Subgroups — #23777349

Order 10112.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099296	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099285	C₂	1	1	yes	maximal, characteristic, complemented
3	#19099276	C₂	1	2	yes	maximal, complemented
4	#19099237	C₂	1	2	yes	maximal, complemented
5	#19099236	C₂	1	2	yes	maximal, complemented
6	#19099226	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099225	C₂	1	1	yes	maximal, characteristic, complemented
8	#19099219	C₂	1	1	yes	maximal, characteristic, complemented
9	#19099208	C₂	1	1	yes	maximal, characteristic, complemented
10	#19099205	C₂	1	2	yes	maximal, complemented
11	#19099204	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099197	C₂	1	1	yes	maximal, characteristic, complemented
13	#19099179	C₂	1	2	yes	maximal, complemented
14	#19099152	C₂	1	2	yes	maximal, complemented
15	#19099146	C₂	1	2	yes	maximal, complemented
16	#19099112	C₂	1	1	yes	maximal, characteristic, complemented
17	#19099098	C₂	1	1	yes	maximal, characteristic, complemented
18	#19099098	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#14579149	C₂	1	1	yes	maximal, characteristic, complemented
20	#124×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#19099035	C₂	1	2	yes	maximal, complemented
22	C₄×#11929624	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11929625	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11929624	C₂²	1	1	yes	characteristic
26	C₂×#11929623	C₂²	1	1	yes	characteristic, complemented
27	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×Q₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₃₁₆	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₇₉	C₂²	1	2	yes	—
31	C₂×D₄×D₇₉	C₂²	1	1	yes	characteristic
32	#14579160	C₂²	1	2	yes	complemented
33	#14579159	C₂²	1	1	yes	characteristic, complemented
34	#14579157	C₂²	1	1	yes	characteristic
35	#14579156	C₂²	1	2	yes	complemented
36	#14579156	C₂²	1	2	yes	complemented
37	#14579156	C₂²	1	2	yes	complemented
38	#14579155	C₂²	1	2	yes	complemented
39	#14579150	C₂²	1	1	yes	characteristic
40	#14579149	C₂²	1	1	yes	characteristic
41	#14579149	C₂²	1	1	yes	characteristic
42	#14579149	C₂²	1	2	yes	complemented
43	#14579149	C₂²	1	2	yes	complemented
44	#14579149	C₂²	1	1	yes	characteristic, complemented
45	#14579149	C₂²	1	2	yes	complemented
46	#14579149	C₂²	1	1	yes	characteristic, complemented
47	#14579148	C₂²	1	1	yes	characteristic, complemented
48	#14579147	C₂²	1	2	yes	complemented
49	#14579147	C₂²	1	2	yes	complemented
50	#14579147	C₂²	1	2	yes	complemented
51	#14579147	C₂²	1	2	yes	complemented
52	#14579146	C₂²	1	2	yes	complemented
