Subgroups — #14419055

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6773	C₂	1	1	yes	maximal, characteristic
2	#11750937	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4828	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65122	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747728	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747726	C₂	1	1	yes	maximal, characteristic, complemented
7	#11747718	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747716	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747592	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747583	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747583	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#1200	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747003	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746995	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746858	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611669	—	3	1	no	maximal, Hall
17	C₂×#6773	C₄	1	1	yes	characteristic
18	C₂×#6705	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
20	C₄×D₆₀	C₂²	1	1	yes	characteristic
21	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
23	#91444	C₄	1	1	yes	characteristic
24	#91444	C₄	1	1	yes	characteristic
25	C₄×#1202	C₂²	1	1	yes	characteristic
26	C₄×#1202	C₂²	1	1	yes	characteristic
27	#91418	C₄	1	1	yes	characteristic
28	#91402	C₄	1	1	yes	characteristic
29	#91402	C₄	1	1	yes	characteristic
30	C₄×#1200	C₂²	1	1	yes	characteristic
31	C₄×#1200	C₂²	1	1	yes	characteristic
32	#91358	C₄	1	1	yes	characteristic
33	Dic₅×Dic₆	C₄	1	1	yes	characteristic
34	C₂×#6651	C₂²	1	1	yes	characteristic
35	C₂×#6649	C₂²	1	1	yes	characteristic
36	C₂×#6649	C₂²	1	1	yes	characteristic
37	C₂×#6648	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	#91104	C₂²	1	1	yes	characteristic
40	#91104	C₂²	1	1	yes	characteristic
41	#91087	C₂²	1	1	yes	characteristic
42	C₅×#815	C₂²	1	1	yes	characteristic
43	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
44	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
46	C₅×#803	C₂²	1	1	yes	characteristic
47	C₃×#3952	C₂²	1	1	yes	characteristic
48	C₃×#3952	C₂²	1	1	yes	characteristic
49	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
50	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
51	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
52	Dic₃⋊#168	C₂²	1	1	yes	characteristic
53	Dic₃⋊#168	C₂²	1	1	yes	characteristic
54	#90957	C₂²	1	1	yes	characteristic
55	#90957	C₂²	1	1	yes	characteristic
56	#90953	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	#79278	—	5	1	no	maximal, Hall
61	C₄×#713	—	3	1	no	—
62	C₅×#446	—	3	1	no	—
63	#65313	—	3	1	no	—
64	#65127	—	3	1	no	—
65	#65125	—	3	1	no	—
66	#65125	—	3	1	no	—
67	#65122	—	3	1	no	—
68	#65122	—	3	1	no	—
69	#65122	D₃	1	1	yes	characteristic, complemented
70	#64996	—	3	1	no	—
71	#64996	—	3	1	no	—
72	#64995	—	3	1	no	—
73	#64995	—	3	1	no	—
74	#64977	—	3	1	no	—
75	C₄×C₈×D₅	—	3	1	no	—
76	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
79	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
83	C₂×#1202	C₂×C₄	1	1	yes	characteristic
84	C₂×#1202	C₂×C₄	1	1	yes	characteristic
85	C₂×#1200	C₂×C₄	1	1	yes	characteristic
86	C₂×#1200	C₂×C₄	1	1	yes	characteristic
87	C₂×#1200	C₂×C₄	1	1	yes	characteristic
88	C₂×#1200	C₂×C₄	1	1	yes	characteristic
89	#6773	—	2	4	no	—
