Subgroups — C₂×#23763642 #34289168

Order 20224.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099330	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098612	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19098587	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098580	C₂	1	1	yes	maximal, characteristic
5	#23763642	C₂	1	8	yes	maximal, direct product factor
6	C₂×#19098335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19098323	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#104×C₇₉	C₂	1	1	yes	maximal, characteristic
9	#19099330	—	2	2	no	—
10	#19099330	—	2	2	no	—
11	#19099330	—	2	2	no	—
12	#19099330	C₂²	1	4	yes	—
13	C₂×#14579168	—	2	2	no	—
14	C₂×#14579168	—	2	2	no	—
15	C₂²×#11929608	—	2	2	no	—
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂²×#11929608	C₂²	1	1	yes	characteristic
18	C₂²×#11929608	C₂²	1	1	yes	characteristic
19	C₂×#14579120	C₂²	1	1	yes	characteristic
20	#19098612	—	2	2	no	—
21	#19098612	C₂²	1	4	yes	complemented
22	C₂×#14579097	—	2	2	no	—
23	#19098587	—	2	2	no	—
24	#19098587	C₂²	1	4	yes	complemented
25	C₂×C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	#19098580	—	2	2	no	—
27	#19098580	C₂²	1	4	yes	—
28	C₂×#14579088	—	2	2	no	—
29	#19098335	C₂²	1	4	yes	complemented
30	#19098323	C₂²	1	4	yes	complemented
31	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#104×C₇₉	C₄	1	2	yes	complemented
35	C₂×#104×C₇₉	C₄	1	4	yes	complemented
36	C₂×#104×C₇₉	C₄	1	2	yes	complemented
37	C₂×#104×C₇₉	C₂²	1	4	yes	—
38	#14579168	—	2	8	no	—
39	#14579168	—	2	8	no	—
40	#14579168	—	2	8	no	—
41	#14579168	—	2	8	no	—
42	C₂×#11929608	—	2	4	no	—
43	C₂×#11929608	—	2	8	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	—	2	1	no	—
50	C₂×#11929608	—	2	1	no	—
51	C₂×#11929608	—	2	8	no	—
52	C₂×#11929608	—	2	1	no	—
53	C₂×#11929608	—	2	1	no	—
54	C₂×#11929608	—	2	1	no	—
55	C₂×#11929608	—	2	1	no	—
56	C₂×#11929608	—	2	1	no	—
57	C₂×#11929608	D₄	1	2	yes	—
58	C₂×#11929608	D₄	1	2	yes	—
59	C₂×#11929608	D₄	1	2	yes	—
60	C₂×#11929608	C₂³	1	2	yes	—
61	C₂×#11929608	C₂³	1	2	yes	—
62	C₂×#11929608	C₂³	1	2	yes	—
63	C₂²×C₇₉⋊C₈	—	2	4	no	—
64	C₂²×C₇₉⋊C₈	—	2	1	no	—
65	C₂²×C₇₉⋊C₈	—	2	1	no	—
66	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
67	#14579120	—	2	1	no	—
68	#14579120	—	2	1	no	—
69	#14579120	—	2	1	no	—
70	#14579120	C₂³	1	2	yes	—
71	C₂×C₄⋊Dic₇₉	—	2	1	no	—
72	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
73	C₂×C₄×Dic₇₉	—	2	1	no	—
74	#14579097	—	2	8	no	—
75	C₄⋊(C₇₉⋊C₈)	—	2	8	no	—
76	#14579088	—	2	8	no	—
77	C₂×#41×C₇₉	—	2	1	no	—
78	C₂×#41×C₇₉	—	2	1	no	—
79	C₂×#41×C₇₉	—	2	1	no	—
80	C₂×#41×C₇₉	—	2	1	no	—
81	C₂×#41×C₇₉	—	2	1	no	—
82	C₂×#41×C₇₉	—	2	1	no	—
83	C₂×#41×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×#41×C₇₉	C₂×C₄	1	2	yes	—
85	C₂×#41×C₇₉	D₄	1	2	yes	—
86	C₂×#41×C₇₉	D₄	1	2	yes	—
87	C₂×#41×C₇₉	Q₈	1	2	yes	—
88	C₂×#41×C₇₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₇₉	Q₈	1	1	yes	characteristic
90	C₂²×D₄×C₇₉	—	2	1	no	—
91	C₂²×D₄×C₇₉	Q₈	1	1	yes	characteristic
92	C₂³×C₄×C₇₉	—	2	1	no	—
93	C₂³×C₄×C₇₉	—	2	1	no	—
94	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₇₉	—	2	1	no	—
