Subgroups — C₂×#23763452 #34287929

Order 20224.

1330 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579168	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14579096	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19098599	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098580	C₂	1	1	yes	maximal, characteristic
5	#23763452	C₂	1	8	yes	maximal, direct product factor
6	C₂×#19098334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19098333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#421×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂×#14579168	—	2	1	no	—
10	C₂×#14579168	—	2	1	no	—
11	C₂×#14579168	—	2	2	no	—
12	C₂×#14579168	—	2	2	no	—
13	C₂×#14579168	C₄	1	2	yes	complemented
14	C₂×#14579168	C₄	1	2	yes	complemented
15	C₂×#14579168	C₄	1	4	yes	complemented
16	C₂×#14579168	C₂²	1	4	yes	—
17	C₂²×#11929608	—	2	1	no	—
18	C₂²×#11929608	C₂²	1	1	yes	characteristic
19	C₂²×#11929608	C₂²	1	1	yes	characteristic
20	C₂³×C₇₉⋊C₈	—	2	1	no	—
21	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×#14579120	C₂²	1	1	yes	characteristic
23	C₂×#14579096	—	2	1	no	—
24	C₂×#14579096	—	2	1	no	—
25	C₂×#14579096	—	2	2	no	—
26	C₂×#14579096	C₂²	1	4	yes	complemented
27	#19098599	—	2	2	no	—
28	#19098599	C₂²	1	4	yes	complemented
29	C₂×#14579094	—	2	1	no	—
30	C₂×#14579092	—	2	1	no	—
31	#19098580	—	2	2	no	—
32	#19098580	C₂²	1	4	yes	—
33	C₂×#14579088	—	2	2	no	—
34	#19098334	C₂²	1	4	yes	complemented
35	#19098333	C₂²	1	4	yes	complemented
36	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
37	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
39	#421×C₇₉	—	2	2	no	—
40	#421×C₇₉	C₂²	1	4	yes	—
41	C₂×#104×C₇₉	—	2	2	no	—
42	#14579168	—	2	4	no	—
43	#14579168	—	2	4	no	—
44	#14579168	—	2	4	no	—
45	#14579168	—	2	4	no	—
46	#14579168	—	2	4	no	—
47	#14579168	—	2	4	no	—
48	#14579168	C₂×C₄	1	8	yes	complemented
49	#14579168	C₂×C₄	1	8	yes	complemented
50	C₂×#11929608	—	2	1	no	—
51	C₂×#11929608	—	2	1	no	—
52	C₂×#11929608	—	2	1	no	—
53	C₂×#11929608	—	2	1	no	—
54	C₂×#11929608	—	2	2	no	—
55	C₂×#11929608	—	2	2	no	—
56	C₂×#11929608	—	2	4	no	—
57	C₂×#11929608	—	2	4	no	—
58	C₂×#11929608	—	2	1	no	—
59	C₂×#11929608	—	2	1	no	—
60	C₂×#11929608	—	2	1	no	—
61	C₂×#11929608	—	2	1	no	—
62	C₂×#11929608	C₂×C₄	1	2	yes	—
63	C₂×#11929608	C₂×C₄	1	2	yes	—
64	C₂×#11929608	C₂³	1	2	yes	—
65	C₂×#11929608	C₂³	1	2	yes	—
66	C₂²×C₇₉⋊C₈	—	2	1	no	—
67	C₂²×C₇₉⋊C₈	—	2	2	no	—
68	C₂²×C₇₉⋊C₈	—	2	2	no	—
69	C₂²×C₇₉⋊C₈	—	2	4	no	—
70	C₂²×C₇₉⋊C₈	—	2	4	no	—
71	C₂²×C₇₉⋊C₈	—	2	1	no	—
72	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
75	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
76	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
77	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
78	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
79	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
80	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
81	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
82	#14579120	—	2	1	no	—
83	#14579120	—	2	1	no	—
