Subgroups — #23777922

Order 10112.

1160 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099311	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099305	C₂	1	1	yes	maximal, characteristic, complemented
3	#19099305	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099297	C₂	1	2	yes	maximal, complemented
5	#19099223	C₂	1	2	yes	maximal, complemented
6	#19099205	C₂	1	2	yes	maximal, complemented
7	#19099204	C₂	1	2	yes	maximal, complemented
8	#19099202	C₂	1	2	yes	maximal, complemented
9	#19099197	C₂	1	2	yes	maximal, complemented
10	#19099183	C₂	1	2	yes	maximal, complemented
11	#19099153	C₂	1	2	yes	maximal, complemented
12	#19099149	C₂	1	2	yes	maximal, complemented
13	#19099145	C₂	1	2	yes	maximal, complemented
14	#19099129	C₂	1	2	yes	maximal, complemented
15	#19099124	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	#124×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#562×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11929625	C₂²	1	1	yes	characteristic, complemented
21	C₂×#11929624	C₂²	1	2	yes	complemented
22	C₂×#11929623	C₂²	1	1	yes	characteristic, complemented
23	C₂×Q₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₃₁₆	C₂²	1	2	yes	complemented
25	C₂×D₄×D₇₉	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₇₉	C₂²	1	2	yes	complemented
27	C₂×D₄×D₇₉	C₂²	1	2	yes	complemented
28	#14579159	C₂²	1	1	yes	characteristic, complemented
29	#14579157	C₂²	1	2	yes	—
30	#14579157	C₂²	1	1	yes	characteristic, complemented
31	#14579156	C₂²	1	2	yes	complemented
32	#14579156	C₂²	1	2	yes	complemented
33	#14579154	C₂²	1	2	yes	complemented
34	#14579150	C₂²	1	1	yes	characteristic, complemented
35	#14579150	C₂²	1	2	yes	complemented
36	#14579150	C₂²	1	2	yes	complemented
37	#14579149	C₂²	1	1	yes	characteristic, complemented
38	#14579149	C₂²	1	1	yes	characteristic, complemented
39	#14579149	C₂²	1	1	yes	characteristic, complemented
40	#14579148	C₂²	1	1	yes	characteristic, complemented
41	#14579147	C₂²	1	2	yes	complemented
42	#14579147	C₂²	1	2	yes	complemented
43	#14579147	C₂²	1	2	yes	complemented
44	#14579147	C₂²	1	2	yes	complemented
45	#14579147	C₂²	1	2	yes	complemented
46	#14579147	C₂²	1	2	yes	complemented
47	#14579147	C₂²	1	2	yes	complemented
48	#14579146	C₂²	1	2	yes	complemented
49	#14579146	C₂²	1	2	yes	complemented
50	#14579146	C₂²	1	2	yes	complemented
51	#14579146	C₂²	1	2	yes	complemented
52	#14579146	C₂²	1	2	yes	complemented
53	#14579144	C₂²	1	2	yes	complemented
54	#14579142	C₂²	1	2	yes	complemented
55	#14579141	C₂²	1	1	yes	characteristic, complemented
56	#14579139	C₂²	1	2	yes	complemented
