Subgroups — #14415733

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#6777	C₂	1	1	yes	maximal, characteristic
4	#11750808	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4706	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64995	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748103	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748103	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747722	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747721	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747696	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#1201	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747015	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746999	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746997	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611214	—	3	1	no	maximal, Hall
17	C₂×#6777	C₄	1	1	yes	characteristic
18	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
20	C₂×#6705	C₂²	1	1	yes	characteristic
21	C₂×#6705	C₂²	1	1	yes	characteristic
22	C₄²×D₁₅	C₂²	1	1	yes	characteristic
23	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
26	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
29	#91473	C₄	1	1	yes	characteristic
30	#91473	C₄	1	1	yes	characteristic
31	#91442	C₄	1	1	yes	characteristic
32	#91442	C₄	1	1	yes	characteristic
33	C₄×#1201	C₂²	1	1	yes	characteristic
34	C₄×#1201	C₂²	1	1	yes	characteristic
35	#91437	C₄	1	1	yes	characteristic
36	#91435	C₄	1	1	yes	characteristic
37	#91434	C₄	1	1	yes	characteristic
38	C₂×#6651	C₂²	1	1	yes	characteristic
39	C₂×#6651	C₂²	1	1	yes	characteristic
40	C₂×#6650	C₂²	1	1	yes	characteristic, complemented
41	C₂×#6649	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₃×#168	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	D₃×#676	—	2	4	no	—
45	D₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
46	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
47	C₈×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
48	C₈×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
49	#91087	C₂²	1	1	yes	characteristic, complemented
50	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
54	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
56	#90983	C₂²	1	1	yes	characteristic, complemented
57	#90983	C₂²	1	1	yes	characteristic, complemented
58	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
59	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
60	#90955	C₂²	1	1	yes	characteristic, complemented
61	#90955	C₂²	1	1	yes	characteristic, complemented
62	#79483	—	5	1	no	maximal, Hall
63	C₂×D₅×M₁₆	—	3	1	no	—
64	C₂²×#676	—	3	1	no	—
65	C₄×D₄×D₅	—	3	1	no	—
66	C₅×#435	—	3	1	no	—
67	#65417	—	3	1	no	—
68	C₈×C₂²⋊D₅	—	3	1	no	—
69	#65300	—	3	1	no	—
70	#65126	—	3	1	no	—
71	#65125	—	3	1	no	—
72	#65018	—	3	1	no	—
73	#65015	—	3	1	no	—
74	#65015	—	3	1	no	—
75	#65014	—	3	1	no	—
76	#64996	—	3	1	no	—
77	#64995	D₃	1	1	yes	characteristic, complemented
78	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
83	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
86	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
89	C₂×#1201	C₂×C₄	1	1	yes	characteristic
90	C₂×#1201	C₂×C₄	1	1	yes	characteristic
91	C₂×#1200	C₂×C₄	1	1	yes	characteristic
