Subgroups — #35151688

Order 20224.

3178 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099329	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14579167	C₂	1	1	yes	maximal, characteristic
3	#23776601	C₂	1	1	yes	maximal, characteristic
4	#23771827	C₂	1	4	yes	maximal, complemented
5	#23771825	C₂	1	4	yes	maximal, complemented
6	#23771822	C₂	1	4	yes	maximal, complemented
7	C₄×#14579167	C₂	1	4	yes	maximal, complemented
8	#23771819	C₂	1	1	yes	maximal, characteristic, complemented
9	#23771818	C₂	1	1	yes	maximal, characteristic, complemented
10	#23771816	C₂	1	4	yes	maximal, complemented
11	C₂×#19098518	C₂	1	1	yes	maximal, characteristic, complemented
12	#405×D₇₉	C₂	1	4	yes	maximal, complemented
13	C₂×#405×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#11929624	C₂²	1	1	yes	characteristic
15	#19099329	C₄	1	16	yes	complemented
16	C₂×#14579169	C₂²	1	4	yes	—
17	C₂×#14579167	C₄	1	16	yes	complemented
18	C₂×#14579167	C₂²	1	2	yes	—
19	C₂×#14579167	C₂²	1	2	yes	—
20	C₂×#14579167	C₂²	1	2	yes	—
21	C₂×#14579167	C₂²	1	2	yes	—
22	C₂×#14579167	C₂²	1	4	yes	—
23	C₂²×#11929608	C₂²	1	1	yes	characteristic
24	C₂²×#11929608	C₂²	1	1	yes	characteristic
25	C₂²×#11929607	C₂²	1	2	yes	—
26	C₂×M₁₆×D₇₉	C₂²	1	4	yes	—
27	C₂²×C₈×D₇₉	C₂²	1	2	yes	—
28	#19099044	C₄	1	4	yes	—
29	#19099043	C₄	1	4	yes	—
30	#19099040	C₄	1	2	yes	—
31	#19099037	C₄	1	2	yes	—
32	#19099036	C₄	1	4	yes	—
33	C₄×#11929624	C₂²	1	4	yes	—
34	#19099031	C₂²	1	4	yes	—
35	C₂×#14579120	C₂²	1	1	yes	characteristic
36	#117×D₇₉	C₂²	1	4	yes	—
37	#19098521	C₂²	1	4	yes	—
38	#19098520	C₂²	1	8	yes	complemented
39	#19098520	C₂²	1	8	yes	complemented
40	#19098519	C₂²	1	4	yes	—
41	#19098519	C₂²	1	4	yes	complemented
42	#19098518	C₂²	1	2	yes	—
43	#19098518	C₂²	1	2	yes	—
44	#19098518	C₂²	1	2	yes	complemented
45	#19098518	C₂²	1	2	yes	complemented
46	#19098518	C₂²	1	4	yes	complemented
47	#19098517	C₂²	1	8	yes	complemented
48	#19098517	C₂²	1	8	yes	complemented
49	C₄×#11929608	C₂²	1	4	yes	complemented
50	#19098515	C₂²	1	8	yes	complemented
51	M₁₆×Dic₇₉	C₂²	1	4	yes	complemented
52	C₄×#11929607	C₂²	1	8	yes	complemented
53	C₂×#14579071	C₂²	1	2	yes	complemented
54	#97×D₇₉	C₂²	1	8	yes	complemented
55	C₂×C₈×Dic₇₉	C₂²	1	2	yes	complemented
56	C₄×C₈×D₇₉	C₂²	1	8	yes	complemented
57	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
58	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
60	#405×C₇₉	C₂²	1	2	yes	—
61	#405×C₇₉	C₂²	1	2	yes	—
62	#405×C₇₉	C₂²	1	2	yes	complemented
63	#405×C₇₉	C₂²	1	2	yes	complemented
64	C₂×#97×C₇₉	C₂²	1	2	yes	complemented
65	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	complemented
66	C₂×#11929624	C₂×C₄	1	8	yes	—