53	#14579146	C₂²	1	2	yes	complemented
54	#14579146	C₂²	1	2	yes	complemented
55	#14579145	C₂²	1	2	yes	complemented
56	#14579144	C₂²	1	2	yes	complemented
57	#14579143	C₂²	1	2	yes	complemented
58	#14579141	C₂²	1	2	yes	complemented
59	#14579141	C₂²	1	1	yes	characteristic, complemented
60	#14579141	C₂²	1	1	yes	characteristic, complemented
61	#14579139	C₂²	1	2	yes	complemented
62	#14579139	C₂²	1	2	yes	complemented
63	#14579138	C₂²	1	2	yes	complemented
64	#14579138	C₂²	1	2	yes	complemented
65	#14579136	C₂²	1	1	yes	characteristic
66	#14579136	C₂²	1	1	yes	characteristic
67	#14579136	C₂²	1	2	yes	complemented
68	#14579136	C₂²	1	2	yes	complemented
69	#14579135	C₂²	1	2	yes	complemented
70	#14579134	C₂²	1	2	yes	—
71	#14579134	C₂²	1	2	yes	complemented
72	#14579134	C₂²	1	2	yes	complemented
73	#14579133	C₂²	1	2	yes	complemented
74	#14579131	C₂²	1	2	yes	—
75	#14579131	C₂²	1	2	yes	complemented
76	#14579131	C₂²	1	2	yes	complemented
77	#14579129	C₂²	1	2	yes	—
78	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
80	#14579126	C₂²	1	1	yes	characteristic, complemented
81	#14579126	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₃₁₆	C₂²	1	2	yes	complemented
85	D₄×Dic₇₉	C₂²	1	2	yes	complemented
86	#14579123	C₂²	1	1	yes	characteristic
87	#14579123	C₂²	1	2	yes	complemented
88	#14579123	C₂²	1	1	yes	characteristic, complemented
89	#14579123	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
95	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	—
96	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
97	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
98	#14579120	C₂²	1	1	yes	characteristic, complemented
99	#14579119	C₂²	1	2	yes	complemented
100	#14579119	C₂²	1	2	yes	complemented
101	#14579118	C₂²	1	1	yes	characteristic, complemented
102	#14579118	C₂²	1	1	yes	characteristic, complemented
103	#14579118	C₂²	1	2	yes	complemented
104	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
105	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
106	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
110	C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
112	#126×C₇₉	C₂²	1	2	yes	complemented
113	#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
114	#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₇₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₇₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
121	#117×C₇₉	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₇₉	C₂³	1	2	yes	—
124	C₂³×D₇₉	C₂³	1	2	yes	—
125	#11929625	—	4	2	no	—
126	#11929624	—	2	4	no	—
127	#11929623	—	4	2	no	—
128	C₂×Dic₁₅₈	—	4	2	no	—