84	#14579120	—	2	1	no	—
85	#14579120	C₂³	1	2	yes	—
86	C₂×C₄⋊Dic₇₉	—	2	1	no	—
87	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
88	C₂×C₄×Dic₇₉	—	2	1	no	—
89	#14579096	—	2	4	no	—
90	#14579096	—	2	4	no	—
91	#14579094	—	2	4	no	—
92	#14579092	—	2	4	no	—
93	#14579088	—	2	8	no	—
94	C₂×#41×C₇₉	—	2	1	no	—
95	C₂×#41×C₇₉	—	2	1	no	—
96	C₂×#41×C₇₉	—	2	1	no	—
97	C₂×#41×C₇₉	—	2	1	no	—
98	C₂×#41×C₇₉	—	2	1	no	—
99	C₂×#41×C₇₉	—	2	1	no	—
100	C₂×#41×C₇₉	C₂×C₄	1	2	yes	—
101	C₂×#41×C₇₉	C₂×C₄	1	2	yes	—
102	C₂×#41×C₇₉	D₄	1	2	yes	—
103	C₂×#41×C₇₉	D₄	1	2	yes	—
104	C₂×#41×C₇₉	Q₈	1	2	yes	—
105	C₂×#41×C₇₉	C₂³	1	2	yes	—
106	C₂²×Q₈×C₇₉	Q₈	1	1	yes	characteristic
107	C₂²×D₄×C₇₉	—	2	1	no	—
108	C₂²×D₄×C₇₉	Q₈	1	1	yes	characteristic
109	C₂³×C₄×C₇₉	—	2	1	no	—
110	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₇₉	—	2	1	no	—
112	C₂×M₁₆×C₇₉	—	2	1	no	—
113	C₂×M₁₆×C₇₉	—	2	1	no	—
114	C₂×M₁₆×C₇₉	—	2	1	no	—
115	C₂×M₁₆×C₇₉	—	2	1	no	—
116	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
117	C₂²×C₈×C₇₉	—	2	1	no	—
118	#117×C₇₉	—	2	1	no	—
119	#117×C₇₉	—	2	1	no	—
120	#117×C₇₉	—	2	1	no	—
121	#117×C₇₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
124	C₂×C₄²×C₇₉	—	2	1	no	—
125	#104×C₇₉	—	2	8	no	—
126	C₂²×Dic₇₉	—	4	1	no	—
127	#11929608	—	2	8	no	—
128	#11929608	—	2	8	no	—
129	#11929608	—	2	2	no	—
130	#11929608	—	2	2	no	—
131	#11929608	—	2	2	no	—
132	#11929608	—	2	2	no	—
133	#11929608	—	2	2	no	—
134	#11929608	—	4	1	no	—
135	#11929608	—	4	1	no	—
136	#11929608	C₂²×C₄	1	4	yes	—
137	C₂×C₇₉⋊C₈	—	2	8	no	—
138	C₂×C₇₉⋊C₈	—	2	8	no	—
139	C₂×C₇₉⋊C₈	—	2	2	no	—
140	C₂×C₇₉⋊C₈	—	2	2	no	—
141	C₂×C₇₉⋊C₈	—	2	2	no	—
142	C₂×C₇₉⋊C₈	—	2	2	no	—
143	C₂×C₇₉⋊C₈	—	4	1	no	—
144	C₂×C₇₉⋊C₈	—	4	1	no	—
145	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
148	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
151	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
152	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
153	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
154	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
155	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
158	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
159	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
160	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
161	C₄⋊Dic₇₉	—	2	2	no	—
162	C₄⋊Dic₇₉	—	4	1	no	—
163	C₂²⋊Dic₇₉	—	2	2	no	—
164	C₂²⋊Dic₇₉	—	4	1	no	—
165	C₄×Dic₇₉	—	2	2	no	—
166	C₄×Dic₇₉	—	4	1	no	—
167	C₂⁴×C₇₉	—	2	1	no	—
168	C₂⁴×C₇₉	#41	1	1	yes	characteristic
169	#41×C₇₉	—	2	2	no	—
170	#41×C₇₉	—	2	2	no	—
171	#41×C₇₉	—	2	2	no	—
172	#41×C₇₉	—	2	2	no	—
173	#41×C₇₉	—	2	2	no	—
174	#41×C₇₉	—	2	2	no	—
175	#41×C₇₉	—	2	2	no	—
176	#41×C₇₉	—	2	2	no	—
177	#41×C₇₉	—	2	2	no	—
178	#41×C₇₉	—	2	2	no	—
179	#41×C₇₉	—	2	2	no	—
180	#41×C₇₉	—	2	2	no	—
181	#41×C₇₉	C₄⋊C₄	1	4	yes	—
182	#41×C₇₉	C₄⋊C₄	1	4	yes	—
183	#41×C₇₉	C₂²×C₄	1	4	yes	—
184	#41×C₇₉	C₂×D₄	1	4	yes	—
185	C₂×Q₈×C₇₉	—	2	1	no	—
186	C₂×Q₈×C₇₉	—	2	1	no	—
187	C₂×Q₈×C₇₉	—	2	1	no	—
188	C₂×Q₈×C₇₉	C₄⋊C₄	1	2	yes	—
