Subgroups — #14418861

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	#11750929	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4837	C₂	1	1	yes	maximal, characteristic
4	C₃×#65117	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747602	C₂	1	1	yes	maximal, characteristic
6	#11747590	C₂	1	1	yes	maximal, characteristic
7	#11747590	C₂	1	1	yes	maximal, characteristic
8	Dic₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
9	#11747569	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747568	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747566	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747564	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747005	C₂	1	1	yes	maximal, characteristic
14	#11746852	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746848	C₂	1	1	yes	maximal, characteristic, complemented
16	#10610777	—	3	1	no	maximal, Hall
17	C₂×D₃×Dic₁₀	C₄	1	1	yes	characteristic
18	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
19	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
21	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
23	C₄×#1204	C₂²	1	1	yes	characteristic
24	C₄×#1204	C₂²	1	1	yes	characteristic
25	D₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
26	D₃×#683	C₄	1	1	yes	characteristic
27	D₃×#683	C₄	1	1	yes	characteristic
28	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
29	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
30	#91340	C₄	1	1	yes	characteristic
31	Dic₃×Dic₁₀	C₄	1	1	yes	characteristic
32	#91324	C₄	1	1	yes	characteristic
33	#91324	C₄	1	1	yes	characteristic
34	C₂×#6650	C₂²	1	1	yes	characteristic
35	C₂×#6650	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	#91099	C₂²	1	1	yes	characteristic
38	#91098	C₂²	1	1	yes	characteristic
39	#91098	C₂²	1	1	yes	characteristic
40	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
41	#91087	C₂²	1	1	yes	characteristic
42	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
44	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
45	C₃×#3947	C₂²	1	1	yes	characteristic
46	C₃×#3946	C₂²	1	1	yes	characteristic
47	C₃×#3946	C₂²	1	1	yes	characteristic
48	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
49	C₃×#3935	C₂²	1	1	yes	characteristic
50	#90983	C₂²	1	1	yes	characteristic
51	#90983	C₂²	1	1	yes	characteristic
52	#90982	C₂²	1	1	yes	characteristic
53	#90982	C₂²	1	1	yes	characteristic
54	#90954	C₂²	1	1	yes	characteristic
55	#90952	C₂²	1	1	yes	characteristic
56	#90951	C₂²	1	1	yes	characteristic
57	Dic₃×#168	C₂²	1	1	yes	characteristic
58	Dic₃×#168	C₂²	1	1	yes	characteristic
59	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	#79962	—	5	1	no	maximal, Hall
61	C₂×C₄×Dic₁₀	—	3	1	no	—
62	C₅×#423	—	3	1	no	—
63	#65407	—	3	1	no	—
64	#65407	—	3	1	no	—
65	M₁₆×Dic₅	—	3	1	no	—
66	M₁₆×Dic₅	—	3	1	no	—
67	C₄×#681	—	3	1	no	—
68	#65120	—	3	1	no	—
69	#65120	—	3	1	no	—
70	#65119	—	3	1	no	—
71	#65119	—	3	1	no	—
72	#65117	—	3	1	no	—
73	#65117	—	3	1	no	—