129	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
132	C₂×Dic₁₅₈	C₂³	1	2	yes	—
133	C₂×Dic₁₅₈	C₂³	1	2	yes	—
134	Q₈×D₇₉	—	4	2	no	—
135	C₂×D₃₁₆	—	4	2	no	—
136	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
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×D₃₁₆	C₂³	1	2	yes	—
142	C₂×D₃₁₆	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
149	D₄×D₇₉	—	2	8	no	—
150	D₄×D₇₉	—	4	2	no	—
151	C₂²×Dic₇₉	C₂³	1	2	yes	—
152	C₂²×Dic₇₉	C₂³	1	2	yes	—
153	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₇₉	C₂³	1	2	yes	—
158	C₂×C₄×D₇₉	C₂³	1	2	yes	—
159	C₂×C₄×D₇₉	C₂³	1	2	yes	—
160	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₇₉	C₂³	1	2	yes	—
163	C₄⋊Dic₇₉	C₂³	1	2	yes	—
164	C₄⋊Dic₇₉	C₂³	1	2	yes	—
165	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
167	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₇₉⋊C₄	C₂³	1	2	yes	—
169	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
171	Dic₇₉⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₇₉⋊C₄	C₂³	1	2	yes	—
173	Dic₇₉⋊C₄	C₂³	1	2	yes	—
174	Dic₇₉⋊C₄	C₂³	1	2	yes	—
175	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
179	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
199	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
205	C₄×Dic₇₉	C₂³	1	2	yes	—
206	C₄×Dic₇₉	C₂³	1	2	yes	—
207	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₇₉	C₂³	1	2	yes	—
210	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
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	1	yes	characteristic
219	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
225	C₄²×C₇₉	C₂³	1	1	yes	characteristic
226	C₄²×C₇₉	C₂³	1	1	yes	characteristic
227	C₄²×C₇₉	C₂³	1	1	yes	characteristic
228	C₄²×C₇₉	C₂³	1	1	yes	characteristic
229	C₄²×C₇₉	C₂³	1	2	yes	—
230	C₂³×C₇₉	C₂⁴	1	2	yes	—
231	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₇₉	—	2	4	no	—
233	C₂²×D₇₉	—	2	4	no	—
234	C₂²×D₇₉	—	4	2	no	—
235	C₂²×D₇₉	—	4	2	no	—
236	C₂²×D₇₉	—	4	2	no	—
237	C₂²×D₇₉	—	4	2	no	—
238	C₂²×D₇₉	C₂⁴	1	2	yes	—
239	C₂²×D₇₉	C₂⁴	1	2	yes	—
240	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
242	Q₈×C₇₉	—	2	2	no	—
243	D₄×C₇₉	—	2	4	no	—
244	D₄×C₇₉	—	2	2	no	—
245	C₂×C₄×C₇₉	—	2	2	no	—
246	C₂×C₄×C₇₉	—	2	2	no	—
247	C₂×C₄×C₇₉	—	4	1	no	—
248	C₂×C₄×C₇₉	—	4	2	no	—
249	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₇₉	—	2	2	no	—
259	C₂²⋊D₇₉	—	2	4	no	—
260	C₂²⋊D₇₉	—	4	2	no	—
261	C₂²⋊D₇₉	—	4	2	no	—
262	C₂²⋊D₇₉	—	4	2	no	—
263	C₂²⋊D₇₉	#41	1	4	yes	complemented
264	C₂×Dic₇₉	—	4	2	no	—
265	C₂×Dic₇₉	—	4	2	no	—
266	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₇₉	C₂⁴	1	2	yes	—
272	C₂×Dic₇₉	C₂⁴	1	2	yes	—