57	#14579139	C₂²	1	2	yes	complemented
58	#14579139	C₂²	1	2	yes	complemented
59	#14579136	C₂²	1	1	yes	characteristic
60	#14579136	C₂²	1	2	yes	complemented
61	#14579136	C₂²	1	2	yes	complemented
62	#14579136	C₂²	1	2	yes	complemented
63	#14579136	C₂²	1	2	yes	complemented
64	#14579135	C₂²	1	2	yes	complemented
65	#14579134	C₂²	1	2	yes	—
66	#14579134	C₂²	1	2	yes	complemented
67	#14579134	C₂²	1	2	yes	complemented
68	#14579134	C₂²	1	2	yes	complemented
69	#14579133	C₂²	1	2	yes	complemented
70	#14579132	C₂²	1	2	yes	complemented
71	#14579131	C₂²	1	2	yes	complemented
72	#14579131	C₂²	1	2	yes	complemented
73	#14579131	C₂²	1	2	yes	complemented
74	#14579131	C₂²	1	2	yes	complemented
75	#14579131	C₂²	1	2	yes	complemented
76	#14579131	C₂²	1	2	yes	complemented
77	#14579129	C₂²	1	2	yes	complemented
78	#14579129	C₂²	1	2	yes	complemented
79	#14579129	C₂²	1	2	yes	complemented
80	#14579129	C₂²	1	2	yes	complemented
81	#14579126	C₂²	1	2	yes	complemented
82	#14579126	C₂²	1	1	yes	characteristic, complemented
83	#14579123	C₂²	1	2	yes	complemented
84	#14579123	C₂²	1	2	yes	complemented
85	#14579123	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
89	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
90	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
91	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
92	#14579119	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
97	C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
98	#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
99	#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
100	#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
101	#123×C₇₉	C₂²	1	2	yes	complemented
102	#123×C₇₉	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	complemented
105	#121×C₇₉	C₂²	1	2	yes	complemented
106	#121×C₇₉	C₂²	1	2	yes	complemented
107	C₂³×D₇₉	C₂³	1	2	yes	—
108	C₂³×D₇₉	C₂³	1	2	yes	—
109	C₂³×D₇₉	C₂³	1	2	yes	—
110	#11929625	—	4	2	no	—
111	#11929624	—	4	4	no	—
112	#11929623	—	4	2	no	—
113	C₂×Dic₁₅₈	C₂³	1	2	yes	—
114	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
115	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
116	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
117	Q₈×D₇₉	—	4	2	no	—
118	C₂×D₃₁₆	—	4	4	no	—
119	C₂×D₃₁₆	C₂³	1	2	yes	—
120	C₂×D₃₁₆	C₂³	1	2	yes	—
121	C₂×D₃₁₆	C₂³	1	2	yes	—
122	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
123	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
124	C₂×D₃₁₆	C₂³	1	2	yes	—
125	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
126	C₂×D₃₁₆	C₂³	1	2	yes	—
127	C₂×D₃₁₆	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