74	#65117	—	3	1	no	—
75	#65117	D₃	1	1	yes	characteristic, complemented
76	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
81	C₂×#1204	C₂×C₄	1	1	yes	characteristic
82	C₂×#1204	C₂×C₄	1	1	yes	characteristic
83	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
87	D₃×Dic₁₀	—	2	4	no	—
88	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
92	#6712	C₂×C₄	1	1	yes	characteristic
93	#6712	C₂×C₄	1	1	yes	characteristic
94	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
95	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
96	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
97	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
98	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
99	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
100	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
103	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
104	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
105	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
106	C₃×#683	C₂×C₄	1	1	yes	characteristic
107	C₃×#683	C₂×C₄	1	1	yes	characteristic
108	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
109	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
110	C₂×C₃×#168	C₂³	1	1	yes	characteristic
111	C₂×C₃×#168	C₂³	1	1	yes	characteristic
112	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
113	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
114	#6669	C₂×C₄	1	1	yes	characteristic
115	#6669	C₂×C₄	1	1	yes	characteristic
116	#6668	C₂×C₄	1	1	yes	characteristic
117	#6668	C₂×C₄	1	1	yes	characteristic
118	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
119	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
120	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
121	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
122	#6650	—	2	2	no	—
123	#6650	Q₈	1	4	yes	complemented
124	C₄×D₃×Q₈	—	5	1	no	—
125	C₃×#446	—	5	1	no	—
126	#5024	—	5	1	no	—
127	#4837	—	5	1	no	—
128	#4837	—	5	1	no	—
129	#4837	D₅	1	1	yes	characteristic
130	#4830	—	5	1	no	—
131	#4828	—	5	1	no	—
132	#4828	—	5	1	no	—
133	#4707	—	5	1	no	—
134	#4707	—	5	1	no	—
135	#4701	—	5	1	no	—
136	#4701	—	5	1	no	—
137	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
138	C₈×Dic₆	—	5	1	no	—
139	C₂²×Dic₁₀	—	3	1	no	—
140	C₂×C₅×M₁₆	—	3	1	no	—
141	C₂×C₅×M₁₆	—	3	1	no	—
142	C₂×C₄²×C₅	—	3	1	no	—
143	C₂×C₄⋊Dic₅	—	3	1	no	—
144	C₂×#683	—	3	1	no	—
145	C₂×#683	—	3	1	no	—
146	C₂×C₄×Dic₅	—	3	1	no	—
147	C₂×C₄×Dic₅	—	3	1	no	—
148	C₂×#681	—	3	1	no	—
149	C₂×#681	—	3	1	no	—
150	C₄×Dic₁₀	—	3	1	no	—
151	C₄×Dic₁₀	—	3	1	no	—
152	C₄×Dic₁₀	—	3	1	no	—
153	C₄×Dic₁₀	—	3	1	no	—
154	C₄×Dic₁₀	—	3	1	no	—
155	C₄×Dic₁₀	—	3	1	no	—
156	C₄×Dic₁₀	—	3	1	no	—
157	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
158	C₅×C₄⋊C₈	—	3	1	no	—
159	C₅×C₄⋊C₈	—	3	1	no	—
160	C₅×C₄⋊C₈	—	3	1	no	—
161	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
162	#3947	—	3	1	no	—
163	#3947	—	3	1	no	—
164	#3947	—	3	1	no	—
165	#3947	C₂×D₃	1	1	yes	characteristic
