Subgroups — C₂×#23772560 #35153371

Order 20224.

1982 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772560	C₂	1	16	yes	maximal, direct product factor
2	C₂×#19098694	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098641	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19098635	C₂	1	2	yes	maximal, complemented
6	C₂×D₄×C₇₉⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#19098624	C₂	1	2	yes	maximal, complemented
9	C₂×#19098616	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19098590	C₂	1	2	yes	maximal, complemented
11	C₂²×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#529×C₇₉	C₂	1	1	yes	maximal, characteristic
13	C₂²×#11929608	C₂²	1	2	yes	—
14	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
16	#19098694	C₂²	1	8	yes	complemented
17	Q₈×C₇₉⋊C₈	C₂²	1	8	yes	complemented
18	#19098641	C₂²	1	8	yes	complemented
19	#19098635	C₂²	1	16	yes	complemented
20	D₄×C₇₉⋊C₈	C₂²	1	16	yes	complemented
21	D₄×C₇₉⋊C₈	C₂²	1	8	yes	complemented
22	#19098624	C₂²	1	16	yes	complemented
23	#19098616	C₂²	1	8	yes	complemented
24	#19098590	C₂²	1	16	yes	complemented
25	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
26	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
30	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
31	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	8	yes	complemented
33	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
36	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
37	C₂×#14579072	C₂²	1	2	yes	—
38	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
41	#529×C₇₉	C₄	1	8	yes	—
42	#529×C₇₉	C₂²	1	8	yes	—
43	C₂×#126×C₇₉	C₄	1	2	yes	—
44	C₂×#125×C₇₉	C₄	1	1	yes	characteristic
45	C₂×#124×C₇₉	C₄	1	1	yes	characteristic
46	C₂×#123×C₇₉	C₄	1	2	yes	—
47	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
48	C₂×#121×C₇₉	C₄	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
51	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×#117×C₇₉	C₂²	1	2	yes	—
53	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×#11929608	—	4	4	no	—
55	C₂×#11929608	C₂³	1	8	yes	—
56	C₂²×C₇₉⋊C₈	—	4	4	no	—
57	C₂²×C₇₉⋊C₈	—	4	4	no	—
58	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
62	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
64	C₂²×C₇₉⋊C₈	C₂³	1	8	yes	—
65	C₂²×C₇₉⋊C₈	C₂³	1	8	yes	—
66	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
67	C₄⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
68	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
69	C₄⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
70	C₄⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
71	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
72	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
73	C₂²⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
74	C₂²⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
75	C₂²⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
76	C₂²⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
77	#14579072	C₂³	1	8	yes	—
78	C₄×C₇₉⋊C₈	C₂³	1	8	yes	—
79	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
80	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
81	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
82	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
83	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
88	#126×C₇₉	C₂×C₄	1	16	yes	—
89	#125×C₇₉	C₂×C₄	1	8	yes	—
90	#124×C₇₉	C₂×C₄	1	8	yes	—
91	#123×C₇₉	C₂×C₄	1	16	yes	—
92	C₂²⋊Q₈×C₇₉	C₂×C₄	1	8	yes	—
93	#121×C₇₉	C₂×C₄	1	8	yes	—
94	C₄×Q₈×C₇₉	C₂×C₄	1	4	yes	—
