Subgroups — C₂×#23765028 #34440971

Order 20224.

1154 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579101	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14579101	C₂	1	1	yes	maximal, characteristic, complemented
3	#23765028	C₂	1	8	yes	maximal, direct product factor
4	C₂×#19098347	C₂	1	4	yes	maximal, complemented
5	C₂²×#131×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#14579101	—	2	1	no	—
7	C₂×#14579101	—	2	1	no	—
8	C₂×#14579101	—	2	2	no	—
9	C₂×#14579101	—	2	1	no	—
10	C₂×#14579101	—	2	2	no	—
11	C₂×#14579101	C₂²	1	2	yes	complemented
12	C₂×#14579101	C₂²	1	4	yes	complemented
13	C₂×#14579101	C₂²	1	4	yes	complemented
14	C₂²×C₇₉⋊C₁₆	—	2	1	no	—
15	C₂²×C₇₉⋊C₁₆	C₂²	1	2	yes	complemented
16	#19098347	C₂²	1	16	yes	complemented
17	C₂²×#41×C₇₉	C₄	1	1	yes	characteristic
18	C₂×#131×C₇₉	—	2	1	no	—
19	C₂×#131×C₇₉	—	2	2	no	—
20	C₂×#131×C₇₉	—	2	1	no	—
21	C₂×#131×C₇₉	—	2	2	no	—
22	C₂×#131×C₇₉	C₄	1	2	yes	—
23	C₂×#131×C₇₉	C₄	1	4	yes	—
24	C₂×#131×C₇₉	C₂²	1	2	yes	—
25	C₂×#131×C₇₉	C₂²	1	4	yes	—
26	C₂²×M₁₆×C₇₉	—	2	1	no	—
27	C₂²×M₁₆×C₇₉	C₄	1	1	yes	characteristic
28	C₂³×C₈×C₇₉	—	2	1	no	—
29	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
30	#14579101	—	2	4	no	—
31	#14579101	—	2	4	no	—
32	#14579101	—	2	2	no	—
33	#14579101	—	2	4	no	—
34	#14579101	C₂³	1	4	yes	complemented
35	C₂×C₇₉⋊C₁₆	—	2	4	no	—
36	C₂×C₇₉⋊C₁₆	—	2	2	no	—
37	C₂×C₇₉⋊C₁₆	—	2	2	no	—
38	C₂×C₇₉⋊C₁₆	—	2	2	no	—
39	C₂×C₇₉⋊C₁₆	C₂³	1	4	yes	complemented
40	C₂×#41×C₇₉	—	2	1	no	—
41	C₂×#41×C₇₉	—	2	2	no	—
42	C₂×#41×C₇₉	—	2	1	no	—
43	C₂×#41×C₇₉	—	2	2	no	—
44	C₂×#41×C₇₉	C₈	1	2	yes	—
45	C₂×#41×C₇₉	C₈	1	4	yes	—
46	C₂×#41×C₇₉	C₂×C₄	1	2	yes	—
47	C₂×#41×C₇₉	C₂×C₄	1	4	yes	—
48	C₂²×Q₈×C₇₉	C₈	1	1	yes	characteristic
49	C₂²×D₄×C₇₉	—	2	1	no	—
50	C₂²×D₄×C₇₉	C₈	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	—	2	1	no	—
52	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
53	#131×C₇₉	—	2	4	no	—
54	#131×C₇₉	—	2	4	no	—
55	#131×C₇₉	—	2	4	no	—
56	#131×C₇₉	—	2	2	no	—
57	#131×C₇₉	—	2	4	no	—
58	#131×C₇₉	—	2	4	no	—
59	#131×C₇₉	—	2	2	no	—
60	#131×C₇₉	C₂×C₄	1	4	yes	—
61	#131×C₇₉	C₂×C₄	1	8	yes	—
62	#131×C₇₉	C₂³	1	4	yes	—
63	C₂×M₁₆×C₇₉	—	2	1	no	—
64	C₂×M₁₆×C₇₉	—	2	2	no	—
65	C₂×M₁₆×C₇₉	—	2	2	no	—
66	C₂×M₁₆×C₇₉	—	2	4	no	—
67	C₂×M₁₆×C₇₉	—	2	2	no	—
68	C₂×M₁₆×C₇₉	—	2	4	no	—
69	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₇₉	C₂×C₄	1	4	yes	—
71	C₂²×C₈×C₇₉	—	2	1	no	—
72	C₂²×C₈×C₇₉	—	2	4	no	—
73	C₂²×C₈×C₇₉	—	2	2	no	—
74	C₂²×C₈×C₇₉	—	2	4	no	—
75	C₂²×C₈×C₇₉	—	2	2	no	—
76	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
78	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₇₉	D₄	1	2	yes	—
83	C₂²×C₈×C₇₉	D₄	1	2	yes	—
84	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
86	C₇₉⋊C₁₆	—	2	4	no	—
87	C₇₉⋊C₁₆	—	2	4	no	—
88	C₂⁴×C₇₉	—	2	1	no	—
89	C₂⁴×C₇₉	M₁₆	1	1	yes	characteristic
90	#41×C₇₉	—	2	4	no	—
91	#41×C₇₉	—	2	4	no	—
92	#41×C₇₉	—	2	4	no	—
93	#41×C₇₉	—	2	2	no	—
94	#41×C₇₉	—	2	4	no	—
95	#41×C₇₉	—	2	2	no	—
96	#41×C₇₉	—	2	4	no	—
97	#41×C₇₉	C₂×C₈	1	4	yes	—
98	#41×C₇₉	C₂×C₈	1	8	yes	—
99	#41×C₇₉	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₇₉	—	2	2	no	—
101	C₂×Q₈×C₇₉	—	2	1	no	—
102	C₂×Q₈×C₇₉	C₂×C₈	1	4	yes	—
103	C₂×Q₈×C₇₉	C₂×C₈	1	2	yes	—
104	C₂×D₄×C₇₉	—	2	2	no	—
105	C₂×D₄×C₇₉	—	2	4	no	—
106	C₂×D₄×C₇₉	—	2	2	no	—
107	C₂×D₄×C₇₉	—	2	4	no	—
108	C₂×D₄×C₇₉	—	2	2	no	—
109	C₂×D₄×C₇₉	—	2	1	no	—
110	C₂×D₄×C₇₉	C₂×C₈	1	4	yes	—
111	C₂×D₄×C₇₉	C₂×C₈	1	2	yes	—
112	C₂²×C₄×C₇₉	—	2	1	no	—
113	C₂²×C₄×C₇₉	—	2	4	no	—
114	C₂²×C₄×C₇₉	—	2	2	no	—
115	C₂²×C₄×C₇₉	—	2	4	no	—
116	C₂²×C₄×C₇₉	—	2	2	no	—
117	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂×C₈	1	2	yes	—
123	C₂²×C₄×C₇₉	M₁₆	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	M₁₆	1	2	yes	—
125	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