273	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
274	D₃₁₆	—	2	4	no	—
275	D₃₁₆	—	2	2	no	—
276	D₃₁₆	—	2	2	no	—
277	D₃₁₆	—	2	2	no	—
278	D₃₁₆	—	4	2	no	—
279	D₃₁₆	—	4	2	no	—
280	D₃₁₆	—	4	2	no	—
281	C₄×D₇₉	—	2	2	no	—
282	C₄×D₇₉	—	2	2	no	—
283	C₄×D₇₉	—	2	2	no	—
284	C₄×D₇₉	—	2	4	no	—
285	C₄×D₇₉	—	2	2	no	—
286	C₄×D₇₉	—	4	1	no	—
287	C₄×D₇₉	—	4	1	no	—
288	C₄×D₇₉	—	4	2	no	—
289	C₄×D₇₉	—	4	2	no	—
290	C₄×D₇₉	—	4	2	no	—
291	Dic₁₅₈	—	2	2	no	—
292	Dic₁₅₈	—	2	2	no	—
293	Dic₁₅₈	—	2	2	no	—
294	Dic₁₅₈	—	4	2	no	—
295	Dic₁₅₈	—	4	2	no	—
296	C₂²×C₇₉	—	2	1	no	—
297	C₂²×C₇₉	—	2	1	no	—
298	C₂²×C₇₉	—	2	2	no	—
299	C₂²×C₇₉	—	2	2	no	—
300	C₂²×C₇₉	—	2	2	no	—
301	C₂²×C₇₉	C₂×#41	1	2	yes	—
302	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
303	C₂×D₇₉	—	2	1	no	—
304	C₂×D₇₉	—	2	1	no	—
305	C₂×D₇₉	—	2	2	no	—
306	C₂×D₇₉	—	2	1	no	—
307	C₂×D₇₉	—	2	2	no	—
308	C₂×D₇₉	—	2	1	no	—
309	C₂×D₇₉	—	2	2	no	—
310	C₂×D₇₉	—	2	2	no	—
311	C₂×D₇₉	—	2	2	no	—
312	C₂×D₇₉	—	2	2	no	—
313	C₂×D₇₉	—	2	1	no	—
314	C₂×D₇₉	—	8	4	no	—
315	C₂×D₇₉	—	8	4	no	—
316	C₂×D₇₉	C₂×#41	1	2	yes	—
317	C₄×C₇₉	—	2	1	no	—
318	C₄×C₇₉	—	2	1	no	—
319	C₄×C₇₉	—	2	2	no	—
320	C₄×C₇₉	—	2	1	no	—
321	C₄×C₇₉	—	2	2	no	—
322	C₄×C₇₉	—	2	1	no	—
323	C₄×C₇₉	—	2	1	no	—
324	C₄×C₇₉	—	2	2	no	—
325	C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
326	Dic₇₉	—	2	1	no	—
327	Dic₇₉	—	2	1	no	—
328	Dic₇₉	—	2	2	no	—
329	Dic₇₉	—	2	2	no	—
330	Dic₇₉	—	2	1	no	—
331	Dic₇₉	—	2	1	no	—
332	Dic₇₉	—	2	1	no	—
333	Dic₇₉	C₂×#41	1	2	yes	—
334	C₂×C₇₉	—	2	2	no	—
335	C₂×C₇₉	—	4	2	no	—
336	C₂×C₇₉	C₂²×#41	1	1	yes	characteristic
337	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₇₉	#585	1	1	yes	characteristic
339	D₇₉	—	2	2	no	—
340	D₇₉	—	4	1	no	—
341	D₇₉	—	4	2	no	—
342	D₇₉	—	4	2	no	—
343	#3514	—	79	1	no	maximal, Sylow
344	C₇₉	#3514	1	1	yes	characteristic, complemented, Sylow
345	#559	—	79	1	no	—
346	#556	—	79	1	no	—
347	#555	—	79	2	no	—
348	#551	—	79	2	no	—
349	#551	—	79	2	no	—
350	D₄×Q₈	—	79	1	no	—
351	#548	—	79	1	no	—
352	#548	—	79	1	no	—
353	#546	—	79	2	no	—
354	#546	—	79	1	no	—
355	#546	—	79	1	no	—
356	D₄²	—	79	1	no	—
357	#542	—	79	2	no	—
358	#538	—	79	2	no	—
359	#538	—	79	2	no	—
360	#532	—	79	1	no	—
361	#529	—	79	1	no	—
362	#529	—	79	1	no	—
363	#529	D₇₉	1	1	yes	characteristic, complemented
364	C₂×#124	—	79	1	no	—
365	C₂×#124	—	79	1	no	—
366	#518	—	79	2	no	—
367	C₄×#41	—	79	1	no	—
368	C₂×#41	—	79	1	no	—
369	C₂×#41	—	79	1	no	—
370	C₂×#41	—	79	1	no	—
371	C₂²×Q₈	—	79	1	no	—
372	C₂²×Q₈	—	79	1	no	—
373	C₂²×D₄	—	79	1	no	—
374	C₂²×D₄	—	79	2	no	—
375	C₂²×D₄	—	79	1	no	—
376	C₄⋊Q₈	—	79	1	no	—
377	C₄⋊Q₈	—	79	2	no	—