95	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
96	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	—
97	C₄×D₄×C₇₉	C₂×C₄	1	8	yes	—
98	C₄×D₄×C₇₉	C₂³	1	8	yes	—
99	C₄×D₄×C₇₉	C₂³	1	4	yes	—
100	#117×C₇₉	C₂×C₄	1	8	yes	—
101	#117×C₇₉	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
104	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
106	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
108	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
109	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
110	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
111	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
112	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
113	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
116	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
119	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
120	#11929608	—	4	8	no	—
121	C₂×C₇₉⋊C₈	—	2	2	no	—
122	C₂×C₇₉⋊C₈	—	2	4	no	—
123	C₂×C₇₉⋊C₈	—	2	4	no	—
124	C₂×C₇₉⋊C₈	—	2	2	no	—
125	C₂×C₇₉⋊C₈	—	2	2	no	—
126	C₂×C₇₉⋊C₈	—	2	2	no	—
127	C₂×C₇₉⋊C₈	—	4	8	no	—
128	C₂×C₇₉⋊C₈	—	4	8	no	—
129	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
130	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
131	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
132	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
133	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
134	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
135	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
136	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×Q₈×C₇₉	—	2	4	no	—
138	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
139	C₂×D₄×C₇₉	—	2	8	no	—
140	C₂×D₄×C₇₉	—	2	4	no	—
141	C₂×D₄×C₇₉	C₂²×C₄	1	8	yes	—
142	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₇₉	—	2	4	no	—
144	C₂²×C₄×C₇₉	—	2	4	no	—
145	C₂²×C₄×C₇₉	—	2	2	no	—
146	C₂²×C₄×C₇₉	—	2	4	no	—
147	C₂²×C₄×C₇₉	—	2	2	no	—
148	C₂²×C₄×C₇₉	—	2	4	no	—
149	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
155	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
160	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
164	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
165	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
166	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
167	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
168	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
169	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
170	C₂²⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
171	C₂²⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
172	C₂²⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
173	C₂²⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
174	C₂²⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
175	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
176	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
177	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
178	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
179	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
180	C₄²×C₇₉	C₂⁴	1	2	yes	—
181	C₄²×C₇₉	C₂⁴	1	2	yes	—
182	C₄²×C₇₉	C₂⁴	1	4	yes	—
183	C₂³×C₇₉	—	2	2	no	—
184	C₂³×C₇₉	—	2	2	no	—
185	C₂³×C₇₉	—	2	4	no	—
186	C₂³×C₇₉	—	2	4	no	—
187	C₂³×C₇₉	—	2	4	no	—
188	C₂³×C₇₉	#131	1	4	yes	—
189	C₂³×C₇₉	C₂³×C₄	1	4	yes	—
190	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
191	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
192	Q₈×C₇₉	—	2	8	no	—
193	D₄×C₇₉	—	2	16	no	—
194	D₄×C₇₉	—	2	8	no	—