136	D₄×D₇₉	—	4	2	no	—
137	D₄×D₇₉	—	4	4	no	—
138	D₄×D₇₉	—	4	4	no	—
139	C₂²×Dic₇₉	C₂³	1	2	yes	—
140	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₇₉	C₂³	1	2	yes	—
143	C₂×C₄×D₇₉	C₂³	1	2	yes	—
144	C₂×C₄×D₇₉	C₂³	1	2	yes	—
145	C₂×C₄×D₇₉	C₂³	1	2	yes	—
146	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₇₉	C₂³	1	2	yes	—
148	C₄⋊Dic₇₉	C₂³	1	2	yes	—
149	Dic₇₉⋊C₄	C₂³	1	2	yes	—
150	Dic₇₉⋊C₄	C₂³	1	2	yes	—
151	Dic₇₉⋊C₄	C₂³	1	2	yes	—
152	Dic₇₉⋊C₄	C₂³	1	2	yes	—
153	Dic₇₉⋊C₄	C₂³	1	2	yes	—
154	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
156	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
157	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
158	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
175	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
176	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
177	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
178	C₄×Dic₇₉	C₂³	1	2	yes	—
179	C₄×Dic₇₉	C₂³	1	2	yes	—
180	C₄×Dic₇₉	C₂³	1	2	yes	—
181	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
182	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
184	C₂×D₄×C₇₉	C₂³	1	2	yes	—
185	C₂×D₄×C₇₉	C₂³	1	2	yes	—
186	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
188	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
190	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
191	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
192	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
193	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
194	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
195	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
201	C₄²×C₇₉	C₂³	1	1	yes	characteristic
202	C₂³×C₇₉	C₂⁴	1	2	yes	—
203	C₂³×C₇₉	C₂⁴	1	2	yes	—
204	C₂²×D₇₉	—	2	4	no	—
205	C₂²×D₇₉	—	4	2	no	—
206	C₂²×D₇₉	—	4	2	no	—
207	C₂²×D₇₉	—	4	2	no	—
208	C₂²×D₇₉	—	4	2	no	—
209	C₂²×D₇₉	—	4	2	no	—
210	C₂²×D₇₉	—	4	2	no	—
211	C₂²×D₇₉	—	4	2	no	—
212	C₂²×D₇₉	—	4	2	no	—
213	C₂²×D₇₉	C₂⁴	1	2	yes	—
214	C₂²×D₇₉	C₂⁴	1	2	yes	—
215	C₂²×D₇₉	C₂⁴	1	2	yes	—
216	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
217	Q₈×C₇₉	—	4	1	no	—
218	Q₈×C₇₉	—	4	1	no	—
219	D₄×C₇₉	—	4	2	no	—
220	D₄×C₇₉	—	4	2	no	—
221	D₄×C₇₉	—	4	1	no	—
222	D₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	4	2	no	—
224	C₂×C₄×C₇₉	—	4	2	no	—
225	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
226	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
229	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
230	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
231	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