166	#3946	—	3	1	no	—
167	#3946	—	3	1	no	—
168	#3946	—	3	1	no	—
169	#3946	—	3	1	no	—
170	#3946	—	3	1	no	—
171	#3946	—	3	1	no	—
172	#3946	C₂×D₃	1	1	yes	characteristic
173	#3946	C₂×D₃	1	1	yes	characteristic
174	C₈×Dic₅	—	3	1	no	—
175	C₈×Dic₅	—	3	1	no	—
176	C₈×Dic₅	—	3	1	no	—
177	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
178	#3935	—	3	1	no	—
179	#3935	C₂×D₃	1	1	yes	characteristic
180	C₄×#168	—	3	1	no	—
181	C₄×#168	—	3	1	no	—
182	Q₈×M₁₆	—	15	1	no	Sylow
183	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
188	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
189	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
191	Dic₃₀	—	2	2	no	—
192	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
195	C₄×C₅×D₃	—	2	2	no	—
196	C₄×C₅×D₃	—	4	1	no	—
197	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
198	C₄×C₅×D₃	#41	1	2	yes	—
199	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
203	C₃×Dic₁₀	—	2	2	no	—
204	#1204	—	2	2	no	—
205	#1204	M₁₆	1	4	yes	complemented
206	D₃×Dic₅	—	2	2	no	—
207	D₃×Dic₅	—	2	2	no	—
208	D₃×Dic₅	—	4	1	no	—
209	D₃×Dic₅	—	4	1	no	—
210	C₃×C₅×C₈	—	2	1	no	—
211	C₃×C₅×C₈	—	2	1	no	—
212	C₃⋊#168	—	2	1	no	—
213	C₃⋊#168	C₂×Q₈	1	2	yes	complemented
214	C₃×#168	—	2	1	no	—
215	C₃×#168	C₂×Q₈	1	2	yes	complemented
216	C₅×C₃⋊C₈	—	2	1	no	—
217	C₅×C₃⋊C₈	—	2	1	no	—
218	C₂×D₃×Q₈	—	5	1	no	—
219	C₃×C₄×Q₈	—	5	1	no	—
220	Q₈×Dic₃	—	5	1	no	—
221	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
222	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
223	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
224	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
225	D₃×C₄⋊C₄	—	5	1	no	—
226	D₃×C₄⋊C₄	—	5	1	no	—
227	D₃×C₄⋊C₄	—	5	1	no	—
228	#887	—	5	1	no	—
229	#887	—	5	1	no	—
230	#887	—	5	1	no	—
231	C₄²×D₃	—	5	1	no	—
232	C₄²×D₃	—	5	1	no	—
233	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
234	C₄×Dic₆	—	5	1	no	—
235	C₄×Dic₆	—	5	1	no	—
236	C₄×Dic₆	—	5	1	no	—
237	C₃×C₄⋊C₈	—	5	1	no	—
238	C₃×C₄⋊C₈	—	5	1	no	—
239	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
240	C₃×#97	—	5	1	no	—
241	C₃×#97	—	5	1	no	—
242	C₃×C₄×C₈	—	5	1	no	—
243	#815	—	5	1	no	—
244	#815	—	5	1	no	—
245	Dic₃⋊C₈	—	5	1	no	—
246	Dic₃⋊C₈	—	5	1	no	—
247	Dic₃⋊C₈	—	5	1	no	—
248	Dic₃⋊C₈	—	5	1	no	—
249	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
250	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
251	C₈×Dic₃	—	5	1	no	—
252	C₈×Dic₃	—	5	1	no	—
253	C₈×Dic₃	—	5	1	no	—
254	C₈×Dic₃	—	5	1	no	—
255	C₄⋊(C₃⋊C₈)	—	5	1	no	—
256	C₄⋊(C₃⋊C₈)	—	5	1	no	—
257	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
258	#803	—	5	1	no	—
259	#803	—	5	1	no	—
260	C₄×C₃⋊C₈	—	5	1	no	—
261	C₂²×C₄×C₅	—	3	1	no	—
262	C₂²×C₄×C₅	—	3	1	no	—
263	C₂²×C₄×C₅	—	3	1	no	—
264	C₂²×Dic₅	—	3	1	no	—
265	C₂²×Dic₅	—	3	1	no	—
266	C₂²×Dic₅	—	3	1	no	—
267	C₂²×Dic₅	—	3	1	no	—
268	C₂×Dic₁₀	—	3	1	no	—
269	C₂×Dic₁₀	—	3	1	no	—
270	C₂×Dic₁₀	—	3	1	no	—
271	C₂×Dic₁₀	—	6	4	no	—
272	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