92	C₂×#1200	C₂×C₄	1	1	yes	characteristic
93	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
94	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
95	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
97	#6777	—	2	4	no	—
98	C₄×D₃×D₅	—	2	2	no	—
99	C₄×D₃×D₅	—	2	2	no	—
100	C₄×D₃×D₅	—	2	2	no	—
101	C₄×D₃×D₅	—	2	2	no	—
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
107	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
108	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
109	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
110	#6705	—	2	2	no	—
111	#6705	D₄	1	4	yes	complemented
112	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
117	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
118	C₅×D₃×C₈	—	2	2	no	—
119	C₃×#685	C₂×C₄	1	1	yes	characteristic
120	C₃×#685	C₂×C₄	1	1	yes	characteristic
121	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
122	C₂×C₃×#168	C₂³	1	1	yes	characteristic
123	C₂×C₃×#168	C₂³	1	1	yes	characteristic
124	C₃×#676	—	2	2	no	—
125	C₃×C₈×D₅	—	2	2	no	—
126	#6669	C₂×C₄	1	1	yes	characteristic
127	#6669	C₂×C₄	1	1	yes	characteristic
128	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
129	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
130	#6665	C₂×C₄	1	1	yes	characteristic
131	#6665	C₂×C₄	1	1	yes	characteristic
132	#6651	—	2	2	no	—
133	#6651	—	2	2	no	—
134	#6650	—	2	2	no	—
135	#6649	—	2	2	no	—
136	D₃×#168	—	2	2	no	—
137	D₅×C₃⋊C₈	—	2	2	no	—
138	C₂×D₃×M₁₆	—	5	1	no	—
139	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
140	C₄×D₃×D₄	—	5	1	no	—
141	C₃×#435	—	5	1	no	—
142	#5128	—	5	1	no	—
143	C₈×#67	—	5	1	no	—
144	#5011	—	5	1	no	—
145	#4837	—	5	1	no	—
146	#4836	—	5	1	no	—
147	#4729	—	5	1	no	—
148	#4726	—	5	1	no	—
149	#4726	—	5	1	no	—
150	#67⋊C₈	—	5	1	no	—
151	#4707	—	5	1	no	—
152	#4706	D₅	1	1	yes	characteristic, complemented
153	C₂×D₄×D₅	—	3	1	no	—
154	C₂²×C₄×D₅	—	3	1	no	—
155	C₂²×C₄×D₅	—	3	1	no	—
156	C₂×C₅×M₁₆	—	3	1	no	—
157	C₂²×C₅×C₈	—	3	1	no	—
158	C₄×C₅×D₄	—	3	1	no	—
159	D₄×Dic₅	—	3	1	no	—
160	C₄×C₂²⋊D₅	—	3	1	no	—
161	C₄×C₂²⋊D₅	—	3	1	no	—
162	C₂×#681	—	3	1	no	—
163	C₂²×#168	—	3	1	no	—
164	D₅×M₁₆	—	6	4	no	—
165	C₂×#676	—	3	1	no	—
166	C₂×#676	—	3	1	no	—
167	C₂×#676	—	3	1	no	—
168	C₂×#676	—	3	1	no	—
169	C₂×#676	—	3	1	no	—
170	C₂×#676	—	6	4	no	—
171	C₂×#676	C₂×D₃	1	1	yes	characteristic, complemented
172	C₂×C₈×D₅	—	3	1	no	—
173	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic, complemented
174	#4039	—	3	1	no	—
175	D₅×C₄⋊C₄	—	3	1	no	—
176	#4027	—	3	1	no	—
177	#4027	—	3	1	no	—
178	D₅×C₂²⋊C₄	—	3	1	no	—
179	D₅×C₂²⋊C₄	—	3	1	no	—
180	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
181	C₄²×D₅	—	3	1	no	—
182	C₅×C₄⋊C₈	—	3	1	no	—
183	C₅×C₂²⋊C₈	—	3	1	no	—
184	C₅×C₂²⋊C₈	—	3	1	no	—
185	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
186	C₂²⋊#168	—	3	1	no	—
187	C₂²⋊#168	—	3	1	no	—
188	#3952	—	3	1	no	—
189	#3952	—	3	1	no	—
190	#3952	C₂×D₃	1	1	yes	characteristic, complemented
191	#3952	C₂×D₃	1	1	yes	characteristic, complemented
192	#3946	—	3	1	no	—
193	#3946	—	3	1	no	—
194	C₈×Dic₅	—	3	1	no	—
195	C₈×Dic₅	—	3	1	no	—
196	C₄⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
197	#3935	—	3	1	no	—
198	D₄×M₁₆	—	15	1	no	Sylow
199	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
204	C₂×D₃×D₅	—	2	2	no	—
205	C₂×D₃×D₅	—	2	2	no	—