232	C₂²⋊D₇₉	—	2	4	no	—
233	C₂²⋊D₇₉	—	2	4	no	—
234	C₂²⋊D₇₉	—	2	4	no	—
235	C₂²⋊D₇₉	—	4	2	no	—
236	C₂²⋊D₇₉	—	4	2	no	—
237	C₂²⋊D₇₉	—	4	2	no	—
238	C₂²⋊D₇₉	—	4	2	no	—
239	C₂²⋊D₇₉	—	4	2	no	—
240	C₂×Dic₇₉	—	4	2	no	—
241	C₂×Dic₇₉	C₂⁴	1	2	yes	—
242	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₇₉	C₂⁴	1	2	yes	—
245	C₂×Dic₇₉	C₂⁴	1	2	yes	—
246	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
247	D₃₁₆	—	2	4	no	—
248	D₃₁₆	—	2	4	no	—
249	D₃₁₆	—	4	2	no	—
250	D₃₁₆	—	4	1	no	—
251	D₃₁₆	—	4	2	no	—
252	D₃₁₆	—	4	2	no	—
253	D₃₁₆	—	4	1	no	—
254	D₃₁₆	—	4	2	no	—
255	D₃₁₆	—	4	1	no	—
256	C₄×D₇₉	—	2	2	no	—
257	C₄×D₇₉	—	2	2	no	—
258	C₄×D₇₉	—	2	4	no	—
259	C₄×D₇₉	—	4	1	no	—
260	C₄×D₇₉	—	4	2	no	—
261	C₄×D₇₉	—	4	2	no	—
262	C₄×D₇₉	—	4	2	no	—
263	C₄×D₇₉	—	4	2	no	—
264	Dic₁₅₈	—	2	4	no	—
265	Dic₁₅₈	—	4	1	no	—
266	Dic₁₅₈	—	4	1	no	—
267	Dic₁₅₈	—	4	1	no	—
268	C₂²×C₇₉	—	2	2	no	—
269	C₂²×C₇₉	—	2	2	no	—
270	C₂²×C₇₉	—	2	2	no	—
271	C₂²×C₇₉	—	2	2	no	—
272	C₂²×C₇₉	—	2	2	no	—
273	C₂²×C₇₉	—	2	2	no	—
274	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
275	C₂×D₇₉	—	2	1	no	—
276	C₂×D₇₉	—	2	1	no	—
277	C₂×D₇₉	—	2	2	no	—
278	C₂×D₇₉	—	2	2	no	—
279	C₂×D₇₉	—	2	2	no	—
280	C₂×D₇₉	—	2	2	no	—
281	C₂×D₇₉	—	2	2	no	—
282	C₂×D₇₉	—	2	2	no	—
283	C₂×D₇₉	—	2	2	no	—
284	C₂×D₇₉	—	2	2	no	—
285	C₂×D₇₉	—	2	2	no	—
286	C₂×D₇₉	—	8	4	no	—
287	C₂×D₇₉	—	8	4	no	—
288	C₂×D₇₉	—	8	4	no	—
289	C₂×D₇₉	H(5,𝔽₂)	1	2	yes	—
290	C₄×C₇₉	—	2	2	no	—
291	C₄×C₇₉	—	2	2	no	—
292	C₄×C₇₉	—	2	2	no	—
293	C₄×C₇₉	—	2	2	no	—
294	C₄×C₇₉	—	2	1	no	—
295	C₄×C₇₉	—	2	1	no	—
296	C₄×C₇₉	—	2	1	no	—
297	Dic₇₉	—	2	2	no	—
298	Dic₇₉	—	2	2	no	—
299	Dic₇₉	—	2	1	no	—
300	Dic₇₉	—	2	2	no	—
301	Dic₇₉	—	2	1	no	—
302	Dic₇₉	H(5,𝔽₂)	1	2	yes	—
303	C₂×C₇₉	—	4	2	no	—
304	C₂×C₇₉	—	4	2	no	—
305	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₇₉	#585	1	1	yes	characteristic
308	D₇₉	—	2	2	no	—
309	D₇₉	—	4	2	no	—
310	D₇₉	—	4	2	no	—
311	D₇₉	—	4	2	no	—
312	#3558	—	79	1	no	maximal, Sylow
313	C₇₉	#3558	1	1	yes	characteristic, complemented, Sylow
314	#562	—	79	1	no	—
315	#562	D₇₉	1	1	yes	characteristic, complemented
316	H(3,𝔽₄)	—	79	1	no	—
317	H(3,𝔽₄)	—	79	1	no	—
318	#559	—	79	2	no	—
319	#548	—	79	2	no	—
320	#546	—	79	2	no	—
321	#546	—	79	2	no	—
322	#546	—	79	2	no	—
323	D₄²	—	79	2	no	—
324	#542	—	79	2	no	—
325	#538	—	79	2	no	—
326	#538	—	79	2	no	—
327	#538	—	79	2	no	—
328	#535	—	79	2	no	—
329	#534	—	79	2	no	—
330	#532	—	79	1	no	—
331	#529	—	79	1	no	—
332	C₂×#124	—	79	1	no	—
333	C₂×#41	—	79	1	no	—
334	C₂×#41	—	79	1	no	—
335	C₂×#41	—	79	2	no	—
336	C₂²×Q₈	—	79	1	no	—
337	C₂²×D₄	—	79	1	no	—
