Subgroups — #14418530

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11752588	C₂	1	1	yes	maximal, characteristic
2	#11750940	C₂	1	1	yes	maximal, characteristic
3	C₅×#4830	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65117	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748054	C₂	1	1	yes	maximal, characteristic
6	#11747820	C₂	1	1	yes	maximal, characteristic, complemented
7	#11747660	C₂	1	1	yes	maximal, characteristic
8	#11747594	C₂	1	1	yes	maximal, characteristic
9	C₈×#1200	C₂	1	1	yes	maximal, characteristic
10	#11747568	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747565	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747565	C₂	1	1	yes	maximal, characteristic, complemented
13	#11746982	C₂	1	1	yes	maximal, characteristic
14	#11746850	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃⋊C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611648	—	3	1	no	maximal, Hall
17	C₂×#6705	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
19	#91761	C₂²	1	1	yes	characteristic
20	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₄×#1204	C₂²	1	1	yes	characteristic
23	C₄×#1204	C₂²	1	1	yes	characteristic
24	#91429	C₄	1	1	yes	characteristic
25	#91424	C₄	1	1	yes	characteristic
26	#91419	C₄	1	1	yes	characteristic
27	#91411	C₄	1	1	yes	characteristic
28	C₄×#1200	C₂²	1	1	yes	characteristic
29	#91386	C₂²	1	1	yes	characteristic
30	#91339	C₄	1	1	yes	characteristic
31	#91336	C₄	1	1	yes	characteristic
32	#91329	C₄	1	1	yes	characteristic
33	#91327	C₄	1	1	yes	characteristic
34	C₂×#6651	C₂²	1	1	yes	characteristic
35	C₂×#6648	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	#91098	C₂²	1	1	yes	characteristic
38	#91098	C₂²	1	1	yes	characteristic
39	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
40	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
42	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
43	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
44	C₄×C₅×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	Dic₃⋊#168	C₂²	1	1	yes	characteristic
51	Dic₃⋊#168	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	#90953	C₂²	1	1	yes	characteristic
56	#90951	C₂²	1	1	yes	characteristic
57	Dic₃×#168	C₂²	1	1	yes	characteristic
58	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
59	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
60	#79958	—	5	1	no	maximal, Hall
61	#65912	—	3	1	no	—
62	C₅×C₈×Q₈	—	3	1	no	—
63	#65313	—	3	1	no	—
64	#65128	—	3	1	no	—
65	#65128	—	3	1	no	—
66	#65126	—	3	1	no	—
67	#65120	—	3	1	no	—
68	#65117	—	3	1	no	—
69	#65117	D₃	1	1	yes	characteristic, complemented
70	#64978	—	3	1	no	—
71	#64978	—	3	1	no	—
72	C₄×C₈×D₅	—	3	1	no	—
73	C₈×Dic₁₀	—	3	1	no	—
74	C₈×Dic₁₀	—	3	1	no	—
75	C₈×Dic₁₀	—	3	1	no	—
76	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