189	C₂×Q₈×C₇₉	C₄⋊C₄	1	2	yes	—
190	C₂×Q₈×C₇₉	C₂×Q₈	1	2	yes	—
191	C₂×D₄×C₇₉	—	2	2	no	—
192	C₂×D₄×C₇₉	—	2	2	no	—
193	C₂×D₄×C₇₉	—	2	2	no	—
194	C₂×D₄×C₇₉	—	2	2	no	—
195	C₂×D₄×C₇₉	—	2	2	no	—
196	C₂×D₄×C₇₉	—	2	2	no	—
197	C₂×D₄×C₇₉	—	2	1	no	—
198	C₂×D₄×C₇₉	—	2	1	no	—
199	C₂×D₄×C₇₉	—	2	1	no	—
200	C₂×D₄×C₇₉	C₄⋊C₄	1	2	yes	—
201	C₂×D₄×C₇₉	C₄⋊C₄	1	2	yes	—
202	C₂×D₄×C₇₉	C₂×Q₈	1	2	yes	—
203	C₂²×C₄×C₇₉	—	2	1	no	—
204	C₂²×C₄×C₇₉	—	2	2	no	—
205	C₂²×C₄×C₇₉	—	2	2	no	—
206	C₂²×C₄×C₇₉	—	2	2	no	—
207	C₂²×C₄×C₇₉	—	2	2	no	—
208	C₂²×C₄×C₇₉	—	2	2	no	—
209	C₂²×C₄×C₇₉	—	2	2	no	—
210	C₂²×C₄×C₇₉	—	4	1	no	—
211	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
220	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
221	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
222	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
223	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
224	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
225	M₁₆×C₇₉	—	2	2	no	—
226	M₁₆×C₇₉	—	2	2	no	—
227	M₁₆×C₇₉	—	4	1	no	—
228	M₁₆×C₇₉	—	4	1	no	—
229	C₂×C₈×C₇₉	—	2	2	no	—
230	C₂×C₈×C₇₉	—	4	1	no	—
231	C₂×C₈×C₇₉	—	4	1	no	—
232	C₄⋊C₄×C₇₉	—	2	2	no	—
233	C₄⋊C₄×C₇₉	—	4	1	no	—
234	C₂²⋊C₄×C₇₉	—	2	2	no	—
235	C₂²⋊C₄×C₇₉	—	4	1	no	—
236	C₄²×C₇₉	—	2	2	no	—
237	C₄²×C₇₉	—	4	1	no	—
238	C₂³×C₇₉	—	2	2	no	—
239	C₂³×C₇₉	—	2	2	no	—
240	C₂³×C₇₉	—	2	2	no	—
241	C₂³×C₇₉	—	4	2	no	—
242	C₂³×C₇₉	—	4	4	no	—
243	C₂³×C₇₉	#117	1	1	yes	characteristic
244	C₂³×C₇₉	#117	1	1	yes	characteristic
245	C₂³×C₇₉	#121	1	1	yes	characteristic
246	C₂³×C₇₉	#121	1	1	yes	characteristic
247	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
250	Q₈×C₇₉	—	2	2	no	—
251	Q₈×C₇₉	—	2	2	no	—
252	Q₈×C₇₉	—	2	2	no	—
253	Q₈×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
254	D₄×C₇₉	—	2	4	no	—
255	D₄×C₇₉	—	2	4	no	—
256	D₄×C₇₉	—	2	4	no	—
257	D₄×C₇₉	—	2	4	no	—
258	D₄×C₇₉	—	2	2	no	—
259	D₄×C₇₉	—	2	2	no	—
260	D₄×C₇₉	—	2	2	no	—
261	D₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
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	4	no	—
266	C₂×C₄×C₇₉	—	2	4	no	—
267	C₂×C₄×C₇₉	—	2	4	no	—
268	C₂×C₄×C₇₉	—	2	4	no	—
269	C₂×C₄×C₇₉	—	4	2	no	—
270	C₂×C₄×C₇₉	—	8	2	no	—
271	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
280	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
281	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
282	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
283	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
284	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
285	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
286	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
287	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
288	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
289	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
290	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
291	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
292	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
293	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
