Subgroups — C₂×#23772414 #35152764

Order 20224.

2254 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772414	C₂	1	16	yes	maximal, direct product factor
2	C₂×#19098694	C₂	1	2	yes	maximal, complemented
3	C₂×#19098635	C₂	1	4	yes	maximal, complemented
4	C₂×D₄×C₇₉⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×#19098620	C₂	1	2	yes	maximal, complemented
6	C₂×#19098620	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#14579072	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×#41×C₇₉	C₂	1	1	yes	maximal, characteristic
10	C₂²×#11929608	C₂²	1	2	yes	—
11	C₂³×C₇₉⋊C₈	C₂²	1	4	yes	—
12	#19098694	C₂²	1	16	yes	complemented
13	#19098635	C₂²	1	32	yes	complemented
14	D₄×C₇₉⋊C₈	C₂²	1	16	yes	complemented
15	#19098620	C₂²	1	16	yes	complemented
16	#19098620	C₂²	1	8	yes	complemented
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
19	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
20	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
21	C₄×#11929608	C₂²	1	8	yes	complemented
22	C₂×#14579072	C₂²	1	2	yes	—
23	C₂×#14579072	C₂²	1	1	yes	characteristic
24	C₂×#14579072	C₂²	1	1	yes	characteristic
25	C₂×#14579072	C₂²	1	4	yes	—
26	C₂×#14579072	C₂²	1	16	yes	complemented
27	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
28	C₂²×#41×C₇₉	C₄	1	1	yes	characteristic
29	C₄×#41×C₇₉	C₄	1	8	yes	—
30	C₄×#41×C₇₉	C₂²	1	8	yes	—
31	C₂×C₄×Q₈×C₇₉	C₄	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₉	C₄	1	2	yes	—
34	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
35	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
37	C₂×#117×C₇₉	C₄	1	1	yes	characteristic
38	C₂×#117×C₇₉	C₄	1	2	yes	—
39	C₂²×C₄²×C₇₉	C₂²	1	2	yes	—
40	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#11929608	—	2	8	no	—
42	C₂×#11929608	C₂³	1	8	yes	—
43	C₂²×C₇₉⋊C₈	—	2	16	no	—
44	C₂²×C₇₉⋊C₈	C₂³	1	16	yes	—
45	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₇₉⋊C₈	C₂³	1	4	yes	—
47	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
48	C₄⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
49	C₄⋊(C₇₉⋊C₈)	C₂³	1	16	yes	—
50	C₂²⋊(C₇₉⋊C₈)	C₂³	1	16	yes	—
51	C₂²⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
52	#14579072	C₂³	1	16	yes	—
53	#14579072	C₂³	1	4	yes	—
54	#14579072	C₂³	1	8	yes	—
55	#14579072	C₂³	1	4	yes	—
56	C₄×C₇₉⋊C₈	C₂³	1	8	yes	—
57	C₂×#41×C₇₉	—	2	8	no	—
58	C₂×#41×C₇₉	C₂×C₄	1	8	yes	—
59	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
61	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₇₉	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇₉	C₂×C₄	1	2	yes	—
66	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₄×Q₈×C₇₉	C₂×C₄	1	8	yes	—
69	C₄×Q₈×C₇₉	C₂×C₄	1	4	yes	—
70	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
71	C₄×D₄×C₇₉	C₂×C₄	1	16	yes	—
72	C₄×D₄×C₇₉	C₂×C₄	1	8	yes	—
73	C₄×D₄×C₇₉	C₂×C₄	1	8	yes	—
74	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	—
75	C₄×D₄×C₇₉	C₂³	1	4	yes	—
76	C₄×D₄×C₇₉	C₂³	1	8	yes	—
77	#117×C₇₉	C₂×C₄	1	8	yes	—
78	#117×C₇₉	C₂×C₄	1	16	yes	—
79	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
87	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
89	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₇₉	C₂×C₄	1	8	yes	—
91	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
92	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₇₉	C₂³	1	8	yes	—
96	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
97	#11929608	—	2	16	no	—
98	C₂×C₇₉⋊C₈	—	2	32	no	—
99	C₂×C₇₉⋊C₈	—	2	8	no	—
100	C₂×C₇₉⋊C₈	—	2	4	no	—
101	C₂×C₇₉⋊C₈	#41	1	8	yes	complemented
102	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
103	C₂×C₇₉⋊C₈	C₂⁴	1	8	yes	—
104	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
105	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
106	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
107	#41×C₇₉	—	2	32	no	—
108	C₂×Q₈×C₇₉	—	2	4	no	—