77	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
79	C₂×#1204	C₂×C₄	1	1	yes	characteristic
80	C₂×#1204	C₂×C₄	1	1	yes	characteristic
81	C₂×#1200	C₂×C₄	1	1	yes	characteristic
82	C₂×#1200	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
86	#6714	C₂×C₄	1	1	yes	characteristic
87	#6714	C₂×C₄	1	1	yes	characteristic
88	#6712	C₂×C₄	1	1	yes	characteristic
89	#6712	C₂×C₄	1	1	yes	characteristic
90	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
91	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
92	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
93	#6705	—	2	2	no	—
94	C₈×D₁₅	—	2	2	no	—
95	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
96	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
102	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
103	C₃×#683	C₂×C₄	1	1	yes	characteristic
104	C₃×#683	C₂×C₄	1	1	yes	characteristic
105	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
106	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
107	C₂×C₃×#168	C₂³	1	1	yes	characteristic
108	C₂×C₃×#168	C₂³	1	1	yes	characteristic
109	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
110	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
111	#6669	C₂×C₄	1	1	yes	characteristic
112	#6669	C₂×C₄	1	1	yes	characteristic
113	#6669	C₂×C₄	1	1	yes	characteristic
114	#6669	C₂×C₄	1	1	yes	characteristic
115	#6668	C₂×C₄	1	1	yes	characteristic
116	#6668	C₂×C₄	1	1	yes	characteristic
117	#6667	C₂×C₄	1	1	yes	characteristic
118	#6667	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	#6651	—	2	2	no	—
122	#6648	Q₈	1	4	yes	complemented
123	#5578	—	5	1	no	—
124	C₃×#446	—	5	1	no	—
125	Q₈×C₃⋊C₈	—	5	1	no	—
126	#4839	—	5	1	no	—
127	#4839	—	5	1	no	—
128	#4837	—	5	1	no	—
129	#4830	—	5	1	no	—
130	#4830	—	5	1	no	—
131	#4830	D₅	1	1	yes	characteristic, complemented
132	#4708	—	5	1	no	—
133	#4708	—	5	1	no	—
134	#4701	—	5	1	no	—
135	#4701	—	5	1	no	—
136	C₄×D₃×C₈	—	5	1	no	—
137	#4679	—	5	1	no	—
138	C₄×C₅×Q₈	—	3	1	no	—
139	#4092	—	3	1	no	—
140	#4090	—	3	1	no	—
141	C₂×#676	—	3	1	no	—
142	C₂×#676	—	3	1	no	—
143	C₂×C₈×D₅	—	3	1	no	—
144	C₂×C₈×D₅	—	3	1	no	—
145	#4043	—	3	1	no	—
146	#4042	—	3	1	no	—
147	#4042	—	3	1	no	—
148	#4035	—	3	1	no	—
149	#4035	—	3	1	no	—
150	#4034	—	3	1	no	—
151	#4018	—	3	1	no	—
152	#4018	—	3	1	no	—
153	C₄²×D₅	—	3	1	no	—
154	C₄×Dic₁₀	—	3	1	no	—
155	C₄×Dic₁₀	—	3	1	no	—
156	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
157	C₅×C₄⋊C₈	—	3	1	no	—
158	C₅×C₄⋊C₈	—	3	1	no	—
159	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
160	C₄×C₅×C₈	—	3	1	no	—
161	C₄×C₅×C₈	—	3	1	no	—
162	C₄×C₅×C₈	—	3	1	no	—
163	#3947	—	3	1	no	—
164	#3947	C₂×D₃	1	1	yes	characteristic
165	#3946	—	3	1	no	—
166	#3946	—	3	1	no	—
167	#3946	—	3	1	no	—
168	#3946	—	3	1	no	—
