Subgroups — #34310056

Order 20224.

788 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098691	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098589	C₂	1	1	yes	maximal, characteristic
3	#23766674	C₂	1	1	yes	maximal, characteristic
4	#23764338	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764123	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764117	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764117	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763964	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763963	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763585	C₂	1	1	yes	maximal, characteristic
11	#23763578	C₂	1	1	yes	maximal, characteristic
12	#23763276	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763186	C₂	1	1	yes	maximal, characteristic
14	#23763168	C₂	1	1	yes	maximal, characteristic
15	C₇₉×#1752	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
18	C₂×#14579120	C₂²	1	1	yes	characteristic
19	#19098691	—	2	4	no	—
20	#19098589	—	2	4	no	—
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×#14579071	C₂²	1	1	yes	characteristic
31	C₂×#14579071	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
34	#19098505	C₄	1	1	yes	characteristic
35	#19098499	C₄	1	1	yes	characteristic
36	#19098497	C₄	1	1	yes	characteristic
37	#19098495	C₄	1	1	yes	characteristic
38	#19098486	C₄	1	1	yes	characteristic
39	#19098486	C₄	1	1	yes	characteristic
40	#19098484	C₄	1	1	yes	characteristic
41	#19098475	C₄	1	1	yes	characteristic
42	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
46	#19098318	C₂²	1	1	yes	characteristic
47	#19098318	C₂²	1	1	yes	characteristic
48	#19098317	C₂²	1	1	yes	characteristic
49	#19098317	C₂²	1	1	yes	characteristic
50	#19098317	C₂²	1	1	yes	characteristic
51	#19098317	C₂²	1	1	yes	characteristic
52	#19098317	C₂²	1	1	yes	characteristic
53	#19098317	C₂²	1	1	yes	characteristic
54	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
57	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
59	#336×C₇₉	C₂²	1	1	yes	characteristic
60	#336×C₇₉	C₂²	1	1	yes	characteristic
61	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
62	C₂×#11929608	—	2	2	no	—
63	C₂×#11929608	—	2	2	no	—
64	C₂×#11929608	—	4	1	no	—
65	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₄×Dic₁₅₈	—	2	2	no	—
70	C₄×Dic₁₅₈	—	2	2	no	—
71	#14579120	—	2	2	no	—
72	#14579120	—	2	2	no	—
73	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
92	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
93	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
94	Dic₇₉⋊C₈	—	2	2	no	—
95	Dic₇₉⋊C₈	—	2	2	no	—
96	Dic₇₉⋊C₈	—	2	2	no	—
97	Dic₇₉⋊C₈	—	2	2	no	—
98	Dic₇₉⋊C₈	—	4	1	no	—
99	Dic₇₉⋊C₈	D₄	1	4	yes	—