195	C₂×C₄×C₇₉	—	2	2	no	—
196	C₂×C₄×C₇₉	—	2	4	no	—
197	C₂×C₄×C₇₉	—	2	8	no	—
198	C₂×C₄×C₇₉	—	2	2	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	2	no	—
201	C₂×C₄×C₇₉	—	2	4	no	—
202	C₂×C₄×C₇₉	—	2	4	no	—
203	C₂×C₄×C₇₉	—	2	4	no	—
204	C₂×C₄×C₇₉	—	2	8	no	—
205	C₂×C₄×C₇₉	—	2	8	no	—
206	C₂×C₄×C₇₉	—	2	2	no	—
207	C₂×C₄×C₇₉	—	2	4	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	2	4	no	—
210	C₂×C₄×C₇₉	#131	1	4	yes	—
211	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
212	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
213	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
216	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
217	C₂×C₄×C₇₉	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
221	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
222	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
223	C₇₉⋊C₈	—	2	4	no	—
224	C₇₉⋊C₈	—	2	2	no	—
225	C₇₉⋊C₈	—	2	4	no	—
226	C₇₉⋊C₈	—	2	2	no	—
227	C₇₉⋊C₈	—	2	2	no	—
228	C₇₉⋊C₈	—	2	2	no	—
229	C₂²×C₇₉	—	2	2	no	—
230	C₂²×C₇₉	—	2	8	no	—
231	C₂²×C₇₉	—	2	2	no	—
232	C₂²×C₇₉	—	2	4	no	—
233	C₂²×C₇₉	—	2	4	no	—
234	C₂²×C₇₉	—	2	4	no	—
235	C₂²×C₇₉	—	4	8	no	—
236	C₂²×C₇₉	#520	1	2	yes	—
237	C₂²×C₇₉	C₂×#131	1	4	yes	—
238	C₂²×C₇₉	C₂×#131	1	2	yes	—
239	C₂²×C₇₉	C₂×#131	1	2	yes	—
240	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
241	C₄×C₇₉	—	2	2	no	—
242	C₄×C₇₉	—	2	4	no	—
243	C₄×C₇₉	—	2	2	no	—
244	C₄×C₇₉	—	2	2	no	—
245	C₄×C₇₉	—	2	2	no	—
246	C₄×C₇₉	—	2	4	no	—
247	C₄×C₇₉	—	2	4	no	—
248	C₄×C₇₉	#520	1	2	yes	—
249	C₄×C₇₉	C₂×#131	1	4	yes	—
250	C₄×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
251	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
252	C₂×#2994	—	79	1	no	maximal, Sylow
253	C₂×C₇₉	—	2	4	no	—
254	C₂×C₇₉	—	4	4	no	—
255	C₂×C₇₉	#2994	1	4	yes	complemented
256	C₂×C₇₉	C₂×#520	1	1	yes	characteristic
257	C₂×C₇₉	C₂²×#131	1	1	yes	characteristic
258	C₂×C₇₉	C₂²×#131	1	1	yes	characteristic
259	C₂×#529	D₇₉	1	1	yes	characteristic
260	#2994	—	79	16	no	—
261	C₂×#446	—	79	1	no	—
262	C₂×C₈×Q₈	—	79	1	no	—
263	C₂×#436	—	79	1	no	—
264	C₂×#435	—	79	2	no	—
265	C₂×C₈×D₄	—	79	2	no	—
266	C₂×C₈×D₄	—	79	1	no	—
267	C₂×#433	—	79	2	no	—
268	C₂×#431	—	79	1	no	—
269	C₂×#424	—	79	2	no	—
270	C₂²×C₄⋊C₈	—	79	1	no	—
271	C₇₉	C₂×#2994	1	1	yes	characteristic, complemented, Sylow
272	C₂²×M₁₆	—	79	2	no	—
273	C₂³×C₈	—	79	2	no	—
274	C₂³×C₈	—	79	2	no	—
275	#529	Dic₇₉	1	8	yes	—
276	#529	C₂×D₇₉	1	8	yes	—
277	C₂×#126	Dic₇₉	1	2	yes	—
278	C₂×#125	Dic₇₉	1	1	yes	characteristic
279	C₂×#124	Dic₇₉	1	1	yes	characteristic
280	C₂×#123	Dic₇₉	1	2	yes	—
281	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
282	C₂×#121	Dic₇₉	1	1	yes	characteristic
283	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	—
285	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
286	C₂×#117	C₂×D₇₉	1	2	yes	—
287	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
288	#446	—	79	8	no	—
289	C₈×Q₈	—	79	8	no	—
290	#436	—	79	8	no	—
291	#435	—	79	16	no	—
292	C₈×D₄	—	79	8	no	—
293	C₈×D₄	—	79	16	no	—
294	#433	—	79	16	no	—
295	#431	—	79	8	no	—
296	#424	—	79	16	no	—
297	C₂×C₄⋊C₈	—	79	2	no	—
298	C₂×C₄⋊C₈	—	79	1	no	—
299	C₂×C₄⋊C₈	—	79	1	no	—
300	C₂×C₄⋊C₈	—	79	8	no	—
301	C₂×C₄⋊C₈	—	79	1	no	—
302	C₂×C₄⋊C₈	—	79	2	no	—
303	C₂×C₄⋊C₈	—	79	2	no	—
304	C₂×C₄⋊C₈	—	79	1	no	—
305	C₂×C₂²⋊C₈	—	79	1	no	—
306	C₂×C₂²⋊C₈	—	79	1	no	—
307	C₂×C₂²⋊C₈	—	79	2	no	—
308	C₂×C₂²⋊C₈	—	79	2	no	—
309	C₂×#97	—	79	2	no	—
310	C₂×C₄×C₈	—	79	1	no	—
311	C₂×C₄×C₈	—	79	1	no	—
312	C₂×C₄×C₈	—	79	2	no	—
313	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