169	#3946	C₂×D₃	1	1	yes	characteristic
170	#3946	C₂×D₃	1	1	yes	characteristic
171	C₈×Dic₅	—	3	1	no	—
172	C₈×Dic₅	—	3	1	no	—
173	C₈×Dic₅	—	3	1	no	—
174	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
175	C₄⋊#168	—	3	1	no	—
176	C₄⋊#168	—	3	1	no	—
177	C₄⋊#168	—	3	1	no	—
178	#3935	—	3	1	no	—
179	#3935	C₂×D₃	1	1	yes	characteristic
180	C₄×#168	—	3	1	no	—
181	#2960	—	15	1	no	Sylow
182	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
188	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
189	C₄×D₁₅	C₂×Q₈	1	2	yes	—
190	C₄×D₁₅	#41	1	2	yes	—
191	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
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	C₅×Dic₆	—	2	2	no	—
196	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
200	C₃×Dic₁₀	—	2	2	no	—
201	#1204	—	2	2	no	—
202	#1204	—	2	2	no	—
203	#1200	—	2	2	no	—
204	#1200	—	2	2	no	—
205	C₃×C₅×C₈	—	2	1	no	—
206	C₃×C₅×C₈	—	2	1	no	—
207	C₃⋊#168	—	2	1	no	—
208	C₃⋊#168	—	2	1	no	—
209	C₃×#168	—	2	1	no	—
210	C₃×#168	C₂×Q₈	1	2	yes	—
211	C₅×C₃⋊C₈	—	2	1	no	—
212	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
213	C₃×C₄×Q₈	—	5	1	no	—
214	#946	—	5	1	no	—
215	#944	—	5	1	no	—
216	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
217	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
218	C₂×D₃×C₈	—	5	1	no	—
219	C₂×D₃×C₈	—	5	1	no	—
220	#897	—	5	1	no	—
221	#896	—	5	1	no	—
222	#896	—	5	1	no	—
223	#889	—	5	1	no	—
224	#889	—	5	1	no	—
225	#888	—	5	1	no	—
226	#872	—	5	1	no	—
227	#872	—	5	1	no	—
228	C₄²×D₃	—	5	1	no	—
229	C₄×Dic₆	—	5	1	no	—
230	C₄×Dic₆	—	5	1	no	—
231	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
232	C₃×C₄⋊C₈	—	5	1	no	—
233	C₃×C₄⋊C₈	—	5	1	no	—
234	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
235	C₃×#97	—	5	1	no	—
236	C₃×#97	—	5	1	no	—
237	C₃×C₄×C₈	—	5	1	no	—
238	#815	—	5	1	no	—
239	#815	—	5	1	no	—
240	Dic₃⋊C₈	—	5	1	no	—
241	Dic₃⋊C₈	—	5	1	no	—
242	Dic₃⋊C₈	—	5	1	no	—
243	Dic₃⋊C₈	—	5	1	no	—
244	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
245	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
246	C₈×Dic₃	—	5	1	no	—
247	C₈×Dic₃	—	5	1	no	—
248	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
249	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
250	C₄⋊(C₃⋊C₈)	—	5	1	no	—
251	C₄⋊(C₃⋊C₈)	—	5	1	no	—
252	C₄⋊(C₃⋊C₈)	—	5	1	no	—
253	C₄×C₃⋊C₈	—	5	1	no	—
254	C₄×C₃⋊C₈	—	5	1	no	—
255	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
256	C₂×C₅×Q₈	—	3	1	no	—
257	C₂×C₄×D₅	—	3	1	no	—
258	C₂×C₄×D₅	—	3	1	no	—
259	C₂×C₄×D₅	—	3	1	no	—
260	C₂×Dic₁₀	—	3	1	no	—
261	C₂×Dic₁₀	—	3	1	no	—
262	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
263	C₂×C₅×C₈	—	3	1	no	—
264	C₂×C₅×C₈	—	3	1	no	—
265	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
266	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
267	C₅×C₄⋊C₄	—	3	1	no	—
