Subgroups — C₂×#23764574 #34315695

Order 20224.

1234 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099116	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098580	C₂	1	1	yes	maximal, characteristic
3	C₂²×#14579088	C₂	1	1	yes	maximal, characteristic
4	#23764574	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19098333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19098322	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19098319	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#410×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11929608	C₂²	1	1	yes	characteristic
10	C₂²×#11929608	C₂²	1	1	yes	characteristic
11	#19099116	—	2	2	no	—
12	#19099116	—	2	2	no	—
13	#19099116	—	2	2	no	—
14	#19099116	C₂²	1	4	yes	complemented
15	C₂×#14579160	—	2	1	no	—
16	C₂×#14579152	—	2	1	no	—
17	C₂×#14579138	—	2	2	no	—
18	C₂×C₄×Dic₁₅₈	—	2	2	no	—
19	C₂×#14579120	C₂²	1	1	yes	characteristic
20	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
21	#19098580	—	2	2	no	—
22	#19098580	C₂²	1	4	yes	—
23	C₂×#14579088	—	2	1	no	—
24	C₂×#14579088	—	2	1	no	—
25	C₂×#14579088	—	2	2	no	—
26	C₂×#14579088	—	2	2	no	—
27	C₂×#14579088	C₂²	1	4	yes	—
28	#19098333	C₂²	1	4	yes	complemented
29	#19098322	C₂²	1	4	yes	complemented
30	#19098319	C₂²	1	4	yes	complemented
31	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
34	#410×C₇₉	—	2	2	no	—
35	#410×C₇₉	C₂²	1	4	yes	—
36	C₂×#99×C₇₉	—	2	2	no	—
37	C₂²×Dic₁₅₈	—	2	2	no	—
38	C₂³×Dic₇₉	—	2	1	no	—
39	C₂×#11929608	—	2	1	no	—
40	C₂×#11929608	—	2	1	no	—
41	C₂×#11929608	—	2	1	no	—
42	C₂×#11929608	—	2	1	no	—
43	C₂×#11929608	—	2	1	no	—
44	C₂×#11929608	—	2	1	no	—
45	C₂×#11929608	—	2	1	no	—
46	C₂×#11929608	—	2	1	no	—
47	C₂×#11929608	—	2	1	no	—
48	C₂×#11929608	—	2	1	no	—
49	C₂×#11929608	C₂³	1	2	yes	—
50	C₂×#11929608	C₂³	1	2	yes	—
51	C₂²×C₇₉⋊C₈	—	2	1	no	—
52	C₂²×C₇₉⋊C₈	—	2	1	no	—
53	#14579160	—	2	4	no	—
54	#14579160	—	2	4	no	—
55	#14579152	—	2	4	no	—
56	#14579152	—	2	4	no	—
57	#14579138	—	2	8	no	—
58	#14579138	—	2	8	no	—
59	C₄×Dic₁₅₈	—	2	8	no	—
60	C₄×Dic₁₅₈	—	2	8	no	—
61	#14579120	—	2	1	no	—
62	#14579120	—	2	1	no	—
63	#14579120	D₄	1	2	yes	—
64	#14579120	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₇₉	—	2	2	no	—
66	C₂×C₄⋊Dic₇₉	—	2	1	no	—
67	C₂×Dic₇₉⋊C₄	—	2	2	no	—
68	C₂×Dic₇₉⋊C₄	—	2	2	no	—
69	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
70	C₂×C₄×Dic₇₉	—	2	1	no	—
71	C₂×C₄×Dic₇₉	—	2	1	no	—
72	C₂×C₄×Dic₇₉	—	2	1	no	—
73	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
74	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
75	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
76	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
77	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
78	#14579088	—	2	4	no	—
79	#14579088	—	2	4	no	—
80	#14579088	—	2	8	no	—
81	C₂×#41×C₇₉	—	2	1	no	—