100	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
101	#14579071	—	2	2	no	—
102	#14579071	—	2	2	no	—
103	C₈×Dic₇₉	—	2	2	no	—
104	C₈×Dic₇₉	—	4	1	no	—
105	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₉	—	2	2	no	—
115	C₂²×C₈×C₇₉	—	2	2	no	—
116	C₂²×C₈×C₇₉	—	4	1	no	—
117	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
125	C₂²⋊C₈×C₇₉	Q₈	1	4	yes	complemented
126	#97×C₇₉	—	2	2	no	—
127	#97×C₇₉	—	4	1	no	—
128	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
129	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
130	C₂×Dic₁₅₈	—	2	2	no	—
131	C₂×Dic₁₅₈	—	4	1	no	—
132	C₂×Dic₁₅₈	—	4	1	no	—
133	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
141	#11929608	—	4	4	no	—
142	C₂×C₇₉⋊C₈	—	2	1	no	—
143	C₂×C₇₉⋊C₈	—	2	1	no	—
144	C₂×C₇₉⋊C₈	—	2	1	no	—
145	C₂×C₇₉⋊C₈	—	2	1	no	—
146	C₂×C₇₉⋊C₈	—	2	1	no	—
147	C₂×C₇₉⋊C₈	—	2	1	no	—
148	C₂×C₇₉⋊C₈	—	2	1	no	—
149	C₂×C₇₉⋊C₈	—	2	1	no	—
150	C₂×C₇₉⋊C₈	—	2	1	no	—
151	C₂×C₇₉⋊C₈	—	2	1	no	—
152	C₂×C₇₉⋊C₈	—	2	1	no	—
153	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
154	C₄⋊Dic₇₉	—	2	2	no	—
155	C₄⋊Dic₇₉	—	2	2	no	—
156	C₄⋊Dic₇₉	—	2	2	no	—
157	C₄⋊Dic₇₉	—	4	1	no	—
158	C₄⋊Dic₇₉	—	4	1	no	—
159	Dic₇₉⋊C₄	—	2	2	no	—
160	Dic₇₉⋊C₄	—	2	2	no	—
161	Dic₇₉⋊C₄	—	2	2	no	—
162	Dic₇₉⋊C₄	—	2	2	no	—
163	Dic₇₉⋊C₄	—	4	1	no	—
164	Dic₇₉⋊C₄	—	4	1	no	—
165	C₂²⋊Dic₇₉	—	2	2	no	—
166	C₂²⋊Dic₇₉	—	2	2	no	—
167	C₂²⋊Dic₇₉	—	2	2	no	—
168	C₂²⋊Dic₇₉	—	4	1	no	—
169	C₄×Dic₇₉	—	2	1	no	—
170	C₄×Dic₇₉	—	2	1	no	—
171	C₄×Dic₇₉	—	2	1	no	—
172	C₄×Dic₇₉	—	2	1	no	—
173	C₄×Dic₇₉	—	2	1	no	—
174	C₄×Dic₇₉	—	2	1	no	—
175	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
176	C₄×Dic₇₉	#41	1	2	yes	—
177	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	1	no	—
180	C₂²×C₄×C₇₉	—	2	1	no	—
181	C₂²×C₄×C₇₉	—	2	1	no	—
182	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
188	C₂²×C₄×C₇₉	#41	1	2	yes	—
189	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
190	C₂×C₈×C₇₉	—	2	1	no	—
191	C₂×C₈×C₇₉	—	2	1	no	—
192	C₂×C₈×C₇₉	—	2	1	no	—
193	C₂×C₈×C₇₉	—	2	1	no	—
194	C₂×C₈×C₇₉	—	2	1	no	—
195	C₂×C₈×C₇₉	—	2	1	no	—
196	C₂×C₈×C₇₉	—	2	1	no	—
197	C₂×C₈×C₇₉	—	2	1	no	—
198	C₂×C₈×C₇₉	—	2	1	no	—
199	C₂×C₈×C₇₉	—	4	4	no	—
200	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
201	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
202	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
203	C₂²⋊C₄×C₇₉	—	4	1	no	—
204	C₂²⋊C₄×C₇₉	—	4	1	no	—
205	C₄²×C₇₉	—	2	1	no	—
206	C₄²×C₇₉	—	2	1	no	—
207	C₄²×C₇₉	—	2	1	no	—
208	C₄²×C₇₉	—	2	1	no	—
209	C₂³×C₇₉	—	2	1	no	—
210	C₂³×C₇₉	—	2	1	no	—
211	C₂³×C₇₉	—	2	1	no	—
212	C₂³×C₇₉	—	2	1	no	—
213	C₂³×C₇₉	—	2	1	no	—
214	C₂³×C₇₉	—	2	1	no	—
215	C₂³×C₇₉	C₄×Q₈	1	2	yes	—
216	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	—	2	1	no	—
218	C₂×C₄×C₇₉	—	2	1	no	—