67	C₂×#11929624	C₂×C₄	1	8	yes	—
68	C₂×#11929624	C₂×C₄	1	2	yes	—
69	C₂×#11929624	C₂×C₄	1	2	yes	—
70	C₂×#11929624	C₂³	1	2	yes	—
71	C₂×#11929624	C₂³	1	2	yes	—
72	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₃₁₆	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₂²⋊D₇₉	C₂×C₄	1	2	yes	—
75	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
76	#14579169	C₂×C₄	1	32	yes	complemented
77	#14579167	C₂×C₄	1	16	yes	complemented
78	#14579167	C₂×C₄	1	16	yes	complemented
79	#14579167	C₂×C₄	1	16	yes	complemented
80	#14579167	C₂×C₄	1	16	yes	complemented
81	#14579167	C₂×C₄	1	32	yes	complemented
82	C₂×#11929608	C₂×C₄	1	8	yes	complemented
83	C₂×#11929608	C₂×C₄	1	8	yes	complemented
84	C₂×#11929608	C₂³	1	2	yes	—
85	C₂×#11929608	C₂³	1	2	yes	—
86	C₂×#11929608	C₂³	1	2	yes	—
87	C₂×#11929608	C₂³	1	2	yes	—
88	C₂×#11929607	C₂×C₄	1	16	yes	complemented
89	C₂×#11929607	C₂³	1	4	yes	—
90	C₂×#11929607	C₂³	1	8	yes	—
91	C₂×#11929607	C₂³	1	4	yes	—
92	M₁₆×D₇₉	C₂×C₄	1	32	yes	complemented
93	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
94	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
95	C₂×C₈×D₇₉	C₂×C₄	1	16	yes	complemented
96	C₂×C₈×D₇₉	C₂³	1	4	yes	—
97	C₂×C₈×D₇₉	C₂³	1	8	yes	—
98	C₂×C₈×D₇₉	C₂³	1	4	yes	—
99	C₄×Dic₁₅₈	C₂×C₄	1	8	yes	—
100	#14579126	C₂×C₄	1	8	yes	—
101	C₄×D₃₁₆	C₂×C₄	1	8	yes	—
102	#14579123	C₂×C₄	1	8	yes	—
103	C₄×C₂²⋊D₇₉	C₂×C₄	1	16	yes	—
104	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	16	yes	—
105	#14579120	C₂×C₄	1	2	yes	—
106	#14579120	C₂×C₄	1	2	yes	—
107	#14579120	C₂³	1	2	yes	—
108	#14579120	C₂³	1	2	yes	—
109	#14579119	C₂×C₄	1	8	yes	—
110	#14579118	C₂³	1	8	yes	—
111	#14579117	C₂×C₄	1	8	yes	—
112	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
113	C₄⋊C₄×D₇₉	C₂×C₄	1	8	yes	—
114	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
115	C₂²⋊C₄×D₇₉	C₂×C₄	1	8	yes	—
116	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
117	C₄²×D₇₉	C₂³	1	8	yes	—
118	#14579072	C₂³	1	8	yes	—
119	#14579071	C₂³	1	4	yes	—
120	#14579071	C₂³	1	8	yes	—
121	#14579071	C₂³	1	4	yes	—
122	C₄×C₇₉⋊C₈	C₂³	1	8	yes	—
123	C₈×Dic₇₉	C₂³	1	4	yes	—
124	C₈×Dic₇₉	C₂³	1	8	yes	—
125	C₈×Dic₇₉	C₂³	1	4	yes	—
126	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₇₉	C₂×C₄	1	8	yes	complemented
128	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
129	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
130	C₂²×C₈×C₇₉	C₂×C₄	1	8	yes	complemented
131	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
138	#117×C₇₉	C₂×C₄	1	2	yes	—
139	#117×C₇₉	C₂×C₄	1	2	yes	—
140	#117×C₇₉	C₂³	1	2	yes	—
141	#117×C₇₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
143	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
