16	no	—
152	C₂³×C₇₉	#95	1	1	yes	characteristic
153	C₂³×C₇₉	#95	1	1	yes	characteristic
154	C₂³×C₇₉	#95	1	1	yes	characteristic
155	C₂³×C₇₉	#95	1	1	yes	characteristic
156	C₂³×C₇₉	#108	1	4	yes	—
157	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	2	2	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	2	2	no	—
170	C₂×C₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	2	2	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	4	1	no	—
176	C₂×C₄×C₇₉	—	4	1	no	—
177	C₂×C₄×C₇₉	—	4	1	no	—
178	C₂×C₄×C₇₉	—	4	1	no	—
179	C₂×C₄×C₇₉	—	4	1	no	—
180	C₂×C₄×C₇₉	—	4	1	no	—
181	C₂×C₄×C₇₉	—	4	1	no	—
182	C₂×C₄×C₇₉	—	4	1	no	—
183	C₂×C₄×C₇₉	—	4	1	no	—
184	C₂×C₄×C₇₉	—	4	1	no	—
185	C₂×C₄×C₇₉	—	4	1	no	—
186	C₂×C₄×C₇₉	—	4	1	no	—
187	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
188	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
189	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
190	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
191	C₂×C₄×C₇₉	#99	1	4	yes	—
192	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₈×C₇₉	—	4	4	no	—
197	C₇₉⋊C₈	—	4	4	no	—
198	C₇₉⋊C₈	—	4	4	no	—
199	C₂²×C₇₉	—	2	8	no	—
200	C₂²×C₇₉	—	2	1	no	—
201	C₂²×C₇₉	—	2	1	no	—
202	C₂²×C₇₉	—	2	1	no	—
203	C₂²×C₇₉	—	2	1	no	—
204	C₂²×C₇₉	—	2	1	no	—
205	C₂²×C₇₉	—	2	1	no	—
206	C₂²×C₇₉	—	2	1	no	—
207	C₂²×C₇₉	—	2	1	no	—
208	C₂²×C₇₉	—	2	1	no	—
209	C₂²×C₇₉	—	2	1	no	—
210	C₂²×C₇₉	—	2	1	no	—
211	C₂²×C₇₉	—	2	1	no	—
212	C₂²×C₇₉	—	2	1	no	—
213	C₂²×C₇₉	—	2	1	no	—
214	C₂²×C₇₉	—	2	1	no	—
215	C₂²×C₇₉	—	2	1	no	—
216	C₂²×C₇₉	—	4	4	no	—
217	C₂²×C₇₉	—	4	4	no	—
218	C₂²×C₇₉	—	4	4	no	—
219	C₂²×C₇₉	—	4	4	no	—
220	C₂²×C₇₉	—	4	4	no	—
221	C₂²×C₇₉	—	4	4	no	—
222	C₂²×C₇₉	#338	1	2	yes	—
223	C₂²×C₇₉	#341	1	2	yes	—
224	C₂²×C₇₉	#341	1	2	yes	—
225	C₂²×C₇₉	#342	1	2	yes	—
226	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
227	C₂²×C₇₉	C₂×#108	1	2	yes	—
228	C₄×C₇₉	—	2	1	no	—
229	C₄×C₇₉	—	2	1	no	—
230	C₄×C₇₉	—	2	1	no	—
231	C₄×C₇₉	—	2	1	no	—
232	C₄×C₇₉	—	2	1	no	—
233	C₄×C₇₉	—	2	1	no	—
234	C₄×C₇₉	#342	1	2	yes	—
235	C₄×C₇₉	C₂×#99	1	2	yes	—
236	C₂×#1293	—	79	1	no	maximal, Sylow
237	C₂×C₇₉	—	2	2	no	—
238	C₂×C₇₉	—	2	2	no	—
239	C₂×C₇₉	—	4	1	no	—
240	C₂×C₇₉	—	4	1	no	—
241	C₂×C₇₉	—	4	1	no	—
242	C₂×C₇₉	—	4	1	no	—
243	C₂×C₇₉	#1293	1	4	yes	complemented
244	C₂×C₇₉	C₂×#338	1	1	yes	characteristic
245	C₂×C₇₉	C₂×#341	1	1	yes	characteristic
246	C₂×C₇₉	C₂×#342	1	1	yes	characteristic
247	C₂×#407	—	79	1	no	—
248	C₂×#407	D₇₉	1	1	yes	characteristic
249	C₂²×C₂²⋊C₈	—	79	1	no	—
250	#1293	—	79	4	no	—
251	C₇₉	C₂×#1293	1	1	yes	characteristic, complemented, Sylow
252	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic
253	C₂²×M₁₆	—	2	1	no	—
254	C₂²×M₁₆	—	158	1	no	—
255	C₂³×C₈	—	79	2	no	—
256	#407	—	2	1	no	—
257	#407	—	2	1	no	—
258	#407	—	79	2	no	—
259	#407	—	79	2	no	—
260	#407	—	158	1	no	—
261	#407	—	158	1	no	—
262	#407	Dic₇₉	1	2	yes	—
263	#407	C₂×D₇₉	1	2	yes	—
264	C₂×C₂²⋊C₈	—	2	1	no	—
265	C₂×C₂²⋊C₈	—	79	2	no	—
266	C₂×C₂²⋊C₈	—	79	2	no	—
267	C₂×C₂²⋊C₈	—	79	2	no	—
268	C₂×C₂²⋊C₈	—	158	1	no	—
269	C₂×C₂²⋊C₈	—	158	1	no	—
270	C₂×C₂²⋊C₈	—	158	1	no	—
271	C₂×C₂²⋊C₈	—	158	1	no	—
272	C₂×C₂²⋊C₈	—	158	1	no	—
273	C₂×C₂²⋊C₈	Dic₇₉	1	2	yes	—
274	C₂⁵	Dic₁₅₈	1	1	yes	characteristic
275	C₂³×C₄	—	4	4	no	—
276	C₂³×C₄	Dic₁₅₈	1	1	yes	characteristic
277	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
278	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
279	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
280	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
281	C₂³×C₄	D₃₁₆	1	1	yes	characteristic
282	C₂³×C₄	D₃₁₆	1	1	yes	characteristic
283	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
284	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
285	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
286	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
287	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
288	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
289	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	4	4	no	—
293	C₂×M₁₆	—	316	4	no	—
294	C₂×M₁₆	—	158	2	no	—
295	C₂×M₁₆	—	158	2	no	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	—	316	4	no	—
298	C₂²×C₈	—	79	4	no	—
299	C₂²×C₈	—	158	2	no	—
300	C₂²×C₈	—	158	2	no	—
301	C₂²×C₈	—	158	2	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	79	4	no	—