338	C₂²×D₄	—	79	2	no	—
339	C₂²×D₄	—	79	2	no	—
340	C₂²×D₄	—	79	2	no	—
341	C₄⋊Q₈	—	79	1	no	—
342	#127	—	79	1	no	—
343	#127	—	79	2	no	—
344	#126	—	79	2	no	—
345	#126	—	79	2	no	—
346	#126	—	79	2	no	—
347	#125	C₂×D₇₉	1	1	yes	characteristic, complemented
348	#124	—	79	1	no	—
349	#124	—	79	2	no	—
350	#124	—	79	2	no	—
351	#124	—	79	1	no	—
352	#124	—	79	2	no	—
353	#124	—	79	2	no	—
354	#124	—	79	2	no	—
355	#124	—	79	2	no	—
356	#124	—	79	2	no	—
357	#124	—	79	2	no	—
358	#124	—	79	2	no	—
359	#124	—	79	1	no	—
360	#124	—	79	1	no	—
361	#124	—	79	1	no	—
362	#124	C₂×D₇₉	1	1	yes	characteristic, complemented
363	#124	C₂×D₇₉	1	1	yes	characteristic, complemented
364	#123	—	79	2	no	—
365	#123	—	79	2	no	—
366	#123	—	79	2	no	—
367	#123	—	79	2	no	—
368	#123	—	79	2	no	—
369	#123	—	79	2	no	—
370	#123	—	79	2	no	—
371	#123	C₂×D₇₉	1	2	yes	complemented
372	#123	C₂×D₇₉	1	2	yes	complemented
373	C₂²⋊Q₈	—	79	1	no	—
374	C₂²⋊Q₈	—	79	2	no	—
375	C₂²⋊Q₈	—	79	2	no	—
376	C₂²⋊Q₈	—	79	2	no	—
377	C₂²⋊Q₈	C₂×D₇₉	1	2	yes	complemented
378	C₂²⋊Q₈	C₂×D₇₉	1	2	yes	complemented
379	#121	—	79	2	no	—
380	#121	—	79	2	no	—
381	#121	—	79	2	no	—
382	#121	—	79	1	no	—
383	#121	—	79	2	no	—
384	#121	—	79	2	no	—
385	#121	—	79	2	no	—
386	#121	—	79	2	no	—
387	#121	—	79	2	no	—
388	#121	—	79	2	no	—
389	#121	—	79	2	no	—
390	#121	—	79	2	no	—
391	#121	C₂×D₇₉	1	2	yes	complemented
392	#121	C₂×D₇₉	1	2	yes	complemented
393	#120	—	79	2	no	—
394	#120	—	79	2	no	—
395	#120	—	79	2	no	—
396	#120	—	79	2	no	—
397	#120	—	79	2	no	—
398	#120	—	79	2	no	—
399	#120	—	79	2	no	—
400	#120	—	79	2	no	—
401	#120	—	79	2	no	—
402	#120	—	79	2	no	—
403	C₄×Q₈	—	79	1	no	—
404	C₄×Q₈	—	79	2	no	—
405	C₄×D₄	—	79	2	no	—
406	C₄×D₄	—	79	2	no	—
407	C₄×D₄	—	79	2	no	—
408	C₄×D₄	—	79	2	no	—
409	C₄×D₄	—	79	1	no	—
410	C₄×D₄	—	79	2	no	—
411	C₄×D₄	—	79	2	no	—
412	C₄×D₄	—	79	2	no	—
413	C₄×D₄	—	79	2	no	—
414	#117	—	79	2	no	—
415	C₂×C₂²⋊C₄	—	79	2	no	—
416	C₂×C₂²⋊C₄	—	79	2	no	—
417	C₂×C₂²⋊C₄	—	79	2	no	—
418	C₂×C₂²⋊C₄	—	79	2	no	—
419	C₂×C₄²	—	79	1	no	—
420	C₂⁴	—	79	2	no	—
421	C₂⁴	—	79	2	no	—
422	C₂⁴	—	79	2	no	—
423	#41	—	316	4	no	—
424	#41	—	316	2	no	—
425	#41	—	316	2	no	—
426	C₂×Q₈	—	316	2	no	—
427	C₂×Q₈	—	79	1	no	—
428	C₂×Q₈	—	79	1	no	—
429	C₂×Q₈	—	79	1	no	—
430	C₂×Q₈	—	79	2	no	—
431	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
432	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
433	C₂×D₄	—	316	4	no	—
434	C₂×D₄	—	316	4	no	—
435	C₂×D₄	—	316	2	no	—
436	C₂×D₄	—	316	4	no	—
437	C₂×D₄	—	79	2	no	—
438	C₂×D₄	—	79	2	no	—
439	C₂×D₄	—	79	2	no	—
440	C₂×D₄	—	79	2	no	—
441	C₂×D₄	—	79	2	no	—
442	C₂×D₄	—	79	2	no	—