378	#127	—	79	1	no	—
379	#126	—	79	2	no	—
380	#126	—	79	2	no	—
381	#126	—	79	2	no	—
382	#126	—	79	2	no	—
383	#126	C₂×D₇₉	1	2	yes	complemented
384	#125	C₂×D₇₉	1	1	yes	characteristic, complemented
385	#124	—	79	1	no	—
386	#124	—	79	1	no	—
387	#124	—	79	2	no	—
388	#124	—	79	2	no	—
389	#124	—	79	2	no	—
390	#124	—	79	2	no	—
391	#124	—	79	1	no	—
392	#124	—	79	1	no	—
393	#124	—	79	2	no	—
394	#124	—	79	1	no	—
395	#124	—	79	1	no	—
396	#124	—	79	2	no	—
397	#124	—	79	2	no	—
398	#124	C₂×D₇₉	1	1	yes	characteristic, complemented
399	#123	—	79	2	no	—
400	#123	—	79	2	no	—
401	#123	—	79	2	no	—
402	#123	—	79	2	no	—
403	#123	—	79	2	no	—
404	#123	—	79	2	no	—
405	#123	C₂×D₇₉	1	2	yes	complemented
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	C₂×D₇₉	1	1	yes	characteristic, complemented
414	#121	—	79	2	no	—
415	#121	—	79	2	no	—
416	#121	—	79	1	no	—
417	#121	—	79	1	no	—
418	#121	—	79	2	no	—
419	#121	—	79	2	no	—
420	#121	—	79	2	no	—
421	#121	—	79	2	no	—
422	#121	—	79	2	no	—
423	#121	C₂×D₇₉	1	1	yes	characteristic
424	#120	—	79	2	no	—
425	#120	—	79	2	no	—
426	#120	—	79	2	no	—
427	#120	—	79	2	no	—
428	C₄×Q₈	—	79	1	no	—
429	C₄×Q₈	—	79	1	no	—
430	C₄×Q₈	—	79	1	no	—
431	C₄×Q₈	—	79	1	no	—
432	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
433	C₄×D₄	—	79	2	no	—
434	C₄×D₄	—	79	1	no	—
435	C₄×D₄	—	79	1	no	—
436	C₄×D₄	—	79	1	no	—
437	C₄×D₄	—	79	1	no	—
438	C₄×D₄	—	79	2	no	—
439	C₄×D₄	—	79	2	no	—
440	C₄×D₄	—	79	1	no	—
441	C₄×D₄	—	79	2	no	—
442	C₄×D₄	—	79	1	no	—
443	C₄×D₄	—	79	2	no	—
444	C₄×D₄	—	79	2	no	—
445	C₄×D₄	—	79	2	no	—
446	C₄×D₄	—	79	1	no	—
447	C₄×D₄	—	79	1	no	—
448	C₄×D₄	—	79	2	no	—
449	C₄×D₄	C₂×D₇₉	1	2	yes	complemented
450	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
451	#117	—	79	1	no	—
452	#117	—	79	2	no	—
453	#117	—	79	2	no	—
454	#117	—	79	1	no	—
455	#117	—	79	1	no	—
456	#117	—	79	2	no	—
457	#117	C₂×D₇₉	1	2	yes	complemented
458	C₂×C₂²⋊C₄	—	79	2	no	—
459	C₂×C₂²⋊C₄	—	79	2	no	—
460	C₂×C₂²⋊C₄	—	79	2	no	—
461	C₂×C₂²⋊C₄	—	79	2	no	—
462	C₂×C₂²⋊C₄	—	79	2	no	—
463	C₂×C₂²⋊C₄	—	79	2	no	—
464	C₂×C₄²	—	79	1	no	—
465	C₂×C₄²	—	79	1	no	—
466	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
467	C₂⁴	—	79	2	no	—
468	C₂⁴	—	79	2	no	—
469	#41	—	316	2	no	—
470	#41	—	316	2	no	—
471	#41	—	158	4	no	—
472	C₂×Q₈	—	316	2	no	—
473	C₂×Q₈	—	316	2	no	—
474	C₂×Q₈	—	79	2	no	—
475	C₂×Q₈	—	79	2	no	—
476	C₂×Q₈	—	79	1	no	—
477	C₂×Q₈	—	79	1	no	—
478	C₂×Q₈	—	79	1	no	—
479	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
480	C₂×D₄	—	316	2	no	—
481	C₂×D₄	—	316	2	no	—
482	C₂×D₄	—	79	2	no	—
483	C₂×D₄	—	79	2	no	—
484	C₂×D₄	—	79	2	no	—
485	C₂×D₄	—	79	1	no	—