206	C₂×D₃×D₅	—	2	2	no	—
207	C₂×D₃×D₅	—	2	2	no	—
208	C₂×D₃×D₅	—	4	1	no	—
209	C₂×D₃×D₅	—	4	1	no	—
210	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
214	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
215	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
216	C₄×D₁₅	—	2	2	no	—
217	C₄×D₁₅	—	4	1	no	—
218	C₄×D₁₅	C₂×D₄	1	2	yes	—
219	C₄×D₁₅	#41	1	2	yes	—
220	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
221	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
222	C₅×D₁₂	—	2	2	no	—
223	C₄×C₅×D₃	—	2	1	no	—
224	C₄×C₅×D₃	—	2	1	no	—
225	C₄×C₅×D₃	—	2	1	no	—
226	C₄×C₅×D₃	—	2	1	no	—
227	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
229	C₃×D₂₀	—	2	2	no	—
230	C₃×C₄×D₅	—	2	1	no	—
231	C₃×C₄×D₅	—	2	1	no	—
232	C₃×C₄×D₅	—	2	1	no	—
233	C₃×C₄×D₅	—	2	1	no	—
234	#1201	—	2	2	no	—
235	#1201	M₁₆	1	4	yes	complemented
236	#1200	—	2	2	no	—
237	#1200	—	2	2	no	—
238	D₃×Dic₅	—	2	2	no	—
239	D₃×Dic₅	—	2	2	no	—
240	D₅×Dic₃	—	2	2	no	—
241	D₅×Dic₃	—	2	2	no	—
242	C₃×C₅×C₈	—	2	1	no	—
243	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
244	C₃⋊#168	—	2	1	no	—
245	C₃⋊#168	C₂×D₄	1	2	yes	complemented
246	C₃×#168	—	2	1	no	—
247	C₃×#168	—	2	1	no	—
248	C₅×C₃⋊C₈	—	2	1	no	—
249	C₅×C₃⋊C₈	—	2	1	no	—
250	C₂×D₃×D₄	—	5	1	no	—
251	C₂²×C₄×D₃	—	5	1	no	—
252	C₂²×C₄×D₃	—	5	1	no	—
253	C₂×C₃×M₁₆	—	5	1	no	—
254	C₂²×C₃×C₈	—	5	1	no	—
255	C₃×C₄×D₄	—	5	1	no	—
256	D₄×Dic₃	—	5	1	no	—
257	C₄×#67	—	5	1	no	—
258	C₄×#67	—	5	1	no	—
259	C₂×#208	—	5	1	no	—
260	C₂²×C₃⋊C₈	—	5	1	no	—
261	D₃×M₁₆	—	10	4	no	—
262	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
263	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
264	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
265	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
266	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
267	C₂×ΓL(1,𝔽₂₅)	—	10	4	no	—
268	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic, complemented
269	C₂×D₃×C₈	—	5	1	no	—
270	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
271	#893	—	5	1	no	—
272	D₃×C₄⋊C₄	—	5	1	no	—
273	#67⋊C₄	—	5	1	no	—
274	#67⋊C₄	—	5	1	no	—
275	D₃×C₂²⋊C₄	—	5	1	no	—
276	D₃×C₂²⋊C₄	—	5	1	no	—
277	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
278	C₄²×D₃	—	5	1	no	—
279	C₃×C₄⋊C₈	—	5	1	no	—
280	C₃×C₂²⋊C₈	—	5	1	no	—
281	C₃×C₂²⋊C₈	—	5	1	no	—
282	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
283	#830	—	5	1	no	—
284	#830	—	5	1	no	—
285	(C₂×D₃)⋊C₈	—	5	1	no	—
286	(C₂×D₃)⋊C₈	—	5	1	no	—
287	(C₂×D₃)⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
288	(C₂×D₃)⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
289	Dic₃⋊C₈	—	5	1	no	—
290	Dic₃⋊C₈	—	5	1	no	—
291	C₈×Dic₃	—	5	1	no	—
292	C₈×Dic₃	—	5	1	no	—
293	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic, complemented
294	#803	—	5	1	no	—
295	C₂³×D₅	—	3	1	no	—
296	C₂³×D₅	—	3	1	no	—
297	C₂×C₅×D₄	—	3	1	no	—
298	C₂²×C₄×C₅	—	3	1	no	—
299	C₂²×C₄×C₅	—	3	1	no	—
300	C₂×C₂²⋊D₅	—	3	1	no	—
301	C₂×C₂²⋊D₅	—	3	1	no	—
302	C₂²×Dic₅	—	3	1	no	—
303	C₂²×Dic₅	—	3	1	no	—
304	D₄×D₅	—	6	4	no	—
305	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
306	C₂×C₄×D₅	—	3	1	no	—
307	C₂×C₄×D₅	—	3	1	no	—
308	C₂×C₄×D₅	—	3	1	no	—
309	C₂×C₄×D₅	—	3	1	no	—
310	C₂×C₄×D₅	—	3	1	no	—
311	C₂×C₄×D₅	—	3	1	no	—
312	C₂×C₄×D₅	—	3	1	no	—
313	C₂×C₄×D₅	—	6	2	no	—