109	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
110	C₂×D₄×C₇₉	—	2	8	no	—
111	C₂×D₄×C₇₉	M₁₆	1	8	yes	complemented
112	C₂×D₄×C₇₉	C₂²×C₄	1	8	yes	—
113	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₇₉	—	2	8	no	—
115	C₂²×C₄×C₇₉	—	2	4	no	—
116	C₂²×C₄×C₇₉	—	2	8	no	—
117	C₂²×C₄×C₇₉	—	2	4	no	—
118	C₂²×C₄×C₇₉	—	4	4	no	—
119	C₂²×C₄×C₇₉	—	4	2	no	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇₉	C₂²×C₄	1	8	yes	—
130	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₇₉	C₂²×C₄	1	8	yes	—
133	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
138	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
139	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
140	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
141	C₂²⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
142	C₂²⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
143	C₂²⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
144	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
145	C₄²×C₇₉	C₂²×C₄	1	8	yes	—
146	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
147	C₄²×C₇₉	C₂²×C₄	1	8	yes	—
148	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
149	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
150	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₇₉	C₂⁴	1	2	yes	—
152	C₄²×C₇₉	C₂⁴	1	2	yes	—
153	C₄²×C₇₉	C₂⁴	1	4	yes	—
154	C₂³×C₇₉	—	2	4	no	—
155	C₂³×C₇₉	—	2	4	no	—
156	C₂³×C₇₉	—	2	2	no	—
157	C₂³×C₇₉	—	2	2	no	—
158	C₂³×C₇₉	—	2	2	no	—
159	C₂³×C₇₉	C₂×M₁₆	1	8	yes	—
160	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
161	C₂³×C₇₉	C₂³×C₄	1	4	yes	—
162	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
163	Q₈×C₇₉	—	2	8	no	—
164	D₄×C₇₉	—	2	16	no	—
165	D₄×C₇₉	C₂×M₁₆	1	16	yes	complemented
166	C₂×C₄×C₇₉	—	2	4	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	2	4	no	—
170	C₂×C₄×C₇₉	—	2	16	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	2	4	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	8	no	—
175	C₂×C₄×C₇₉	—	2	4	no	—
176	C₂×C₄×C₇₉	—	2	8	no	—
177	C₂×C₄×C₇₉	—	2	8	no	—
178	C₂×C₄×C₇₉	—	2	4	no	—
179	C₂×C₄×C₇₉	—	4	8	no	—
180	C₂×C₄×C₇₉	—	4	4	no	—
181	C₂×C₄×C₇₉	C₂×M₁₆	1	4	yes	—
182	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
185	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
186	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
187	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
188	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
189	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
192	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
193	C₇₉⋊C₈	—	2	8	no	—
194	C₇₉⋊C₈	—	2	4	no	—
195	C₇₉⋊C₈	C₂×#41	1	8	yes	complemented
196	C₂²×C₇₉	—	2	4	no	—
197	C₂²×C₇₉	—	2	16	no	—
198	C₂²×C₇₉	—	2	4	no	—
199	C₂²×C₇₉	—	2	2	no	—
200	C₂²×C₇₉	—	2	2	no	—
201	C₂²×C₇₉	—	2	2	no	—
202	C₂²×C₇₉	—	4	4	no	—
203	C₂²×C₇₉	C₄×#41	1	2	yes	—
204	C₂²×C₇₉	C₂²×M₁₆	1	8	yes	—
205	C₂²×C₇₉	C₂²×M₁₆	1	2	yes	—
206	C₂²×C₇₉	#568	1	2	yes	—
207	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
208	C₄×C₇₉	—	2	4	no	—
209	C₄×C₇₉	—	2	2	no	—
210	C₄×C₇₉	—	2	2	no	—
211	C₄×C₇₉	—	2	4	no	—
212	C₄×C₇₉	—	2	2	no	—
213	C₄×C₇₉	—	2	4	no	—
214	C₄×C₇₉	—	2	2	no	—
215	C₄×C₇₉	C₄×#41	1	2	yes	—
216	C₄×C₇₉	C₂²×M₁₆	1	4	yes	—
217	C₄×C₇₉	C₂²×#41	1	2	yes	—
218	C₂×#2970	—	79	1	no	maximal, Sylow
219	C₂×C₇₉	—	2	8	no	—
220	C₂×C₇₉	—	4	2	no	—
221	C₂×C₇₉	#2970	1	4	yes	complemented
222	C₂×C₇₉	C₂×C₄×#41	1	1	yes	characteristic
223	C₂×C₇₉	C₂³×M₁₆	1	1	yes	characteristic
224	C₂×C₇₉	C₂×#568	1	1	yes	characteristic
225	C₂×C₄×#41	D₇₉	1	1	yes	characteristic
226	#2970	—	79	16	no	—
227	C₂×#446	—	79	2	no	—
228	C₂×#435	—	79	4	no	—
229	C₂×C₈×D₄	—	79	2	no	—
230	C₂×#432	—	79	1	no	—
231	C₂×#432	—	79	2	no	—
232	C₂×C₄×M₁₆	—	79	1	no	—
233	C₂²×#97	—	79	2	no	—
234	C₇₉	C₂×#2970	1	1	yes	characteristic, complemented, Sylow