219	C₂×C₄×C₇₉	—	2	2	no	—
220	C₂×C₄×C₇₉	—	2	2	no	—
221	C₂×C₄×C₇₉	—	2	2	no	—
222	C₂×C₄×C₇₉	—	2	2	no	—
223	C₂×C₄×C₇₉	—	2	1	no	—
224	C₂×C₄×C₇₉	—	2	1	no	—
225	C₂×C₄×C₇₉	—	2	1	no	—
226	C₂×C₄×C₇₉	—	2	1	no	—
227	C₂×C₄×C₇₉	—	2	1	no	—
228	C₂×C₄×C₇₉	—	2	1	no	—
229	C₂×C₄×C₇₉	—	2	1	no	—
230	C₂×C₄×C₇₉	—	2	1	no	—
231	C₂×C₄×C₇₉	—	2	1	no	—
232	C₂×C₄×C₇₉	—	2	1	no	—
233	C₂×C₄×C₇₉	—	2	1	no	—
234	C₂×C₄×C₇₉	—	2	1	no	—
235	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
236	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
242	C₂×Dic₇₉	—	2	1	no	—
243	C₂×Dic₇₉	—	2	1	no	—
244	C₂×Dic₇₉	—	2	1	no	—
245	C₂×Dic₇₉	—	2	1	no	—
246	C₂×Dic₇₉	—	2	1	no	—
247	C₂×Dic₇₉	—	2	1	no	—
248	C₂×Dic₇₉	—	2	1	no	—
249	C₂×Dic₇₉	—	2	1	no	—
250	C₂×Dic₇₉	—	2	1	no	—
251	C₂×Dic₇₉	—	2	1	no	—
252	C₂×Dic₇₉	—	2	1	no	—
253	C₂×Dic₇₉	—	2	1	no	—
254	C₂×Dic₇₉	—	2	1	no	—
255	C₂×Dic₇₉	—	2	1	no	—
256	C₂×Dic₇₉	—	2	1	no	—
257	C₂×Dic₇₉	—	2	1	no	—
258	C₂×Dic₇₉	—	2	1	no	—
259	C₂×Dic₇₉	—	2	1	no	—
260	C₂×Dic₇₉	—	2	1	no	—
261	C₂×Dic₇₉	—	2	1	no	—
262	C₂×Dic₇₉	—	2	1	no	—
263	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
264	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
265	C₂×Dic₇₉	#131	1	2	yes	—
266	Dic₁₅₈	—	4	4	no	—
267	C₈×C₇₉	—	2	2	no	—
268	C₈×C₇₉	—	2	2	no	—
269	C₈×C₇₉	—	2	2	no	—
270	C₈×C₇₉	—	4	1	no	—
271	C₇₉⋊C₈	—	2	2	no	—
272	C₇₉⋊C₈	—	4	1	no	—
273	C₇₉⋊C₈	—	4	1	no	—
274	C₇₉⋊C₈	—	4	1	no	—
275	C₂²×C₇₉	—	2	2	no	—
276	C₂²×C₇₉	—	2	2	no	—
277	C₂²×C₇₉	—	2	2	no	—
278	C₂²×C₇₉	—	4	1	no	—
279	C₂²×C₇₉	—	4	1	no	—
280	C₂²×C₇₉	—	4	1	no	—
281	C₂²×C₇₉	—	4	1	no	—
282	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
284	C₂²×C₇₉	#520	1	1	yes	characteristic
285	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
286	C₂²×C₇₉	#568	1	1	yes	characteristic
287	C₂²×C₇₉	#568	1	1	yes	characteristic
288	C₂²×C₇₉	#568	1	1	yes	characteristic
289	C₄×C₇₉	—	2	2	no	—
290	C₄×C₇₉	—	4	1	no	—
291	C₄×C₇₉	—	4	1	no	—
292	C₄×C₇₉	—	4	1	no	—
293	C₄×C₇₉	—	4	1	no	—
294	C₄×C₇₉	#546	1	1	yes	characteristic
295	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
296	C₄×C₇₉	#552	1	1	yes	characteristic
297	C₄×C₇₉	#554	1	1	yes	characteristic
298	Dic₇₉	—	2	2	no	—
299	Dic₇₉	—	2	2	no	—
300	Dic₇₉	—	2	2	no	—
301	Dic₇₉	—	4	1	no	—
302	Dic₇₉	—	4	1	no	—
303	Dic₇₉	—	4	1	no	—
304	Dic₇₉	—	4	1	no	—
305	Dic₇₉	—	4	1	no	—
306	#22961	—	79	1	no	maximal, Sylow
307	C₂×C₇₉	—	4	2	no	—
308	C₂×C₇₉	#2360	1	1	yes	characteristic
309	C₂×C₇₉	#2930	1	1	yes	characteristic
310	C₂×C₇₉	#2935	1	1	yes	characteristic
311	C₂×C₇₉	#2961	1	1	yes	characteristic
312	C₂×C₇₉	#2962	1	1	yes	characteristic
313	C₂×C₇₉	#2992	1	1	yes	characteristic
314	C₂×C₇₉	#2995	1	1	yes	characteristic
315	C₂×#446	—	79	1	no	—
316	C₂×#424	—	79	1	no	—
317	#2396	—	79	1	no	—