314	C₂×C₄×D₅	—	6	2	no	—
315	C₂×C₄×D₅	—	6	2	no	—
316	C₂×C₄×D₅	—	6	2	no	—
317	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
318	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
319	C₅×M₁₆	—	6	2	no	—
320	C₂×C₅×C₈	—	3	1	no	—
321	C₂×C₅×C₈	—	3	1	no	—
322	C₂×C₅×C₈	—	6	2	no	—
323	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
324	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
325	C₅×C₄⋊C₄	—	3	1	no	—
326	C₅×C₂²⋊C₄	—	3	1	no	—
327	C₅×C₂²⋊C₄	—	3	1	no	—
328	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
329	C₂²⋊Dic₅	—	3	1	no	—
330	C₂²⋊Dic₅	—	3	1	no	—
331	#685	—	3	1	no	—
332	#685	—	3	1	no	—
333	#685	C₄×D₃	1	1	yes	characteristic
334	#685	C₄×D₃	1	1	yes	characteristic
335	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
336	#683	—	3	1	no	—
337	#683	—	3	1	no	—
338	C₄×Dic₅	—	3	1	no	—
339	C₄×Dic₅	—	3	1	no	—
340	C₄×Dic₅	—	3	1	no	—
341	#681	—	6	2	no	—
342	C₂×#168	—	3	1	no	—
343	C₂×#168	—	3	1	no	—
344	C₂×#168	—	6	2	no	—
345	C₂×#168	C₂²×D₃	1	1	yes	characteristic
346	C₂×#168	C₂²×D₃	1	1	yes	characteristic
347	#676	—	2	2	no	—
348	#676	—	3	4	no	—
349	#676	—	6	2	no	—
350	#676	—	6	2	no	—
351	#676	—	6	2	no	—
352	#676	—	6	2	no	—
353	C₈×D₅	—	2	2	no	—
354	C₈×D₅	—	6	2	no	—
355	C₂²×M₁₆	—	15	1	no	—
356	C₂²×M₁₆	—	15	1	no	—
357	C₂×C₄×D₄	—	15	1	no	—
358	#436	—	15	1	no	—
359	#436	—	15	1	no	—
360	#435	—	3	1	no	—
361	#435	—	5	1	no	—
362	#435	—	15	1	no	—
363	#435	—	15	1	no	—
364	C₈×D₄	—	15	1	no	—
365	C₈×D₄	—	15	1	no	—
366	#423	—	15	1	no	—
367	#407	—	15	1	no	—
368	#407	—	15	1	no	—
369	C₄×M₁₆	—	15	1	no	—
370	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
371	C₂×D₁₅	—	2	1	no	—
372	C₂×D₁₅	—	2	1	no	—
373	C₂×D₁₅	C₄×D₄	1	2	yes	—
374	C₂×C₅×D₃	—	2	1	no	—
375	C₂×C₅×D₃	—	2	1	no	—
376	C₂×C₅×D₃	—	2	1	no	—
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	complemented
380	C₂×C₃×D₅	—	2	1	no	—
381	C₂×C₃×D₅	—	2	1	no	—
382	C₂×C₃×D₅	—	2	1	no	—
383	C₂×C₃×D₅	—	2	1	no	—
384	C₂×C₃×D₅	—	2	1	no	—
385	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	complemented
386	D₃×D₅	—	4	4	no	—
387	D₃×D₅	—	4	4	no	—
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
391	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
392	Dic₁₅	—	2	1	no	—
393	Dic₁₅	C₄×D₄	1	2	yes	—
394	Dic₁₅	C₂×M₁₆	1	2	yes	complemented
395	C₃×Dic₅	—	2	1	no	—
396	C₃×Dic₅	—	2	1	no	—
397	C₅×Dic₃	—	2	1	no	—
398	C₅×Dic₃	—	2	1	no	—
399	C₂³×D₃	—	5	1	no	—
400	C₂³×D₃	—	5	1	no	—
401	C₂×C₃×D₄	—	5	1	no	—
402	C₂²×C₃×C₄	—	5	1	no	—
403	C₂²×C₃×C₄	—	5	1	no	—
404	C₂×#67	—	5	1	no	—
405	C₂×#67	—	5	1	no	—
406	C₂²×Dic₃	—	5	1	no	—
407	C₂²×Dic₃	—	5	1	no	—
408	D₃×D₄	—	10	4	no	—
409	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
410	C₂×C₄×D₃	—	5	1	no	—
411	C₂×C₄×D₃	—	5	1	no	—
412	C₂×C₄×D₃	—	5	1	no	—
413	C₂×C₄×D₃	—	5	1	no	—
414	C₂×C₄×D₃	—	5	1	no	—
415	C₂×C₄×D₃	—	5	1	no	—
416	C₂×C₄×D₃	—	5	1	no	—
417	C₂×C₄×D₃	—	10	2	no	—
418	C₂×C₄×D₃	—	10	2	no	—
419	C₂×C₄×D₃	—	10	2	no	—
420	C₂×C₄×D₃	—	10	2	no	—
421	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
422	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
423	C₃×M₁₆	—	10	2	no	—
424	C₂×C₃×C₈	—	5	1	no	—
425	C₂×C₃×C₈	—	5	1	no	—
426	C₂×C₃×C₈	—	10	2	no	—
427	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
428	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
429	C₃×C₄⋊C₄	—	5	1	no	—
