Subgroups — #23777696

Order 10112.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099315	C₂	1	2	yes	maximal, complemented
2	#19099310	C₂	1	2	yes	maximal, complemented
3	#19099281	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099269	C₂	1	2	yes	maximal, complemented
5	#19099268	C₂	1	1	yes	maximal, characteristic, complemented
6	#19099266	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099257	C₂	1	2	yes	maximal, complemented
8	Q₈×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#19099223	C₂	1	1	yes	maximal, characteristic, complemented
10	#19099223	C₂	1	1	yes	maximal, characteristic, complemented
11	#19099218	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099185	C₂	1	1	yes	maximal, characteristic, complemented
13	#19099184	C₂	1	2	yes	maximal, complemented
14	#19099176	C₂	1	1	yes	maximal, characteristic, complemented
15	#19099161	C₂	1	2	yes	maximal, complemented
16	#19099152	C₂	1	2	yes	maximal, complemented
17	#19099149	C₂	1	2	yes	maximal, complemented
18	#19099144	C₂	1	1	yes	maximal, characteristic, complemented
19	#19099136	C₂	1	1	yes	maximal, characteristic, complemented
20	#19099075	C₂	1	1	yes	maximal, characteristic, complemented
21	#19099072	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11929624	C₂²	1	1	yes	characteristic
25	C₂×#11929624	C₂²	1	1	yes	characteristic
26	C₂×#11929624	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₇₉	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
30	#14579161	C₂²	1	1	yes	characteristic, complemented
31	#14579161	C₂²	1	2	yes	complemented
32	#14579160	C₂²	1	2	yes	complemented
33	#14579160	C₂²	1	1	yes	characteristic, complemented
34	#14579156	C₂²	1	2	yes	—
35	#14579156	C₂²	1	2	yes	—
36	#14579156	C₂²	1	2	yes	complemented
37	#14579155	C₂²	1	2	yes	complemented
38	#14579155	C₂²	1	2	yes	complemented
39	#14579154	C₂²	1	2	yes	—
40	#14579152	C₂²	1	2	yes	complemented
41	#14579152	C₂²	1	2	yes	complemented
42	#14579151	C₂²	1	2	yes	complemented
43	#14579150	C₂²	1	1	yes	characteristic, complemented
44	#14579149	C₂²	1	2	yes	—
45	#14579147	C₂²	1	2	yes	—
46	#14579147	C₂²	1	2	yes	—
47	#14579147	C₂²	1	2	yes	—
48	#14579147	C₂²	1	2	yes	complemented
49	#14579146	C₂²	1	2	yes	—
50	#14579146	C₂²	1	2	yes	—
51	#14579146	C₂²	1	1	yes	characteristic
52	#14579146	C₂²	1	2	yes	complemented
53	#14579145	C₂²	1	2	yes	—
54	#14579143	C₂²	1	2	yes	—
55	#14579143	C₂²	1	1	yes	characteristic
56	#14579143	C₂²	1	2	yes	complemented
57	#14579143	C₂²	1	2	yes	complemented
58	#14579141	C₂²	1	1	yes	characteristic
59	#14579141	C₂²	1	1	yes	characteristic
60	#14579141	C₂²	1	2	yes	—
61	#14579141	C₂²	1	1	yes	characteristic
62	#14579141	C₂²	1	1	yes	characteristic, complemented
63	#14579141	C₂²	1	2	yes	complemented