96	C₂×M₁₆×C₇₉	—	2	1	no	—
97	C₂×M₁₆×C₇₉	—	2	1	no	—
98	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
99	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
100	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
101	C₂²×C₈×C₇₉	—	2	1	no	—
102	C₂×C₄²×C₇₉	—	2	1	no	—
103	C₂×C₄²×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	—	2	1	no	—
105	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
107	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
109	#104×C₇₉	C₂×C₄	1	8	yes	complemented
110	#104×C₇₉	C₂×C₄	1	8	yes	complemented
111	C₂²×Dic₇₉	—	4	1	no	—
112	#11929608	—	2	16	no	—
113	#11929608	—	2	2	no	—
114	#11929608	—	2	2	no	—
115	#11929608	—	2	2	no	—
116	#11929608	—	2	2	no	—
117	#11929608	—	2	2	no	—
118	#11929608	—	2	2	no	—
119	#11929608	—	2	2	no	—
120	#11929608	—	2	2	no	—
121	#11929608	—	2	2	no	—
122	#11929608	—	4	1	no	—
123	#11929608	—	4	1	no	—
124	#11929608	C₂×D₄	1	4	yes	—
125	C₂×C₇₉⋊C₈	—	2	16	no	—
126	C₂×C₇₉⋊C₈	—	2	2	no	—
127	C₂×C₇₉⋊C₈	—	2	2	no	—
128	C₂×C₇₉⋊C₈	—	2	2	no	—
129	C₂×C₇₉⋊C₈	—	2	2	no	—
130	C₂×C₇₉⋊C₈	—	2	2	no	—
131	C₂×C₇₉⋊C₈	—	2	2	no	—
132	C₂×C₇₉⋊C₈	—	4	1	no	—
133	C₂×C₇₉⋊C₈	—	4	1	no	—
134	C₂×C₇₉⋊C₈	C₂×D₄	1	4	yes	—
135	C₄⋊Dic₇₉	—	2	2	no	—
136	C₄⋊Dic₇₉	—	4	1	no	—
137	C₂²⋊Dic₇₉	—	2	2	no	—
138	C₂²⋊Dic₇₉	—	4	1	no	—
139	C₄×Dic₇₉	—	2	2	no	—
140	C₄×Dic₇₉	—	4	1	no	—
141	C₂⁴×C₇₉	—	2	1	no	—
142	C₂⁴×C₇₉	#41	1	1	yes	characteristic
143	#41×C₇₉	—	2	2	no	—
144	#41×C₇₉	—	2	2	no	—
145	#41×C₇₉	—	2	2	no	—
146	#41×C₇₉	—	2	2	no	—
147	#41×C₇₉	—	2	2	no	—
148	#41×C₇₉	—	2	2	no	—
149	#41×C₇₉	—	2	2	no	—
150	#41×C₇₉	—	2	2	no	—
151	#41×C₇₉	—	2	2	no	—
152	#41×C₇₉	—	2	2	no	—
153	#41×C₇₉	—	2	2	no	—
154	#41×C₇₉	—	2	2	no	—
155	#41×C₇₉	C₄⋊C₄	1	4	yes	—
156	#41×C₇₉	C₄⋊C₄	1	4	yes	—
157	#41×C₇₉	C₂²×C₄	1	4	yes	—
158	#41×C₇₉	C₂×D₄	1	4	yes	—
159	C₂×Q₈×C₇₉	—	2	1	no	—
160	C₂×Q₈×C₇₉	—	2	1	no	—
161	C₂×Q₈×C₇₉	—	2	1	no	—
162	C₂×Q₈×C₇₉	C₄⋊C₄	1	2	yes	—
163	C₂×Q₈×C₇₉	C₄⋊C₄	1	2	yes	—
164	C₂×Q₈×C₇₉	C₂×Q₈	1	2	yes	—
165	C₂×D₄×C₇₉	—	2	2	no	—
166	C₂×D₄×C₇₉	—	2	2	no	—
167	C₂×D₄×C₇₉	—	2	2	no	—
168	C₂×D₄×C₇₉	—	2	2	no	—
169	C₂×D₄×C₇₉	—	2	2	no	—
170	C₂×D₄×C₇₉	—	2	2	no	—
171	C₂×D₄×C₇₉	—	2	1	no	—
172	C₂×D₄×C₇₉	—	2	1	no	—
173	C₂×D₄×C₇₉	—	2	1	no	—
174	C₂×D₄×C₇₉	C₄⋊C₄	1	2	yes	—
175	C₂×D₄×C₇₉	C₄⋊C₄	1	2	yes	—
176	C₂×D₄×C₇₉	C₂×Q₈	1	2	yes	—
177	C₂²×C₄×C₇₉	—	2	1	no	—
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	2	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	—	2	2	no	—
185	C₂²×C₄×C₇₉	—	2	2	no	—
186	C₂²×C₄×C₇₉	—	2	1	no	—
187	C₂²×C₄×C₇₉	—	2	2	no	—
188	C₂²×C₄×C₇₉	—	4	4	no	—
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×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	1	yes	characteristic
198	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
199	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
200	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
201	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
202	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
203	M₁₆×C₇₉	—	2	2	no	—
204	M₁₆×C₇₉	—	2	2	no	—
205	M₁₆×C₇₉	—	2	2	no	—
206	M₁₆×C₇₉	C₂²×C₄	1	4	yes	—
207	C₂×C₈×C₇₉	—	2	2	no	—