486	C₂×D₄	—	79	1	no	—
487	C₂×D₄	—	79	2	no	—
488	C₂×D₄	—	79	2	no	—
489	C₂×D₄	—	79	2	no	—
490	C₂×D₄	—	79	2	no	—
491	C₂×D₄	—	79	1	no	—
492	C₂×D₄	—	79	2	no	—
493	C₂×D₄	—	79	1	no	—
494	C₂×D₄	—	79	1	no	—
495	C₂×D₄	—	158	8	no	—
496	C₂×D₄	C₂²×D₇₉	1	2	yes	—
497	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
498	C₂²×C₄	—	79	2	no	—
499	C₂²×C₄	—	79	2	no	—
500	C₂²×C₄	—	79	1	no	—
501	C₂²×C₄	—	79	1	no	—
502	C₂²×C₄	—	79	2	no	—
503	C₂²×C₄	—	79	2	no	—
504	C₂²×C₄	—	79	2	no	—
505	C₂²×C₄	—	79	1	no	—
506	C₂²×C₄	—	79	1	no	—
507	C₂²×C₄	—	79	1	no	—
508	C₂²×C₄	—	79	1	no	—
509	C₂²×C₄	—	79	2	no	—
510	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
514	C₄⋊C₄	—	79	1	no	—
515	C₄⋊C₄	—	79	2	no	—
516	C₄⋊C₄	—	79	1	no	—
517	C₄⋊C₄	—	79	1	no	—
518	C₄⋊C₄	—	79	1	no	—
519	C₄⋊C₄	—	79	2	no	—
520	C₄⋊C₄	—	79	2	no	—
521	C₄⋊C₄	—	79	2	no	—
522	C₄⋊C₄	—	79	2	no	—
523	C₄⋊C₄	—	79	1	no	—
524	C₄⋊C₄	—	79	1	no	—
525	C₄⋊C₄	—	79	2	no	—
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	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
532	C₂²⋊C₄	—	79	1	no	—
533	C₂²⋊C₄	—	79	2	no	—
534	C₂²⋊C₄	—	79	2	no	—
535	C₂²⋊C₄	—	79	1	no	—
536	C₂²⋊C₄	—	79	1	no	—
537	C₂²⋊C₄	—	79	2	no	—
538	C₂²⋊C₄	—	79	2	no	—
539	C₂²⋊C₄	—	79	2	no	—
540	C₂²⋊C₄	—	79	2	no	—
541	C₂²⋊C₄	—	79	2	no	—
542	C₂²⋊C₄	—	79	2	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	2	no	—
548	C₂²⋊C₄	—	79	2	no	—
549	C₂²⋊C₄	—	79	1	no	—
550	C₂²⋊C₄	—	79	1	no	—
551	C₂²⋊C₄	—	79	1	no	—
552	C₂²⋊C₄	—	79	2	no	—
553	C₂²⋊C₄	—	79	2	no	—
554	C₂²⋊C₄	—	79	2	no	—
555	C₂²⋊C₄	—	79	2	no	—
556	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
561	C₄²	—	79	1	no	—
562	C₄²	—	79	1	no	—
563	C₄²	—	79	1	no	—
564	C₄²	—	79	1	no	—
565	C₄²	—	79	1	no	—
566	C₄²	—	79	1	no	—
567	C₄²	—	79	2	no	—
568	C₄²	—	79	2	no	—
569	C₄²	C₂²×D₇₉	1	1	yes	characteristic
570	C₄²	C₂²×D₇₉	1	1	yes	characteristic
571	C₄²	C₂²×D₇₉	1	1	yes	characteristic
572	C₄²	C₂²×D₇₉	1	1	yes	characteristic
573	C₄²	C₂²×D₇₉	1	2	yes	—
574	C₂³	—	316	2	no	—
575	C₂³	—	316	2	no	—
576	C₂³	—	316	2	no	—
577	C₂³	—	316	2	no	—
578	C₂³	—	79	1	no	—
579	C₂³	—	79	2	no	—
580	C₂³	—	79	2	no	—
581	C₂³	—	79	1	no	—
582	C₂³	—	158	4	no	—
583	C₂³	—	158	4	no	—
584	C₂³	C₂³×D₇₉	1	2	yes	—
585	C₂³	C₂³×D₇₉	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	316	2	no	—
588	Q₈	—	316	2	no	—
589	Q₈	—	158	2	no	—
590	Q₈	—	158	2	no	—
591	Q₈	—	158	2	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	316	2	no	—
595	D₄	—	316	2	no	—
596	D₄	—	316	2	no	—
597	D₄	—	316	2	no	—
598	D₄	—	316	2	no	—
599	D₄	—	316	2	no	—
600	D₄	—	79	4	no	—
601	D₄	—	158	4	no	—
602	D₄	—	158	2	no	—
603	D₄	—	158	4	no	—
604	D₄	—	158	2	no	—