298	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
299	C₂×Dic₇₉	—	4	2	no	—
300	C₂×Dic₇₉	—	8	2	no	—
301	C₈×C₇₉	—	4	2	no	—
302	C₇₉⋊C₈	—	2	4	no	—
303	C₇₉⋊C₈	—	4	2	no	—
304	C₇₉⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
305	C₇₉⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
306	C₇₉⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
307	C₇₉⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂²×C₇₉	—	2	2	no	—
309	C₂²×C₇₉	—	2	2	no	—
310	C₂²×C₇₉	—	2	2	no	—
311	C₂²×C₇₉	—	2	4	no	—
312	C₂²×C₇₉	—	4	1	no	—
313	C₂²×C₇₉	—	4	1	no	—
314	C₂²×C₇₉	—	4	1	no	—
315	C₂²×C₇₉	—	4	1	no	—
316	C₂²×C₇₉	—	4	4	no	—
317	C₂²×C₇₉	—	4	4	no	—
318	C₂²×C₇₉	—	4	4	no	—
319	C₂²×C₇₉	#380	1	1	yes	characteristic
320	C₂²×C₇₉	#380	1	1	yes	characteristic
321	C₂²×C₇₉	#380	1	1	yes	characteristic
322	C₂²×C₇₉	#380	1	1	yes	characteristic
323	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
324	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
325	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
326	C₄×C₇₉	—	2	4	no	—
327	C₄×C₇₉	—	8	2	no	—
328	C₄×C₇₉	#380	1	1	yes	characteristic
329	C₄×C₇₉	#380	1	1	yes	characteristic
330	C₄×C₇₉	#380	1	1	yes	characteristic
331	C₄×C₇₉	#380	1	1	yes	characteristic
332	C₄×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
333	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
334	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
335	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
336	Dic₇₉	—	8	2	no	—
337	C₂×#1814	—	79	1	no	maximal, Sylow
338	C₂×C₇₉	—	2	1	no	—
339	C₂×C₇₉	—	2	1	no	—
340	C₂×C₇₉	—	2	1	no	—
341	C₂×C₇₉	—	2	1	no	—
342	C₂×C₇₉	—	2	1	no	—
343	C₂×C₇₉	—	2	1	no	—
344	C₂×C₇₉	—	4	4	no	—
345	C₂×C₇₉	#1814	1	2	yes	complemented
346	C₂×C₇₉	C₂×#380	1	1	yes	characteristic
347	C₂²×#131	—	79	1	no	—
348	C₂²×#108	—	79	1	no	—
349	C₂×#427	—	79	1	no	—
350	C₂×#421	—	79	1	no	—
351	C₂×#421	D₇₉	1	1	yes	characteristic
352	#1814	—	79	8	no	—
353	C₂×#344	—	79	1	no	—
354	C₂×#344	—	79	1	no	—
355	C₇₉	C₂×#1814	1	1	yes	characteristic, complemented, Sylow
356	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
357	C₂×#131	—	79	4	no	—
358	C₂×#131	—	79	2	no	—
359	C₂×#131	—	79	2	no	—
360	C₂×#131	—	79	4	no	—
361	C₂×#131	—	158	1	no	—
362	C₂×#131	—	158	1	no	—
363	C₂×#131	—	158	2	no	—
364	C₂×#131	—	158	2	no	—
365	C₂²×M₁₆	—	79	1	no	—
366	C₂²×M₁₆	—	79	1	no	—
367	C₂²×M₁₆	—	158	1	no	—
368	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
369	C₂³×C₈	—	79	1	no	—
370	C₂³×C₈	—	158	1	no	—
371	C₂×#117	—	79	1	no	—
372	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
373	C₂×#108	—	79	4	no	—
374	C₂×#108	—	158	1	no	—
375	C₂×#108	—	158	1	no	—
376	C₂×#108	—	158	2	no	—
377	#427	—	79	4	no	—
378	#427	—	158	2	no	—
379	C₂×#107	—	158	1	no	—
380	C₂×#106	—	158	1	no	—
381	#421	—	2	2	no	—
382	#421	—	79	4	no	—
383	#421	—	158	2	no	—
384	#421	C₂×D₇₉	1	4	yes	—
385	C₂×#104	—	2	2	no	—
386	C₂×#104	—	158	2	no	—
387	#344	—	79	4	no	—
388	#344	—	79	4	no	—
389	C₂×#41	—	2	1	no	—
390	C₂×#41	—	2	1	no	—