64	#14579141	C₂²	1	2	yes	complemented
65	#14579140	C₂²	1	1	yes	characteristic
66	#14579140	C₂²	1	1	yes	characteristic, complemented
67	#14579140	C₂²	1	2	yes	complemented
68	#14579139	C₂²	1	2	yes	—
69	#14579139	C₂²	1	2	yes	—
70	#14579139	C₂²	1	1	yes	characteristic
71	#14579139	C₂²	1	2	yes	complemented
72	#14579139	C₂²	1	2	yes	complemented
73	#14579139	C₂²	1	2	yes	complemented
74	#14579138	C₂²	1	2	yes	—
75	#14579138	C₂²	1	1	yes	characteristic
76	#14579137	C₂²	1	1	yes	characteristic
77	#14579136	C₂²	1	2	yes	—
78	#14579136	C₂²	1	1	yes	characteristic
79	#14579136	C₂²	1	2	yes	—
80	#14579136	C₂²	1	1	yes	characteristic
81	#14579136	C₂²	1	1	yes	characteristic, complemented
82	#14579135	C₂²	1	2	yes	—
83	#14579135	C₂²	1	2	yes	complemented
84	#14579134	C₂²	1	2	yes	—
85	#14579134	C₂²	1	2	yes	—
86	#14579134	C₂²	1	1	yes	characteristic
87	#14579133	C₂²	1	1	yes	characteristic
88	#14579132	C₂²	1	2	yes	—
89	#14579131	C₂²	1	2	yes	—
90	#14579131	C₂²	1	1	yes	characteristic
91	#14579129	C₂²	1	1	yes	characteristic
92	C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
93	#14579126	C₂²	1	1	yes	characteristic, complemented
94	#14579126	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₃₁₆	C₂²	1	2	yes	—
96	C₄×D₃₁₆	C₂²	1	2	yes	—
97	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
98	C₄×D₃₁₆	C₂²	1	2	yes	—
99	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
100	#14579123	C₂²	1	2	yes	—
101	#14579123	C₂²	1	2	yes	—
102	#14579123	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
106	#14579119	C₂²	1	1	yes	characteristic, complemented
107	#14579118	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
109	C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₇₉	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
112	#126×C₇₉	C₂²	1	2	yes	—
113	#125×C₇₉	C₂²	1	2	yes	complemented
114	#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₇₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
120	#117×C₇₉	C₂²	1	1	yes	characteristic
121	#117×C₇₉	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₇₉	C₂³	1	1	yes	characteristic
124	#11929624	—	4	2	no	—
125	#11929624	—	4	2	no	—
126	#11929624	—	4	2	no	—
127	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₅₈	C₂³	1	2	yes	—
130	C₂×Dic₁₅₈	C₂³	1	2	yes	—
131	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
132	C₂×Dic₁₅₈	C₂³	1	2	yes	—
133	Q₈×D₇₉	—	4	2	no	—
134	Q₈×D₇₉	—	4	2	no	—
135	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
136	C₂×D₃₁₆	C₂³	1	2	yes	—
137	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
138	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
139	C₂×D₃₁₆	C₂³	1	2	yes	—
140	C₂×D₃₁₆	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