605	D₄	—	158	2	no	—
606	D₄	—	158	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	316	2	no	—
612	C₂×C₄	—	316	2	no	—
613	C₂×C₄	—	316	1	no	—
614	C₂×C₄	—	316	1	no	—
615	C₂×C₄	—	316	2	no	—
616	C₂×C₄	—	316	2	no	—
617	C₂×C₄	—	316	2	no	—
618	C₂×C₄	—	79	1	no	—
619	C₂×C₄	—	79	1	no	—
620	C₂×C₄	—	79	1	no	—
621	C₂×C₄	—	79	1	no	—
622	C₂×C₄	—	79	1	no	—
623	C₂×C₄	—	79	1	no	—
624	C₂×C₄	—	79	2	no	—
625	C₂×C₄	—	79	2	no	—
626	C₂×C₄	—	158	4	no	—
627	C₂×C₄	—	158	2	no	—
628	C₂×C₄	—	158	2	no	—
629	C₂×C₄	—	158	2	no	—
630	C₂×C₄	—	158	2	no	—
631	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₇₉	1	2	yes	—
634	C₂×C₄	C₂³×D₇₉	1	2	yes	—
635	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₇₉	1	2	yes	—
639	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	79	2	no	—
646	C₂²	—	632	4	no	—
647	C₂²	—	632	4	no	—
648	C₂²	—	158	2	no	—
649	C₂²	—	158	1	no	—
650	C₂²	—	158	2	no	—
651	C₂²	—	158	1	no	—
652	C₂²	—	158	2	no	—
653	C₂²	—	158	2	no	—
654	C₂²	—	158	1	no	—
655	C₂²	—	158	2	no	—
656	C₂²	—	158	2	no	—
657	C₂²	—	158	1	no	—
658	C₂²	—	158	1	no	—
659	C₂²	#41×D₇₉	1	2	yes	—
660	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	79	2	no	—
670	C₄	—	158	1	no	—
671	C₄	—	158	2	no	—
672	C₄	—	158	2	no	—
673	C₄	—	158	1	no	—
674	C₄	—	158	1	no	—
675	C₄	—	158	1	no	—
676	C₄	—	158	1	no	—
677	C₄	#14579207	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	316	2	no	—
681	C₂	—	316	2	no	—
682	C₂	—	316	1	no	—
683	C₂	—	158	2	no	—
684	C₂	C₂×#41×D₇₉	1	1	yes	characteristic
685	C₂	C₂×#14579207	1	1	yes	characteristic
686	C₂	#19099399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#529×C₇₉	C₂
hypercenter	#529	D₇₉
hypocenter	C₇₉	#3514
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #19099296	C₂	semidirect
2. #19099285	C₂	semidirect
3. #19099276	C₂	semidirect
4. #19099237	C₂	semidirect
5. #19099236	C₂	semidirect
6. #19099226	C₂	semidirect
7. #19099225	C₂	semidirect
8. #19099219	C₂	semidirect
9. #19099208	C₂	semidirect
10. #19099205	C₂	semidirect
11. #19099204	C₂	semidirect
12. #19099197	C₂	semidirect
13. #19099179	C₂	semidirect
14. #19099152	C₂	semidirect
15. #19099146	C₂	semidirect
16. #19099112	C₂	semidirect
17. #19099098	C₂	semidirect
18. #19099098	C₂	semidirect
19. C₂×#14579149	C₂	semidirect
20. #124×D₇₉	C₂	semidirect
21. #19099035	C₂	semidirect
22. C₄×#11929624	C₂	semidirect
23. #529×C₇₉	C₂	semidirect
24. C₂×#11929625	C₂²	semidirect
26. C₂×#11929623	C₂²	semidirect
27. C₂²×Dic₁₅₈	C₂²	semidirect
28. C₂×Q₈×D₇₉	C₂²	semidirect
32. #14579160	C₂²	semidirect
33. #14579159	C₂²	semidirect
35. #14579156	C₂²	semidirect
36. #14579156	C₂²	semidirect