314	C₂²×D₄	C₂×Dic₇₉	1	2	yes	—
315	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
316	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
317	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
318	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
319	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
320	C₂×M₁₆	—	316	4	no	—
321	C₂×M₁₆	—	79	8	no	—
322	C₂²×C₈	—	316	4	no	—
323	C₂²×C₈	—	316	4	no	—
324	C₂²×C₈	—	79	8	no	—
325	C₂²×C₈	—	79	8	no	—
326	C₂²×C₈	—	79	2	no	—
327	C₂²×C₈	—	79	1	no	—
328	C₂²×C₈	—	79	2	no	—
329	C₂²×C₈	—	79	1	no	—
330	C₂²×C₈	—	79	1	no	—
331	C₂²×C₈	—	79	1	no	—
332	#126	C₂×Dic₇₉	1	16	yes	—
333	#125	C₂×Dic₇₉	1	8	yes	—
334	#124	C₂×Dic₇₉	1	8	yes	—
335	#123	C₂×Dic₇₉	1	16	yes	—
336	C₂²⋊Q₈	C₂×Dic₇₉	1	8	yes	—
337	#121	C₂×Dic₇₉	1	8	yes	—
338	C₄×Q₈	C₂×Dic₇₉	1	4	yes	—
339	C₄×Q₈	C₂²×D₇₉	1	4	yes	—
340	C₄×D₄	C₂×Dic₇₉	1	4	yes	—
341	C₄×D₄	C₂×Dic₇₉	1	8	yes	—
342	C₄×D₄	C₂²×D₇₉	1	8	yes	—
343	C₄×D₄	C₂²×D₇₉	1	4	yes	—
344	#117	C₂×Dic₇₉	1	8	yes	—
345	#117	C₂²×D₇₉	1	8	yes	—
346	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
348	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
350	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
357	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
358	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
359	C₂×C₄²	C₂×Dic₇₉	1	4	yes	—
360	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
361	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
362	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
363	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
364	C₄⋊C₈	—	79	8	no	—
365	C₄⋊C₈	—	79	4	no	—
366	C₄⋊C₈	—	79	4	no	—
367	C₄⋊C₈	—	79	4	no	—
368	C₄⋊C₈	—	79	8	no	—
369	C₄⋊C₈	—	79	8	no	—
370	C₄⋊C₈	—	79	4	no	—
371	C₂²⋊C₈	—	79	4	no	—
372	C₂²⋊C₈	—	79	4	no	—
373	C₂²⋊C₈	—	79	8	no	—
374	C₂²⋊C₈	—	79	8	no	—
375	#97	—	79	8	no	—
376	C₄×C₈	—	79	4	no	—
377	C₄×C₈	—	79	4	no	—
378	C₄×C₈	—	79	8	no	—
379	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
380	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	C₂²×Dic₇₉	1	4	yes	—
383	C₂×D₄	—	2	8	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	C₂²×Dic₇₉	1	8	yes	—
386	C₂×D₄	C₂²×Dic₇₉	1	4	yes	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
394	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
397	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
398	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
399	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
400	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
401	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
402	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
403	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
404	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
405	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
406	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
407	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
408	M₁₆	—	316	8	no	—
409	C₂×C₈	—	316	8	no	—
410	C₂×C₈	—	316	8	no	—
411	C₂×C₈	—	79	2	no	—
412	C₂×C₈	—	79	2	no	—
413	C₂×C₈	—	79	2	no	—
414	C₂×C₈	—	79	4	no	—
415	C₂×C₈	—	79	2	no	—
416	C₂×C₈	—	79	4	no	—
417	C₂×C₈	—	158	2	no	—
418	C₂×C₈	—	158	4	no	—
419	C₂×C₈	—	158	4	no	—
420	C₂×C₈	—	158	2	no	—
421	C₂×C₈	—	158	2	no	—
422	C₂×C₈	—	158	2	no	—
423	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
424	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
425	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
426	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
427	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