208	C₂×C₈×C₇₉	—	2	2	no	—
209	C₂×C₈×C₇₉	—	2	2	no	—
210	C₄²×C₇₉	—	2	1	no	—
211	C₄²×C₇₉	—	2	2	no	—
212	C₄²×C₇₉	—	2	1	no	—
213	C₄²×C₇₉	—	2	2	no	—
214	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
215	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
216	C₂³×C₇₉	—	2	2	no	—
217	C₂³×C₇₉	—	2	2	no	—
218	C₂³×C₇₉	—	2	2	no	—
219	C₂³×C₇₉	—	4	2	no	—
220	C₂³×C₇₉	—	8	2	no	—
221	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
222	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
223	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×C₇₉	#123	1	1	yes	characteristic
226	C₂³×C₇₉	#123	1	1	yes	characteristic
227	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
228	Q₈×C₇₉	—	2	2	no	—
229	Q₈×C₇₉	—	2	2	no	—
230	Q₈×C₇₉	—	2	2	no	—
231	Q₈×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
232	D₄×C₇₉	—	2	4	no	—
233	D₄×C₇₉	—	2	4	no	—
234	D₄×C₇₉	—	2	4	no	—
235	D₄×C₇₉	—	2	4	no	—
236	D₄×C₇₉	—	2	2	no	—
237	D₄×C₇₉	—	2	2	no	—
238	D₄×C₇₉	—	2	2	no	—
239	D₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
240	C₂×C₄×C₇₉	—	2	4	no	—
241	C₂×C₄×C₇₉	—	2	2	no	—
242	C₂×C₄×C₇₉	—	2	2	no	—
243	C₂×C₄×C₇₉	—	2	2	no	—
244	C₂×C₄×C₇₉	—	2	2	no	—
245	C₂×C₄×C₇₉	—	2	4	no	—
246	C₂×C₄×C₇₉	—	2	4	no	—
247	C₂×C₄×C₇₉	—	2	4	no	—
248	C₂×C₄×C₇₉	—	2	4	no	—
249	C₂×C₄×C₇₉	—	2	2	no	—
250	C₂×C₄×C₇₉	—	4	4	no	—
251	C₂×C₄×C₇₉	—	4	4	no	—
252	C₂×C₄×C₇₉	—	4	2	no	—
253	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
263	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
264	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
265	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
266	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
267	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
274	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
275	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
280	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
281	C₂×Dic₇₉	—	4	2	no	—
282	C₂×Dic₇₉	—	8	2	no	—
283	C₈×C₇₉	—	2	4	no	—
284	C₇₉⋊C₈	—	2	4	no	—
285	C₇₉⋊C₈	—	2	4	no	—
286	C₇₉⋊C₈	—	4	2	no	—
287	C₂²×C₇₉	—	2	2	no	—
288	C₂²×C₇₉	—	2	2	no	—
289	C₂²×C₇₉	—	2	2	no	—
290	C₂²×C₇₉	—	2	4	no	—
291	C₂²×C₇₉	—	4	1	no	—
292	C₂²×C₇₉	—	4	1	no	—
293	C₂²×C₇₉	—	4	1	no	—
294	C₂²×C₇₉	—	4	1	no	—
295	C₂²×C₇₉	—	4	4	no	—
296	C₂²×C₇₉	—	8	2	no	—
297	C₂²×C₇₉	—	8	2	no	—
298	C₂²×C₇₉	#385	1	1	yes	characteristic
299	C₂²×C₇₉	#385	1	1	yes	characteristic
300	C₂²×C₇₉	#385	1	1	yes	characteristic
301	C₂²×C₇₉	#385	1	1	yes	characteristic
302	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
304	C₂²×C₇₉	C₂×#123	1	1	yes	characteristic
305	C₄×C₇₉	—	2	4	no	—
306	C₄×C₇₉	—	2	4	no	—
307	C₄×C₇₉	—	4	2	no	—
308	C₄×C₇₉	#385	1	1	yes	characteristic
309	C₄×C₇₉	#385	1	1	yes	characteristic
310	C₄×C₇₉	#385	1	1	yes	characteristic
311	C₄×C₇₉	#385	1	1	yes	characteristic
312	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
313	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
314	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
315	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
316	Dic₇₉	—	8	2	no	—
317	C₂×#1861	—	79	1	no	maximal, Sylow
318	C₂×C₇₉	—	2	1	no	—