147	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₇₉	—	4	2	no	—
149	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₇₉	C₂³	1	2	yes	—
153	C₂×C₄×D₇₉	C₂³	1	2	yes	—
154	C₂×C₄×D₇₉	C₂³	1	2	yes	—
155	C₂×C₄×D₇₉	C₂³	1	2	yes	—
156	C₂×C₄×D₇₉	C₂³	1	2	yes	—
157	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₇₉	C₂³	1	2	yes	—
159	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₇₉	C₂³	1	2	yes	—
162	C₄⋊Dic₇₉	C₂³	1	2	yes	—
163	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₇₉	C₂³	1	2	yes	—
165	C₄⋊Dic₇₉	C₂³	1	2	yes	—
166	C₄⋊Dic₇₉	C₂³	1	2	yes	—
167	C₄⋊Dic₇₉	C₂³	1	2	yes	—
168	Dic₇₉⋊C₄	C₂³	1	2	yes	—
169	Dic₇₉⋊C₄	C₂³	1	2	yes	—
170	Dic₇₉⋊C₄	C₂³	1	2	yes	—
171	Dic₇₉⋊C₄	C₂³	1	2	yes	—
172	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
176	Dic₇₉⋊C₄	C₂³	1	2	yes	—
177	Dic₇₉⋊C₄	C₂³	1	2	yes	—
178	Dic₇₉⋊C₄	C₂³	1	2	yes	—
179	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
183	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
201	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₇₉	C₂³	1	2	yes	—
203	C₄×Dic₇₉	C₂³	1	2	yes	—
204	C₄×Dic₇₉	C₂³	1	2	yes	—
205	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
225	C₄²×C₇₉	C₂³	1	2	yes	—
226	C₄²×C₇₉	C₂³	1	2	yes	—
227	C₄²×C₇₉	C₂³	1	1	yes	characteristic
228	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₇₉	—	2	2	no	—
231	C₂²×D₇₉	—	4	1	no	—
232	C₂²×D₇₉	—	4	1	no	—
233	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₇₉	C₂⁴	1	2	yes	—
235	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
237	Q₈×C₇₉	—	2	2	no	—
238	D₄×C₇₉	—	4	1	no	—
239	C₂×C₄×C₇₉	—	2	2	no	—
240	C₂×C₄×C₇₉	—	2	2	no	—
241	C₂×C₄×C₇₉	—	4	2	no	—
242	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₇₉	—	2	2	no	—
252	C₂²⋊D₇₉	—	4	1	no	—
253	C₂²⋊D₇₉	—	4	2	no	—
254	C₂²⋊D₇₉	—	4	2	no	—
255	C₂²⋊D₇₉	—	4	1	no	—
256	C₂²⋊D₇₉	—	4	1	no	—
257	C₂×Dic₇₉	—	4	1	no	—
258	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₇₉	C₂⁴	1	2	yes	—
262	C₂×Dic₇₉	C₂⁴	1	2	yes	—
263	C₂×Dic₇₉	C₂⁴	1	2	yes	—
264	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
266	D₃₁₆	—	2	4	no	—
267	D₃₁₆	—	2	2	no	—
268	D₃₁₆	—	2	2	no	—
269	D₃₁₆	—	4	2	no	—
270	D₃₁₆	—	4	2	no	—
271	D₃₁₆	—	4	1	no	—
272	C₄×D₇₉	—	2	2	no	—
273	C₄×D₇₉	—	2	2	no	—
274	C₄×D₇₉	—	2	2	no	—
275	C₄×D₇₉	—	4	1	no	—
276	C₄×D₇₉	—	4	1	no	—
277	C₄×D₇₉	—	4	2	no	—
278	C₄×D₇₉	—	4	2	no	—
279	C₄×D₇₉	—	4	2	no	—
280	C₄×D₇₉	—	4	2	no	—
281	C₄×D₇₉	—	4	2	no	—
282	C₄×D₇₉	—	4	2	no	—
283	Dic₁₅₈	—	2	2	no	—
284	Dic₁₅₈	—	2	2	no	—
285	Dic₁₅₈	—	4	2	no	—
286	Dic₁₅₈	—	4	2	no	—
287	Dic₁₅₈	—	4	2	no	—
288	Dic₁₅₈	—	4	1	no	—
289	C₂²×C₇₉	—	2	1	no	—
290	C₂²×C₇₉	—	2	1	no	—
291	C₂²×C₇₉	—	2	1	no	—
292	C₂²×C₇₉	—	2	1	no	—
293	C₂²×C₇₉	—	2	1	no	—
294	C₂²×C₇₉	—	2	1	no	—
295	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
296	C₂×D₇₉	—	2	1	no	—