443	C₂×D₄	—	79	2	no	—
444	C₂×D₄	—	79	2	no	—
445	C₂×D₄	—	79	1	no	—
446	C₂×D₄	—	79	2	no	—
447	C₂×D₄	—	79	2	no	—
448	C₂×D₄	—	79	1	no	—
449	C₂×D₄	—	79	1	no	—
450	C₂×D₄	—	79	2	no	—
451	C₂×D₄	—	79	2	no	—
452	C₂×D₄	—	79	2	no	—
453	C₂×D₄	—	79	2	no	—
454	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
456	C₂×D₄	C₂²×D₇₉	1	2	yes	—
457	C₂×D₄	C₂²×D₇₉	1	2	yes	—
458	C₂²×C₄	—	79	2	no	—
459	C₂²×C₄	—	79	1	no	—
460	C₂²×C₄	—	79	2	no	—
461	C₂²×C₄	—	79	2	no	—
462	C₂²×C₄	—	79	2	no	—
463	C₂²×C₄	—	79	2	no	—
464	C₂²×C₄	—	79	1	no	—
465	C₂²×C₄	—	79	1	no	—
466	C₂²×C₄	—	79	2	no	—
467	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
468	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
469	C₄⋊C₄	—	79	2	no	—
470	C₄⋊C₄	—	79	2	no	—
471	C₄⋊C₄	—	79	2	no	—
472	C₄⋊C₄	—	79	2	no	—
473	C₄⋊C₄	—	79	2	no	—
474	C₄⋊C₄	—	79	2	no	—
475	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
476	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
477	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
478	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
480	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
481	C₂²⋊C₄	—	79	2	no	—
482	C₂²⋊C₄	—	79	2	no	—
483	C₂²⋊C₄	—	79	2	no	—
484	C₂²⋊C₄	—	79	2	no	—
485	C₂²⋊C₄	—	79	2	no	—
486	C₂²⋊C₄	—	79	2	no	—
487	C₂²⋊C₄	—	79	2	no	—
488	C₂²⋊C₄	—	79	2	no	—
489	C₂²⋊C₄	—	79	2	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	2	no	—
495	C₂²⋊C₄	—	79	2	no	—
496	C₂²⋊C₄	—	79	2	no	—
497	C₂²⋊C₄	—	79	2	no	—
498	C₂²⋊C₄	—	79	2	no	—
499	C₂²⋊C₄	—	79	2	no	—
500	C₂²⋊C₄	—	79	2	no	—
501	C₂²⋊C₄	—	79	2	no	—
502	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
503	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
506	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
508	C₄²	—	79	1	no	—
509	C₄²	—	79	1	no	—
510	C₄²	—	79	1	no	—
511	C₄²	—	79	2	no	—
512	C₄²	—	79	2	no	—
513	C₄²	—	79	2	no	—
514	C₄²	C₂²×D₇₉	1	1	yes	characteristic
515	C₂³	—	316	2	no	—
516	C₂³	—	316	2	no	—
517	C₂³	—	316	2	no	—
518	C₂³	—	316	2	no	—
519	C₂³	—	316	2	no	—
520	C₂³	—	316	2	no	—
521	C₂³	—	316	2	no	—
522	C₂³	—	316	2	no	—
523	C₂³	—	79	1	no	—
524	C₂³	—	79	2	no	—
525	C₂³	—	79	2	no	—
526	C₂³	—	79	2	no	—
527	C₂³	—	158	4	no	—
528	C₂³	C₂³×D₇₉	1	2	yes	—
529	C₂³	C₂³×D₇₉	1	2	yes	—
530	Q₈	—	4	1	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	316	1	no	—
533	Q₈	—	316	1	no	—
534	Q₈	—	316	1	no	—
535	Q₈	—	158	4	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	316	2	no	—
541	D₄	—	316	2	no	—
542	D₄	—	316	2	no	—
543	D₄	—	316	1	no	—
544	D₄	—	316	2	no	—
545	D₄	—	316	1	no	—
546	D₄	—	316	1	no	—
547	D₄	—	316	2	no	—
548	D₄	—	316	2	no	—
549	D₄	—	316	2	no	—