319	C₂×C₇₉	—	2	1	no	—
320	C₂×C₇₉	—	2	1	no	—
321	C₂×C₇₉	—	2	1	no	—
322	C₂×C₇₉	—	2	1	no	—
323	C₂×C₇₉	—	2	1	no	—
324	C₂×C₇₉	—	4	4	no	—
325	C₂×C₇₉	#1861	1	2	yes	complemented
326	C₂×C₇₉	C₂×#385	1	1	yes	characteristic
327	C₂×#568	—	79	1	no	—
328	C₂×#430	—	79	1	no	—
329	C₂×#423	—	79	1	no	—
330	C₂×#421	—	79	1	no	—
331	C₂²×#104	D₇₉	1	1	yes	characteristic
332	#1861	—	79	8	no	—
333	C₂×#344	—	79	1	no	—
334	C₂×#339	—	79	1	no	—
335	C₇₉	C₂×#1861	1	1	yes	characteristic, complemented, Sylow
336	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
337	#568	—	79	4	no	—
338	#568	—	158	2	no	—
339	#568	—	158	2	no	—
340	#568	—	158	2	no	—
341	C₂×#131	—	158	2	no	—
342	C₂×#131	—	158	2	no	—
343	C₂²×M₁₆	—	79	1	no	—
344	C₂²×M₁₆	—	79	1	no	—
345	C₂²×M₁₆	—	79	1	no	—
346	C₂²×M₁₆	—	158	2	no	—
347	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
348	C₂×#117	—	79	1	no	—
349	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
350	#430	—	79	4	no	—
351	#430	—	158	2	no	—
352	C₂×#108	—	158	2	no	—
353	#423	—	79	4	no	—
354	#423	—	158	2	no	—
355	C₂×C₄⋊C₈	—	158	2	no	—
356	#421	—	79	4	no	—
357	#421	—	158	2	no	—
358	C₂×#104	—	158	2	no	—
359	C₂×#104	Dic₇₉	1	2	yes	complemented
360	C₂×#104	Dic₇₉	1	4	yes	complemented
361	C₂×#104	Dic₇₉	1	2	yes	complemented
362	C₂×#104	C₂×D₇₉	1	4	yes	—
363	#344	—	79	4	no	—
364	#339	—	79	4	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	Dic₁₅₈	1	2	yes	—
372	C₂×#41	D₃₁₆	1	2	yes	—
373	C₂×#41	D₃₁₆	1	2	yes	—
374	C₂×#41	C₂×Dic₇₉	1	2	yes	—
375	C₂×#41	C₂×Dic₇₉	1	2	yes	—
376	C₂×#41	C₂²×D₇₉	1	2	yes	—
377	C₂²×Q₈	Dic₁₅₈	1	1	yes	characteristic
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	Dic₁₅₈	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
383	#131	—	158	8	no	—
384	#131	—	158	8	no	—
385	#131	—	158	8	no	—
386	#131	—	158	8	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	79	2	no	—
391	C₂×M₁₆	—	79	2	no	—
392	C₂×M₁₆	—	79	2	no	—
393	C₂×M₁₆	—	79	2	no	—
394	C₂×M₁₆	—	79	2	no	—
395	C₂×M₁₆	—	79	2	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	8	no	—
402	C₂×M₁₆	—	158	4	no	—
403	C₂×M₁₆	—	158	8	no	—
404	C₂×M₁₆	—	158	1	no	—
405	C₂×M₁₆	—	158	1	no	—
406	C₂×M₁₆	—	158	1	no	—
407	C₂×M₁₆	—	158	1	no	—
408	C₂×M₁₆	—	158	1	no	—
409	C₂×M₁₆	—	158	1	no	—
410	C₂×M₁₆	—	158	1	no	—
411	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
412	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
413	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
414	C₂²×C₈	—	2	1	no	—
415	C₂²×C₈	—	79	2	no	—
416	C₂²×C₈	—	158	1	no	—
417	C₂²×C₈	—	158	4	no	—
418	C₂²×C₈	—	158	1	no	—
419	#117	—	79	2	no	—
420	#117	—	158	1	no	—
421	#117	—	158	1	no	—
422	#117	—	158	1	no	—
423	C₂×C₄⋊C₄	—	158	1	no	—
424	C₂×C₂²⋊C₄	—	158	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	158	1	no	—
429	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
430	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
431	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
432	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
433	#108	—	158	8	no	—
434	C₄⋊C₈	—	158	8	no	—
435	#104	—	158	8	no	—
436	#104	C₂×Dic₇₉	1	8	yes	complemented