127	M₁₆×C₇₉	—	2	4	no	—
128	M₁₆×C₇₉	—	2	8	no	—
129	M₁₆×C₇₉	—	2	4	no	—
130	M₁₆×C₇₉	—	2	2	no	—
131	M₁₆×C₇₉	—	2	4	no	—
132	M₁₆×C₇₉	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₇₉	—	2	8	no	—
134	C₂×C₈×C₇₉	—	2	4	no	—
135	C₂×C₈×C₇₉	—	2	4	no	—
136	C₂×C₈×C₇₉	—	2	4	no	—
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
139	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
142	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
143	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
144	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
145	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
156	C₂³×C₇₉	—	2	4	no	—
157	C₂³×C₇₉	—	2	2	no	—
158	C₂³×C₇₉	—	4	2	no	—
159	C₂³×C₇₉	—	4	4	no	—
160	C₂³×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
161	C₂³×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
162	C₂³×C₇₉	C₂²⋊C₈	1	2	yes	—
163	C₂³×C₇₉	C₂×M₁₆	1	1	yes	characteristic
164	C₂³×C₇₉	C₂×M₁₆	1	2	yes	—
165	Q₈×C₇₉	—	2	2	no	—
166	Q₈×C₇₉	—	2	4	no	—
167	Q₈×C₇₉	C₂²×C₈	1	4	yes	—
168	D₄×C₇₉	—	2	4	no	—
169	D₄×C₇₉	—	2	8	no	—
170	D₄×C₇₉	—	2	4	no	—
171	D₄×C₇₉	—	2	2	no	—
172	D₄×C₇₉	—	2	4	no	—
173	D₄×C₇₉	C₂²×C₈	1	4	yes	—
174	C₂×C₄×C₇₉	—	2	4	no	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	2	4	no	—
177	C₂×C₄×C₇₉	—	2	8	no	—
178	C₂×C₄×C₇₉	—	2	4	no	—
179	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
180	C₂×C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
182	C₂×C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
184	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
185	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
186	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
191	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
192	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
193	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
196	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
197	C₈×C₇₉	—	2	4	no	—
198	C₈×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
199	C₈×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₈×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₈×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
202	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
204	C₂²×C₇₉	—	2	2	no	—
205	C₂²×C₇₉	—	2	2	no	—
206	C₂²×C₇₉	—	2	2	no	—
207	C₂²×C₇₉	—	2	4	no	—
208	C₂²×C₇₉	—	4	2	no	—
209	C₂²×C₇₉	—	4	2	no	—
210	C₂²×C₇₉	—	4	8	no	—
211	C₂²×C₇₉	—	4	4	no	—
212	C₂²×C₇₉	C₂×C₂²⋊C₈	1	2	yes	—
213	C₂²×C₇₉	C₂×C₂²⋊C₈	1	2	yes	—
214	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
215	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
216	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
217	C₄×C₇₉	—	2	4	no	—
218	C₄×C₇₉	C₂×C₂²⋊C₈	1	2	yes	—
219	C₄×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
220	C₄×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
221	C₄×C₇₉	C₂×C₂²⋊C₈	1	2	yes	—
222	C₄×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₇₉	C₂³×C₈	1	1	yes	characteristic
224	C₂×#2117	—	79	1	no	maximal, Sylow
225	C₂×C₇₉	—	2	2	no	—
226	C₂×C₇₉	—	2	1	no	—
227	C₂×C₇₉	—	2	2	no	—
228	C₂×C₇₉	—	2	1	no	—
229	C₂×C₇₉	—	4	4	no	—
230	C₂×C₇₉	#2117	1	2	yes	complemented
231	C₂×C₇₉	C₂²×C₂²⋊C₈	1	1	yes	characteristic
232	C₂²×#131	D₇₉	1	1	yes	characteristic
233	C₂²×M₃₂	—	79	1	no	—
234	C₂²×M₃₂	—	79	1	no	—
235	#2117	—	79	8	no	—
236	C₂×#350	—	79	4	no	—
237	C₇₉	C₂×#2117	1	1	yes	characteristic, complemented, Sylow
238	C₂²×#41	Dic₇₉	1	1	yes	characteristic
239	C₂×#131	—	2	1	no	—
240	C₂×#131	—	2	2	no	—
241	C₂×#131	—	2	2	no	—
242	C₂×#131	—	2	1	no	—
243	C₂×#131	Dic₇₉	1	2	yes	—
244	C₂×#131	Dic₇₉	1	4	yes	—
245	C₂×#131	C₂×D₇₉	1	2	yes	—
246	C₂×#131	C₂×D₇₉	1	4	yes	—
247	C₂²×M₁₆	—	2	1	no	—
248	C₂²×M₁₆	Dic₇₉	1	1	yes	characteristic
249	C₂³×C₈	—	2	1	no	—