82	C₂×#41×C₇₉	—	2	1	no	—
83	C₂×#41×C₇₉	—	2	1	no	—
84	C₂×#41×C₇₉	—	2	1	no	—
85	C₂×#41×C₇₉	—	2	1	no	—
86	C₂×#41×C₇₉	—	2	1	no	—
87	C₂×#41×C₇₉	—	2	1	no	—
88	C₂×#41×C₇₉	—	2	1	no	—
89	C₂×#41×C₇₉	—	2	1	no	—
90	C₂×#41×C₇₉	—	2	1	no	—
91	C₂×#41×C₇₉	Q₈	1	2	yes	complemented
92	C₂×#41×C₇₉	C₂³	1	2	yes	—
93	C₂²×Q₈×C₇₉	Q₈	1	1	yes	characteristic, complemented
94	C₂²×D₄×C₇₉	—	2	1	no	—
95	C₂²×D₄×C₇₉	Q₈	1	1	yes	characteristic, complemented
96	C₂³×C₄×C₇₉	—	2	1	no	—
97	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
98	#117×C₇₉	—	2	1	no	—
99	#117×C₇₉	—	2	1	no	—
100	#117×C₇₉	—	2	1	no	—
101	#117×C₇₉	—	2	1	no	—
102	#117×C₇₉	—	2	1	no	—
103	#117×C₇₉	D₄	1	2	yes	—
104	#117×C₇₉	C₂³	1	2	yes	—
105	#117×C₇₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
110	C₂×C₄²×C₇₉	—	2	1	no	—
111	C₂×C₄²×C₇₉	—	2	1	no	—
112	#99×C₇₉	—	2	8	no	—
113	C₂×Dic₁₅₈	—	2	8	no	—
114	C₂×Dic₁₅₈	—	4	8	no	—
115	C₂²×Dic₇₉	—	2	1	no	—
116	C₂²×Dic₇₉	—	2	2	no	—
117	C₂²×Dic₇₉	—	2	1	no	—
118	C₂²×Dic₇₉	—	2	2	no	—
119	C₂²×Dic₇₉	—	2	2	no	—
120	C₂²×Dic₇₉	—	4	4	no	—
121	#11929608	—	2	2	no	—
122	#11929608	—	2	2	no	—
123	#11929608	—	2	2	no	—
124	#11929608	—	2	2	no	—
125	#11929608	—	4	1	no	—
126	#11929608	—	4	1	no	—
127	#11929608	—	4	1	no	—
128	#11929608	—	4	1	no	—
129	C₂×C₇₉⋊C₈	—	2	2	no	—
130	C₂×C₇₉⋊C₈	—	2	2	no	—
131	C₂×C₇₉⋊C₈	—	4	1	no	—
132	C₂×C₇₉⋊C₈	—	4	1	no	—
133	C₂×C₇₉⋊C₈	—	4	1	no	—
134	C₂×C₇₉⋊C₈	—	4	1	no	—
135	C₄⋊Dic₇₉	—	2	8	no	—
136	C₄⋊Dic₇₉	—	2	2	no	—
137	C₄⋊Dic₇₉	—	2	2	no	—
138	Dic₇₉⋊C₄	—	2	8	no	—
139	Dic₇₉⋊C₄	—	2	8	no	—
140	C₂²⋊Dic₇₉	—	2	2	no	—
141	C₂²⋊Dic₇₉	—	2	2	no	—
142	C₄×Dic₇₉	—	2	2	no	—
143	C₄×Dic₇₉	—	2	1	no	—
144	C₄×Dic₇₉	—	2	1	no	—
145	C₄×Dic₇₉	—	2	2	no	—
146	C₄×Dic₇₉	—	2	2	no	—
147	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
148	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
149	C₄×Dic₇₉	C₂×D₄	1	4	yes	—
150	C₂⁴×C₇₉	—	2	1	no	—
151	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
152	#41×C₇₉	—	2	2	no	—
153	#41×C₇₉	—	2	2	no	—
154	#41×C₇₉	—	2	2	no	—
155	#41×C₇₉	—	2	2	no	—
156	#41×C₇₉	—	2	2	no	—
157	#41×C₇₉	—	2	2	no	—
158	#41×C₇₉	—	2	2	no	—
159	#41×C₇₉	—	2	2	no	—
160	#41×C₇₉	—	4	1	no	—
161	#41×C₇₉	—	4	1	no	—
162	#41×C₇₉	—	4	1	no	—
163	#41×C₇₉	—	4	1	no	—
164	#41×C₇₉	—	4	1	no	—
165	#41×C₇₉	—	4	1	no	—
166	#41×C₇₉	—	4	1	no	—
167	#41×C₇₉	—	4	1	no	—
168	C₂×Q₈×C₇₉	—	2	1	no	—
169	C₂×Q₈×C₇₉	—	2	1	no	—
170	C₂×Q₈×C₇₉	—	2	1	no	—
171	C₂×Q₈×C₇₉	—	2	1	no	—
172	C₂×Q₈×C₇₉	—	2	1	no	—
173	C₂×Q₈×C₇₉	C₂×Q₈	1	2	yes	complemented
174	C₂×D₄×C₇₉	—	2	2	no	—
175	C₂×D₄×C₇₉	—	2	2	no	—
176	C₂×D₄×C₇₉	—	2	1	no	—
177	C₂×D₄×C₇₉	—	2	1	no	—
178	C₂×D₄×C₇₉	—	2	1	no	—
179	C₂×D₄×C₇₉	—	2	1	no	—
180	C₂×D₄×C₇₉	—	2	1	no	—
181	C₂×D₄×C₇₉	—	4	1	no	—
182	C₂×D₄×C₇₉	—	4	1	no	—
183	C₂×D₄×C₇₉	—	4	1	no	—
184	C₂×D₄×C₇₉	—	4	1	no	—
185	C₂×D₄×C₇₉	C₂×Q₈	1	2	yes	complemented
186	C₂²×C₄×C₇₉	—	2	2	no	—