437	#104	C₂×Dic₇₉	1	8	yes	complemented
438	C₂⁴	—	2	1	no	—
439	C₂⁴	#11929623	1	1	yes	characteristic
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	C₄⋊Dic₇₉	1	4	yes	—
453	#41	C₄⋊Dic₇₉	1	4	yes	—
454	#41	C₂²×Dic₇₉	1	4	yes	—
455	#41	C₂×D₃₁₆	1	4	yes	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	C₄⋊Dic₇₉	1	2	yes	—
460	C₂×Q₈	C₄⋊Dic₇₉	1	2	yes	—
461	C₂×Q₈	C₂×Dic₁₅₈	1	2	yes	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₄⋊Dic₇₉	1	2	yes	—
472	C₂×D₄	C₄⋊Dic₇₉	1	2	yes	—
473	C₂×D₄	C₂×Dic₁₅₈	1	2	yes	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	316	1	no	—
487	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
489	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
490	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
491	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
492	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
495	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
496	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
497	C₂²×C₄	#11929623	1	1	yes	characteristic
498	C₂²×C₄	#11929623	1	1	yes	characteristic
499	C₂²×C₄	#11929623	1	1	yes	characteristic
500	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	316	1	no	—
505	M₁₆	—	316	1	no	—
506	M₁₆	—	79	4	no	—
507	M₁₆	—	158	2	no	—
508	M₁₆	—	158	2	no	—
509	M₁₆	—	158	16	no	—
510	M₁₆	—	158	2	no	—
511	M₁₆	—	158	2	no	—
512	M₁₆	—	158	2	no	—
513	M₁₆	—	158	2	no	—
514	M₁₆	—	158	2	no	—
515	M₁₆	—	158	2	no	—
516	M₁₆	—	158	2	no	—
517	M₁₆	C₂²×Dic₇₉	1	4	yes	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	316	1	no	—
522	C₂×C₈	—	316	1	no	—
523	C₂×C₈	—	79	4	no	—
524	C₂×C₈	—	158	2	no	—
525	C₂×C₈	—	158	16	no	—
526	C₂×C₈	—	158	2	no	—
527	C₂×C₈	—	158	2	no	—
528	C₂×C₈	—	158	2	no	—
529	C₂×C₈	—	158	2	no	—
530	C₂×C₈	—	158	2	no	—
531	C₄⋊C₄	—	316	1	no	—
532	C₄⋊C₄	—	158	2	no	—
533	C₂²⋊C₄	—	316	1	no	—
534	C₂²⋊C₄	—	158	2	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	316	1	no	—
540	C₄²	—	158	2	no	—
541	C₄²	C₂²×Dic₇₉	1	2	yes	—
542	C₄²	C₂²×Dic₇₉	1	2	yes	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
549	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
550	C₂³	#14579138	1	1	yes	characteristic
551	C₂³	#14579138	1	1	yes	characteristic
552	C₂³	#14579145	1	1	yes	characteristic
553	C₂³	#14579145	1	1	yes	characteristic
554	C₂³	C₂×#11929623	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	C₂×C₄⋊Dic₇₉	1	4	yes	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	C₂×C₄⋊Dic₇₉	1	4	yes	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	316	2	no	—
581	C₂×C₄	—	632	2	no	—
582	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
583	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
584	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
585	C₂×C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
586	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
587	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
588	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
589	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
590	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
591	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