235	C₂²×#41	Dic₇₉	1	1	yes	characteristic
236	C₂²×M₁₆	—	79	2	no	—
237	C₂³×C₈	—	79	4	no	—
238	C₄×#41	Dic₇₉	1	8	yes	—
239	C₄×#41	C₂×D₇₉	1	8	yes	—
240	C₂×C₄×Q₈	Dic₇₉	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
242	C₂×C₄×D₄	Dic₇₉	1	2	yes	—
243	C₂×C₄×D₄	Dic₇₉	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	—
246	C₂×#117	Dic₇₉	1	1	yes	characteristic
247	C₂×#117	Dic₇₉	1	2	yes	—
248	C₂²×C₄²	C₂×D₇₉	1	2	yes	—
249	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
250	#446	—	79	16	no	—
251	#435	—	79	32	no	—
252	C₈×D₄	—	79	16	no	—
253	#432	—	79	8	no	—
254	#432	—	79	16	no	—
255	C₂×C₄⋊C₈	—	79	2	no	—
256	C₂×C₄⋊C₈	—	79	4	no	—
257	C₂×C₂²⋊C₈	—	79	4	no	—
258	C₂×C₂²⋊C₈	—	79	2	no	—
259	C₄×M₁₆	—	79	8	no	—
260	C₂×#97	—	79	1	no	—
261	C₂×#97	—	79	2	no	—
262	C₂×#97	—	79	4	no	—
263	C₂×#97	—	79	16	no	—
264	C₂×#97	—	79	1	no	—
265	C₂×C₄×C₈	—	79	2	no	—
266	C₂×#41	—	2	8	no	—
267	C₂×#41	C₂×Dic₇₉	1	8	yes	—
268	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
269	C₂²×D₄	C₂×Dic₇₉	1	2	yes	—
270	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
271	C₂³×C₄	C₂×Dic₇₉	1	2	yes	—
272	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
273	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
274	C₂³×C₄	C₂×Dic₇₉	1	2	yes	—
275	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
276	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
277	C₂×M₁₆	—	79	8	no	—
278	C₂×M₁₆	—	158	8	no	—
279	C₂²×C₈	—	79	2	no	—
280	C₂²×C₈	—	79	16	no	—
281	C₂²×C₈	—	79	4	no	—
282	C₂²×C₈	—	79	2	no	—
283	C₂²×C₈	—	158	16	no	—
284	C₄×Q₈	C₂×Dic₇₉	1	8	yes	—
285	C₄×Q₈	C₂×Dic₇₉	1	4	yes	—
286	C₄×Q₈	C₂²×D₇₉	1	4	yes	—
287	C₄×D₄	C₂×Dic₇₉	1	16	yes	—
288	C₄×D₄	C₂×Dic₇₉	1	8	yes	—
289	C₄×D₄	C₂×Dic₇₉	1	8	yes	—
290	C₄×D₄	C₂×Dic₇₉	1	4	yes	—
291	C₄×D₄	C₂²×D₇₉	1	4	yes	—
292	C₄×D₄	C₂²×D₇₉	1	8	yes	—
293	#117	C₂×Dic₇₉	1	8	yes	—
294	#117	C₂×Dic₇₉	1	16	yes	—
295	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
302	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
303	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
304	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
305	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
306	C₂×C₄²	C₂×Dic₇₉	1	8	yes	—
307	C₂×C₄²	C₂×Dic₇₉	1	4	yes	—
308	C₂×C₄²	C₂²×D₇₉	1	8	yes	—
309	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
310	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
311	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
312	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
313	C₄⋊C₈	—	79	8	no	—
314	C₄⋊C₈	—	79	16	no	—
315	C₂²⋊C₈	—	79	16	no	—
316	C₂²⋊C₈	—	79	8	no	—
317	#97	—	79	4	no	—
318	#97	—	79	8	no	—
319	#97	—	79	16	no	—
320	#97	—	79	4	no	—
321	C₄×C₈	—	79	8	no	—
322	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
323	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
324	#41	—	2	32	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	C₂²×Dic₇₉	1	4	yes	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	#11929608	1	8	yes	complemented
329	C₂×D₄	C₂²×Dic₇₉	1	8	yes	—
330	C₂×D₄	C₂²×Dic₇₉	1	4	yes	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
338	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
339	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
340	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
341	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
342	C₂²×C₄	C₂²×Dic₇₉	1	8	yes	—
343	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
344	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
345	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
347	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
348	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
349	C₂²×C₄	C₂²×Dic₇₉	1	8	yes	—
350	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
351	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