144	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
145	#97×C₇₉	C₂³	1	4	yes	—
146	#97×C₇₉	C₂³	1	4	yes	—
147	C₄×C₈×C₇₉	C₂³	1	4	yes	—
148	C₄×C₈×C₇₉	C₂³	1	4	yes	—
149	C₂³×D₇₉	C₂²×C₄	1	2	yes	—
150	#11929624	C₄²	1	16	yes	—
151	#11929624	C₄²	1	16	yes	—
152	#11929624	C₂²×C₄	1	8	yes	—
153	#11929624	C₂²×C₄	1	8	yes	—
154	#11929624	C₂²×C₄	1	8	yes	—
155	#11929624	C₂²×C₄	1	8	yes	—
156	C₂×Dic₁₅₈	C₄²	1	8	yes	—
157	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
158	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
159	C₂×D₃₁₆	C₄²	1	8	yes	—
160	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
161	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
162	C₂×C₂²⋊D₇₉	C₄²	1	16	yes	—
163	C₂×C₂²⋊D₇₉	C₂²×C₄	1	4	yes	—
164	C₂×C₂²⋊D₇₉	C₂²×C₄	1	4	yes	—
165	C₂²×Dic₇₉	C₂²×C₄	1	4	yes	—
166	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
167	C₂×C₄×D₇₉	C₂²×C₄	1	8	yes	—
168	C₂×C₄×D₇₉	C₂²×C₄	1	8	yes	—
169	C₂×C₄×D₇₉	C₂²×C₄	1	16	yes	—
170	C₂×C₄×D₇₉	C₂²×C₄	1	4	yes	—
171	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
172	#11929608	C₂²×C₄	1	8	yes	—
173	#11929608	C₂²×C₄	1	8	yes	—
174	#11929608	C₂²×C₄	1	8	yes	—
175	#11929608	C₂²×C₄	1	8	yes	—
176	#11929607	C₂²×C₄	1	32	yes	—
177	#11929607	C₂²×C₄	1	16	yes	—
178	#11929607	C₂²×C₄	1	16	yes	—
179	C₂×C₇₉⋊C₈	C₂²×C₄	1	8	yes	—
180	C₂×C₇₉⋊C₈	C₂²×C₄	1	8	yes	—
181	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
182	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
183	C₈×D₇₉	C₂²×C₄	1	16	yes	—
184	C₈×D₇₉	C₂²×C₄	1	16	yes	—
185	C₈×D₇₉	C₂²×C₄	1	32	yes	—
186	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
187	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
188	Dic₇₉⋊C₄	C₂²×C₄	1	16	yes	—
189	C₂²⋊Dic₇₉	C₂²×C₄	1	4	yes	—
190	C₂²⋊Dic₇₉	C₂²×C₄	1	4	yes	—
191	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	16	yes	—
192	C₄×Dic₇₉	C₂²×C₄	1	16	yes	—
193	C₄×Dic₇₉	C₂²×C₄	1	4	yes	—
194	C₄×Dic₇₉	C₂⁴	1	4	yes	—
195	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
205	M₁₆×C₇₉	C₂²×C₄	1	8	yes	—
206	M₁₆×C₇₉	C₂²×C₄	1	8	yes	—
207	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
208	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
209	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
210	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
211	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
212	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
213	C₂×C₈×C₇₉	C₂²×C₄	1	8	yes	—
214	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
215	C₂×C₈×C₇₉	C₂⁴	1	4	yes	—
216	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
217	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
218	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