297	C₂×D₇₉	—	2	1	no	—
298	C₂×D₇₉	—	2	2	no	—
299	C₂×D₇₉	—	2	1	no	—
300	C₂×D₇₉	—	2	1	no	—
301	C₂×D₇₉	—	2	1	no	—
302	C₂×D₇₉	—	2	2	no	—
303	C₂×D₇₉	—	2	1	no	—
304	C₂×D₇₉	—	2	1	no	—
305	C₂×D₇₉	—	2	1	no	—
306	C₂×D₇₉	—	2	2	no	—
307	C₂×D₇₉	—	4	4	no	—
308	C₂×D₇₉	2₋¹⁺⁴	1	2	yes	—
309	C₄×C₇₉	—	2	1	no	—
310	C₄×C₇₉	—	2	1	no	—
311	C₄×C₇₉	—	2	2	no	—
312	C₄×C₇₉	—	2	2	no	—
313	C₄×C₇₉	—	2	1	no	—
314	C₄×C₇₉	—	2	2	no	—
315	C₄×C₇₉	—	2	2	no	—
316	C₄×C₇₉	—	2	1	no	—
317	C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
318	Dic₇₉	—	2	2	no	—
319	Dic₇₉	—	2	2	no	—
320	Dic₇₉	—	2	1	no	—
321	Dic₇₉	—	2	1	no	—
322	Dic₇₉	—	2	1	no	—
323	Dic₇₉	—	2	1	no	—
324	Dic₇₉	—	2	1	no	—
325	Dic₇₉	—	2	2	no	—
326	C₂×C₇₉	—	4	1	no	—
327	C₂×C₇₉	—	4	1	no	—
328	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
330	C₂×C₇₉	#585	1	1	yes	characteristic
331	D₇₉	—	2	2	no	—
332	D₇₉	—	4	2	no	—
333	D₇₉	—	4	1	no	—
334	D₇₉	—	4	1	no	—
335	#3541	—	79	1	no	maximal, Sylow
336	C₇₉	#3541	1	1	yes	characteristic, complemented, Sylow
337	#563	—	79	2	no	—
338	#562	—	79	2	no	—
339	#556	—	79	1	no	—
340	#554	—	79	2	no	—
341	#554	—	79	1	no	—
342	#553	—	79	1	no	—
343	#553	—	79	2	no	—
344	#552	D₇₉	1	1	yes	characteristic, complemented
345	D₄×Q₈	—	79	1	no	—
346	#548	—	79	1	no	—
347	#548	—	79	1	no	—
348	#547	—	79	1	no	—
349	#542	—	79	1	no	—
350	#542	—	79	2	no	—
351	#541	—	79	1	no	—
352	#539	—	79	2	no	—
353	#538	—	79	2	no	—
354	#538	—	79	2	no	—
355	#537	—	79	1	no	—
356	#536	—	79	1	no	—
357	#525	—	79	1	no	—
358	#525	—	79	1	no	—
359	C₂×C₂²⋊Q₈	—	79	1	no	—
360	C₂×#41	—	79	1	no	—
361	C₂×#41	—	79	1	no	—
362	C₂×#41	—	79	1	no	—
363	C₂²×Q₈	—	79	1	no	—
364	C₂²×Q₈	—	79	1	no	—
365	C₂³×C₄	—	79	1	no	—
366	C₄⋊Q₈	—	79	2	no	—
367	C₄⋊Q₈	—	79	1	no	—
368	C₄⋊Q₈	—	79	1	no	—
369	C₄⋊Q₈	—	79	2	no	—
370	#126	—	79	2	no	—
371	#126	—	79	2	no	—
372	#126	—	79	2	no	—
373	#126	—	79	2	no	—
374	#126	—	79	2	no	—
375	#126	—	79	2	no	—
376	#126	C₂×D₇₉	1	2	yes	—
377	#125	—	79	2	no	—
378	#125	—	79	2	no	—
379	#125	—	79	2	no	—
380	#125	C₂×D₇₉	1	2	yes	complemented
381	#125	C₂×D₇₉	1	1	yes	characteristic, complemented
382	#124	—	79	1	no	—
383	#124	—	79	2	no	—
384	#124	—	79	2	no	—
385	#124	—	79	2	no	—
386	#124	—	79	2	no	—
387	#124	—	79	2	no	—
388	#123	—	79	1	no	—
389	#123	—	79	2	no	—
390	#123	—	79	2	no	—
391	#123	—	79	2	no	—
392	#123	—	79	1	no	—
393	#123	—	79	2	no	—
394	#123	—	79	2	no	—
395	#123	—	79	2	no	—
396	#123	—	79	2	no	—
397	#123	C₂×D₇₉	1	2	yes	—
398	C₂²⋊Q₈	—	79	1	no	—
399	C₂²⋊Q₈	—	79	1	no	—
400	C₂²⋊Q₈	—	79	1	no	—
401	C₂²⋊Q₈	—	79	2	no	—
402	C₂²⋊Q₈	—	79	1	no	—
403	C₂²⋊Q₈	—	79	2	no	—
404	C₂²⋊Q₈	—	79	1	no	—
405	C₂²⋊Q₈	—	79	1	no	—
406	C₂²⋊Q₈	—	79	1	no	—
407	C₂²⋊Q₈	—	79	1	no	—
408	C₂²⋊Q₈	—	79	2	no	—
409	C₂²⋊Q₈	—	79	2	no	—
410	C₂²⋊Q₈	—	79	2	no	—