250	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
251	C₂×M₃₂	—	79	4	no	—
252	C₂×M₃₂	—	79	2	no	—
253	C₂×M₃₂	—	79	4	no	—
254	C₂×M₃₂	—	158	1	no	—
255	C₂×M₃₂	—	158	1	no	—
256	C₂×M₃₂	—	158	2	no	—
257	C₂×M₃₂	—	158	2	no	—
258	C₂×M₃₂	—	158	1	no	—
259	C₂²×C₁₆	—	79	2	no	—
260	C₂²×C₁₆	—	158	1	no	—
261	#350	—	79	16	no	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	1	no	—
264	C₂×#41	—	2	1	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	C₇₉⋊C₈	1	2	yes	—
267	C₂×#41	C₇₉⋊C₈	1	4	yes	—
268	C₂×#41	C₂×Dic₇₉	1	2	yes	—
269	C₂×#41	C₂×Dic₇₉	1	4	yes	—
270	C₂²×Q₈	C₇₉⋊C₈	1	1	yes	characteristic
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	C₇₉⋊C₈	1	1	yes	characteristic
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
275	#131	—	2	4	no	—
276	#131	—	2	4	no	—
277	#131	—	2	4	no	—
278	#131	—	2	2	no	—
279	#131	—	2	4	no	—
280	#131	—	2	4	no	—
281	#131	—	2	2	no	—
282	#131	C₂×Dic₇₉	1	4	yes	—
283	#131	C₂×Dic₇₉	1	8	yes	—
284	#131	C₂²×D₇₉	1	4	yes	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	4	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	4	no	—
291	C₂×M₁₆	C₂×Dic₇₉	1	2	yes	—
292	C₂×M₁₆	C₂×Dic₇₉	1	4	yes	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	4	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	2	4	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
299	C₂²×C₈	C₂×Dic₇₉	1	2	yes	—
300	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
302	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
303	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
304	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
305	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
307	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
308	M₃₂	—	79	4	no	—
309	M₃₂	—	158	4	no	—
310	M₃₂	—	158	4	no	—
311	M₃₂	—	158	4	no	—
312	M₃₂	—	158	2	no	—
313	C₂×C₁₆	—	79	4	no	—
314	C₂×C₁₆	—	158	2	no	—
315	C₂×C₁₆	—	158	2	no	—
316	C₂×C₁₆	—	158	4	no	—
317	C₂×C₁₆	—	158	2	no	—
318	C₂⁴	—	2	1	no	—
319	C₂⁴	#11929608	1	1	yes	characteristic
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	2	2	no	—
324	#41	—	2	4	no	—
325	#41	—	2	2	no	—
326	#41	—	2	4	no	—
327	#41	C₂×C₇₉⋊C₈	1	4	yes	—
328	#41	C₂×C₇₉⋊C₈	1	8	yes	—
329	#41	C₂²×Dic₇₉	1	4	yes	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	C₂×C₇₉⋊C₈	1	4	yes	—
333	C₂×Q₈	C₂×C₇₉⋊C₈	1	2	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	C₂×C₇₉⋊C₈	1	4	yes	—
341	C₂×D₄	C₂×C₇₉⋊C₈	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
348	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
349	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₇₉⋊C₈	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₇₉⋊C₈	1	2	yes	—
353	C₂²×C₄	#11929608	1	1	yes	characteristic
354	C₂²×C₄	#11929608	1	2	yes	—
355	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
356	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	8	no	—
361	M₁₆	—	2	4	no	—
362	M₁₆	C₂²×Dic₇₉	1	4	yes	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	8	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
369	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
370	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
371	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
372	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
373	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
374	C₂×C₈	C₂²⋊Dic₇₉	1	2	yes	—
375	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
376	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
377	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
380	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
381	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
382	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
383	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