318	#1985	—	79	1	no	—
319	#1940	—	79	1	no	—
320	#1939	—	79	1	no	—
321	#1939	—	79	1	no	—
322	#1917	—	79	1	no	—
323	#1917	—	79	1	no	—
324	#1851	—	79	1	no	—
325	#1850	—	79	1	no	—
326	#1771	—	79	1	no	—
327	#1753	—	79	1	no	—
328	#1752	D₇₉	1	1	yes	characteristic
329	#1750	—	79	1	no	—
330	C₇₉	#22961	1	1	yes	characteristic, complemented, Sylow
331	C₂²×M₁₆	—	79	1	no	—
332	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
333	C₂×C₄×Q₈	—	79	1	no	—
334	C₂×#117	—	79	1	no	—
335	#446	—	158	4	no	—
336	#424	—	158	4	no	—
337	C₂×C₄⋊C₈	—	79	1	no	—
338	C₂×C₄⋊C₈	—	79	1	no	—
339	C₂×C₄⋊C₈	—	79	1	no	—
340	C₂×C₄⋊C₈	—	79	1	no	—
341	C₂×C₄⋊C₈	—	79	1	no	—
342	C₂×C₄⋊C₈	—	79	1	no	—
343	C₂×C₄⋊C₈	—	79	1	no	—
344	C₂×C₄⋊C₈	—	79	1	no	—
345	C₂×C₂²⋊C₈	—	79	1	no	—
346	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
347	C₂×#97	—	79	1	no	—
348	C₂×#97	—	79	1	no	—
349	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
350	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
351	C₂×C₄×C₈	—	79	1	no	—
352	C₂×C₄×C₈	—	79	1	no	—
353	#400	—	79	1	no	—
354	#399	—	79	1	no	—
355	#398	—	79	1	no	—
356	#398	—	79	1	no	—
357	#396	—	79	1	no	—
358	#396	—	79	1	no	—
359	#395	—	79	1	no	—
360	#393	—	79	1	no	—
361	C₄×C₄⋊C₄	—	79	1	no	—
362	C₄×C₄⋊C₄	—	79	1	no	—
363	C₄×C₄⋊C₄	—	79	1	no	—
364	C₄×C₂²⋊C₄	—	79	1	no	—
365	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
366	#336	—	79	1	no	—
367	#336	—	79	1	no	—
368	#336	—	79	1	no	—
369	#336	—	79	1	no	—
370	#336	—	79	1	no	—
371	#336	—	79	1	no	—
372	#336	—	79	1	no	—
373	#336	—	79	1	no	—
374	#336	C₂×D₇₉	1	1	yes	characteristic
375	#336	C₂×D₇₉	1	1	yes	characteristic
376	C₂²×Q₈	—	79	1	no	—
377	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
378	C₂×M₁₆	—	316	1	no	—
379	C₂×M₁₆	—	158	2	no	—
380	C₂×M₁₆	—	158	2	no	—
381	C₂²×C₈	—	2	2	no	—
382	C₂²×C₈	—	2	2	no	—
383	C₂²×C₈	—	4	1	no	—
384	C₂²×C₈	—	79	1	no	—
385	C₂²×C₈	—	79	1	no	—
386	C₂²×C₈	—	79	1	no	—
387	C₂²×C₈	—	79	1	no	—
388	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
389	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
390	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
391	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
392	C₄×Q₈	—	158	2	no	—
393	C₄×Q₈	—	158	2	no	—
394	#117	—	158	2	no	—
395	#117	—	158	2	no	—
396	C₂×C₄⋊C₄	—	79	1	no	—
397	C₂×C₄⋊C₄	—	79	1	no	—
398	C₂×C₄⋊C₄	—	79	1	no	—
399	C₂×C₄⋊C₄	—	79	1	no	—
400	C₂×C₄⋊C₄	—	79	1	no	—
401	C₂×C₄⋊C₄	—	79	1	no	—
402	C₂×C₄⋊C₄	—	79	1	no	—
403	C₂×C₄⋊C₄	—	79	1	no	—
404	C₂×C₄⋊C₄	—	79	1	no	—
405	C₂×C₄⋊C₄	—	79	1	no	—
406	C₂×C₄⋊C₄	—	79	1	no	—
407	C₂×C₂²⋊C₄	—	79	1	no	—
408	C₂×C₂²⋊C₄	—	79	1	no	—
409	C₂×C₂²⋊C₄	—	79	1	no	—
410	C₂×C₂²⋊C₄	—	79	1	no	—
411	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
413	C₂×C₄²	—	79	1	no	—