268	C₅×C₄⋊C₄	—	3	1	no	—
269	C₅×C₄⋊C₄	—	3	1	no	—
270	C₄²×C₅	—	3	1	no	—
271	C₄²×C₅	—	3	1	no	—
272	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
273	#685	—	3	1	no	—
274	#685	—	3	1	no	—
275	#685	—	3	1	no	—
276	#685	—	3	1	no	—
277	C₄⋊Dic₅	—	3	1	no	—
278	C₄⋊Dic₅	—	3	1	no	—
279	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
280	#683	—	3	1	no	—
281	#683	—	3	1	no	—
282	#683	—	3	1	no	—
283	#683	—	3	1	no	—
284	#683	—	3	1	no	—
285	#683	—	3	1	no	—
286	#683	—	3	1	no	—
287	#683	—	3	1	no	—
288	#683	C₄×D₃	1	1	yes	characteristic
289	#683	C₄×D₃	1	1	yes	characteristic
290	C₄×Dic₅	—	3	1	no	—
291	C₄×Dic₅	—	3	1	no	—
292	C₄×Dic₅	—	3	1	no	—
293	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
294	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
295	C₂×#168	—	3	1	no	—
296	C₂×#168	—	3	1	no	—
297	C₂×#168	C₂²×D₃	1	1	yes	characteristic
298	C₂×#168	C₂²×D₃	1	1	yes	characteristic
299	#676	—	6	2	no	—
300	#676	—	6	2	no	—
301	C₈×D₅	—	3	4	no	—
302	C₈×D₅	—	6	2	no	—
303	#533	—	15	1	no	—
304	#446	—	5	1	no	—
305	#446	—	15	1	no	—
306	#446	—	15	1	no	—
307	#446	—	15	1	no	—
308	C₈×Q₈	—	3	1	no	—
309	C₈×Q₈	—	15	1	no	—
310	C₈×Q₈	—	15	1	no	—
311	C₈×Q₈	—	15	1	no	—
312	#424	—	15	1	no	—
313	#424	—	15	1	no	—
314	#423	—	15	1	no	—
315	#405	—	15	1	no	—
316	#405	—	15	1	no	—
317	C₂×C₄×C₈	—	15	1	no	—
318	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
319	C₂×D₁₅	—	2	1	no	—
320	C₂×D₁₅	—	2	1	no	—
321	C₂×D₁₅	C₄×Q₈	1	2	yes	—
322	C₃×C₄×C₅	—	2	1	no	—
323	C₃×C₄×C₅	—	2	1	no	—
324	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
325	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
326	Dic₁₅	—	2	1	no	—
327	Dic₁₅	—	2	1	no	—
328	Dic₁₅	C₄×Q₈	1	2	yes	—
329	C₃×Dic₅	—	2	1	no	—
330	C₃×Dic₅	—	2	1	no	—
331	C₃×Dic₅	—	2	1	no	—
332	C₃×Dic₅	#131	1	2	yes	—
333	C₅×Dic₃	—	2	1	no	—
334	C₅×Dic₃	—	2	1	no	—
335	C₅×Dic₃	—	2	1	no	—
336	C₅×Dic₃	#131	1	2	yes	—
337	C₂×C₃×Q₈	—	5	1	no	—
338	C₂×C₄×D₃	—	5	1	no	—
339	C₂×C₄×D₃	—	5	1	no	—
340	C₂×C₄×D₃	—	5	1	no	—
341	C₂×Dic₆	—	5	1	no	—
342	C₂×Dic₆	—	5	1	no	—
343	C₂×Dic₆	C₄×D₅	1	1	yes	characteristic
344	C₂×C₃×C₈	—	5	1	no	—
345	C₂×C₃×C₈	—	5	1	no	—
346	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
347	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
348	C₃×C₄⋊C₄	—	5	1	no	—
349	C₃×C₄⋊C₄	—	5	1	no	—
350	C₃×C₄⋊C₄	—	5	1	no	—
351	C₃×C₄²	—	5	1	no	—
352	C₃×C₄²	—	5	1	no	—
353	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
354	(C₂×D₃)⋊C₄	—	5	1	no	—
355	(C₂×D₃)⋊C₄	—	5	1	no	—
356	(C₂×D₃)⋊C₄	—	5	1	no	—
357	(C₂×D₃)⋊C₄	—	5	1	no	—
358	C₄⋊Dic₃	—	5	1	no	—
359	C₄⋊Dic₃	—	5	1	no	—
360	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
361	Dic₃⋊C₄	—	5	1	no	—
362	Dic₃⋊C₄	—	5	1	no	—
363	Dic₃⋊C₄	—	5	1	no	—
364	Dic₃⋊C₄	—	5	1	no	—
365	Dic₃⋊C₄	—	5	1	no	—
366	Dic₃⋊C₄	—	5	1	no	—