187	C₂²×C₄×C₇₉	—	2	1	no	—
188	C₂²×C₄×C₇₉	—	2	2	no	—
189	C₂²×C₄×C₇₉	—	2	2	no	—
190	C₂²×C₄×C₇₉	—	4	1	no	—
191	C₂²×C₄×C₇₉	—	4	1	no	—
192	C₂²×C₄×C₇₉	—	4	1	no	—
193	C₂²×C₄×C₇₉	—	4	1	no	—
194	C₂²×C₄×C₇₉	—	4	1	no	—
195	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
201	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
202	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
203	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
204	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
205	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
206	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
207	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
208	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
209	C₄⋊C₄×C₇₉	—	2	2	no	—
210	C₄⋊C₄×C₇₉	—	2	2	no	—
211	C₄⋊C₄×C₇₉	—	2	2	no	—
212	C₄⋊C₄×C₇₉	—	4	1	no	—
213	C₂²⋊C₄×C₇₉	—	2	2	no	—
214	C₂²⋊C₄×C₇₉	—	2	2	no	—
215	C₂²⋊C₄×C₇₉	—	4	1	no	—
216	C₂²⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
217	C₄²×C₇₉	—	2	2	no	—
218	C₄²×C₇₉	—	2	2	no	—
219	C₄²×C₇₉	—	2	2	no	—
220	C₄²×C₇₉	—	4	1	no	—
221	C₂³×C₇₉	—	2	2	no	—
222	C₂³×C₇₉	—	4	2	no	—
223	C₂³×C₇₉	—	4	1	no	—
224	C₂³×C₇₉	—	4	1	no	—
225	C₂³×C₇₉	—	8	2	no	—
226	C₂³×C₇₉	#120	1	1	yes	characteristic
227	C₂³×C₇₉	#120	1	1	yes	characteristic
228	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
230	C₂³×C₇₉	#124	1	1	yes	characteristic
231	C₂³×C₇₉	#124	1	1	yes	characteristic
232	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₇₉	—	2	2	no	—
234	Q₈×C₇₉	—	2	2	no	—
235	Q₈×C₇₉	—	4	1	no	—
236	Q₈×C₇₉	—	4	1	no	—
237	D₄×C₇₉	—	2	2	no	—
238	D₄×C₇₉	—	2	2	no	—
239	D₄×C₇₉	—	4	2	no	—
240	D₄×C₇₉	—	4	2	no	—
241	D₄×C₇₉	—	4	2	no	—
242	D₄×C₇₉	—	4	2	no	—
243	D₄×C₇₉	—	4	1	no	—
244	D₄×C₇₉	—	4	1	no	—
245	C₂×C₄×C₇₉	—	2	4	no	—
246	C₂×C₄×C₇₉	—	2	2	no	—
247	C₂×C₄×C₇₉	—	4	4	no	—
248	C₂×C₄×C₇₉	—	4	1	no	—
249	C₂×C₄×C₇₉	—	4	1	no	—
250	C₂×C₄×C₇₉	—	4	2	no	—
251	C₂×C₄×C₇₉	—	4	2	no	—
252	C₂×C₄×C₇₉	—	4	2	no	—
253	C₂×C₄×C₇₉	—	4	2	no	—
254	C₂×C₄×C₇₉	—	4	2	no	—
255	C₂×C₄×C₇₉	—	8	2	no	—
256	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
258	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
260	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
269	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
270	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
271	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
272	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
273	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
274	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
275	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
276	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
277	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
278	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