592	C₂×C₄	#14579131	1	1	yes	characteristic
593	C₂×C₄	#14579131	1	1	yes	characteristic
594	C₂×C₄	#14579131	1	1	yes	characteristic
595	C₂×C₄	#14579131	1	1	yes	characteristic
596	C₂×C₄	#14579138	1	1	yes	characteristic
597	C₂×C₄	#14579138	1	1	yes	characteristic
598	C₂×C₄	#14579138	1	1	yes	characteristic
599	C₂×C₄	#14579138	1	1	yes	characteristic
600	C₂×C₄	#14579138	1	1	yes	characteristic
601	C₂×C₄	#14579138	1	1	yes	characteristic
602	C₂×C₄	#14579145	1	1	yes	characteristic
603	C₂×C₄	#14579145	1	1	yes	characteristic
604	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
605	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
606	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
608	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
609	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	316	2	no	—
612	C₈	—	158	4	no	—
613	C₈	—	158	4	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	#19098438	1	1	yes	characteristic
626	C₂²	#19098438	1	1	yes	characteristic
627	C₂²	#19098438	1	1	yes	characteristic
628	C₂²	#19098438	1	1	yes	characteristic
629	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
630	C₂²	C₂×#14579138	1	1	yes	characteristic
631	C₂²	C₂×#14579145	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	632	2	no	—
636	C₄	#19098438	1	1	yes	characteristic
637	C₄	#19098438	1	1	yes	characteristic
638	C₄	#19098438	1	1	yes	characteristic
639	C₄	#19098438	1	1	yes	characteristic
640	C₄	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
641	C₄	C₂×D₄×Dic₇₉	1	1	yes	characteristic
642	C₄	C₂×#14579131	1	1	yes	characteristic
643	C₄	C₂×#14579138	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	4	4	no	—
651	C₂	#23763642	1	2	yes	direct product factor
652	C₂	C₂×#19098438	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579131
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂²×#104×C₇₉	C₂
socle	C₂²×C₇₉	#385
prime radical	C₂²×#41×C₇₉	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂²×#104	D₇₉
hypocenter	C₇₉	C₂×#1861
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

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

N	H ≅ G/N	type
2. C₂×#19098612	C₂	semidirect
3. C₂×#19098587	C₂	semidirect
5. #23763642	C₂	direct (N × H)
6. C₂×#19098335	C₂	semidirect
7. C₂×#19098323	C₂	semidirect
21. #19098612	C₂²	semidirect
24. #19098587	C₂²	semidirect
29. #19098335	C₂²	semidirect
30. #19098323	C₂²	semidirect
34. C₂×#104×C₇₉	C₄	semidirect
35. C₂×#104×C₇₉	C₄	semidirect
36. C₂×#104×C₇₉	C₄	semidirect
109. #104×C₇₉	C₂×C₄	semidirect
110. #104×C₇₉	C₂×C₄	semidirect
325. C₂×C₇₉	#1861	semidirect
335. C₇₉	C₂×#1861	semidirect
359. C₂×#104	Dic₇₉	semidirect
360. C₂×#104	Dic₇₉	semidirect
361. C₂×#104	Dic₇₉	semidirect
436. #104	C₂×Dic₇₉	semidirect
437. #104	C₂×Dic₇₉	semidirect
651. C₂	#23763642	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×#19099330	2
C₂×#19098612	2
C₂×#19098587	2
C₂×#19098580	2
#23763642	2
C₂×#19098335	2
C₂×#19098323	2
C₂²×#104×C₇₉	2
C₂×#1861	79

Subgroups — C2×#23763642 #34289168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23763642 #34289168