391	C₂×#41	—	2	1	no	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	—	2	1	no	—
394	C₂×#41	—	2	1	no	—
395	C₂×#41	Dic₁₅₈	1	2	yes	—
396	C₂×#41	C₄×D₇₉	1	2	yes	—
397	C₂×#41	C₄×D₇₉	1	2	yes	—
398	C₂×#41	C₂²⋊D₇₉	1	2	yes	—
399	C₂×#41	C₂²⋊D₇₉	1	2	yes	—
400	C₂×#41	C₂²×D₇₉	1	2	yes	—
401	C₂²×Q₈	Dic₁₅₈	1	1	yes	characteristic
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	Dic₁₅₈	1	1	yes	characteristic
404	C₂³×C₄	—	2	1	no	—
405	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
406	#131	—	79	8	no	—
407	#131	—	79	8	no	—
408	#131	—	158	4	no	—
409	#131	—	158	4	no	—
410	#131	—	158	4	no	—
411	#131	—	158	4	no	—
412	#131	—	158	4	no	—
413	#131	—	158	4	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₂×M₁₆	—	2	1	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	—	2	1	no	—
418	C₂×M₁₆	—	2	1	no	—
419	C₂×M₁₆	—	79	2	no	—
420	C₂×M₁₆	—	79	2	no	—
421	C₂×M₁₆	—	79	2	no	—
422	C₂×M₁₆	—	79	2	no	—
423	C₂×M₁₆	—	158	1	no	—
424	C₂×M₁₆	—	158	1	no	—
425	C₂×M₁₆	—	158	1	no	—
426	C₂×M₁₆	—	158	1	no	—
427	C₂×M₁₆	—	158	2	no	—
428	C₂×M₁₆	—	158	2	no	—
429	C₂×M₁₆	—	158	4	no	—
430	C₂×M₁₆	—	158	4	no	—
431	C₂×M₁₆	—	158	1	no	—
432	C₂×M₁₆	—	158	1	no	—
433	C₂×M₁₆	—	158	1	no	—
434	C₂×M₁₆	—	158	1	no	—
435	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
436	C₂²×C₈	—	2	1	no	—
437	C₂²×C₈	—	79	1	no	—
438	C₂²×C₈	—	79	1	no	—
439	C₂²×C₈	—	79	2	no	—
440	C₂²×C₈	—	79	1	no	—
441	C₂²×C₈	—	79	1	no	—
442	C₂²×C₈	—	79	1	no	—
443	C₂²×C₈	—	79	1	no	—
444	C₂²×C₈	—	79	2	no	—
445	C₂²×C₈	—	79	2	no	—
446	C₂²×C₈	—	79	2	no	—
447	C₂²×C₈	—	158	1	no	—
448	C₂²×C₈	—	158	2	no	—
449	C₂²×C₈	—	158	2	no	—
450	C₂²×C₈	—	158	4	no	—
451	C₂²×C₈	—	158	4	no	—
452	C₂²×C₈	—	158	1	no	—
453	#117	—	2	1	no	—
454	#117	—	2	1	no	—
455	#117	—	2	1	no	—
456	#117	—	79	2	no	—
457	#117	—	158	1	no	—
458	#117	—	158	1	no	—
459	#117	—	158	1	no	—
460	#117	C₂²×D₇₉	1	2	yes	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	158	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	158	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	158	1	no	—
467	#108	—	158	4	no	—
468	#108	—	158	4	no	—
469	#107	—	158	4	no	—
470	#106	—	158	4	no	—
471	#104	—	2	8	no	—
472	#104	—	158	8	no	—
473	C₂⁴	—	2	1	no	—
474	C₂⁴	#11929623	1	1	yes	characteristic
475	#41	—	2	2	no	—
476	#41	—	2	2	no	—
477	#41	—	2	2	no	—
478	#41	—	2	2	no	—
479	#41	—	2	2	no	—
480	#41	—	2	2	no	—
481	#41	—	2	2	no	—
482	#41	—	2	2	no	—
483	#41	—	2	2	no	—
484	#41	—	2	2	no	—
485	#41	—	2	2	no	—
486	#41	—	2	2	no	—
487	#41	Dic₇₉⋊C₄	1	4	yes	—
488	#41	Dic₇₉⋊C₄	1	4	yes	—
489	#41	C₂×C₄×D₇₉	1	4	yes	—
490	#41	C₂×C₂²⋊D₇₉	1	4	yes	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	Dic₇₉⋊C₄	1	2	yes	—
495	C₂×Q₈	Dic₇₉⋊C₄	1	2	yes	—
496	C₂×Q₈	C₂×Dic₁₅₈	1	2	yes	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	Dic₇₉⋊C₄	1	2	yes	—
507	C₂×D₄	Dic₇₉⋊C₄	1	2	yes	—
508	C₂×D₄	C₂×Dic₁₅₈	1	2	yes	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	4	1	no	—
517	C₂²×C₄	—	316	1	no	—
518	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
520	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