414	C₂×C₄²	—	79	1	no	—
415	C₂×C₄²	—	79	1	no	—
416	C₂×C₄²	—	79	1	no	—
417	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
418	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
419	C₄⋊C₈	—	316	1	no	—
420	C₄⋊C₈	—	316	1	no	—
421	C₄⋊C₈	—	79	4	no	—
422	C₄⋊C₈	—	158	2	no	—
423	C₄⋊C₈	—	158	2	no	—
424	C₄⋊C₈	—	158	2	no	—
425	C₄⋊C₈	—	158	2	no	—
426	C₄⋊C₈	—	158	2	no	—
427	C₂²⋊C₈	—	158	2	no	—
428	C₂²⋊C₈	Dic₁₅₈	1	4	yes	complemented
429	#97	—	2	2	no	—
430	#97	—	4	1	no	—
431	#97	—	158	2	no	—
432	#97	—	158	2	no	—
433	C₄×C₈	—	316	1	no	—
434	C₄×C₈	—	158	2	no	—
435	#95	—	79	1	no	—
436	#95	—	79	1	no	—
437	#95	—	79	1	no	—
438	#95	—	79	1	no	—
439	#95	—	79	1	no	—
440	#95	—	79	1	no	—
441	#95	—	79	1	no	—
442	#95	—	79	1	no	—
443	#95	C₄×D₇₉	1	1	yes	characteristic
444	#95	C₄×D₇₉	1	1	yes	characteristic
445	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
446	C₂×Q₈	—	316	1	no	—
447	C₂×Q₈	—	316	1	no	—
448	C₂×Q₈	—	158	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	79	1	no	—
454	C₂²×C₄	—	79	1	no	—
455	C₂²×C₄	—	79	1	no	—
456	C₂²×C₄	—	79	1	no	—
457	C₂²×C₄	—	79	1	no	—
458	C₂²×C₄	—	79	1	no	—
459	C₂²×C₄	—	79	1	no	—
460	C₂²×C₄	—	79	1	no	—
461	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
467	C₂²×C₄	#11929624	1	2	yes	—
468	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
469	M₁₆	—	316	4	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	4	4	no	—
480	C₂×C₈	—	79	2	no	—
481	C₂×C₈	—	158	1	no	—
482	C₂×C₈	—	158	1	no	—
483	C₂×C₈	—	158	1	no	—
484	C₂×C₈	—	158	1	no	—
485	C₂×C₈	—	158	1	no	—
486	C₂×C₈	—	158	1	no	—
487	C₂×C₈	—	158	1	no	—
488	C₂×C₈	—	158	1	no	—
489	C₂×C₈	—	158	1	no	—
490	C₂×C₈	—	158	1	no	—
491	C₂×C₈	—	158	1	no	—
492	C₂×C₈	D₄×D₇₉	1	2	yes	—
493	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
494	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
495	C₄⋊C₄	—	316	1	no	—
496	C₄⋊C₄	—	316	1	no	—
497	C₄⋊C₄	—	316	1	no	—
498	C₄⋊C₄	—	316	1	no	—
499	C₄⋊C₄	—	158	2	no	—
500	C₄⋊C₄	—	158	2	no	—
501	C₄⋊C₄	—	158	2	no	—
502	C₄⋊C₄	—	158	2	no	—
503	C₄⋊C₄	—	158	2	no	—
504	C₄⋊C₄	—	158	2	no	—
505	C₄⋊C₄	—	158	2	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	316	1	no	—
509	C₂²⋊C₄	—	158	2	no	—
510	C₂²⋊C₄	—	158	2	no	—
511	C₂²⋊C₄	—	158	2	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	79	2	no	—
517	C₄²	—	79	2	no	—
518	C₄²	—	158	1	no	—
519	C₄²	—	158	1	no	—
520	C₄²	—	158	1	no	—
521	C₄²	—	158	1	no	—
522	C₄²	—	158	1	no	—
523	C₄²	—	158	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	C₄×Dic₁₅₈	1	2	yes	—
531	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
532	Q₈	—	316	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	79	2	no	—
552	C₂×C₄	—	79	2	no	—
553	C₂×C₄	—	79	2	no	—
554	C₂×C₄	—	158	1	no	—
555	C₂×C₄	—	158	1	no	—
556	C₂×C₄	—	158	1	no	—