384	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
385	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
386	C₁₆	—	158	4	no	—
387	C₁₆	—	158	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	4	no	—
392	C₂³	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
393	C₂³	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
394	C₂³	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
395	C₂³	C₂×#11929608	1	1	yes	characteristic
396	C₂³	C₂×#11929608	1	2	yes	—
397	Q₈	—	2	2	no	—
398	Q₈	—	2	4	no	—
399	Q₈	C₂²×C₇₉⋊C₈	1	4	yes	—
400	D₄	—	2	8	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	4	no	—
405	D₄	C₂²×C₇₉⋊C₈	1	4	yes	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
412	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
413	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
414	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
415	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
416	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
417	C₂×C₄	C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
418	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
419	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
420	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
421	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
423	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₇₉⋊C₈	1	2	yes	—
425	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
426	C₂×C₄	C₂×#11929608	1	2	yes	—
427	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
428	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
429	C₈	—	2	4	no	—
430	C₈	C₂×C₂²⋊Dic₇₉	1	2	yes	—
431	C₈	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
432	C₈	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
433	C₈	C₂×C₂²⋊Dic₇₉	1	2	yes	—
434	C₈	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
435	C₈	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	8	no	—
443	C₂²	—	4	4	no	—
444	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
445	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
446	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
447	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
448	C₂²	C₂²×#11929608	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	C₂×C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
451	C₄	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
452	C₄	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
453	C₄	C₂×C₂²⋊(C₇₉⋊C₈)	1	2	yes	—
454	C₄	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
455	C₄	C₂³×C₇₉⋊C₈	1	1	yes	characteristic
456	C₂	—	2	2	no	—
457	C₂	—	2	2	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	4	4	no	—
461	C₂	#23765028	1	2	yes	direct product factor
462	C₂	C₂²×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₉
commutator	C₄×C₇₉	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₂²×#131×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₂²⋊C₈
prime radical	C₂²×#41×C₇₉	C₄
cosocle	C₂×C₈×C₇₉	C₂⁴
hypercenter	C₂²×#131	D₇₉
hypocenter	C₇₉	C₂×#2117
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂²×#14579101	C₂	semidirect
2. C₂²×#14579101	C₂	semidirect
3. #23765028	C₂	direct (N × H)
4. C₂×#19098347	C₂	semidirect
11. C₂×#14579101	C₂²	semidirect
12. C₂×#14579101	C₂²	semidirect
13. C₂×#14579101	C₂²	semidirect
15. C₂²×C₇₉⋊C₁₆	C₂²	semidirect
16. #19098347	C₂²	semidirect
34. #14579101	C₂³	semidirect
39. C₂×C₇₉⋊C₁₆	C₂³	semidirect
230. C₂×C₇₉	#2117	semidirect
237. C₇₉	C₂×#2117	semidirect
461. C₂	#23765028	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×#14579101	2
#23765028	2
C₂×#19098347	2
C₂²×#131×C₇₉	2
C₂×#2117	79

Subgroups — C2×#23765028 #34440971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23765028 #34440971