428	C₄⋊C₄	C₂²×Dic₇₉	1	8	yes	—
429	C₂²⋊C₄	C₂²×Dic₇₉	1	8	yes	—
430	C₂²⋊C₄	C₂²×Dic₇₉	1	8	yes	—
431	C₂²⋊C₄	C₂²×Dic₇₉	1	8	yes	—
432	C₂²⋊C₄	C₂²×Dic₇₉	1	8	yes	—
433	C₂²⋊C₄	C₂²×Dic₇₉	1	8	yes	—
434	C₄²	C₂²×Dic₇₉	1	2	yes	—
435	C₄²	C₂²×Dic₇₉	1	2	yes	—
436	C₄²	C₂²×Dic₇₉	1	4	yes	—
437	C₄²	C₂²×Dic₇₉	1	4	yes	—
438	C₄²	C₂²×Dic₇₉	1	4	yes	—
439	C₄²	C₂³×D₇₉	1	2	yes	—
440	C₄²	C₂³×D₇₉	1	4	yes	—
441	C₄²	C₂³×D₇₉	1	2	yes	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	#14579168	1	4	yes	—
448	C₂³	C₂³×Dic₇₉	1	4	yes	—
449	C₂³	C₂³×Dic₇₉	1	2	yes	—
450	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
451	Q₈	—	2	8	no	—
452	D₄	—	2	16	no	—
453	D₄	—	2	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	#14579168	1	4	yes	—
470	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
471	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
472	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
473	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
474	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
475	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
476	C₂×C₄	C₂³×Dic₇₉	1	4	yes	—
477	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
478	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
479	C₂×C₄	#14579207	1	2	yes	—
480	C₂×C₄	#14579208	1	2	yes	—
481	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
482	C₈	—	158	2	no	—
483	C₈	—	158	4	no	—
484	C₈	—	158	4	no	—
485	C₈	—	158	2	no	—
486	C₈	—	158	2	no	—
487	C₈	—	158	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	4	8	no	—
495	C₂²	#19099046	1	2	yes	—
496	C₂²	C₂×#14579168	1	4	yes	—
497	C₂²	C₂×#14579168	1	2	yes	—
498	C₂²	C₂×#14579168	1	2	yes	—
499	C₂²	C₂⁴×Dic₇₉	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	4	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	4	no	—
507	C₄	#19099046	1	2	yes	—
508	C₄	C₂×#14579168	1	4	yes	—
509	C₄	C₂×#14579207	1	1	yes	characteristic
510	C₄	C₂×#14579208	1	1	yes	characteristic
511	C₂	—	2	4	no	—
512	C₂	—	4	4	no	—
513	C₂	#23772560	1	4	yes	direct product factor
514	C₂	C₂×#19099046	1	1	yes	characteristic
515	C₂	C₂²×#14579168	1	1	yes	characteristic
516	C₂	C₂²×#14579168	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₂×#529×C₇₉	C₂
socle	C₂³×C₇₉	C₂³×C₄
prime radical	C₂×#121×C₇₉	C₄
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	C₂×#529	D₇₉
hypocenter	C₇₉	C₂×#2994
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #23772560	C₂	direct (N × H)
2. C₂×#19098694	C₂	semidirect
3. C₂×Q₈×C₇₉⋊C₈	C₂	semidirect
4. C₂×#19098641	C₂	semidirect
5. C₂×#19098635	C₂	semidirect
6. C₂×D₄×C₇₉⋊C₈	C₂	semidirect
7. C₂×D₄×C₇₉⋊C₈	C₂	semidirect
8. C₂×#19098624	C₂	semidirect
9. C₂×#19098616	C₂	semidirect
10. C₂×#19098590	C₂	semidirect
11. C₂²×C₄⋊(C₇₉⋊C₈)	C₂	semidirect
16. #19098694	C₂²	semidirect
17. Q₈×C₇₉⋊C₈	C₂²	semidirect
18. #19098641	C₂²	semidirect
19. #19098635	C₂²	semidirect
20. D₄×C₇₉⋊C₈	C₂²	semidirect
21. D₄×C₇₉⋊C₈	C₂²	semidirect
22. #19098624	C₂²	semidirect
23. #19098616	C₂²	semidirect
24. #19098590	C₂²	semidirect
32. C₂×C₄⋊(C₇₉⋊C₈)	C₂²	semidirect
255. C₂×C₇₉	#2994	semidirect
271. C₇₉	C₂×#2994	semidirect
513. C₂	#23772560	direct (N × H)

Maximal subgroups

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

subgroup	index
#23772560	2
C₂×#19098694	2
C₂×Q₈×C₇₉⋊C₈	2
C₂×#19098641	2
C₂×#19098635	2
C₂×D₄×C₇₉⋊C₈	2
C₂×#19098624	2
C₂×#19098616	2
C₂×#19098590	2
C₂²×C₄⋊(C₇₉⋊C₈)	2
C₂×#529×C₇₉	2
C₂×#2994	79

Subgroups — C2×#23772560 #35153371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23772560 #35153371