352	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
353	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
354	M₁₆	—	158	16	no	—
355	C₂×C₈	—	79	8	no	—
356	C₂×C₈	—	79	4	no	—
357	C₂×C₈	—	79	4	no	—
358	C₂×C₈	—	79	8	no	—
359	C₂×C₈	—	158	32	no	—
360	C₂×C₈	—	158	8	no	—
361	C₂×C₈	—	158	4	no	—
362	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
363	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
364	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
365	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
366	C₂²⋊C₄	C₂²×Dic₇₉	1	8	yes	—
367	C₂²⋊C₄	C₂²×Dic₇₉	1	8	yes	—
368	C₂²⋊C₄	C₂²×Dic₇₉	1	8	yes	—
369	C₄²	C₂²×Dic₇₉	1	2	yes	—
370	C₄²	C₂²×Dic₇₉	1	8	yes	—
371	C₄²	C₂²×Dic₇₉	1	4	yes	—
372	C₄²	C₂²×Dic₇₉	1	8	yes	—
373	C₄²	C₂²×Dic₇₉	1	4	yes	—
374	C₄²	C₂²×Dic₇₉	1	4	yes	—
375	C₄²	C₂²×Dic₇₉	1	2	yes	—
376	C₄²	C₂³×D₇₉	1	2	yes	—
377	C₄²	C₂³×D₇₉	1	2	yes	—
378	C₄²	C₂³×D₇₉	1	4	yes	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	C₂×#11929608	1	8	yes	—
385	C₂³	C₂³×Dic₇₉	1	2	yes	—
386	C₂³	C₂³×Dic₇₉	1	4	yes	—
387	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	D₄	—	2	16	no	—
390	D₄	C₂×#11929608	1	16	yes	complemented
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	C₂×#11929608	1	4	yes	—
407	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
408	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
409	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
410	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
411	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
412	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
413	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
414	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
415	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
416	C₂×C₄	#41×D₇₉	1	4	yes	—
417	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
418	C₈	—	79	8	no	—
419	C₈	—	158	8	no	—
420	C₈	—	158	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	16	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	#41×Dic₇₉	1	2	yes	—
429	C₂²	C₂²×#11929608	1	8	yes	—
430	C₂²	C₂²×#11929608	1	2	yes	—
431	C₂²	#19099330	1	2	yes	—
432	C₂²	C₂⁴×Dic₇₉	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	#41×Dic₇₉	1	2	yes	—
441	C₄	C₂²×#11929608	1	4	yes	—
442	C₄	C₂×#41×D₇₉	1	2	yes	—
443	C₂	—	2	8	no	—
444	C₂	—	4	2	no	—
445	C₂	#23772414	1	4	yes	direct product factor
446	C₂	C₂×#41×Dic₇₉	1	1	yes	characteristic
447	C₂	C₂³×#11929608	1	1	yes	characteristic
448	C₂	C₂×#19099330	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₂×C₄×#41×C₇₉	C₂
socle	C₂³×C₇₉	C₂³×C₄
prime radical	C₂²×#41×C₇₉	C₄
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	C₂×C₄×#41	D₇₉
hypocenter	C₇₉	C₂×#2970
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #23772414	C₂	direct (N × H)
2. C₂×#19098694	C₂	semidirect
3. C₂×#19098635	C₂	semidirect
4. C₂×D₄×C₇₉⋊C₈	C₂	semidirect
5. C₂×#19098620	C₂	semidirect
6. C₂×#19098620	C₂	semidirect
7. C₂×C₄×#11929608	C₂	semidirect
8. C₂²×#14579072	C₂	semidirect
12. #19098694	C₂²	semidirect
13. #19098635	C₂²	semidirect
14. D₄×C₇₉⋊C₈	C₂²	semidirect
15. #19098620	C₂²	semidirect
16. #19098620	C₂²	semidirect
21. C₄×#11929608	C₂²	semidirect
26. C₂×#14579072	C₂²	semidirect
101. C₂×C₇₉⋊C₈	#41	semidirect
111. C₂×D₄×C₇₉	M₁₆	semidirect
165. D₄×C₇₉	C₂×M₁₆	semidirect
195. C₇₉⋊C₈	C₂×#41	semidirect
221. C₂×C₇₉	#2970	semidirect
234. C₇₉	C₂×#2970	semidirect
328. C₂×D₄	#11929608	semidirect
390. D₄	C₂×#11929608	semidirect
445. C₂	#23772414	direct (N × H)

Maximal subgroups

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

subgroup	index
#23772414	2
C₂×#19098694	2
C₂×#19098635	2
C₂×D₄×C₇₉⋊C₈	2
C₂×#19098620	2
C₂×C₄×#11929608	2
C₂²×#14579072	2
C₂×C₄×#41×C₇₉	2
C₂×#2970	79

Subgroups — C2×#23772414 #35152764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23772414 #35152764