557	C₂×C₄	—	158	1	no	—
558	C₂×C₄	—	158	1	no	—
559	C₂×C₄	—	158	1	no	—
560	C₂×C₄	—	158	1	no	—
561	C₂×C₄	—	158	1	no	—
562	C₂×C₄	—	158	1	no	—
563	C₂×C₄	—	158	1	no	—
564	C₂×C₄	—	158	1	no	—
565	C₂×C₄	—	158	1	no	—
566	C₂×C₄	—	158	1	no	—
567	C₂×C₄	—	158	1	no	—
568	C₂×C₄	—	158	1	no	—
569	C₂×C₄	—	158	1	no	—
570	C₂×C₄	—	158	1	no	—
571	C₂×C₄	—	158	1	no	—
572	C₂×C₄	—	158	1	no	—
573	C₂×C₄	—	158	1	no	—
574	C₂×C₄	—	158	1	no	—
575	C₂×C₄	C₄×Dic₁₅₈	1	2	yes	—
576	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
577	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
578	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
579	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
580	C₂×C₄	#14579206	1	1	yes	characteristic
581	C₂×C₄	#14579208	1	1	yes	characteristic
582	C₈	—	2	2	no	—
583	C₈	—	2	2	no	—
584	C₈	—	2	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	316	1	no	—
587	C₈	—	316	1	no	—
588	C₈	—	316	1	no	—
589	C₈	—	158	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
598	C₂²	C₂×C₄×Dic₁₅₈	1	1	yes	characteristic
599	C₂²	#19099042	1	1	yes	characteristic
600	C₂²	#131×D₇₉	1	1	yes	characteristic
601	C₂²	#19099328	1	1	yes	characteristic
602	C₂²	#19099329	1	1	yes	characteristic
603	C₂²	#19099329	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	316	1	no	—
610	C₄	—	316	1	no	—
611	C₄	—	316	1	no	—
612	C₄	—	316	1	no	—
613	C₄	—	316	1	no	—
614	C₄	—	158	2	no	—
615	C₄	—	158	2	no	—
616	C₄	—	158	2	no	—
617	C₄	#19099203	1	1	yes	characteristic
618	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
619	C₄	#19099246	1	1	yes	characteristic
620	C₄	#19099272	1	1	yes	characteristic
621	C₂	—	4	2	no	—
622	C₂	#23766406	1	1	yes	characteristic
623	C₂	#23772098	1	1	yes	characteristic
624	C₂	#23772141	1	1	yes	characteristic
625	C₂	#23772340	1	1	yes	characteristic
626	C₂	#23772344	1	1	yes	characteristic
627	C₂	#23772535	1	1	yes	characteristic
628	C₂	#23772571	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1752	C₂
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1752	D₇₉
hypocenter	C₇₉	#22961
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1752

Complements

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

N	H ≅ G/N	type
1. C₂×#19098691	C₂	semidirect
4. #23764338	C₂	semidirect
5. #23764123	C₂	semidirect
6. #23764117	C₂	semidirect
7. #23764117	C₂	semidirect
8. #23763964	C₂	semidirect
9. #23763963	C₂	semidirect
12. #23763276	C₂	semidirect
125. C₂²⋊C₈×C₇₉	Q₈	semidirect
330. C₇₉	#22961	semidirect
428. C₂²⋊C₈	Dic₁₅₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098691	2
C₂×#19098589	2
#23766674	2
#23764338	2
#23764123	2
#23764117	2
#23763964	2
#23763963	2
#23763585	2
#23763578	2
#23763276	2
#23763186	2
#23763168	2
C₇₉×#1752	2
#22961	79