281	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
284	C₂×Dic₇₉	—	2	4	no	—
285	C₂×Dic₇₉	—	2	2	no	—
286	C₂×Dic₇₉	—	2	2	no	—
287	C₂×Dic₇₉	—	2	4	no	—
288	C₂×Dic₇₉	—	4	4	no	—
289	C₂×Dic₇₉	—	4	4	no	—
290	C₂×Dic₇₉	—	4	2	no	—
291	C₂×Dic₇₉	—	4	4	no	—
292	Dic₁₅₈	—	4	16	no	—
293	C₇₉⋊C₈	—	4	2	no	—
294	C₇₉⋊C₈	—	4	2	no	—
295	C₂²×C₇₉	—	2	2	no	—
296	C₂²×C₇₉	—	2	2	no	—
297	C₂²×C₇₉	—	2	2	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	2	no	—
303	C₂²×C₇₉	—	8	2	no	—
304	C₂²×C₇₉	—	8	2	no	—
305	C₂²×C₇₉	—	8	2	no	—
306	C₂²×C₇₉	#393	1	1	yes	characteristic
307	C₂²×C₇₉	#393	1	1	yes	characteristic
308	C₂²×C₇₉	#393	1	1	yes	characteristic
309	C₂²×C₇₉	#393	1	1	yes	characteristic
310	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
311	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
312	C₂²×C₇₉	C₂×#124	1	1	yes	characteristic
313	C₄×C₇₉	—	4	4	no	—
314	C₄×C₇₉	—	4	2	no	—
315	C₄×C₇₉	—	8	2	no	—
316	C₄×C₇₉	#393	1	1	yes	characteristic
317	C₄×C₇₉	#393	1	1	yes	characteristic
318	C₄×C₇₉	#393	1	1	yes	characteristic
319	C₄×C₇₉	#393	1	1	yes	characteristic
320	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
321	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
322	C₄×C₇₉	C₂×#124	1	1	yes	characteristic
323	C₄×C₇₉	C₂×#124	1	1	yes	characteristic
324	Dic₇₉	—	2	4	no	—
325	Dic₇₉	—	4	4	no	—
326	Dic₇₉	—	4	2	no	—
327	C₂×#2031	—	79	1	no	maximal, Sylow
328	C₂×C₇₉	—	2	1	no	—
329	C₂×C₇₉	—	2	1	no	—
330	C₂×C₇₉	—	2	1	no	—
331	C₂×C₇₉	—	2	1	no	—
332	C₂×C₇₉	—	2	1	no	—
333	C₂×C₇₉	—	2	1	no	—
334	C₂×C₇₉	—	8	2	no	—
335	C₂×C₇₉	#2031	1	2	yes	complemented
336	C₂×C₇₉	C₂×#393	1	1	yes	characteristic
337	C₂×#533	—	79	1	no	—
338	C₂×#421	—	79	1	no	—
339	C₂²×#104	—	79	1	no	—
340	C₂×#410	D₇₉	1	1	yes	characteristic
341	#2031	—	79	8	no	—
342	C₂×#344	—	79	1	no	—
343	C₂×#339	—	79	1	no	—
344	C₂×H(3,ℤ/4)	—	79	1	no	—
345	C₇₉	C₂×#2031	1	1	yes	characteristic, complemented, Sylow
346	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
347	C₂²×M₁₆	—	79	1	no	—
348	C₂²×M₁₆	—	79	1	no	—
349	#533	—	79	4	no	—
350	#533	—	158	2	no	—
351	#533	—	158	2	no	—
352	#533	—	158	2	no	—
353	C₂×C₄⋊Q₈	—	158	1	no	—
354	C₂×#125	—	158	1	no	—
355	C₂×C₂²⋊Q₈	—	158	2	no	—
356	C₂×C₄×Q₈	—	158	2	no	—
357	C₂×#117	—	79	1	no	—
358	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
359	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
360	C₂²×C₄²	—	79	1	no	—
361	#421	—	79	4	no	—
362	#421	—	158	2	no	—
363	C₂×#104	—	79	4	no	—
364	C₂×#104	—	158	1	no	—
365	C₂×#104	—	158	1	no	—
366	C₂×#104	—	158	2	no	—
367	C₂×#104	—	158	2	no	—
368	#410	—	2	2	no	—
369	#410	C₂×D₇₉	1	4	yes	—
370	C₂×#99	—	2	2	no	—
371	#344	—	79	4	no	—
372	#339	—	79	4	no	—
373	H(3,ℤ/4)	—	79	4	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	1	no	—
377	C₂×#41	—	2	1	no	—
378	C₂×#41	—	2	1	no	—
379	C₂×#41	—	2	1	no	—
380	C₂×#41	—	2	1	no	—
381	C₂×#41	—	2	1	no	—