430	C₃×C₂²⋊C₄	—	5	1	no	—
431	C₃×C₂²⋊C₄	—	5	1	no	—
432	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
433	#217	—	5	1	no	—
434	#217	—	5	1	no	—
435	(C₂×D₃)⋊C₄	—	5	1	no	—
436	(C₂×D₃)⋊C₄	—	5	1	no	—
437	(C₂×D₃)⋊C₄	C₄×D₅	1	1	yes	characteristic
438	(C₂×D₃)⋊C₄	C₄×D₅	1	1	yes	characteristic
439	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
440	Dic₃⋊C₄	—	5	1	no	—
441	Dic₃⋊C₄	—	5	1	no	—
442	C₄×Dic₃	—	5	1	no	—
443	C₄×Dic₃	—	5	1	no	—
444	C₄×Dic₃	—	5	1	no	—
445	#208	—	10	2	no	—
446	C₂×C₃⋊C₈	—	5	1	no	—
447	C₂×C₃⋊C₈	—	5	1	no	—
448	C₂×C₃⋊C₈	—	10	2	no	—
449	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
450	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
451	ΓL(1,𝔽₂₅)	—	2	2	no	—
452	ΓL(1,𝔽₂₅)	—	5	4	no	—
453	ΓL(1,𝔽₂₅)	—	10	2	no	—
454	ΓL(1,𝔽₂₅)	—	10	2	no	—
455	ΓL(1,𝔽₂₅)	—	10	2	no	—
456	ΓL(1,𝔽₂₅)	—	10	2	no	—
457	D₃×C₈	—	2	2	no	—
458	D₃×C₈	—	10	2	no	—
459	C₂³×C₅	—	3	1	no	—
460	C₂³×C₅	—	3	1	no	—
461	C₂²×D₅	—	3	1	no	—
462	C₂²×D₅	—	6	2	no	—
463	C₂²×D₅	—	6	2	no	—
464	C₂²×D₅	—	6	2	no	—
465	C₂²×D₅	—	6	2	no	—
466	C₂²×D₅	—	12	1	no	—
467	C₂²×D₅	—	12	1	no	—
468	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
469	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
470	C₅×D₄	—	6	2	no	—
471	C₂×C₄×C₅	—	3	1	no	—
472	C₂×C₄×C₅	—	3	1	no	—
473	C₂×C₄×C₅	—	6	1	no	—
474	C₂×C₄×C₅	—	6	1	no	—
475	C₂×C₄×C₅	—	6	1	no	—
476	C₂×C₄×C₅	—	6	1	no	—
477	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
478	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
479	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
480	C₂²⋊D₅	—	3	4	no	—
481	C₂²⋊D₅	—	6	2	no	—
482	C₂×Dic₅	—	3	1	no	—
483	C₂×Dic₅	—	3	1	no	—
484	C₂×Dic₅	—	3	1	no	—
485	C₂×Dic₅	—	6	2	no	—
486	C₂×Dic₅	—	6	2	no	—
487	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
488	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
489	D₂₀	—	2	2	no	—
490	C₄×D₅	—	2	1	no	—
491	C₄×D₅	—	2	1	no	—
492	C₄×D₅	—	2	1	no	—
493	C₄×D₅	—	2	1	no	—
494	C₄×D₅	—	3	2	no	—
495	C₄×D₅	—	3	2	no	—
496	C₄×D₅	—	6	2	no	—
497	C₄×D₅	—	6	2	no	—
498	C₄×D₅	—	6	2	no	—
499	C₄×D₅	—	6	2	no	—
500	C₄×D₅	—	6	2	no	—
501	C₄×D₅	—	12	1	no	—
502	C₅×C₈	—	2	1	no	—
503	C₅×C₈	—	6	1	no	—
504	C₅×C₈	—	6	1	no	—
505	C₅×C₈	D₃×D₄	1	2	yes	complemented
506	#168	—	2	1	no	—
507	#168	—	2	1	no	—
508	#168	—	3	2	no	—
509	#168	—	6	1	no	—
510	C₂²×D₄	—	15	1	no	—
511	C₂³×C₄	—	15	1	no	—
512	C₂³×C₄	—	15	1	no	—
513	C₂×M₁₆	—	3	1	no	—
514	C₂×M₁₆	—	5	1	no	—
515	C₂×M₁₆	—	15	1	no	—
516	C₂×M₁₆	—	15	1	no	—
517	C₂×M₁₆	—	15	1	no	—
518	C₂×M₁₆	—	15	1	no	—
519	C₂×M₁₆	—	15	1	no	—
520	C₂×M₁₆	—	15	1	no	—
521	C₂×M₁₆	—	30	4	no	—
522	C₂×M₁₆	—	30	4	no	—
523	C₂²×C₈	—	3	1	no	—
524	C₂²×C₈	—	5	1	no	—
525	C₂²×C₈	—	15	1	no	—
526	C₂²×C₈	—	15	1	no	—
527	C₄×D₄	—	3	1	no	—
528	C₄×D₄	—	5	1	no	—
529	C₄×D₄	—	15	1	no	—
530	C₄×D₄	—	15	1	no	—
531	C₄×D₄	—	15	1	no	—
532	C₄×D₄	—	15	1	no	—
533	C₄×D₄	—	15	1	no	—
534	C₄×D₄	—	15	1	no	—
535	C₂×C₄⋊C₄	—	15	1	no	—
536	C₂×C₂²⋊C₄	—	15	1	no	—
537	C₂×C₂²⋊C₄	—	15	1	no	—
538	C₂×C₄²	—	15	1	no	—
539	C₄⋊C₈	—	3	1	no	—
540	C₄⋊C₈	—	5	1	no	—
541	C₄⋊C₈	—	15	1	no	—
542	C₄⋊C₈	—	15	1	no	—
543	C₂²⋊C₈	—	3	1	no	—
544	C₂²⋊C₈	—	3	1	no	—
545	C₂²⋊C₈	—	5	1	no	—
546	C₂²⋊C₈	—	5	1	no	—
547	C₂²⋊C₈	—	15	1	no	—
548	C₂²⋊C₈	—	15	1	no	—
549	C₂²⋊C₈	—	15	1	no	—
550	C₂²⋊C₈	—	15	1	no	—
551	#97	—	15	1	no	—