521	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
522	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
523	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
526	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
527	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
528	C₂²×C₄	#11929623	1	1	yes	characteristic
529	C₂²×C₄	#11929623	1	1	yes	characteristic
530	C₂²×C₄	#11929623	1	1	yes	characteristic
531	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	2	no	—
534	M₁₆	—	4	1	no	—
535	M₁₆	—	4	1	no	—
536	M₁₆	—	316	1	no	—
537	M₁₆	—	316	1	no	—
538	M₁₆	—	79	4	no	—
539	M₁₆	—	158	2	no	—
540	M₁₆	—	158	2	no	—
541	M₁₆	—	158	8	no	—
542	M₁₆	—	158	8	no	—
543	M₁₆	—	158	2	no	—
544	M₁₆	—	158	2	no	—
545	M₁₆	—	158	2	no	—
546	C₂×C₈	—	2	2	no	—
547	C₂×C₈	—	4	1	no	—
548	C₂×C₈	—	4	1	no	—
549	C₂×C₈	—	316	1	no	—
550	C₂×C₈	—	316	1	no	—
551	C₂×C₈	—	79	1	no	—
552	C₂×C₈	—	79	1	no	—
553	C₂×C₈	—	79	2	no	—
554	C₂×C₈	—	79	1	no	—
555	C₂×C₈	—	79	1	no	—
556	C₂×C₈	—	79	2	no	—
557	C₂×C₈	—	79	2	no	—
558	C₂×C₈	—	79	2	no	—
559	C₂×C₈	—	79	2	no	—
560	C₂×C₈	—	79	2	no	—
561	C₂×C₈	—	79	2	no	—
562	C₂×C₈	—	79	2	no	—
563	C₂×C₈	—	79	2	no	—
564	C₂×C₈	—	79	2	no	—
565	C₂×C₈	—	79	2	no	—
566	C₂×C₈	—	79	2	no	—
567	C₂×C₈	—	158	2	no	—
568	C₂×C₈	—	158	8	no	—
569	C₂×C₈	—	158	8	no	—
570	C₂×C₈	—	158	2	no	—
571	C₂×C₈	—	158	2	no	—
572	C₂×C₈	—	158	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	316	1	no	—
576	C₄⋊C₄	—	158	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	4	1	no	—
579	C₂²⋊C₄	—	316	1	no	—
580	C₂²⋊C₄	—	158	2	no	—
581	C₄²	—	2	2	no	—
582	C₄²	—	4	1	no	—
583	C₄²	—	316	1	no	—
584	C₄²	—	158	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	4	4	no	—
590	C₂³	#14579117	1	1	yes	characteristic
591	C₂³	#14579117	1	1	yes	characteristic
592	C₂³	#14579133	1	1	yes	characteristic
593	C₂³	#14579133	1	1	yes	characteristic
594	C₂³	#14579138	1	1	yes	characteristic
595	C₂³	#14579138	1	1	yes	characteristic
596	C₂³	C₂×#11929623	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	C₂×Dic₇₉⋊C₄	1	4	yes	—
601	D₄	—	2	4	no	—
602	D₄	—	2	4	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	2	no	—
608	D₄	C₂×Dic₇₉⋊C₄	1	4	yes	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	8	2	no	—
618	C₂×C₄	—	316	2	no	—
619	C₂×C₄	—	632	2	no	—
620	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
621	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
622	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
623	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
624	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
625	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
626	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
627	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
628	C₂×C₄	#14579117	1	1	yes	characteristic
629	C₂×C₄	#14579117	1	1	yes	characteristic
630	C₂×C₄	#14579133	1	1	yes	characteristic
631	C₂×C₄	#14579133	1	1	yes	characteristic
632	C₂×C₄	#14579133	1	1	yes	characteristic
633	C₂×C₄	#14579133	1	1	yes	characteristic