382	C₂×#41	—	2	1	no	—
383	C₂×#41	—	2	1	no	—
384	C₂×#41	Dic₁₅₈	1	2	yes	complemented
385	C₂×#41	C₂²×D₇₉	1	2	yes	—
386	C₂²×Q₈	—	158	2	no	—
387	C₂²×Q₈	Dic₁₅₈	1	1	yes	characteristic, complemented
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	Dic₁₅₈	1	1	yes	characteristic, complemented
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	—	158	1	no	—
392	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
393	C₂×M₁₆	—	79	2	no	—
394	C₂×M₁₆	—	79	2	no	—
395	C₂×M₁₆	—	158	1	no	—
396	C₂×M₁₆	—	158	1	no	—
397	C₂×M₁₆	—	158	1	no	—
398	C₂×M₁₆	—	158	1	no	—
399	C₂×M₁₆	—	158	1	no	—
400	C₂×M₁₆	—	158	1	no	—
401	C₂×M₁₆	—	158	1	no	—
402	C₂×M₁₆	—	158	1	no	—
403	C₂×M₁₆	—	158	1	no	—
404	C₂×M₁₆	—	158	1	no	—
405	C₂²×C₈	—	158	1	no	—
406	C₂²×C₈	—	158	1	no	—
407	C₄⋊Q₈	—	158	4	no	—
408	C₄⋊Q₈	—	158	4	no	—
409	#125	—	158	4	no	—
410	#125	—	158	4	no	—
411	C₂²⋊Q₈	—	158	8	no	—
412	C₂²⋊Q₈	—	158	8	no	—
413	C₄×Q₈	—	158	8	no	—
414	C₄×Q₈	—	158	8	no	—
415	#117	—	2	1	no	—
416	#117	—	2	1	no	—
417	#117	—	2	1	no	—
418	#117	—	2	1	no	—
419	#117	—	2	1	no	—
420	#117	—	79	2	no	—
421	#117	—	79	2	no	—
422	#117	—	158	1	no	—
423	#117	—	158	1	no	—
424	#117	C₂²⋊D₇₉	1	2	yes	—
425	#117	C₂²×D₇₉	1	2	yes	—
426	#117	C₂²×D₇₉	1	2	yes	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	158	2	no	—
430	C₂×C₄⋊C₄	—	158	2	no	—
431	C₂×C₄⋊C₄	—	158	2	no	—
432	C₂×C₄⋊C₄	—	158	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	158	1	no	—
435	C₂×C₂²⋊C₄	C₂²⋊D₇₉	1	2	yes	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	79	2	no	—
439	C₂×C₄²	—	79	1	no	—
440	C₂×C₄²	—	79	1	no	—
441	C₂×C₄²	—	79	2	no	—
442	C₂×C₄²	—	79	2	no	—
443	C₂×C₄²	—	158	1	no	—
444	C₂×C₄²	—	158	1	no	—
445	C₂×C₄²	—	158	1	no	—
446	#104	—	158	4	no	—
447	#104	—	158	4	no	—
448	#104	—	158	8	no	—
449	#99	—	2	8	no	—
450	C₂⁴	—	2	1	no	—
451	C₂⁴	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	2	2	no	—
460	#41	—	4	1	no	—
461	#41	—	4	1	no	—
462	#41	—	4	1	no	—
463	#41	—	4	1	no	—
464	#41	—	4	1	no	—
465	#41	—	4	1	no	—
466	#41	—	4	1	no	—
467	#41	—	4	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	316	8	no	—
474	C₂×Q₈	—	158	8	no	—
475	C₂×Q₈	C₂×Dic₁₅₈	1	2	yes	complemented
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	C₂×Dic₁₅₈	1	2	yes	complemented
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	4	1	no	—
493	C₂²×C₄	—	4	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	—	316	4	no	—
498	C₂²×C₄	—	158	1	no	—
499	C₂²×C₄	—	158	2	no	—
500	C₂²×C₄	—	158	2	no	—
501	C₂²×C₄	—	158	2	no	—
502	C₂²×C₄	—	158	1	no	—
503	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
504	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
505	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
506	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
509	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