90	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	#6714	C₂×C₄	1	1	yes	characteristic
94	#6714	C₂×C₄	1	1	yes	characteristic
95	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
97	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
98	#6705	—	2	2	no	—
99	C₈×D₁₅	—	2	2	no	—
100	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
101	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
104	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
106	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
107	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
108	C₃×C₄×Dic₅	C₂×C₄	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	#6667	C₂×C₄	1	1	yes	characteristic
115	#6667	C₂×C₄	1	1	yes	characteristic
116	#6665	C₂×C₄	1	1	yes	characteristic
117	#6665	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	#6651	—	2	2	no	—
123	#6649	—	2	2	no	—
124	#6649	—	2	2	no	—
125	#6648	—	2	2	no	—
126	C₄×#235	—	5	1	no	—
127	C₃×#431	—	5	1	no	—
128	C₄×#208	—	5	1	no	—
129	#4836	—	5	1	no	—
130	#4836	—	5	1	no	—
131	#4828	—	5	1	no	—
132	#4828	D₅	1	1	yes	characteristic, complemented
133	#4729	—	5	1	no	—
134	#4729	—	5	1	no	—
135	#4728	—	5	1	no	—
136	#4728	—	5	1	no	—
137	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
138	#4685	—	5	1	no	—
139	#4685	—	5	1	no	—
140	C₄×D₃×C₈	—	5	1	no	—
141	C₂×#713	—	3	1	no	—
142	C₄×C₅×Q₈	—	3	1	no	—
143	Q₈×Dic₅	—	3	1	no	—
144	C₂×#676	—	3	1	no	—
145	C₂×#676	—	3	1	no	—
146	C₂×#676	—	3	1	no	—
147	C₂×#676	—	3	1	no	—
148	C₂×C₈×D₅	—	3	1	no	—
149	C₂×C₈×D₅	—	3	1	no	—
150	#4039	—	3	1	no	—
151	#4039	—	3	1	no	—
152	#4039	—	3	1	no	—
153	#4038	—	3	1	no	—
154	#4038	—	3	1	no	—
155	#4038	—	3	1	no	—
156	C₄×D₂₀	—	3	1	no	—
157	C₄×D₂₀	—	3	1	no	—
158	C₄×D₂₀	—	3	1	no	—
159	C₄²×D₅	—	3	1	no	—
160	C₄²×D₅	—	3	1	no	—
161	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
162	C₅×C₄⋊C₈	—	3	1	no	—
163	C₅×C₄⋊C₈	—	3	1	no	—
164	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
165	C₅×#97	—	3	1	no	—
166	C₅×#97	—	3	1	no	—
167	C₄×C₅×C₈	—	3	1	no	—
168	#3952	—	3	1	no	—
169	#3952	—	3	1	no	—
170	#3952	—	3	1	no	—
171	#3952	—	3	1	no	—
172	#3952	C₂×D₃	1	1	yes	characteristic
173	#3952	C₂×D₃	1	1	yes	characteristic
174	C₈×Dic₅	—	3	1	no	—
175	C₈×Dic₅	—	3	1	no	—
176	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
177	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
178	C₄⋊#168	—	3	1	no	—
179	C₄⋊#168	—	3	1	no	—
180	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
181	#3935	—	3	1	no	—
182	#3935	—	3	1	no	—
183	C₄×#168	—	3	1	no	—
184	#2965	—	15	1	no	Sylow
185	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
186	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
192	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
193	D₆₀	—	2	2	no	—
194	C₄×D₁₅	—	2	1	no	—
195	C₄×D₁₅	—	2	1	no	—
196	C₄×D₁₅	—	2	1	no	—
197	C₄×D₁₅	—	2	1	no	—
198	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
202	C₅×Dic₆	—	2	2	no	—
203	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
206	C₃×C₄×D₅	—	2	1	no	—
207	C₃×C₄×D₅	—	2	1	no	—
208	C₃×C₄×D₅	—	2	2	no	—
209	C₃×C₄×D₅	—	2	2	no	—
210	#1202	—	2	2	no	—
211	#1202	—	2	2	no	—
212	#1200	—	2	2	no	—
213	#1200	—	2	2	no	—
214	#1200	—	2	2	no	—
215	#1200	M₁₆	1	4	yes	complemented
216	C₃×C₅×C₈	—	2	1	no	—
217	C₃×C₅×C₈	—	2	1	no	—
218	C₃⋊#168	—	2	1	no	—
219	C₃⋊#168	#41	1	2	yes	complemented
220	C₃×#168	—	2	1	no	—
221	C₃×#168	—	2	1	no	—