411	C₂²⋊Q₈	—	79	2	no	—
412	C₂²⋊Q₈	—	79	2	no	—
413	C₂²⋊Q₈	—	79	2	no	—
414	C₂²⋊Q₈	—	79	2	no	—
415	C₂²⋊Q₈	—	79	2	no	—
416	C₂²⋊Q₈	—	79	1	no	—
417	C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
419	#121	—	79	1	no	—
420	#121	—	79	2	no	—
421	#121	—	79	2	no	—
422	#121	—	79	2	no	—
423	#121	—	79	1	no	—
424	#121	—	79	1	no	—
425	#121	—	79	2	no	—
426	#121	—	79	1	no	—
427	#121	—	79	2	no	—
428	#121	—	79	1	no	—
429	#121	—	79	2	no	—
430	#121	—	79	2	no	—
431	#120	—	79	1	no	—
432	#120	—	79	1	no	—
433	#120	—	79	2	no	—
434	C₄×Q₈	—	79	1	no	—
435	C₄×Q₈	—	79	1	no	—
436	C₄×Q₈	—	79	2	no	—
437	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
438	C₄×D₄	—	79	1	no	—
439	C₄×D₄	—	79	1	no	—
440	C₄×D₄	—	79	2	no	—
441	C₄×D₄	—	79	2	no	—
442	C₄×D₄	—	79	2	no	—
443	C₄×D₄	—	79	2	no	—
444	C₄×D₄	—	79	2	no	—
445	C₄×D₄	—	79	1	no	—
446	C₄×D₄	—	79	2	no	—
447	C₄×D₄	—	79	2	no	—
448	C₄×D₄	—	79	1	no	—
449	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
450	#117	—	79	1	no	—
451	#117	—	79	1	no	—
452	#117	C₂×D₇₉	1	1	yes	characteristic
453	#117	C₂×D₇₉	1	2	yes	complemented
454	C₂×C₄⋊C₄	—	79	2	no	—
455	C₂×C₄⋊C₄	—	79	1	no	—
456	C₂×C₄⋊C₄	—	79	2	no	—
457	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
458	C₂×C₂²⋊C₄	—	79	2	no	—
459	C₂⁴	—	79	1	no	—
460	#41	—	316	2	no	—
461	#41	—	316	2	no	—
462	#41	—	316	2	no	—
463	C₂×Q₈	—	316	2	no	—
464	C₂×Q₈	—	316	2	no	—
465	C₂×Q₈	—	79	2	no	—
466	C₂×Q₈	—	79	2	no	—
467	C₂×Q₈	—	79	1	no	—
468	C₂×Q₈	—	79	2	no	—
469	C₂×Q₈	—	79	1	no	—
470	C₂×Q₈	—	79	1	no	—
471	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
472	C₂×D₄	—	79	1	no	—
473	C₂×D₄	—	79	2	no	—
474	C₂×D₄	—	79	1	no	—
475	C₂×D₄	—	79	1	no	—
476	C₂×D₄	—	79	2	no	—
477	C₂×D₄	—	79	1	no	—
478	C₂×D₄	—	79	2	no	—
479	C₂×D₄	—	79	2	no	—
480	C₂×D₄	—	79	1	no	—
481	C₂×D₄	—	79	2	no	—
482	C₂×D₄	—	79	1	no	—
483	C₂×D₄	—	79	1	no	—
484	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
485	C₂²×C₄	—	316	2	no	—
486	C₂²×C₄	—	79	1	no	—
487	C₂²×C₄	—	79	2	no	—
488	C₂²×C₄	—	79	2	no	—
489	C₂²×C₄	—	79	1	no	—
490	C₂²×C₄	—	79	2	no	—
491	C₂²×C₄	—	79	2	no	—
492	C₂²×C₄	—	79	2	no	—
493	C₂²×C₄	—	79	2	no	—
494	C₂²×C₄	—	79	1	no	—
495	C₂²×C₄	—	79	1	no	—
496	C₂²×C₄	—	79	1	no	—
497	C₂²×C₄	—	79	1	no	—
498	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
501	C₄⋊C₄	—	79	2	no	—
502	C₄⋊C₄	—	79	2	no	—
503	C₄⋊C₄	—	79	2	no	—
504	C₄⋊C₄	—	79	2	no	—
505	C₄⋊C₄	—	79	1	no	—
506	C₄⋊C₄	—	79	1	no	—
507	C₄⋊C₄	—	79	1	no	—
508	C₄⋊C₄	—	79	1	no	—
509	C₄⋊C₄	—	79	2	no	—
510	C₄⋊C₄	—	79	2	no	—
511	C₄⋊C₄	—	79	2	no	—
512	C₄⋊C₄	—	79	1	no	—
513	C₄⋊C₄	—	79	2	no	—
514	C₄⋊C₄	—	79	2	no	—
515	C₄⋊C₄	—	79	2	no	—
516	C₄⋊C₄	—	79	2	no	—
517	C₄⋊C₄	—	79	1	no	—
518	C₄⋊C₄	—	79	2	no	—
519	C₄⋊C₄	—	79	2	no	—
520	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