306	C₂²⋊C₈	—	158	2	no	—
307	C₂²⋊C₈	—	158	2	no	—
308	C₂²⋊C₈	—	158	2	no	—
309	C₂²⋊C₈	—	158	2	no	—
310	C₂²⋊C₈	—	158	2	no	—
311	C₂²⋊C₈	—	158	2	no	—
312	C₂²⋊C₈	—	158	2	no	—
313	C₂²⋊C₈	C₂×Dic₇₉	1	4	yes	—
314	C₂⁴	—	2	4	no	—
315	C₂⁴	—	4	2	no	—
316	C₂⁴	—	4	2	no	—
317	C₂⁴	Dic₇₉⋊C₄	1	1	yes	characteristic
318	C₂⁴	Dic₇₉⋊C₄	1	1	yes	characteristic
319	C₂⁴	Dic₇₉⋊C₄	1	1	yes	characteristic
320	C₂⁴	Dic₇₉⋊C₄	1	1	yes	characteristic
321	C₂⁴	C₄⋊Dic₇₉	1	1	yes	characteristic
322	C₂⁴	C₄⋊Dic₇₉	1	1	yes	characteristic
323	C₂⁴	C₂×Dic₁₅₈	1	1	yes	characteristic
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
339	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
340	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
341	C₂²×C₄	C₄×Dic₇₉	1	1	yes	characteristic
342	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
343	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
344	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
345	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
346	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
347	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
348	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
349	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
350	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
352	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
353	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
354	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
356	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
357	C₂²×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
358	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
359	C₂²×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
362	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
366	M₁₆	—	4	4	no	—
367	M₁₆	—	4	4	no	—
368	M₁₆	—	316	4	no	—
369	M₁₆	—	316	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	4	4	no	—
372	C₂×C₈	—	316	4	no	—
373	C₂×C₈	—	316	4	no	—
374	C₂×C₈	—	316	4	no	—
375	C₂×C₈	—	316	4	no	—
376	C₂×C₈	—	158	4	no	—
377	C₂×C₈	—	158	4	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	16	no	—
399	C₂³	C₇₉⋊#95	1	1	yes	characteristic
400	C₂³	C₇₉⋊#95	1	1	yes	characteristic
401	C₂³	C₇₉⋊#95	1	1	yes	characteristic
402	C₂³	C₇₉⋊#95	1	1	yes	characteristic
403	C₂³	#14579096	1	4	yes	—
404	C₂³	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
405	C₂³	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
406	C₂³	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
435	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
436	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
437	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
438	C₂×C₄	#14579075	1	4	yes	—
439	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
440	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
441	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
442	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
443	C₈	—	4	4	no	—
444	C₈	—	316	4	no	—
445	C₈	—	316	4	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	C₇₉⋊#338	1	2	yes	—
470	C₂²	#19098327	1	2	yes	—
471	C₂²	#19098327	1	2	yes	—
472	C₂²	#19098329	1	2	yes	—
473	C₂²	C₂×C₇₉⋊#95	1	1	yes	characteristic
474	C₂²	C₂×#14579096	1	2	yes	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	#19098329	1	2	yes	—
482	C₄	C₂×#14579075	1	2	yes	—
483	C₂	—	2	2	no	—
484	C₂	—	2	2	no	—
485	C₂	—	4	1	no	—
486	C₂	—	4	1	no	—
487	C₂	—	4	1	no	—
488	C₂	—	4	1	no	—
489	C₂	#23761276	1	4	yes	direct product factor
490	C₂	C₂×C₇₉⋊#338	1	1	yes	characteristic
491	C₂	C₂×#19098327	1	1	yes	characteristic
492	C₂	C₂×#19098329	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₇₉⋊#95
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₂×#407×C₇₉	C₂
socle	C₂³×C₇₉	#95
prime radical	C₂⁵×C₇₉	Q₈
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	C₂×#407	D₇₉
hypocenter	C₇₉	C₂×#1293
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
3. #23761276	C₂	direct (N × H)
243. C₂×C₇₉	#1293	semidirect
251. C₇₉	C₂×#1293	semidirect
489. C₂	#23761276	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×#19098527	2
C₂²×C₂²⋊(C₇₉⋊C₈)	2
#23761276	2
C₂×#407×C₇₉	2
C₂×#1293	79

Subgroups — C2×#23761276 #34178232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23761276 #34178232