550	D₄	—	316	2	no	—
551	D₄	—	316	2	no	—
552	D₄	—	158	4	no	—
553	D₄	—	158	4	no	—
554	D₄	—	158	4	no	—
555	D₄	—	158	4	no	—
556	D₄	—	158	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	316	2	no	—
560	C₂×C₄	—	316	2	no	—
561	C₂×C₄	—	316	2	no	—
562	C₂×C₄	—	316	2	no	—
563	C₂×C₄	—	316	1	no	—
564	C₂×C₄	—	316	2	no	—
565	C₂×C₄	—	79	1	no	—
566	C₂×C₄	—	79	2	no	—
567	C₂×C₄	—	79	1	no	—
568	C₂×C₄	—	79	1	no	—
569	C₂×C₄	—	79	2	no	—
570	C₂×C₄	—	79	2	no	—
571	C₂×C₄	—	158	2	no	—
572	C₂×C₄	—	158	4	no	—
573	C₂×C₄	—	158	2	no	—
574	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
575	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
576	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
577	C₂×C₄	C₂³×D₇₉	1	2	yes	—
578	C₂×C₄	C₂³×D₇₉	1	2	yes	—
579	C₂×C₄	C₂³×D₇₉	1	2	yes	—
580	C₂×C₄	C₂³×D₇₉	1	2	yes	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	79	2	no	—
588	C₂²	—	632	4	no	—
589	C₂²	—	632	4	no	—
590	C₂²	—	632	4	no	—
591	C₂²	—	158	2	no	—
592	C₂²	—	158	2	no	—
593	C₂²	—	158	2	no	—
594	C₂²	—	158	2	no	—
595	C₂²	—	158	2	no	—
596	C₂²	—	158	2	no	—
597	C₂²	—	158	2	no	—
598	C₂²	—	158	2	no	—
599	C₂²	—	158	2	no	—
600	C₂²	—	158	1	no	—
601	C₂²	—	158	1	no	—
602	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	79	2	no	—
611	C₄	—	158	1	no	—
612	C₄	—	158	2	no	—
613	C₄	—	158	2	no	—
614	C₄	—	158	1	no	—
615	C₄	—	158	2	no	—
616	C₂	—	4	2	no	—
617	C₂	—	4	2	no	—
618	C₂	—	316	2	no	—
619	C₂	—	316	2	no	—
620	C₂	—	316	2	no	—
621	C₂	—	158	2	no	—
622	C₂	H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
623	C₂	H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
624	C₂	#19099400	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#562×C₇₉	C₂
hypercenter	#562	D₇₉
hypocenter	C₇₉	#3558
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #19099311	C₂	semidirect
2. #19099305	C₂	semidirect
3. #19099305	C₂	semidirect
4. #19099297	C₂	semidirect
5. #19099223	C₂	semidirect
6. #19099205	C₂	semidirect
7. #19099204	C₂	semidirect
8. #19099202	C₂	semidirect
9. #19099197	C₂	semidirect
10. #19099183	C₂	semidirect
11. #19099153	C₂	semidirect
12. #19099149	C₂	semidirect
13. #19099145	C₂	semidirect
14. #19099129	C₂	semidirect
15. #19099124	C₂	semidirect
16. #19099112	C₂	semidirect
17. #19099098	C₂	semidirect
18. #124×D₇₉	C₂	semidirect
19. #562×C₇₉	C₂	semidirect
20. C₂×#11929625	C₂²	semidirect
21. C₂×#11929624	C₂²	semidirect
22. C₂×#11929623	C₂²	semidirect
23. C₂×Q₈×D₇₉	C₂²	semidirect
24. C₂²×D₃₁₆	C₂²	semidirect
26. C₂×D₄×D₇₉	C₂²	semidirect
27. C₂×D₄×D₇₉	C₂²	semidirect
28. #14579159	C₂²	semidirect
30. #14579157	C₂²	semidirect