367	Dic₃⋊C₄	—	5	1	no	—
368	Dic₃⋊C₄	—	5	1	no	—
369	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
370	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
371	C₄×Dic₃	—	5	1	no	—
372	C₄×Dic₃	—	5	1	no	—
373	C₄×Dic₃	—	5	1	no	—
374	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
375	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
376	C₂×C₃⋊C₈	—	5	1	no	—
377	C₂×C₃⋊C₈	—	5	1	no	—
378	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
379	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
380	ΓL(1,𝔽₂₅)	—	10	2	no	—
381	ΓL(1,𝔽₂₅)	—	10	2	no	—
382	D₃×C₈	—	5	4	no	—
383	D₃×C₈	—	10	2	no	—
384	C₂²×D₅	—	3	1	no	—
385	C₅×Q₈	—	6	2	no	—
386	C₂×C₄×C₅	—	3	1	no	—
387	C₂×C₄×C₅	—	3	1	no	—
388	C₂×C₄×C₅	—	3	1	no	—
389	C₂×C₄×C₅	—	3	1	no	—
390	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
391	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
392	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
393	C₂×Dic₅	—	3	1	no	—
394	C₂×Dic₅	—	3	1	no	—
395	C₂×Dic₅	—	3	1	no	—
396	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
397	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
398	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
399	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
400	C₄×D₅	—	3	2	no	—
401	C₄×D₅	—	3	2	no	—
402	C₄×D₅	—	6	2	no	—
403	C₄×D₅	—	6	2	no	—
404	Dic₁₀	—	2	2	no	—
405	Dic₁₀	—	6	2	no	—
406	Dic₁₀	—	6	2	no	—
407	C₅×C₈	—	2	1	no	—
408	C₅×C₈	—	2	1	no	—
409	C₅×C₈	—	3	2	no	—
410	C₅×C₈	—	6	1	no	—
411	#168	—	2	1	no	—
412	#168	—	6	1	no	—
413	#168	—	6	1	no	—
414	#168	D₃×Q₈	1	2	yes	—
415	C₂×M₁₆	—	15	1	no	—
416	C₂×M₁₆	—	15	1	no	—
417	C₂²×C₈	—	15	1	no	—
418	C₂²×C₈	—	15	1	no	—
419	C₄⋊Q₈	—	15	1	no	—
420	C₄⋊Q₈	—	15	1	no	—
421	#125	—	15	1	no	—
422	#125	—	15	1	no	—
423	C₂²⋊Q₈	—	15	1	no	—
424	C₂²⋊Q₈	—	15	1	no	—
425	C₂²⋊Q₈	—	15	1	no	—
426	C₂²⋊Q₈	—	15	1	no	—
427	C₄×Q₈	—	3	1	no	—
428	C₄×Q₈	—	5	1	no	—
429	C₄×Q₈	—	15	1	no	—
430	C₄×Q₈	—	15	1	no	—
431	#117	—	15	1	no	—
432	#117	—	15	1	no	—
433	C₂×C₄²	—	15	1	no	—
434	C₄⋊C₈	—	3	1	no	—
435	C₄⋊C₈	—	3	1	no	—
436	C₄⋊C₈	—	5	1	no	—
437	C₄⋊C₈	—	5	1	no	—
438	C₄⋊C₈	—	15	1	no	—
439	C₄⋊C₈	—	15	1	no	—
440	C₄⋊C₈	—	15	1	no	—
441	C₄⋊C₈	—	15	1	no	—
442	C₄⋊C₈	—	15	1	no	—
443	C₄⋊C₈	—	15	1	no	—
444	C₄⋊C₈	—	15	1	no	—
445	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic
446	#97	—	5	1	no	—
447	#97	—	5	1	no	—
448	#97	—	15	1	no	—
449	#97	—	15	1	no	—
450	C₄×C₈	—	3	1	no	—
451	C₄×C₈	—	3	1	no	—
452	C₄×C₈	—	3	1	no	—
453	C₄×C₈	—	5	1	no	—
454	C₄×C₈	—	15	1	no	—
455	C₄×C₈	—	15	1	no	—
456	C₄×C₈	—	15	1	no	—
457	C₄×C₈	—	15	1	no	—
458	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
459	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
460	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
461	D₁₅	—	2	2	no	—
462	C₂²×D₃	—	5	1	no	—
463	C₃×Q₈	—	10	2	no	—