552	#97	D₃×D₅	1	1	yes	characteristic, complemented
553	C₄×C₈	—	15	1	no	—
554	C₄×C₈	—	15	1	no	—
555	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
556	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
557	C₂×C₃×C₅	#568	1	1	yes	characteristic
558	D₁₅	—	2	2	no	—
559	C₃×D₅	—	2	2	no	—
560	C₃×D₅	—	4	1	no	—
561	C₅×D₃	—	2	2	no	—
562	C₅×D₃	—	4	1	no	—
563	C₂³×C₃	—	5	1	no	—
564	C₂³×C₃	—	5	1	no	—
565	C₂²×D₃	—	5	1	no	—
566	C₂²×D₃	—	10	2	no	—
567	C₂²×D₃	—	10	2	no	—
568	C₂²×D₃	—	10	2	no	—
569	C₂²×D₃	—	10	2	no	—
570	C₂²×D₃	—	20	1	no	—
571	C₂²×D₃	—	20	1	no	—
572	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
573	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
574	C₃×D₄	—	10	2	no	—
575	C₂×C₃×C₄	—	5	1	no	—
576	C₂×C₃×C₄	—	5	1	no	—
577	C₂×C₃×C₄	—	10	1	no	—
578	C₂×C₃×C₄	—	10	1	no	—
579	C₂×C₃×C₄	—	10	1	no	—
580	C₂×C₃×C₄	—	10	1	no	—
581	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
582	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
584	#67	—	5	4	no	—
585	#67	—	10	2	no	—
586	C₂×Dic₃	—	5	1	no	—
587	C₂×Dic₃	—	5	1	no	—
588	C₂×Dic₃	—	5	1	no	—
589	C₂×Dic₃	—	10	2	no	—
590	C₂×Dic₃	—	10	2	no	—
591	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
592	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
593	D₁₂	—	2	2	no	—
594	C₄×D₃	—	2	1	no	—
595	C₄×D₃	—	2	1	no	—
596	C₄×D₃	—	2	1	no	—
597	C₄×D₃	—	2	1	no	—
598	C₄×D₃	—	5	2	no	—
599	C₄×D₃	—	5	2	no	—
600	C₄×D₃	—	10	2	no	—
601	C₄×D₃	—	10	2	no	—
602	C₄×D₃	—	10	2	no	—
603	C₄×D₃	—	10	2	no	—
604	C₄×D₃	—	10	2	no	—
605	C₄×D₃	—	20	1	no	—
606	C₃×C₈	—	2	1	no	—
607	C₃×C₈	—	10	1	no	—
608	C₃×C₈	—	10	1	no	—
609	C₃×C₈	D₄×D₅	1	2	yes	complemented
610	C₃⋊C₈	—	2	1	no	—
611	C₃⋊C₈	—	2	1	no	—
612	C₃⋊C₈	—	5	2	no	—
613	C₃⋊C₈	—	10	1	no	—
614	C₂²×C₅	—	3	2	no	—
615	C₂²×C₅	—	6	1	no	—
616	C₂²×C₅	—	6	1	no	—
617	C₂²×C₅	—	6	1	no	—
618	C₂²×C₅	—	6	1	no	—
619	C₂²×C₅	—	6	1	no	—
620	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
621	C₂×D₅	—	2	1	no	—
622	C₂×D₅	—	2	1	no	—
623	C₂×D₅	—	2	1	no	—
624	C₂×D₅	—	2	1	no	—
625	C₂×D₅	—	2	1	no	—
626	C₂×D₅	—	3	2	no	—
627	C₂×D₅	—	6	1	no	—
628	C₂×D₅	—	6	1	no	—
629	C₂×D₅	—	12	4	no	—
630	C₂×D₅	—	12	4	no	—
631	C₂×D₅	D₃×M₁₆	1	2	yes	complemented
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	2	1	no	—
634	C₄×C₅	—	6	1	no	—
635	C₄×C₅	—	6	1	no	—
636	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
637	C₄×C₅	D₃×#41	1	1	yes	characteristic
638	Dic₅	—	2	1	no	—
639	Dic₅	—	2	1	no	—
640	Dic₅	—	3	2	no	—
641	Dic₅	—	3	2	no	—
642	Dic₅	—	6	1	no	—
643	C₂⁴	—	15	1	no	—
644	C₂⁴	—	15	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	5	1	no	—
647	C₂×D₄	—	15	1	no	—
648	C₂×D₄	—	15	1	no	—
649	C₂×D₄	—	30	4	no	—
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	5	1	no	—
653	C₂²×C₄	—	5	1	no	—
654	C₂²×C₄	—	15	1	no	—
655	C₂²×C₄	—	15	1	no	—
656	C₂²×C₄	—	15	1	no	—
657	C₂²×C₄	—	15	1	no	—
658	C₂²×C₄	—	15	1	no	—
659	C₂²×C₄	—	15	1	no	—
660	C₂²×C₄	—	15	1	no	—
661	C₂²×C₄	—	15	1	no	—
662	C₂²×C₄	—	15	1	no	—
663	C₂²×C₄	—	30	2	no	—
664	C₂²×C₄	—	30	2	no	—
665	C₂²×C₄	—	30	2	no	—
666	C₂²×C₄	—	30	2	no	—
667	M₁₆	—	6	2	no	—
668	M₁₆	—	10	2	no	—
669	M₁₆	—	15	4	no	—
670	M₁₆	—	30	2	no	—
671	M₁₆	—	30	2	no	—
672	M₁₆	—	30	2	no	—
673	M₁₆	—	30	2	no	—
674	M₁₆	—	30	2	no	—
675	C₂×C₈	—	3	1	no	—
676	C₂×C₈	—	3	1	no	—
677	C₂×C₈	—	5	1	no	—
678	C₂×C₈	—	5	1	no	—