273	C₅×M₁₆	—	6	2	no	—
274	C₅×M₁₆	—	6	2	no	—
275	C₂×C₅×C₈	—	3	1	no	—
276	C₂×C₅×C₈	—	3	1	no	—
277	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
278	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
279	C₄²×C₅	—	3	1	no	—
280	C₄²×C₅	—	3	1	no	—
281	C₄²×C₅	—	3	1	no	—
282	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
283	C₄⋊Dic₅	—	3	1	no	—
284	C₄⋊Dic₅	—	3	1	no	—
285	C₄⋊Dic₅	—	3	1	no	—
286	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
287	#683	—	3	1	no	—
288	#683	—	3	1	no	—
289	#683	—	3	1	no	—
290	#683	—	3	1	no	—
291	#683	—	3	1	no	—
292	#683	—	3	1	no	—
293	#683	C₄×D₃	1	1	yes	characteristic
294	#683	C₄×D₃	1	1	yes	characteristic
295	C₄×Dic₅	—	3	1	no	—
296	C₄×Dic₅	—	3	1	no	—
297	C₄×Dic₅	—	3	1	no	—
298	C₄×Dic₅	—	3	1	no	—
299	C₄×Dic₅	—	3	1	no	—
300	C₄×Dic₅	—	3	1	no	—
301	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
302	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
303	#681	—	3	4	no	—
304	#681	—	6	2	no	—
305	C₂×#168	—	3	1	no	—
306	C₂×#168	—	3	1	no	—
307	C₂×#168	C₂²×D₃	1	1	yes	characteristic
308	C₂×#168	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₄×Q₈	—	15	1	no	—
310	#446	—	5	1	no	—
311	#446	—	15	1	no	—
312	#446	—	15	1	no	—
313	#446	—	15	1	no	—
314	#446	—	15	1	no	—
315	#446	—	15	1	no	—
316	C₈×Q₈	—	15	1	no	—
317	C₈×Q₈	—	15	1	no	—
318	#423	—	3	1	no	—
319	#423	—	15	1	no	—
320	#423	—	15	1	no	—
321	C₄×M₁₆	—	15	1	no	—
322	C₄×M₁₆	—	15	1	no	—
323	C₄×M₁₆	—	15	1	no	—
324	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
325	C₂×C₅×D₃	—	2	1	no	—
326	C₂×C₅×D₃	—	2	1	no	—
327	C₂×C₅×D₃	C₄×Q₈	1	2	yes	—
328	C₃×C₄×C₅	—	2	1	no	—
329	C₃×C₄×C₅	—	2	1	no	—
330	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
331	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
332	Dic₁₅	—	2	1	no	—
333	Dic₁₅	—	2	1	no	—
334	Dic₁₅	—	2	1	no	—
335	Dic₁₅	C₂×M₁₆	1	2	yes	—
336	C₃×Dic₅	—	2	1	no	—
337	C₃×Dic₅	—	2	1	no	—
338	C₃×Dic₅	—	2	1	no	—
339	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
340	C₅×Dic₃	—	2	1	no	—
341	C₅×Dic₃	C₄×Q₈	1	2	yes	—
342	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
343	C₂×C₃×Q₈	—	5	1	no	—
344	D₃×Q₈	—	10	4	no	—
345	C₂×C₄×D₃	—	5	1	no	—
346	C₂×C₄×D₃	—	5	1	no	—
347	C₂×C₄×D₃	—	5	1	no	—
348	C₂×C₄×D₃	—	5	1	no	—
349	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
350	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
351	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
352	C₂×Dic₆	—	5	1	no	—
353	C₂×Dic₆	—	5	1	no	—
354	C₂×Dic₆	—	5	1	no	—
355	C₂×C₃×C₈	—	5	1	no	—
356	C₂×C₃×C₈	—	5	1	no	—
357	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
358	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
359	C₃×C₄⋊C₄	—	5	1	no	—
360	C₃×C₄⋊C₄	—	5	1	no	—
361	C₃×C₄⋊C₄	—	5	1	no	—
362	C₃×C₄²	—	5	1	no	—
363	C₃×C₄²	—	5	1	no	—
364	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
365	C₄⋊Dic₃	—	5	1	no	—
366	C₄⋊Dic₃	—	5	1	no	—
367	C₄⋊Dic₃	—	5	1	no	—
368	Dic₃⋊C₄	—	5	1	no	—
369	Dic₃⋊C₄	—	5	1	no	—
370	Dic₃⋊C₄	—	5	1	no	—
371	Dic₃⋊C₄	—	5	1	no	—