222	C₅×C₃⋊C₈	—	2	1	no	—
223	C₅×C₃⋊C₈	#41	1	2	yes	complemented
224	C₂×#235	—	5	1	no	—
225	C₂×C₃×C₄²	—	5	1	no	—
226	C₄×#67	—	5	1	no	—
227	C₄×#67	—	5	1	no	—
228	C₄×#67	—	5	1	no	—
229	C₄×#67	—	5	1	no	—
230	#926	—	5	1	no	—
231	C₂×#208	—	5	1	no	—
232	C₂×#208	—	5	1	no	—
233	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
234	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
235	C₂×D₃×C₈	—	5	1	no	—
236	C₂×D₃×C₈	—	5	1	no	—
237	C₄×D₁₂	—	5	1	no	—
238	C₄×D₁₂	—	5	1	no	—
239	#872	—	5	1	no	—
240	#872	—	5	1	no	—
241	C₄²×D₃	—	5	1	no	—
242	C₄²×D₃	—	5	1	no	—
243	C₄×Dic₆	—	5	1	no	—
244	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
245	C₃×C₄⋊C₈	—	5	1	no	—
246	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
247	C₃×C₂²⋊C₈	—	5	1	no	—
248	C₃×C₂²⋊C₈	—	5	1	no	—
249	C₃×C₄×C₈	—	5	1	no	—
250	C₃×C₄×C₈	—	5	1	no	—
251	(C₂×D₃)⋊C₈	—	5	1	no	—
252	(C₂×D₃)⋊C₈	—	5	1	no	—
253	(C₂×D₃)⋊C₈	—	5	1	no	—
254	(C₂×D₃)⋊C₈	—	5	1	no	—
255	#815	—	5	1	no	—
256	#815	C₂×D₅	1	1	yes	characteristic
257	Dic₃⋊C₈	—	5	1	no	—
258	Dic₃⋊C₈	—	5	1	no	—
259	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
260	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
261	C₈×Dic₃	—	5	1	no	—
262	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
263	#803	—	5	1	no	—
264	#803	C₂×D₅	1	1	yes	characteristic
265	C₄×C₃⋊C₈	—	5	1	no	—
266	C₄×C₃⋊C₈	—	5	1	no	—
267	C₂×C₅×Q₈	—	3	1	no	—
268	#713	—	6	4	no	—
269	C₂×D₂₀	—	3	1	no	—
270	C₂×D₂₀	—	3	1	no	—
271	C₂×D₂₀	—	3	1	no	—
272	C₂×C₄×D₅	—	3	1	no	—
273	C₂×C₄×D₅	—	3	1	no	—
274	C₂×C₄×D₅	—	3	1	no	—
275	C₂×C₄×D₅	—	3	1	no	—
276	C₂×C₄×D₅	—	3	1	no	—
277	C₂×C₄×D₅	—	3	1	no	—
278	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
279	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
280	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
281	C₂×C₅×C₈	—	3	1	no	—
282	C₂×C₅×C₈	—	3	1	no	—
283	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
285	C₅×C₄⋊C₄	—	3	1	no	—
286	C₅×C₄⋊C₄	—	3	1	no	—
287	C₅×C₄⋊C₄	—	3	1	no	—
288	C₄²×C₅	—	3	1	no	—
289	C₄²×C₅	—	3	1	no	—
290	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
291	#685	—	3	1	no	—
292	#685	—	3	1	no	—
293	#685	—	3	1	no	—
294	#685	—	3	1	no	—
295	#685	—	3	1	no	—
296	#685	—	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	—	3	1	no	—
302	C₄×Dic₅	—	3	1	no	—
303	C₄×Dic₅	—	3	1	no	—
304	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
305	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
306	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
307	C₂×#168	—	3	1	no	—
308	C₂×#168	—	3	1	no	—
309	C₂×#168	C₂²×D₃	1	1	yes	characteristic
310	C₂×#168	C₂²×D₃	1	1	yes	characteristic
311	#676	—	6	2	no	—
312	#676	—	6	2	no	—
313	#676	—	6	2	no	—
314	#676	—	6	2	no	—
315	C₈×D₅	—	6	2	no	—
316	C₈×D₅	—	6	2	no	—
317	C₄×#41	—	15	1	no	—
318	#446	—	3	1	no	—
319	#446	—	15	1	no	—
320	#436	—	15	1	no	—
321	#436	—	15	1	no	—
322	#435	—	15	1	no	—
323	#435	—	15	1	no	—
324	#435	—	15	1	no	—
325	#435	—	15	1	no	—
326	#431	—	5	1	no	—
327	#431	—	15	1	no	—
328	#431	—	15	1	no	—
329	C₄×M₁₆	—	15	1	no	—
330	C₄×M₁₆	—	15	1	no	—
331	C₂×C₄×C₈	—	15	1	no	—
332	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
333	C₂×D₁₅	—	2	1	no	—
334	C₂×D₁₅	—	2	1	no	—
335	C₂×D₁₅	—	2	1	no	—
336	C₂×D₁₅	—	2	1	no	—
337	C₂×D₁₅	—	2	1	no	—
338	C₂×D₁₅	C₂×M₁₆	1	2	yes	—
339	C₂×C₃×D₅	—	2	1	no	—
340	C₂×C₃×D₅	—	2	1	no	—
341	C₂×C₃×D₅	—	2	1	no	—