219	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
221	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
222	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
223	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
224	C₄²×C₇₉	C₂⁴	1	4	yes	—
225	C₂³×C₇₉	—	4	2	no	—
226	C₂³×C₇₉	C₂×C₄²	1	4	yes	—
227	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
228	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
229	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
230	C₂²×D₇₉	—	4	4	no	—
231	C₂²×D₇₉	C₂×C₄²	1	8	yes	—
232	C₂²×D₇₉	C₂³×C₄	1	4	yes	—
233	C₂×C₄×C₇₉	—	4	4	no	—
234	C₂×C₄×C₇₉	C₂×C₄²	1	4	yes	—
235	C₂×C₄×C₇₉	C₂×C₄²	1	4	yes	—
236	C₂×C₄×C₇₉	C₂×C₄²	1	4	yes	—
237	C₂×C₄×C₇₉	C₂³×C₄	1	8	yes	—
238	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
239	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
240	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
241	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
242	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
243	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
244	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
248	C₂²⋊D₇₉	C₂×C₄²	1	16	yes	—
249	C₂²⋊D₇₉	C₂×C₄²	1	16	yes	—
250	C₂×Dic₇₉	—	4	4	no	—
251	C₂×Dic₇₉	C₂×C₄²	1	8	yes	—
252	C₂×Dic₇₉	C₂³×C₄	1	8	yes	—
253	C₂×Dic₇₉	C₂³×C₄	1	4	yes	—
254	D₃₁₆	C₂×C₄²	1	8	yes	—
255	D₃₁₆	C₂×C₄²	1	8	yes	—
256	C₄×D₇₉	—	4	16	no	—
257	C₄×D₇₉	C₂×C₄²	1	16	yes	—
258	C₄×D₇₉	C₂³×C₄	1	8	yes	—
259	C₄×D₇₉	C₂³×C₄	1	8	yes	—
260	Dic₁₅₈	C₂×C₄²	1	8	yes	—
261	Dic₁₅₈	C₂×C₄²	1	8	yes	—
262	C₈×C₇₉	C₂³×C₄	1	2	yes	—
263	C₈×C₇₉	C₂³×C₄	1	2	yes	—
264	C₈×C₇₉	C₂³×C₄	1	8	yes	—
265	C₈×C₇₉	C₂³×C₄	1	2	yes	—
266	C₈×C₇₉	C₂³×C₄	1	2	yes	—
267	C₇₉⋊C₈	C₂³×C₄	1	8	yes	—
268	C₇₉⋊C₈	C₂³×C₄	1	8	yes	—
269	C₂²×C₇₉	—	2	2	no	—
270	C₂²×C₇₉	—	2	2	no	—
271	C₂²×C₇₉	—	2	2	no	—
272	C₂²×C₇₉	—	4	4	no	—
273	C₂²×C₇₉	C₂²×C₄²	1	2	yes	—
274	C₂²×C₇₉	C₂²×C₄²	1	2	yes	—
275	C₂²×C₇₉	C₂²×C₄²	1	2	yes	—
276	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
277	C₂×D₇₉	—	2	8	no	—
278	C₂×D₇₉	—	4	8	no	—
279	C₂×D₇₉	C₂²×C₄²	1	8	yes	—
280	C₄×C₇₉	—	2	8	no	—
281	C₄×C₇₉	C₂²×C₄²	1	2	yes	—
282	C₄×C₇₉	C₂²×C₄²	1	2	yes	—
283	C₄×C₇₉	C₂²×C₄²	1	2	yes	—
284	C₄×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
285	C₄×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
286	Dic₇₉	—	2	8	no	—
287	Dic₇₉	C₂²×C₄²	1	8	yes	—
288	#60058	—	79	1	no	maximal, Sylow
289	C₂×C₇₉	—	2	2	no	—
290	C₂×C₇₉	—	2	2	no	—
291	C₂×C₇₉	—	2	2	no	—
292	C₂×C₇₉	C₂³×C₄²	1	1	yes	characteristic
293	C₂×C₇₉	#3573	1	2	yes	—
294	D₇₉	—	2	8	no	—
295	C₂×#568	—	79	1	no	—
296	C₂²×#131	—	79	1	no	—
297	#3428	—	79	1	no	—
298	#2875	—	79	4	no	—
299	#2875	—	79	4	no	—