31. #14579156	C₂²	semidirect
32. #14579156	C₂²	semidirect
33. #14579154	C₂²	semidirect
34. #14579150	C₂²	semidirect
35. #14579150	C₂²	semidirect
36. #14579150	C₂²	semidirect
37. #14579149	C₂²	semidirect
38. #14579149	C₂²	semidirect
39. #14579149	C₂²	semidirect
40. #14579148	C₂²	semidirect
41. #14579147	C₂²	semidirect
42. #14579147	C₂²	semidirect
43. #14579147	C₂²	semidirect
44. #14579147	C₂²	semidirect
45. #14579147	C₂²	semidirect
46. #14579147	C₂²	semidirect
47. #14579147	C₂²	semidirect
48. #14579146	C₂²	semidirect
49. #14579146	C₂²	semidirect
50. #14579146	C₂²	semidirect
51. #14579146	C₂²	semidirect
52. #14579146	C₂²	semidirect
53. #14579144	C₂²	semidirect
54. #14579142	C₂²	semidirect
55. #14579141	C₂²	semidirect
56. #14579139	C₂²	semidirect
57. #14579139	C₂²	semidirect
58. #14579139	C₂²	semidirect
60. #14579136	C₂²	semidirect
61. #14579136	C₂²	semidirect
62. #14579136	C₂²	semidirect
63. #14579136	C₂²	semidirect
64. #14579135	C₂²	semidirect
66. #14579134	C₂²	semidirect
67. #14579134	C₂²	semidirect
68. #14579134	C₂²	semidirect
69. #14579133	C₂²	semidirect
70. #14579132	C₂²	semidirect
71. #14579131	C₂²	semidirect
72. #14579131	C₂²	semidirect
73. #14579131	C₂²	semidirect
74. #14579131	C₂²	semidirect
75. #14579131	C₂²	semidirect
76. #14579131	C₂²	semidirect
77. #14579129	C₂²	semidirect
78. #14579129	C₂²	semidirect
79. #14579129	C₂²	semidirect
80. #14579129	C₂²	semidirect
81. #14579126	C₂²	semidirect
82. #14579126	C₂²	semidirect
83. #14579123	C₂²	semidirect
84. #14579123	C₂²	semidirect
85. #14579123	C₂²	semidirect
86. C₄×C₂²⋊D₇₉	C₂²	semidirect
87. C₄×C₂²⋊D₇₉	C₂²	semidirect
88. C₄×C₂²⋊D₇₉	C₂²	semidirect
89. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
90. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
91. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
92. #14579119	C₂²	semidirect
93. C₂×(C₂×D₇₉)⋊C₄	C₂²	semidirect
94. C₂²⋊C₄×D₇₉	C₂²	semidirect
95. C₂²⋊C₄×D₇₉	C₂²	semidirect
96. C₂²⋊C₄×D₇₉	C₂²	semidirect
97. C₄²×D₇₉	C₂²	semidirect
98. #125×C₇₉	C₂²	semidirect
99. #124×C₇₉	C₂²	semidirect
100. #124×C₇₉	C₂²	semidirect
101. #123×C₇₉	C₂²	semidirect
102. #123×C₇₉	C₂²	semidirect
103. C₂²⋊Q₈×C₇₉	C₂²	semidirect
104. C₂²⋊Q₈×C₇₉	C₂²	semidirect
105. #121×C₇₉	C₂²	semidirect
106. #121×C₇₉	C₂²	semidirect
313. C₇₉	#3558	semidirect
315. #562	D₇₉	semidirect
347. #125	C₂×D₇₉	semidirect
362. #124	C₂×D₇₉	semidirect
363. #124	C₂×D₇₉	semidirect
371. #123	C₂×D₇₉	semidirect
372. #123	C₂×D₇₉	semidirect
377. C₂²⋊Q₈	C₂×D₇₉	semidirect
378. C₂²⋊Q₈	C₂×D₇₉	semidirect
391. #121	C₂×D₇₉	semidirect
392. #121	C₂×D₇₉	semidirect