523	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
525	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
527	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
528	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
529	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
530	C₂²⋊C₄	—	79	2	no	—
531	C₂²⋊C₄	—	79	1	no	—
532	C₂²⋊C₄	—	79	2	no	—
533	C₂²⋊C₄	—	79	1	no	—
534	C₂²⋊C₄	—	79	2	no	—
535	C₂²⋊C₄	—	79	2	no	—
536	C₂²⋊C₄	—	79	1	no	—
537	C₂²⋊C₄	—	79	1	no	—
538	C₂²⋊C₄	—	79	2	no	—
539	C₂²⋊C₄	—	79	1	no	—
540	C₂²⋊C₄	—	79	1	no	—
541	C₂²⋊C₄	—	79	2	no	—
542	C₂²⋊C₄	—	79	1	no	—
543	C₂²⋊C₄	—	79	2	no	—
544	C₂²⋊C₄	—	79	2	no	—
545	C₂²⋊C₄	—	79	2	no	—
546	C₂²⋊C₄	—	79	2	no	—
547	C₂²⋊C₄	—	79	1	no	—
548	C₂²⋊C₄	—	79	2	no	—
549	C₂²⋊C₄	—	79	2	no	—
550	C₂²⋊C₄	—	79	2	no	—
551	C₂²⋊C₄	—	79	2	no	—
552	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
557	C₄²	—	79	1	no	—
558	C₄²	—	79	2	no	—
559	C₄²	—	79	2	no	—
560	C₄²	—	79	2	no	—
561	C₄²	C₂²×D₇₉	1	1	yes	characteristic
562	C₄²	C₂²×D₇₉	1	2	yes	—
563	C₄²	C₂²×D₇₉	1	2	yes	—
564	C₂³	—	316	1	no	—
565	C₂³	—	316	1	no	—
566	C₂³	—	79	1	no	—
567	C₂³	—	79	1	no	—
568	C₂³	—	79	1	no	—
569	C₂³	—	79	2	no	—
570	C₂³	—	158	2	no	—
571	C₂³	C₂³×D₇₉	1	1	yes	characteristic
572	C₂³	C₂³×D₇₉	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	316	2	no	—
575	Q₈	—	316	2	no	—
576	Q₈	—	316	1	no	—
577	Q₈	—	316	2	no	—
578	Q₈	—	158	2	no	—
579	Q₈	—	158	2	no	—
580	D₄	—	4	1	no	—
581	D₄	—	316	1	no	—
582	D₄	—	316	2	no	—
583	D₄	—	316	2	no	—
584	D₄	—	316	1	no	—
585	D₄	—	316	1	no	—
586	D₄	—	316	2	no	—
587	D₄	—	316	2	no	—
588	D₄	—	316	1	no	—
589	D₄	—	158	4	no	—
590	D₄	—	158	2	no	—
591	D₄	—	158	2	no	—
592	D₄	—	158	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	316	1	no	—
597	C₂×C₄	—	316	1	no	—
598	C₂×C₄	—	316	2	no	—
599	C₂×C₄	—	316	2	no	—
600	C₂×C₄	—	316	2	no	—
601	C₂×C₄	—	316	2	no	—
602	C₂×C₄	—	316	2	no	—
603	C₂×C₄	—	316	2	no	—
604	C₂×C₄	—	316	1	no	—
605	C₂×C₄	—	79	1	no	—
606	C₂×C₄	—	79	1	no	—
607	C₂×C₄	—	79	1	no	—
608	C₂×C₄	—	79	2	no	—
609	C₂×C₄	—	79	2	no	—
610	C₂×C₄	—	79	2	no	—
611	C₂×C₄	—	79	1	no	—
612	C₂×C₄	—	79	1	no	—
613	C₂×C₄	—	158	2	no	—
614	C₂×C₄	—	158	2	no	—
615	C₂×C₄	—	158	2	no	—
616	C₂×C₄	C₂³×D₇₉	1	2	yes	—
617	C₂×C₄	C₂³×D₇₉	1	2	yes	—
618	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₇₉	1	2	yes	—
620	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₇₉	1	2	yes	—
622	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	316	4	no	—
632	C₂²	—	79	2	no	—
633	C₂²	—	158	1	no	—
634	C₂²	—	158	2	no	—
635	C₂²	—	158	1	no	—
636	C₂²	—	158	1	no	—
637	C₂²	—	158	2	no	—
638	C₂²	—	158	1	no	—
639	C₂²	—	158	2	no	—
640	C₂²	—	158	1	no	—
641	C₂²	—	158	1	no	—
642	C₂²	—	158	1	no	—
643	C₂²	—	158	1	no	—