300	C₄×#131	—	79	4	no	—
301	C₄×#131	—	79	4	no	—
302	#2873	—	79	4	no	—
303	#2873	—	79	1	no	—
304	#2873	—	79	1	no	—
305	C₂×#405	—	79	4	no	—
306	C₂×#405	—	79	1	no	—
307	C₂×#405	D₇₉	1	1	yes	characteristic, complemented
308	C₇₉	#60058	1	1	yes	characteristic, complemented, Sylow
309	C₂²×#41	—	79	1	no	—
310	#568	—	79	16	no	—
311	C₂×#131	—	79	4	no	—
312	C₂×#131	—	79	2	no	—
313	C₂×#131	—	79	2	no	—
314	C₂×#131	—	79	4	no	—
315	C₂×#131	—	79	2	no	—
316	C₂×#131	—	79	2	no	—
317	C₂×#131	—	79	16	no	—
318	C₂²×M₁₆	—	79	1	no	—
319	C₂²×M₁₆	—	79	1	no	—
320	C₂²×M₁₆	—	79	4	no	—
321	C₂²×M₁₆	—	79	2	no	—
322	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
323	C₂³×C₈	—	79	2	no	—
324	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
325	#520	—	79	4	no	—
326	#520	—	79	4	no	—
327	#519	—	79	2	no	—
328	#518	—	79	2	no	—
329	#518	—	79	4	no	—
330	C₄×#41	—	79	4	no	—
331	C₄×#41	—	79	4	no	—
332	C₂×#117	—	79	1	no	—
333	C₂×#117	—	79	4	no	—
334	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
335	#405	—	79	4	no	—
336	#405	—	79	2	no	—
337	#405	—	79	2	no	—
338	#405	—	79	2	no	—
339	#405	—	79	2	no	—
340	#405	—	79	4	no	—
341	#405	—	79	4	no	—
342	#405	—	79	4	no	—
343	#405	—	79	8	no	—
344	#405	—	79	8	no	—
345	#405	—	79	8	no	—
346	#405	—	79	8	no	—
347	#405	C₂×D₇₉	1	2	yes	—
348	#405	C₂×D₇₉	1	2	yes	—
349	#405	C₂×D₇₉	1	2	yes	complemented
350	#405	C₂×D₇₉	1	2	yes	complemented
351	C₄×M₁₆	—	79	4	no	—
352	C₄×M₁₆	—	79	4	no	—
353	C₄×M₁₆	—	79	8	no	—
354	C₄×M₁₆	—	79	8	no	—
355	C₂×#97	—	79	2	no	—
356	C₂×#97	—	79	8	no	—
357	C₂×#97	C₂×D₇₉	1	2	yes	complemented
358	C₂×C₄×C₈	—	79	2	no	—
359	C₂×C₄×C₈	—	79	8	no	—
360	C₂×C₄×C₈	C₂×D₇₉	1	2	yes	complemented
361	C₂×#41	—	79	2	no	—
362	C₂×#41	—	79	2	no	—
363	C₂×#41	—	79	8	no	—
364	C₂×#41	—	79	8	no	—
365	C₂×#41	—	79	2	no	—
366	C₂×#41	—	79	2	no	—
367	C₂²×Q₈	—	79	1	no	—
368	C₂²×D₄	—	79	2	no	—
369	C₂²×D₄	—	79	1	no	—
370	C₂³×C₄	—	79	2	no	—
371	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
372	#131	—	79	32	no	—
373	#131	—	79	16	no	—
374	#131	—	79	16	no	—
375	#131	—	79	16	no	—
376	#131	—	79	16	no	—
377	#131	—	79	32	no	—
378	C₂×M₁₆	—	79	8	no	—
379	C₂×M₁₆	—	79	8	no	—
380	C₂×M₁₆	—	79	2	no	—
381	C₂×M₁₆	—	79	2	no	—
382	C₂×M₁₆	—	79	2	no	—
383	C₂×M₁₆	—	79	2	no	—
384	C₂×M₁₆	—	79	32	no	—
385	C₂×M₁₆	—	79	16	no	—
386	C₂×M₁₆	—	79	4	no	—
387	C₂×M₁₆	—	79	8	no	—
388	C₂×M₁₆	—	79	4	no	—
389	C₂×M₁₆	C₄×D₇₉	1	8	yes	complemented
390	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
391	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
392	C₂²×C₈	—	79	2	no	—
393	C₂²×C₈	—	79	2	no	—
394	C₂²×C₈	—	79	16	no	—
395	C₂²×C₈	—	79	4	no	—
396	C₂²×C₈	—	79	8	no	—
397	C₂²×C₈	—	79	4	no	—
398	C₂²×C₈	C₄×D₇₉	1	8	yes	complemented