372	Dic₃⋊C₄	—	5	1	no	—
373	Dic₃⋊C₄	—	5	1	no	—
374	C₄×Dic₃	—	5	1	no	—
375	C₄×Dic₃	—	5	1	no	—
376	C₄×Dic₃	—	5	1	no	—
377	C₄×Dic₃	—	5	1	no	—
378	C₄×Dic₃	—	5	1	no	—
379	C₄×Dic₃	—	5	1	no	—
380	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
381	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
382	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
383	C₂×C₃⋊C₈	—	5	1	no	—
384	C₂×C₃⋊C₈	—	5	1	no	—
385	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
386	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
387	ΓL(1,𝔽₂₅)	—	2	2	no	—
388	ΓL(1,𝔽₂₅)	—	2	2	no	—
389	ΓL(1,𝔽₂₅)	—	5	4	no	—
390	ΓL(1,𝔽₂₅)	—	10	2	no	—
391	C₂³×C₅	—	3	1	no	—
392	C₂×C₄×C₅	—	3	1	no	—
393	C₂×C₄×C₅	—	3	1	no	—
394	C₂×C₄×C₅	—	3	2	no	—
395	C₂×C₄×C₅	—	3	2	no	—
396	C₂×C₄×C₅	—	3	1	no	—
397	C₂×C₄×C₅	—	6	2	no	—
398	C₂×C₄×C₅	—	12	1	no	—
399	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
400	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
401	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
402	C₂×Dic₅	—	3	1	no	—
403	C₂×Dic₅	—	3	1	no	—
404	C₂×Dic₅	—	3	1	no	—
405	C₂×Dic₅	—	3	1	no	—
406	C₂×Dic₅	—	6	2	no	—
407	C₂×Dic₅	—	6	2	no	—
408	C₂×Dic₅	—	12	1	no	—
409	C₂×Dic₅	—	12	1	no	—
410	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
411	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
412	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
413	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
414	Dic₁₀	—	2	2	no	—
415	Dic₁₀	—	3	4	no	—
416	Dic₁₀	—	6	2	no	—
417	Dic₁₀	—	6	2	no	—
418	C₅×C₈	—	2	1	no	—
419	C₅×C₈	—	2	1	no	—
420	C₅×C₈	—	6	1	no	—
421	C₅×C₈	—	6	1	no	—
422	#168	—	2	1	no	—
423	#168	—	3	2	no	—
424	#168	—	6	1	no	—
425	#168	D₃×Q₈	1	2	yes	complemented
426	C₂²×Q₈	—	15	1	no	—
427	C₂×M₁₆	—	3	1	no	—
428	C₂×M₁₆	—	3	1	no	—
429	C₂×M₁₆	—	15	1	no	—
430	C₂×M₁₆	—	15	1	no	—
431	C₄×Q₈	—	5	1	no	—
432	C₄×Q₈	—	15	1	no	—
433	C₄×Q₈	—	15	1	no	—
434	C₄×Q₈	—	15	1	no	—
435	C₄×Q₈	—	15	1	no	—
436	C₄×Q₈	—	15	1	no	—
437	C₄×Q₈	—	15	1	no	—
438	C₄×Q₈	—	15	1	no	—
439	C₂×C₄⋊C₄	—	15	1	no	—
440	C₂×C₄⋊C₄	—	15	1	no	—
441	C₂×C₄⋊C₄	—	15	1	no	—
442	C₂×C₄²	—	3	1	no	—
443	C₂×C₄²	—	15	1	no	—
444	C₂×C₄²	—	15	1	no	—
445	C₄⋊C₈	—	3	1	no	—
446	C₄⋊C₈	—	3	1	no	—
447	C₄⋊C₈	—	3	1	no	—
448	C₄⋊C₈	—	5	1	no	—
449	C₄⋊C₈	—	5	1	no	—
450	C₄⋊C₈	—	15	1	no	—
451	C₄⋊C₈	—	15	1	no	—
452	C₄⋊C₈	—	15	1	no	—
453	C₄⋊C₈	—	15	1	no	—
454	C₄⋊C₈	—	15	1	no	—
455	C₄⋊C₈	—	15	1	no	—
456	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic
457	#97	—	5	1	no	—
458	#97	—	5	1	no	—
459	#97	—	15	1	no	—
460	#97	—	15	1	no	—
461	#97	—	15	1	no	—
462	#97	—	15	1	no	—
463	C₄×C₈	—	5	1	no	—
464	C₄×C₈	—	15	1	no	—
465	C₄×C₈	—	15	1	no	—
466	C₄×C₈	—	15	1	no	—
467	C₄×C₈	—	15	1	no	—
468	C₄×C₈	—	15	1	no	—
469	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
470	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
471	C₂×C₃×C₅	#568	1	1	yes	characteristic
472	C₅×D₃	—	2	2	no	—
473	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
474	C₃×Q₈	—	10	2	no	—