510	C₂²×C₄	#11929623	1	1	yes	characteristic
511	C₂²×C₄	#11929623	1	1	yes	characteristic
512	C₂²×C₄	#11929623	1	1	yes	characteristic
513	C₂²×C₄	#11929623	1	1	yes	characteristic
514	C₂²×C₄	#11929624	1	1	yes	characteristic
515	C₂²×C₄	#11929624	1	1	yes	characteristic
516	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
517	M₁₆	—	316	1	no	—
518	M₁₆	—	316	1	no	—
519	M₁₆	—	316	1	no	—
520	M₁₆	—	316	1	no	—
521	M₁₆	—	158	2	no	—
522	M₁₆	—	158	2	no	—
523	M₁₆	—	158	2	no	—
524	M₁₆	—	158	2	no	—
525	C₂×C₈	—	316	1	no	—
526	C₂×C₈	—	316	1	no	—
527	C₂×C₈	—	316	1	no	—
528	C₂×C₈	—	316	1	no	—
529	C₂×C₈	—	158	2	no	—
530	C₂×C₈	—	158	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₄⋊C₄	—	158	8	no	—
536	C₄⋊C₄	—	158	8	no	—
537	C₄⋊C₄	—	158	8	no	—
538	C₄⋊C₄	—	158	2	no	—
539	C₄⋊C₄	—	158	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	4	1	no	—
543	C₂²⋊C₄	—	158	2	no	—
544	C₂²⋊C₄	—	158	2	no	—
545	C₂²⋊C₄	C₂×C₂²⋊D₇₉	1	4	yes	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	4	1	no	—
550	C₄²	—	79	2	no	—
551	C₄²	—	79	2	no	—
552	C₄²	—	79	4	no	—
553	C₄²	—	158	2	no	—
554	C₄²	—	158	1	no	—
555	C₄²	—	158	1	no	—
556	C₄²	—	158	2	no	—
557	C₄²	—	158	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	8	2	no	—
563	C₂³	#14579129	1	1	yes	characteristic
564	C₂³	#14579129	1	1	yes	characteristic
565	C₂³	#14579140	1	1	yes	characteristic
566	C₂³	#14579140	1	1	yes	characteristic
567	C₂³	#14579148	1	1	yes	characteristic
568	C₂³	#14579148	1	1	yes	characteristic
569	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
570	Q₈	—	2	2	no	—
571	Q₈	—	2	2	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	—	316	16	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	8	2	no	—
594	C₂×C₄	—	316	2	no	—
595	C₂×C₄	—	316	4	no	—
596	C₂×C₄	—	316	4	no	—
597	C₂×C₄	—	316	4	no	—
598	C₂×C₄	—	158	2	no	—
599	C₂×C₄	—	158	4	no	—
600	C₂×C₄	—	158	4	no	—
601	C₂×C₄	—	158	2	no	—
602	C₂×C₄	#14579129	1	1	yes	characteristic
603	C₂×C₄	#14579129	1	1	yes	characteristic
604	C₂×C₄	#14579138	1	1	yes	characteristic
605	C₂×C₄	#14579138	1	1	yes	characteristic
606	C₂×C₄	#14579138	1	1	yes	characteristic
607	C₂×C₄	#14579138	1	1	yes	characteristic
608	C₂×C₄	#14579138	1	1	yes	characteristic
609	C₂×C₄	#14579138	1	1	yes	characteristic
610	C₂×C₄	#14579138	1	1	yes	characteristic
611	C₂×C₄	#14579138	1	1	yes	characteristic
612	C₂×C₄	#14579140	1	1	yes	characteristic
613	C₂×C₄	#14579140	1	1	yes	characteristic
614	C₂×C₄	#14579147	1	1	yes	characteristic
615	C₂×C₄	#14579147	1	1	yes	characteristic
616	C₂×C₄	#14579147	1	1	yes	characteristic
617	C₂×C₄	#14579147	1	1	yes	characteristic
618	C₂×C₄	#14579147	1	1	yes	characteristic
619	C₂×C₄	#14579147	1	1	yes	characteristic
620	C₂×C₄	#14579147	1	1	yes	characteristic
621	C₂×C₄	#14579147	1	1	yes	characteristic
622	C₂×C₄	#14579148	1	1	yes	characteristic
623	C₂×C₄	#14579148	1	1	yes	characteristic