679	C₂×C₈	—	6	2	no	—
680	C₂×C₈	—	10	2	no	—
681	C₂×C₈	—	15	1	no	—
682	C₂×C₈	—	15	1	no	—
683	C₂×C₈	—	30	2	no	—
684	C₂×C₈	—	30	2	no	—
685	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
686	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
687	C₄⋊C₄	—	3	1	no	—
688	C₄⋊C₄	—	5	1	no	—
689	C₄⋊C₄	—	15	1	no	—
690	C₄⋊C₄	—	15	1	no	—
691	C₂²⋊C₄	—	3	1	no	—
692	C₂²⋊C₄	—	3	1	no	—
693	C₂²⋊C₄	—	5	1	no	—
694	C₂²⋊C₄	—	5	1	no	—
695	C₂²⋊C₄	—	15	1	no	—
696	C₂²⋊C₄	—	15	1	no	—
697	C₂²⋊C₄	—	15	1	no	—
698	C₂²⋊C₄	—	15	1	no	—
699	C₄²	—	15	1	no	—
700	C₄²	—	15	1	no	—
701	C₄²	—	15	1	no	—
702	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
703	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
704	C₂²×C₃	—	5	2	no	—
705	C₂²×C₃	—	10	1	no	—
706	C₂²×C₃	—	10	1	no	—
707	C₂²×C₃	—	10	1	no	—
708	C₂²×C₃	—	10	1	no	—
709	C₂²×C₃	—	10	1	no	—
710	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
711	C₂×D₃	—	2	1	no	—
712	C₂×D₃	—	2	1	no	—
713	C₂×D₃	—	2	1	no	—
714	C₂×D₃	—	2	1	no	—
715	C₂×D₃	—	2	1	no	—
716	C₂×D₃	—	5	2	no	—
717	C₂×D₃	—	10	1	no	—
718	C₂×D₃	—	10	1	no	—
719	C₂×D₃	—	20	4	no	—
720	C₂×D₃	—	20	4	no	—
721	C₂×D₃	D₅×M₁₆	1	2	yes	complemented
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	10	1	no	—
725	C₃×C₄	—	10	1	no	—
726	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
727	C₃×C₄	D₅×#41	1	1	yes	characteristic
728	Dic₃	—	2	1	no	—
729	Dic₃	—	2	1	no	—
730	Dic₃	—	5	2	no	—
731	Dic₃	—	5	2	no	—
732	Dic₃	—	10	1	no	—
733	C₂×C₅	—	6	2	no	—
734	C₂×C₅	—	12	1	no	—
735	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
736	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
737	C₂×C₅	#5750	1	1	yes	characteristic
738	D₅	—	2	2	no	—
739	D₅	—	4	1	no	—
740	D₅	—	6	2	no	—
741	C₂³	—	3	1	no	—
742	C₂³	—	3	1	no	—
743	C₂³	—	5	1	no	—
744	C₂³	—	5	1	no	—
745	C₂³	—	15	1	no	—
746	C₂³	—	30	2	no	—
747	C₂³	—	30	2	no	—
748	C₂³	—	30	2	no	—
749	C₂³	—	30	2	no	—
750	C₂³	—	60	1	no	—
751	C₂³	—	60	1	no	—
752	D₄	—	6	2	no	—
753	D₄	—	10	2	no	—
754	D₄	—	15	4	no	—
755	D₄	—	30	2	no	—
756	C₂×C₄	—	3	1	no	—
757	C₂×C₄	—	3	1	no	—
758	C₂×C₄	—	5	1	no	—
759	C₂×C₄	—	5	1	no	—
760	C₂×C₄	—	6	1	no	—
761	C₂×C₄	—	6	1	no	—
762	C₂×C₄	—	6	1	no	—
763	C₂×C₄	—	6	1	no	—
764	C₂×C₄	—	10	1	no	—
765	C₂×C₄	—	10	1	no	—
766	C₂×C₄	—	10	1	no	—
767	C₂×C₄	—	10	1	no	—
768	C₂×C₄	—	15	1	no	—
769	C₂×C₄	—	15	1	no	—
770	C₂×C₄	—	15	2	no	—
771	C₂×C₄	—	15	2	no	—
772	C₂×C₄	—	15	1	no	—
773	C₂×C₄	—	30	2	no	—
774	C₂×C₄	—	30	2	no	—
775	C₂×C₄	—	30	2	no	—
776	C₂×C₄	—	30	2	no	—
777	C₂×C₄	—	30	2	no	—
778	C₂×C₄	—	30	2	no	—
779	C₂×C₄	—	30	2	no	—
780	C₂×C₄	—	60	1	no	—
781	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
782	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
784	C₈	—	2	1	no	—
785	C₈	—	6	1	no	—
786	C₈	—	6	1	no	—
787	C₈	—	10	1	no	—
788	C₈	—	10	1	no	—
789	C₈	—	15	2	no	—
790	C₈	—	30	1	no	—
791	C₈	#6777	1	2	yes	complemented
792	C₂×C₃	—	10	2	no	—
793	C₂×C₃	—	20	1	no	—
794	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
795	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
796	C₂×C₃	#66084	1	1	yes	characteristic
797	D₃	—	2	2	no	—
798	D₃	—	4	1	no	—
799	D₃	—	10	2	no	—
800	C₅	#79483	1	1	yes	characteristic, complemented, Sylow
801	C₂²	—	3	2	no	—
802	C₂²	—	5	2	no	—
803	C₂²	—	6	1	no	—
804	C₂²	—	6	1	no	—
805	C₂²	—	6	1	no	—
806	C₂²	—	6	1	no	—
807	C₂²	—	6	1	no	—