475	C₂×C₃×C₄	—	5	1	no	—
476	C₂×C₃×C₄	—	5	1	no	—
477	C₂×C₃×C₄	—	5	1	no	—
478	C₂×C₃×C₄	—	5	1	no	—
479	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
480	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
482	C₂×Dic₃	—	5	1	no	—
483	C₂×Dic₃	—	5	1	no	—
484	C₂×Dic₃	—	5	1	no	—
485	C₂×Dic₃	—	5	1	no	—
486	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
487	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
488	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
489	C₄×D₃	—	2	2	no	—
490	C₄×D₃	—	4	1	no	—
491	C₄×D₃	—	10	2	no	—
492	C₄×D₃	—	10	2	no	—
493	C₄×D₃	—	20	1	no	—
494	C₄×D₃	—	20	1	no	—
495	C₄×D₃	#711	1	2	yes	—
496	C₄×D₃	Q₈×D₅	1	2	yes	—
497	Dic₆	—	5	4	no	—
498	Dic₆	—	10	2	no	—
499	Dic₆	—	10	2	no	—
500	C₃×C₈	—	2	1	no	—
501	C₃×C₈	—	2	1	no	—
502	C₃×C₈	—	5	2	no	—
503	C₃×C₈	—	10	1	no	—
504	C₃⋊C₈	—	2	1	no	—
505	C₃⋊C₈	—	2	1	no	—
506	C₃⋊C₈	—	5	2	no	—
507	C₃⋊C₈	—	10	1	no	—
508	C₂²×C₅	—	3	2	no	—
509	C₂²×C₅	—	6	1	no	—
510	C₂²×C₅	—	6	1	no	—
511	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
512	C₄×C₅	—	2	1	no	—
513	C₄×C₅	—	2	1	no	—
514	C₄×C₅	—	3	2	no	—
515	C₄×C₅	—	3	2	no	—
516	C₄×C₅	—	6	1	no	—
517	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
518	C₄×C₅	D₃×#41	1	1	yes	characteristic
519	Dic₅	—	2	1	no	—
520	Dic₅	—	2	1	no	—
521	Dic₅	—	2	1	no	—
522	Dic₅	—	3	2	no	—
523	Dic₅	—	6	1	no	—
524	Dic₅	—	6	1	no	—
525	Dic₅	—	6	1	no	—
526	Dic₅	D₃×M₁₆	1	2	yes	—
527	C₂×Q₈	—	5	1	no	—
528	C₂×Q₈	—	15	1	no	—
529	C₂×Q₈	—	15	1	no	—
530	C₂×Q₈	—	15	1	no	—
531	C₂×Q₈	—	30	4	no	—
532	C₂²×C₄	—	3	1	no	—
533	C₂²×C₄	—	3	1	no	—
534	C₂²×C₄	—	3	1	no	—
535	C₂²×C₄	—	15	1	no	—
536	C₂²×C₄	—	15	1	no	—
537	C₂²×C₄	—	15	1	no	—
538	C₂²×C₄	—	15	1	no	—
539	M₁₆	—	6	2	no	—
540	M₁₆	—	6	2	no	—
541	M₁₆	—	15	4	no	—
542	M₁₆	—	30	2	no	—
543	C₂×C₈	—	3	1	no	—
544	C₂×C₈	—	3	1	no	—
545	C₂×C₈	—	5	1	no	—
546	C₂×C₈	—	5	1	no	—
547	C₂×C₈	—	15	1	no	—
548	C₂×C₈	—	15	1	no	—
549	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
550	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
551	C₄⋊C₄	—	5	1	no	—
552	C₄⋊C₄	—	5	1	no	—
553	C₄⋊C₄	—	5	1	no	—
554	C₄⋊C₄	—	15	1	no	—
555	C₄⋊C₄	—	15	1	no	—
556	C₄⋊C₄	—	15	1	no	—
557	C₄⋊C₄	—	15	1	no	—
558	C₄⋊C₄	—	15	1	no	—
559	C₄⋊C₄	—	15	1	no	—
560	C₄⋊C₄	—	15	1	no	—
561	C₄⋊C₄	—	15	1	no	—
562	C₄⋊C₄	—	15	1	no	—
563	C₄²	—	3	1	no	—
564	C₄²	—	3	1	no	—
565	C₄²	—	3	1	no	—
566	C₄²	—	5	1	no	—
567	C₄²	—	5	1	no	—
568	C₄²	—	15	1	no	—
569	C₄²	—	15	1	no	—
570	C₄²	—	15	1	no	—
571	C₄²	—	15	1	no	—
572	C₄²	—	15	1	no	—
573	C₄²	—	15	1	no	—
574	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
575	C₃×C₅	Q₈×M₁₆	1	1	yes	characteristic, complemented, Hall
576	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
577	C₂×D₃	—	2	1	no	—
578	C₂×D₃	—	2	1	no	—
579	C₂×D₃	#4033	1	2	yes	—
580	C₃×C₄	—	2	1	no	—
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	5	2	no	—
583	C₃×C₄	—	10	1	no	—
584	C₃×C₄	—	10	1	no	—
585	C₃×C₄	—	10	1	no	—
586	C₃×C₄	C₂×#711	1	1	yes	characteristic
587	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