644	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	158	1	no	—
654	C₄	—	158	1	no	—
655	C₄	—	158	2	no	—
656	C₄	—	158	2	no	—
657	C₄	—	158	1	no	—
658	C₄	—	158	1	no	—
659	C₄	—	158	2	no	—
660	C₄	—	158	1	no	—
661	C₄	#14579207	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	4	1	no	—
664	C₂	—	316	1	no	—
665	C₂	—	316	1	no	—
666	C₂	—	316	2	no	—
667	C₂	—	158	2	no	—
668	C₂	C₂×#14579207	1	1	yes	characteristic
669	C₂	2₋¹⁺⁴×D₇₉	1	1	yes	characteristic
670	C₂	#19099399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#552×C₇₉	C₂
hypercenter	#552	D₇₉
hypocenter	C₇₉	#3541
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #19099315	C₂	semidirect
2. #19099310	C₂	semidirect
3. #19099281	C₂	semidirect
4. #19099269	C₂	semidirect
5. #19099268	C₂	semidirect
6. #19099266	C₂	semidirect
7. #19099257	C₂	semidirect
8. Q₈×D₃₁₆	C₂	semidirect
9. #19099223	C₂	semidirect
10. #19099223	C₂	semidirect
11. #19099218	C₂	semidirect
12. #19099185	C₂	semidirect
13. #19099184	C₂	semidirect
14. #19099176	C₂	semidirect
15. #19099161	C₂	semidirect
16. #19099152	C₂	semidirect
17. #19099149	C₂	semidirect
18. #19099144	C₂	semidirect
19. #19099136	C₂	semidirect
20. #19099075	C₂	semidirect
21. #19099072	C₂	semidirect
22. C₂²⋊Q₈×D₇₉	C₂	semidirect
23. #552×C₇₉	C₂	semidirect
26. C₂×#11929624	C₂²	semidirect
28. C₂×Q₈×D₇₉	C₂²	semidirect
30. #14579161	C₂²	semidirect
31. #14579161	C₂²	semidirect
32. #14579160	C₂²	semidirect
33. #14579160	C₂²	semidirect
36. #14579156	C₂²	semidirect
37. #14579155	C₂²	semidirect
38. #14579155	C₂²	semidirect
40. #14579152	C₂²	semidirect
41. #14579152	C₂²	semidirect
42. #14579151	C₂²	semidirect
43. #14579150	C₂²	semidirect
48. #14579147	C₂²	semidirect
52. #14579146	C₂²	semidirect
56. #14579143	C₂²	semidirect
57. #14579143	C₂²	semidirect
62. #14579141	C₂²	semidirect
63. #14579141	C₂²	semidirect
64. #14579141	C₂²	semidirect
66. #14579140	C₂²	semidirect
67. #14579140	C₂²	semidirect
71. #14579139	C₂²	semidirect
72. #14579139	C₂²	semidirect
73. #14579139	C₂²	semidirect
81. #14579136	C₂²	semidirect
83. #14579135	C₂²	semidirect
92. C₄×Dic₁₅₈	C₂²	semidirect
93. #14579126	C₂²	semidirect
94. #14579126	C₂²	semidirect
99. C₄×D₃₁₆	C₂²	semidirect
102. #14579123	C₂²	semidirect
106. #14579119	C₂²	semidirect
110. C₄⋊C₄×D₇₉	C₂²	semidirect
113. #125×C₇₉	C₂²	semidirect
114. #125×C₇₉	C₂²	semidirect
117. C₂²⋊Q₈×C₇₉	C₂²	semidirect
118. C₄×Q₈×C₇₉	C₂²	semidirect
121. #117×C₇₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₇₉	C₂²	semidirect
336. C₇₉	#3541	semidirect
344. #552	D₇₉	semidirect
380. #125	C₂×D₇₉	semidirect
381. #125	C₂×D₇₉	semidirect
418. C₂²⋊Q₈	C₂×D₇₉	semidirect
437. C₄×Q₈	C₂×D₇₉	semidirect
453. #117	C₂×D₇₉	semidirect
457. C₂×C₄⋊C₄	C₂×D₇₉	semidirect