464	C₂×C₃×C₄	—	5	1	no	—
465	C₂×C₃×C₄	—	5	1	no	—
466	C₂×C₃×C₄	—	5	1	no	—
467	C₂×C₃×C₄	—	5	1	no	—
468	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
469	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
471	C₂×Dic₃	—	5	1	no	—
472	C₂×Dic₃	—	5	1	no	—
473	C₂×Dic₃	—	5	1	no	—
474	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
475	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
476	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
477	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
478	C₄×D₃	—	5	2	no	—
479	C₄×D₃	—	5	2	no	—
480	C₄×D₃	—	10	2	no	—
481	C₄×D₃	—	10	2	no	—
482	Dic₆	—	2	2	no	—
483	Dic₆	—	10	2	no	—
484	Dic₆	—	10	2	no	—
485	C₃×C₈	—	2	1	no	—
486	C₃×C₈	—	2	1	no	—
487	C₃×C₈	—	5	2	no	—
488	C₃×C₈	—	10	1	no	—
489	C₃⋊C₈	—	2	1	no	—
490	C₃⋊C₈	—	10	1	no	—
491	C₃⋊C₈	—	10	1	no	—
492	C₃⋊C₈	Q₈×D₅	1	2	yes	—
493	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
494	C₂×D₅	—	3	2	no	—
495	C₂×D₅	—	6	1	no	—
496	C₂×D₅	—	6	1	no	—
497	C₄×C₅	—	2	1	no	—
498	C₄×C₅	—	2	1	no	—
499	C₄×C₅	—	3	2	no	—
500	C₄×C₅	—	6	1	no	—
501	C₄×C₅	—	6	1	no	—
502	C₄×C₅	—	6	1	no	—
503	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
504	C₄×C₅	D₃×#41	1	1	yes	characteristic
505	Dic₅	—	2	1	no	—
506	Dic₅	—	2	1	no	—
507	Dic₅	—	2	1	no	—
508	Dic₅	—	3	2	no	—
509	Dic₅	—	6	1	no	—
510	Dic₅	—	6	1	no	—
511	Dic₅	#907	1	2	yes	—
512	C₂×Q₈	—	3	1	no	—
513	C₂×Q₈	—	5	1	no	—
514	C₂×Q₈	—	15	1	no	—
515	C₂×Q₈	—	15	1	no	—
516	C₂²×C₄	—	15	1	no	—
517	C₂²×C₄	—	15	1	no	—
518	C₂²×C₄	—	15	1	no	—
519	M₁₆	—	30	2	no	—
520	M₁₆	—	30	2	no	—
521	C₂×C₈	—	3	1	no	—
522	C₂×C₈	—	3	1	no	—
523	C₂×C₈	—	5	1	no	—
524	C₂×C₈	—	5	1	no	—
525	C₂×C₈	—	15	4	no	—
526	C₂×C₈	—	15	1	no	—
527	C₂×C₈	—	15	1	no	—
528	C₂×C₈	—	30	2	no	—
529	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
530	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
531	C₄⋊C₄	—	3	1	no	—
532	C₄⋊C₄	—	3	1	no	—
533	C₄⋊C₄	—	3	1	no	—
534	C₄⋊C₄	—	5	1	no	—
535	C₄⋊C₄	—	5	1	no	—
536	C₄⋊C₄	—	5	1	no	—
537	C₄⋊C₄	—	15	1	no	—
538	C₄⋊C₄	—	15	1	no	—
539	C₄⋊C₄	—	15	1	no	—
540	C₄⋊C₄	—	15	1	no	—
541	C₄⋊C₄	—	15	1	no	—
542	C₄⋊C₄	—	15	1	no	—
543	C₄⋊C₄	—	15	1	no	—
544	C₄⋊C₄	—	15	1	no	—
545	C₄⋊C₄	—	15	1	no	—
546	C₄⋊C₄	—	15	1	no	—
547	C₂²⋊C₄	—	15	1	no	—
548	C₂²⋊C₄	—	15	1	no	—
549	C₂²⋊C₄	—	15	1	no	—
550	C₂²⋊C₄	—	15	1	no	—
551	C₄²	—	3	1	no	—
552	C₄²	—	3	1	no	—
553	C₄²	—	5	1	no	—
554	C₄²	—	5	1	no	—
555	C₄²	—	15	1	no	—
556	C₄²	—	15	1	no	—
557	C₄²	—	15	1	no	—
558	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
559	C₃×C₅	#2960	1	1	yes	characteristic, complemented, Hall
560	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
561	C₂×D₃	—	5	2	no	—
562	C₂×D₃	—	10	1	no	—
563	C₂×D₃	—	10	1	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	5	2	no	—
567	C₃×C₄	—	10	1	no	—
568	C₃×C₄	—	10	1	no	—