588	Dic₃	—	2	1	no	—
589	Dic₃	—	5	2	no	—
590	Dic₃	—	10	1	no	—
591	Dic₃	—	10	1	no	—
592	Dic₃	—	10	1	no	—
593	Dic₃	#4033	1	2	yes	—
594	Dic₃	D₅×M₁₆	1	2	yes	—
595	C₂×C₅	—	6	2	no	—
596	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
597	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
598	C₂×C₅	#5750	1	1	yes	characteristic
599	C₂³	—	3	1	no	—
600	Q₈	—	10	2	no	—
601	Q₈	—	15	4	no	—
602	Q₈	—	30	2	no	—
603	Q₈	—	30	2	no	—
604	C₂×C₄	—	3	1	no	—
605	C₂×C₄	—	3	1	no	—
606	C₂×C₄	—	3	2	no	—
607	C₂×C₄	—	3	2	no	—
608	C₂×C₄	—	3	1	no	—
609	C₂×C₄	—	5	1	no	—
610	C₂×C₄	—	5	1	no	—
611	C₂×C₄	—	5	1	no	—
612	C₂×C₄	—	5	1	no	—
613	C₂×C₄	—	6	2	no	—
614	C₂×C₄	—	12	1	no	—
615	C₂×C₄	—	15	1	no	—
616	C₂×C₄	—	15	1	no	—
617	C₂×C₄	—	15	1	no	—
618	C₂×C₄	—	15	1	no	—
619	C₂×C₄	—	30	2	no	—
620	C₂×C₄	—	30	2	no	—
621	C₂×C₄	—	60	1	no	—
622	C₂×C₄	—	60	1	no	—
623	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
624	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
625	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
626	C₈	—	2	1	no	—
627	C₈	—	2	1	no	—
628	C₈	—	5	2	no	—
629	C₈	—	6	1	no	—
630	C₈	—	6	1	no	—
631	C₈	—	10	1	no	—
632	C₈	—	15	2	no	—
633	C₈	—	30	1	no	—
634	C₂×C₃	C₂×#4033	1	1	yes	characteristic
635	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
636	C₂×C₃	#66079	1	1	yes	characteristic
637	D₃	—	2	2	no	—
638	C₅	#79962	1	1	yes	characteristic, complemented, Sylow
639	C₂²	—	3	2	no	—
640	C₂²	—	6	1	no	—
641	C₂²	—	6	1	no	—
642	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
643	C₄	—	2	1	no	—
644	C₄	—	2	1	no	—
645	C₄	—	3	2	no	—
646	C₄	—	3	2	no	—
647	C₄	—	5	2	no	—
648	C₄	—	6	1	no	—
649	C₄	—	10	1	no	—
650	C₄	—	10	1	no	—
651	C₄	—	10	1	no	—
652	C₄	—	15	2	no	—
653	C₄	—	30	1	no	—
654	C₄	—	30	1	no	—
655	C₄	—	30	1	no	—
656	C₄	D₃×#711	1	1	yes	characteristic
657	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
658	C₃	#10610777	1	1	yes	characteristic, complemented, Sylow
659	C₂	—	6	2	no	—
660	C₂	D₃×#4033	1	1	yes	characteristic
661	C₂	#11753951	1	1	yes	characteristic
662	C₂	D₃×D₅×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×C₄⋊C₈	C₂²
prime radical	C₂²×C₅×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄⋊C₈	D₃×D₅
hypocenter	C₃×C₅	Q₈×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #11750929	C₂	semidirect
4. C₃×#65117	C₂	semidirect
9. #11747569	C₂	semidirect
10. #11747568	C₂	semidirect
11. #11747566	C₂	semidirect
12. #11747564	C₂	semidirect
14. #11746852	C₂	semidirect
15. #11746848	C₂	semidirect
75. #65117	D₃	semidirect
123. #6650	Q₈	semidirect
205. #1204	M₁₆	semidirect
213. C₃⋊#168	C₂×Q₈	semidirect
215. C₃×#168	C₂×Q₈	semidirect
425. #168	D₃×Q₈	semidirect
575. C₃×C₅	Q₈×M₁₆	semidirect
638. C₅	#79962	semidirect
658. C₃	#10610777	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₃×Dic₁₀	2
#11750929	2
C₅×#4837	2
C₃×#65117	2
#11747602	2
#11747590	2
Dic₅×ΓL(1,𝔽₂₅)	2
#11747569	2
#11747568	2
#11747566	2
#11747564	2
#11747005	2
#11746852	2
#11746848	2
#10610777	3
#79962	5