399	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
400	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
401	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
402	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
403	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
404	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
405	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
406	C₄×Q₈	—	79	8	no	—
407	C₄×Q₈	—	79	8	no	—
408	C₄×D₄	—	79	16	no	—
409	C₄×D₄	—	79	8	no	—
410	C₄×D₄	—	79	16	no	—
411	C₄×D₄	—	79	8	no	—
412	#117	—	79	2	no	—
413	#117	—	79	2	no	—
414	#117	—	79	2	no	—
415	#117	—	79	2	no	—
416	#117	—	79	8	no	—
417	#117	—	79	8	no	—
418	#117	—	79	8	no	—
419	#117	C₄×D₇₉	1	2	yes	—
420	#117	C₄×D₇₉	1	2	yes	—
421	#117	C₂²×D₇₉	1	2	yes	—
422	#117	C₂²×D₇₉	1	2	yes	—
423	C₂×C₄⋊C₄	—	79	2	no	—
424	C₂×C₄⋊C₄	—	79	8	no	—
425	C₂×C₄⋊C₄	C₄×D₇₉	1	2	yes	—
426	C₂×C₂²⋊C₄	—	79	2	no	—
427	C₂×C₂²⋊C₄	—	79	8	no	—
428	C₂×C₂²⋊C₄	C₄×D₇₉	1	2	yes	—
429	C₂×C₄²	—	79	2	no	—
430	C₂×C₄²	—	79	8	no	—
431	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
432	#97	—	79	4	no	—
433	#97	—	79	8	no	—
434	#97	—	79	4	no	—
435	#97	—	79	8	no	—
436	#97	C₂²×D₇₉	1	4	yes	—
437	#97	C₂²×D₇₉	1	4	yes	—
438	C₄×C₈	—	79	4	no	—
439	C₄×C₈	—	79	8	no	—
440	C₄×C₈	—	79	4	no	—
441	C₄×C₈	—	79	8	no	—
442	C₄×C₈	C₂²×D₇₉	1	4	yes	—
443	C₄×C₈	C₂²×D₇₉	1	4	yes	—
444	C₂⁴	—	79	2	no	—
445	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
446	#41	—	79	16	no	—
447	#41	—	79	16	no	—
448	#41	—	79	8	no	—
449	#41	—	79	8	no	—
450	#41	—	79	8	no	—
451	#41	—	79	8	no	—
452	C₂×Q₈	—	79	8	no	—
453	C₂×Q₈	—	79	2	no	—
454	C₂×Q₈	—	79	2	no	—
455	C₂×D₄	—	79	16	no	—
456	C₂×D₄	—	79	4	no	—
457	C₂×D₄	—	79	4	no	—
458	C₂×D₄	—	79	8	no	—
459	C₂×D₄	—	79	2	no	—
460	C₂×D₄	—	79	2	no	—
461	C₂²×C₄	—	79	4	no	—
462	C₂²×C₄	—	79	16	no	—
463	C₂²×C₄	—	79	2	no	—
464	C₂²×C₄	—	79	4	no	—
465	C₂²×C₄	—	79	4	no	—
466	C₂²×C₄	—	79	8	no	—
467	C₂²×C₄	—	79	8	no	—
468	C₂²×C₄	C₂×C₄×D₇₉	1	4	yes	—
469	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₇₉	1	4	yes	—
473	C₂²×C₄	C₂×C₄×D₇₉	1	4	yes	—
474	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
475	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
476	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
477	M₁₆	—	79	8	no	—
478	M₁₆	—	79	8	no	—
479	M₁₆	—	79	8	no	—
480	M₁₆	—	79	8	no	—
481	M₁₆	—	79	32	no	—
482	M₁₆	—	79	16	no	—
483	M₁₆	—	79	16	no	—
484	M₁₆	C₂×C₄×D₇₉	1	8	yes	—
485	M₁₆	C₂×C₄×D₇₉	1	8	yes	—
486	C₂×C₈	—	79	4	no	—
487	C₂×C₈	—	79	4	no	—
488	C₂×C₈	—	79	8	no	—
489	C₂×C₈	—	79	8	no	—
490	C₂×C₈	—	79	16	no	—
491	C₂×C₈	—	79	16	no	—
492	C₂×C₈	—	79	32	no	—
493	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