624	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
625	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
626	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
627	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
628	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
629	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
630	C₈	—	316	2	no	—
631	C₈	—	316	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	8	2	no	—
641	C₂²	—	8	2	no	—
642	C₂²	—	8	2	no	—
643	C₂²	#19098475	1	1	yes	characteristic
644	C₂²	#19098475	1	1	yes	characteristic
645	C₂²	#19098475	1	1	yes	characteristic
646	C₂²	#19098475	1	1	yes	characteristic
647	C₂²	C₂×#14579129	1	1	yes	characteristic
648	C₂²	C₂×#14579140	1	1	yes	characteristic
649	C₂²	C₂×#14579148	1	1	yes	characteristic
650	C₄	—	4	4	no	—
651	C₄	—	4	2	no	—
652	C₄	—	8	2	no	—
653	C₄	—	316	2	no	—
654	C₄	—	316	4	no	—
655	C₄	—	158	4	no	—
656	C₄	#19098475	1	1	yes	characteristic
657	C₄	#19098475	1	1	yes	characteristic
658	C₄	#19098475	1	1	yes	characteristic
659	C₄	#19098475	1	1	yes	characteristic
660	C₄	C₂×#14579138	1	1	yes	characteristic
661	C₄	C₂×#14579138	1	1	yes	characteristic
662	C₄	C₂×#14579147	1	1	yes	characteristic
663	C₄	C₂×#14579147	1	1	yes	characteristic
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	2	1	no	—
667	C₂	—	2	1	no	—
668	C₂	—	2	1	no	—
669	C₂	—	2	1	no	—
670	C₂	—	8	2	no	—
671	C₂	#23764574	1	2	yes	direct product factor
672	C₂	C₂×#19098475	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579147
commutator, cosocle	C₂²×C₄×C₇₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#410×C₇₉	C₂
socle	C₂²×C₇₉	#393
prime radical	C₂²×#41×C₇₉	C₂²
hypercenter	C₂×#410	D₇₉
hypocenter	C₇₉	C₂×#2031
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#410

Complements

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

N	H ≅ G/N	type
1. C₂×#19099116	C₂	semidirect
4. #23764574	C₂	direct (N × H)
5. C₂×#19098333	C₂	semidirect
6. C₂×#19098322	C₂	semidirect
7. C₂×#19098319	C₂	semidirect
14. #19099116	C₂²	semidirect
28. #19098333	C₂²	semidirect
29. #19098322	C₂²	semidirect
30. #19098319	C₂²	semidirect
91. C₂×#41×C₇₉	Q₈	semidirect
93. C₂²×Q₈×C₇₉	Q₈	semidirect
95. C₂²×D₄×C₇₉	Q₈	semidirect
173. C₂×Q₈×C₇₉	C₂×Q₈	semidirect
185. C₂×D₄×C₇₉	C₂×Q₈	semidirect
335. C₂×C₇₉	#2031	semidirect
345. C₇₉	C₂×#2031	semidirect
384. C₂×#41	Dic₁₅₈	semidirect
387. C₂²×Q₈	Dic₁₅₈	semidirect
389. C₂²×D₄	Dic₁₅₈	semidirect
475. C₂×Q₈	C₂×Dic₁₅₈	semidirect
487. C₂×D₄	C₂×Dic₁₅₈	semidirect
671. C₂	#23764574	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×#19099116	2
C₂×#19098580	2
C₂²×#14579088	2
#23764574	2
C₂×#19098333	2
C₂×#19098322	2
C₂×#19098319	2
C₂×#410×C₇₉	2
C₂×#2031	79

Subgroups — C2×#23764574 #34315695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23764574 #34315695