37. #14579156	C₂²	semidirect
38. #14579155	C₂²	semidirect
42. #14579149	C₂²	semidirect
43. #14579149	C₂²	semidirect
44. #14579149	C₂²	semidirect
45. #14579149	C₂²	semidirect
46. #14579149	C₂²	semidirect
47. #14579148	C₂²	semidirect
48. #14579147	C₂²	semidirect
49. #14579147	C₂²	semidirect
50. #14579147	C₂²	semidirect
51. #14579147	C₂²	semidirect
52. #14579146	C₂²	semidirect
53. #14579146	C₂²	semidirect
54. #14579146	C₂²	semidirect
55. #14579145	C₂²	semidirect
56. #14579144	C₂²	semidirect
57. #14579143	C₂²	semidirect
58. #14579141	C₂²	semidirect
59. #14579141	C₂²	semidirect
60. #14579141	C₂²	semidirect
61. #14579139	C₂²	semidirect
62. #14579139	C₂²	semidirect
63. #14579138	C₂²	semidirect
64. #14579138	C₂²	semidirect
67. #14579136	C₂²	semidirect
68. #14579136	C₂²	semidirect
69. #14579135	C₂²	semidirect
71. #14579134	C₂²	semidirect
72. #14579134	C₂²	semidirect
73. #14579133	C₂²	semidirect
75. #14579131	C₂²	semidirect
76. #14579131	C₂²	semidirect
78. C₄×Dic₁₅₈	C₂²	semidirect
79. C₄×Dic₁₅₈	C₂²	semidirect
80. #14579126	C₂²	semidirect
81. #14579126	C₂²	semidirect
82. C₄×D₃₁₆	C₂²	semidirect
83. C₄×D₃₁₆	C₂²	semidirect
84. C₄×D₃₁₆	C₂²	semidirect
85. D₄×Dic₇₉	C₂²	semidirect
87. #14579123	C₂²	semidirect
88. #14579123	C₂²	semidirect
89. #14579123	C₂²	semidirect
92. C₄×C₂²⋊D₇₉	C₂²	semidirect
93. C₄×C₂²⋊D₇₉	C₂²	semidirect
94. C₄×C₂²⋊D₇₉	C₂²	semidirect
96. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
97. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
98. #14579120	C₂²	semidirect
99. #14579119	C₂²	semidirect
100. #14579119	C₂²	semidirect
101. #14579118	C₂²	semidirect
102. #14579118	C₂²	semidirect
103. #14579118	C₂²	semidirect
104. C₂×(C₂×D₇₉)⋊C₄	C₂²	semidirect
105. C₂×(C₂×D₇₉)⋊C₄	C₂²	semidirect
106. C₂×(C₂×D₇₉)⋊C₄	C₂²	semidirect
107. C₂²⋊C₄×D₇₉	C₂²	semidirect
108. C₂²⋊C₄×D₇₉	C₂²	semidirect
109. C₂²⋊C₄×D₇₉	C₂²	semidirect
110. C₄²×D₇₉	C₂²	semidirect
111. C₄²×D₇₉	C₂²	semidirect
112. #126×C₇₉	C₂²	semidirect
113. #125×C₇₉	C₂²	semidirect
114. #124×C₇₉	C₂²	semidirect
115. #123×C₇₉	C₂²	semidirect
116. C₂²⋊Q₈×C₇₉	C₂²	semidirect
118. C₄×Q₈×C₇₉	C₂²	semidirect
119. C₄×D₄×C₇₉	C₂²	semidirect
120. C₄×D₄×C₇₉	C₂²	semidirect
121. #117×C₇₉	C₂²	semidirect
122. C₂×C₄²×C₇₉	C₂²	semidirect
263. C₂²⋊D₇₉	#41	semidirect
344. C₇₉	#3514	semidirect
363. #529	D₇₉	semidirect
383. #126	C₂×D₇₉	semidirect
384. #125	C₂×D₇₉	semidirect
398. #124	C₂×D₇₉	semidirect
405. #123	C₂×D₇₉	semidirect
413. C₂²⋊Q₈	C₂×D₇₉	semidirect
432. C₄×Q₈	C₂×D₇₉	semidirect
449. C₄×D₄	C₂×D₇₉	semidirect
450. C₄×D₄	C₂×D₇₉	semidirect
457. #117	C₂×D₇₉	semidirect
466. C₂×C₄²	C₂×D₇₉	semidirect