494	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
495	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
496	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
497	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
498	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
499	C₂×C₈	C₂×C₄×D₇₉	1	8	yes	—
500	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
501	C₂×C₈	C₂³×D₇₉	1	4	yes	—
502	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
503	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
504	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
505	C₄⋊C₄	—	79	16	no	—
506	C₄⋊C₄	—	79	4	no	—
507	C₄⋊C₄	—	79	4	no	—
508	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
509	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
510	C₂²⋊C₄	—	79	4	no	—
511	C₂²⋊C₄	—	79	4	no	—
512	C₂²⋊C₄	—	79	16	no	—
513	C₂²⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
514	C₂²⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
515	C₄²	—	79	4	no	—
516	C₄²	—	79	16	no	—
517	C₄²	—	79	4	no	—
518	C₄²	C₂×C₄×D₇₉	1	4	yes	—
519	C₄²	C₂³×D₇₉	1	4	yes	—
520	C₂³	—	4	2	no	—
521	C₂³	—	316	4	no	—
522	C₂³	—	79	8	no	—
523	C₂³	—	79	4	no	—
524	C₂³	C₄²×D₇₉	1	4	yes	—
525	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
526	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
527	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
528	Q₈	—	79	8	no	—
529	Q₈	—	79	8	no	—
530	D₄	—	79	16	no	—
531	D₄	—	79	16	no	—
532	D₄	—	79	8	no	—
533	D₄	—	79	8	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	316	16	no	—
536	C₂×C₄	—	316	4	no	—
537	C₂×C₄	—	79	8	no	—
538	C₂×C₄	—	79	4	no	—
539	C₂×C₄	—	79	16	no	—
540	C₂×C₄	—	79	8	no	—
541	C₂×C₄	—	79	8	no	—
542	C₂×C₄	—	79	8	no	—
543	C₂×C₄	C₄²×D₇₉	1	4	yes	—
544	C₂×C₄	C₄²×D₇₉	1	4	yes	—
545	C₂×C₄	C₄²×D₇₉	1	4	yes	—
546	C₂×C₄	C₂²×C₄×D₇₉	1	8	yes	—
547	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
548	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
550	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
551	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
552	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
553	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
554	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
555	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
556	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
557	C₈	—	79	8	no	—
558	C₈	—	79	8	no	—
559	C₈	C₂²×C₄×D₇₉	1	2	yes	—
560	C₈	C₂²×C₄×D₇₉	1	2	yes	—
561	C₈	C₂²×C₄×D₇₉	1	8	yes	—
562	C₈	C₂²×C₄×D₇₉	1	2	yes	—
563	C₈	C₂²×C₄×D₇₉	1	2	yes	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	316	8	no	—
569	C₂²	—	79	8	no	—
570	C₂²	—	158	8	no	—