569	C₃×C₄	—	10	1	no	—
570	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
571	C₃×C₄	D₅×#41	1	1	yes	characteristic
572	Dic₃	—	2	1	no	—
573	Dic₃	—	2	1	no	—
574	Dic₃	—	2	1	no	—
575	Dic₃	—	5	2	no	—
576	Dic₃	—	10	1	no	—
577	Dic₃	—	10	1	no	—
578	Dic₃	#4047	1	2	yes	—
579	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
580	C₂×C₅	C₂×#907	1	1	yes	characteristic
581	C₂×C₅	D₃×#131	1	1	yes	characteristic
582	D₅	—	6	2	no	—
583	C₂³	—	15	1	no	—
584	Q₈	—	6	2	no	—
585	Q₈	—	10	2	no	—
586	Q₈	—	30	2	no	—
587	Q₈	—	30	2	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	3	1	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	5	1	no	—
593	C₂×C₄	—	5	1	no	—
594	C₂×C₄	—	5	1	no	—
595	C₂×C₄	—	5	1	no	—
596	C₂×C₄	—	15	1	no	—
597	C₂×C₄	—	15	2	no	—
598	C₂×C₄	—	15	2	no	—
599	C₂×C₄	—	15	1	no	—
600	C₂×C₄	—	15	1	no	—
601	C₂×C₄	—	30	2	no	—
602	C₂×C₄	—	30	2	no	—
603	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
604	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	3	2	no	—
609	C₈	—	5	2	no	—
610	C₈	—	6	1	no	—
611	C₈	—	10	1	no	—
612	C₈	—	30	1	no	—
613	C₈	—	30	1	no	—
614	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
615	C₂×C₃	C₂×#4047	1	1	yes	characteristic
616	C₂×C₃	D₅×#131	1	1	yes	characteristic
617	D₃	—	10	2	no	—
618	C₅	#79958	1	1	yes	characteristic, complemented, Sylow
619	C₂²	—	15	2	no	—
620	C₂²	—	30	1	no	—
621	C₂²	—	30	1	no	—
622	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	3	2	no	—
626	C₄	—	5	2	no	—
627	C₄	—	6	1	no	—
628	C₄	—	6	1	no	—
629	C₄	—	6	1	no	—
630	C₄	—	10	1	no	—
631	C₄	—	10	1	no	—
632	C₄	—	10	1	no	—
633	C₄	—	15	2	no	—
634	C₄	—	30	1	no	—
635	C₄	—	30	1	no	—
636	C₄	#92024	1	1	yes	characteristic
637	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
638	C₃	#10611648	1	1	yes	characteristic, complemented, Sylow
639	C₂	—	30	2	no	—
640	C₂	#11753409	1	1	yes	characteristic
641	C₂	D₃×#4047	1	1	yes	characteristic
642	C₂	D₅×#907	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×D₁₅	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄⋊C₈	D₃×D₅
hypocenter	C₃×C₅	#2960
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
3. C₅×#4830	C₂	semidirect
4. C₃×#65117	C₂	semidirect
6. #11747820	C₂	semidirect
10. #11747568	C₂	semidirect
11. #11747565	C₂	semidirect
12. #11747565	C₂	semidirect
14. #11746850	C₂	semidirect
15. C₃⋊C₈×Dic₁₀	C₂	semidirect
69. #65117	D₃	semidirect
122. #6648	Q₈	semidirect
131. #4830	D₅	semidirect
559. C₃×C₅	#2960	semidirect
618. C₅	#79958	semidirect
638. C₃	#10611648	semidirect

Maximal subgroups

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

subgroup	index
#11752588	2
#11750940	2
C₅×#4830	2
C₃×#65117	2
#11748054	2
#11747820	2
#11747660	2
#11747594	2
C₈×#1200	2
#11747568	2
#11747565	2
#11746982	2
#11746850	2
C₃⋊C₈×Dic₁₀	2
#10611648	3
#79958	5