808	C₂²	—	10	1	no	—
809	C₂²	—	10	1	no	—
810	C₂²	—	10	1	no	—
811	C₂²	—	10	1	no	—
812	C₂²	—	10	1	no	—
813	C₂²	—	15	2	no	—
814	C₂²	—	30	1	no	—
815	C₂²	—	30	1	no	—
816	C₂²	—	60	4	no	—
817	C₂²	—	60	4	no	—
818	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	6	1	no	—
822	C₄	—	6	1	no	—
823	C₄	—	10	1	no	—
824	C₄	—	10	1	no	—
825	C₄	—	15	2	no	—
826	C₄	—	15	2	no	—
827	C₄	—	30	1	no	—
828	C₄	C₂×#6777	1	1	yes	characteristic
829	C₄	#92016	1	1	yes	characteristic
830	C₃	#10611214	1	1	yes	characteristic, complemented, Sylow
831	C₂	—	6	2	no	—
832	C₂	—	10	2	no	—
833	C₂	—	12	1	no	—
834	C₂	—	20	1	no	—
835	C₂	—	30	2	no	—
836	C₂	C₄×#6777	1	1	yes	characteristic
837	C₂	D₃×D₅×M₁₆	1	1	yes	characteristic
838	C₂	#11754018	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#97	C₂²
prime radical	C₂×#6777	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#97	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×#676	C₂	semidirect
2. C₂×D₅×ΓL(1,𝔽₂₅)	C₂	semidirect
4. #11750808	C₂	semidirect
5. C₅×#4706	C₂	semidirect
6. C₃×#64995	C₂	semidirect
7. #11748103	C₂	semidirect
8. #11748103	C₂	semidirect
9. #11747722	C₂	semidirect
10. #11747721	C₂	semidirect
11. #11747696	C₂	semidirect
12. C₈×#1201	C₂	semidirect
13. #11747015	C₂	semidirect
14. #11746999	C₂	semidirect
15. #11746997	C₂	semidirect
23. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
24. C₂×C₅×D₃×C₈	C₂²	semidirect
26. C₂×C₃×#676	C₂²	semidirect
27. C₂×C₃×C₈×D₅	C₂²	semidirect
40. C₂×#6650	C₂²	semidirect
41. C₂×#6649	C₂²	semidirect
42. C₂×D₃×#168	C₂²	semidirect
43. C₂×D₅×C₃⋊C₈	C₂²	semidirect
46. C₃×C₅×#97	C₂²	semidirect
47. C₈×Dic₁₅	C₂²	semidirect
48. C₈×Dic₁₅	C₂²	semidirect
49. #91087	C₂²	semidirect
50. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
51. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
52. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
53. C₃×#3952	C₂²	semidirect
54. C₃×#3952	C₂²	semidirect
55. C₃×C₄⋊#168	C₂²	semidirect
56. #90983	C₂²	semidirect
57. #90983	C₂²	semidirect
58. (C₂×D₃)⋊#168	C₂²	semidirect
59. (C₂×D₃)⋊#168	C₂²	semidirect
60. #90955	C₂²	semidirect
61. #90955	C₂²	semidirect
77. #64995	D₃	semidirect
111. #6705	D₄	semidirect
152. #4706	D₅	semidirect
171. C₂×#676	C₂×D₃	semidirect
173. C₂×C₈×D₅	C₂×D₃	semidirect
185. C₅×#97	C₂×D₃	semidirect
190. #3952	C₂×D₃	semidirect
191. #3952	C₂×D₃	semidirect
196. C₄⋊#168	C₂×D₃	semidirect
235. #1201	M₁₆	semidirect
243. C₃×C₅×C₈	C₂×D₄	semidirect
245. C₃⋊#168	C₂×D₄	semidirect
268. C₂×ΓL(1,𝔽₂₅)	C₂×D₅	semidirect
270. C₂×D₃×C₈	C₂×D₅	semidirect
282. C₃×#97	C₂×D₅	semidirect
287. (C₂×D₃)⋊C₈	C₂×D₅	semidirect
288. (C₂×D₃)⋊C₈	C₂×D₅	semidirect
293. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
379. C₂×C₅×D₃	C₂×M₁₆	semidirect
385. C₂×C₃×D₅	C₂×M₁₆	semidirect
394. Dic₁₅	C₂×M₁₆	semidirect
505. C₅×C₈	D₃×D₄	semidirect
552. #97	D₃×D₅	semidirect
609. C₃×C₈	D₄×D₅	semidirect
631. C₂×D₅	D₃×M₁₆	semidirect
703. C₃×C₅	D₄×M₁₆	semidirect
721. C₂×D₃	D₅×M₁₆	semidirect
791. C₈	#6777	semidirect
800. C₅	#79483	semidirect
830. C₃	#10611214	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×#676	2
C₂×D₅×ΓL(1,𝔽₂₅)	2
C₄×#6777	2
#11750808	2
C₅×#4706	2
C₃×#64995	2
#11748103	2
#11747722	2
#11747721	2
#11747696	2
C₈×#1201	2
#11747015	2
#11746999	2
#11746997	2
#10611214	3
#79483	5