571	C₂²	C₂×C₄²×D₇₉	1	2	yes	—
572	C₂²	C₂×C₄²×D₇₉	1	2	yes	—
573	C₂²	C₂×C₄²×D₇₉	1	2	yes	—
574	C₂²	C₂³×C₄×D₇₉	1	1	yes	characteristic
575	C₄	—	2	8	no	—
576	C₄	—	79	8	no	—
577	C₄	—	158	8	no	—
578	C₄	C₂×C₄²×D₇₉	1	2	yes	—
579	C₄	C₂×C₄²×D₇₉	1	2	yes	—
580	C₄	C₂×C₄²×D₇₉	1	2	yes	—
581	C₄	C₂³×C₄×D₇₉	1	1	yes	characteristic
582	C₄	C₂³×C₄×D₇₉	1	1	yes	characteristic
583	C₂	—	2	2	no	—
584	C₂	—	2	2	no	—
585	C₂	—	2	2	no	—
586	C₂	—	158	8	no	—
587	C₂	C₂²×C₄²×D₇₉	1	1	yes	characteristic
588	C₂	#23778111	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂³×D₇₉
commutator	C₂×C₇₉	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₂×#405×C₇₉	C₂
socle	C₂²×C₇₉	C₂⁴×C₄
prime radical	C₂²×#11929624	C₂²
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	C₂×#405	D₇₉
hypocenter	C₇₉	#60058
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
4. #23771827	C₂	semidirect
5. #23771825	C₂	semidirect
6. #23771822	C₂	semidirect
7. C₄×#14579167	C₂	semidirect
8. #23771819	C₂	semidirect
9. #23771818	C₂	semidirect
10. #23771816	C₂	semidirect
11. C₂×#19098518	C₂	semidirect
12. #405×D₇₉	C₂	semidirect
13. C₂×#405×C₇₉	C₂	semidirect
15. #19099329	C₄	semidirect
17. C₂×#14579167	C₄	semidirect
38. #19098520	C₂²	semidirect
39. #19098520	C₂²	semidirect
41. #19098519	C₂²	semidirect
44. #19098518	C₂²	semidirect
45. #19098518	C₂²	semidirect
46. #19098518	C₂²	semidirect
47. #19098517	C₂²	semidirect
48. #19098517	C₂²	semidirect
49. C₄×#11929608	C₂²	semidirect
50. #19098515	C₂²	semidirect
51. M₁₆×Dic₇₉	C₂²	semidirect
52. C₄×#11929607	C₂²	semidirect
53. C₂×#14579071	C₂²	semidirect
54. #97×D₇₉	C₂²	semidirect
55. C₂×C₈×Dic₇₉	C₂²	semidirect
56. C₄×C₈×D₇₉	C₂²	semidirect
62. #405×C₇₉	C₂²	semidirect
63. #405×C₇₉	C₂²	semidirect
64. C₂×#97×C₇₉	C₂²	semidirect
65. C₂×C₄×C₈×C₇₉	C₂²	semidirect
76. #14579169	C₂×C₄	semidirect
77. #14579167	C₂×C₄	semidirect
78. #14579167	C₂×C₄	semidirect
79. #14579167	C₂×C₄	semidirect
80. #14579167	C₂×C₄	semidirect
81. #14579167	C₂×C₄	semidirect
82. C₂×#11929608	C₂×C₄	semidirect
83. C₂×#11929608	C₂×C₄	semidirect
88. C₂×#11929607	C₂×C₄	semidirect
92. M₁₆×D₇₉	C₂×C₄	semidirect
95. C₂×C₈×D₇₉	C₂×C₄	semidirect
127. C₂×M₁₆×C₇₉	C₂×C₄	semidirect
130. C₂²×C₈×C₇₉	C₂×C₄	semidirect
307. C₂×#405	D₇₉	semidirect
308. C₇₉	#60058	semidirect
349. #405	C₂×D₇₉	semidirect
350. #405	C₂×D₇₉	semidirect
357. C₂×#97	C₂×D₇₉	semidirect
360. C₂×C₄×C₈	C₂×D₇₉	semidirect
389. C₂×M₁₆	C₄×D₇₉	semidirect
398. C₂²×C₈	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19099329	2
C₂²×#14579167	2
#23776601	2
#23771827	2
#23771825	2
#23771822	2
C₄×#14579167	2
#23771819	2
#23771818	2
#23771816	2
C₂×#19098518	2
#405×D₇₉	2
C₂×#405×C₇₉	2
#60058	79