634	C₂×C₄	#14579133	1	1	yes	characteristic
635	C₂×C₄	#14579133	1	1	yes	characteristic
636	C₂×C₄	#14579138	1	1	yes	characteristic
637	C₂×C₄	#14579138	1	1	yes	characteristic
638	C₂×C₄	#14579138	1	1	yes	characteristic
639	C₂×C₄	#14579138	1	1	yes	characteristic
640	C₂×C₄	#14579138	1	1	yes	characteristic
641	C₂×C₄	#14579138	1	1	yes	characteristic
642	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
643	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
644	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
645	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
646	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
647	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
648	C₈	—	4	2	no	—
649	C₈	—	316	2	no	—
650	C₈	—	79	2	no	—
651	C₈	—	79	2	no	—
652	C₈	—	79	2	no	—
653	C₈	—	79	2	no	—
654	C₈	—	158	4	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	4	no	—
665	C₂²	—	4	4	no	—
666	C₂²	#19098421	1	1	yes	characteristic
667	C₂²	#19098421	1	1	yes	characteristic
668	C₂²	#19098421	1	1	yes	characteristic
669	C₂²	#19098421	1	1	yes	characteristic
670	C₂²	C₂×#14579117	1	1	yes	characteristic
671	C₂²	C₂×#14579133	1	1	yes	characteristic
672	C₂²	C₂×#14579138	1	1	yes	characteristic
673	C₄	—	2	4	no	—
674	C₄	—	8	2	no	—
675	C₄	—	632	2	no	—
676	C₄	#19098421	1	1	yes	characteristic
677	C₄	#19098421	1	1	yes	characteristic
678	C₄	#19098421	1	1	yes	characteristic
679	C₄	#19098421	1	1	yes	characteristic
680	C₄	C₂×C₂²⋊C₄×D₇₉	1	1	yes	characteristic
681	C₄	C₂²×Dic₇₉⋊C₄	1	1	yes	characteristic
682	C₄	C₂×#14579133	1	1	yes	characteristic
683	C₄	C₂×#14579138	1	1	yes	characteristic
684	C₂	—	2	1	no	—
685	C₂	—	2	1	no	—
686	C₂	—	2	1	no	—
687	C₂	—	2	1	no	—
688	C₂	—	2	1	no	—
689	C₂	—	2	1	no	—
690	C₂	—	4	4	no	—
691	C₂	#23763452	1	2	yes	direct product factor
692	C₂	C₂×#19098421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579133
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#421×C₇₉	C₂
socle	C₂²×C₇₉	#380
prime radical	C₂²×#41×C₇₉	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#421	D₇₉
hypocenter	C₇₉	C₂×#1814
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#421

Complements

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

N	H ≅ G/N	type
2. C₂²×#14579096	C₂	semidirect
3. C₂×#19098599	C₂	semidirect
5. #23763452	C₂	direct (N × H)
6. C₂×#19098334	C₂	semidirect
7. C₂×#19098333	C₂	semidirect
13. C₂×#14579168	C₄	semidirect
14. C₂×#14579168	C₄	semidirect
15. C₂×#14579168	C₄	semidirect
26. C₂×#14579096	C₂²	semidirect
28. #19098599	C₂²	semidirect
34. #19098334	C₂²	semidirect
35. #19098333	C₂²	semidirect
48. #14579168	C₂×C₄	semidirect
49. #14579168	C₂×C₄	semidirect
345. C₂×C₇₉	#1814	semidirect
355. C₇₉	C₂×#1814	semidirect
691. C₂	#23763452	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14579168	2
C₂²×#14579096	2
C₂×#19098599	2
C₂×#19098580	2
#23763452	2
C₂×#19098334	2
C₂×#19098333	2
C₂×#421×C₇₉	2
C₂×#1814	79

Subgroups — C2×#23763452 #34287929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23763452 #34287929