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	—	2	1	no	—
344	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
345	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
346	Dic₁₅	—	2	1	no	—
347	Dic₁₅	—	2	1	no	—
348	C₃×Dic₅	—	2	1	no	—
349	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
350	C₃×Dic₅	#131	1	2	yes	—
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	—	2	1	no	—
353	C₅×Dic₃	—	2	1	no	—
354	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
355	C₂²×C₃×C₄	—	5	1	no	—
356	C₂²×C₃×C₄	—	5	1	no	—
357	C₂²×C₃×C₄	—	5	1	no	—
358	C₂×#67	—	5	1	no	—
359	C₂×#67	—	5	1	no	—
360	#235	—	10	4	no	—
361	C₂×D₁₂	—	5	1	no	—
362	C₂×C₄×D₃	—	5	1	no	—
363	C₂×C₄×D₃	—	5	1	no	—
364	C₂×C₄×D₃	—	5	1	no	—
365	C₂×C₄×D₃	—	5	1	no	—
366	C₂×C₄×D₃	—	5	1	no	—
367	C₂×C₄×D₃	—	5	1	no	—
368	C₂×Dic₆	C₄×D₅	1	1	yes	characteristic
369	C₂×C₃×C₈	—	5	1	no	—
370	C₂×C₃×C₈	—	5	1	no	—
371	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
372	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
373	C₃×C₄²	—	5	1	no	—
374	C₃×C₄²	—	5	1	no	—
375	C₃×C₄²	—	5	1	no	—
376	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
377	#217	—	5	1	no	—
378	#217	—	5	1	no	—
379	(C₂×D₃)⋊C₄	—	5	1	no	—
380	(C₂×D₃)⋊C₄	—	5	1	no	—
381	(C₂×D₃)⋊C₄	—	5	1	no	—
382	(C₂×D₃)⋊C₄	—	5	1	no	—
383	C₄⋊Dic₃	—	5	1	no	—
384	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
385	Dic₃⋊C₄	—	5	1	no	—
386	Dic₃⋊C₄	—	5	1	no	—
387	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
388	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
389	C₄×Dic₃	—	5	1	no	—
390	C₄×Dic₃	—	5	1	no	—
391	C₄×Dic₃	—	5	1	no	—
392	C₄×Dic₃	—	5	1	no	—
393	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
394	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
395	#208	—	10	2	no	—
396	#208	—	10	2	no	—
397	C₂×C₃⋊C₈	—	5	1	no	—
398	C₂×C₃⋊C₈	—	5	1	no	—
399	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
400	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
401	ΓL(1,𝔽₂₅)	—	10	2	no	—
402	ΓL(1,𝔽₂₅)	—	10	2	no	—
403	D₃×C₈	—	10	2	no	—
404	D₃×C₈	—	10	2	no	—
405	C₂²×D₅	—	3	1	no	—
406	C₂²×D₅	—	3	1	no	—
407	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
408	C₅×Q₈	—	6	2	no	—
409	C₂×C₄×C₅	—	3	1	no	—
410	C₂×C₄×C₅	—	3	1	no	—
411	C₂×C₄×C₅	—	3	1	no	—
412	C₂×C₄×C₅	—	3	1	no	—
413	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
414	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
415	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
416	C₂×Dic₅	—	3	1	no	—
417	C₂×Dic₅	—	3	1	no	—
418	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
419	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
420	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
421	D₂₀	—	6	2	no	—
422	D₂₀	—	6	2	no	—
423	D₂₀	—	6	2	no	—
424	C₄×D₅	—	2	1	no	—
425	C₄×D₅	—	2	1	no	—
426	C₄×D₅	—	2	2	no	—
427	C₄×D₅	—	2	2	no	—
428	C₄×D₅	—	3	4	no	—
429	C₄×D₅	—	6	1	no	—
430	C₄×D₅	—	6	1	no	—
431	C₄×D₅	—	6	1	no	—
432	C₄×D₅	—	6	1	no	—
433	C₄×D₅	—	6	2	no	—
434	C₄×D₅	—	6	2	no	—
435	C₄×D₅	—	6	2	no	—
436	C₅×C₈	—	2	1	no	—
437	C₅×C₈	—	2	1	no	—
438	C₅×C₈	—	3	2	no	—
439	C₅×C₈	—	6	1	no	—
440	#168	—	2	1	no	—
441	#168	—	2	1	no	—
442	#168	—	3	2	no	—
443	#168	—	6	1	no	—
444	C₂×#41	—	15	1	no	—
445	C₂×M₁₆	—	15	1	no	—
446	C₂×M₁₆	—	15	1	no	—
447	C₂×M₁₆	—	15	1	no	—
448	C₂×M₁₆	—	15	1	no	—
449	C₂²×C₈	—	15	1	no	—
450	C₂²×C₈	—	15	1	no	—
451	C₄×Q₈	—	3	1	no	—
452	C₄×Q₈	—	15	1	no	—
453	C₄×D₄	—	15	1	no	—
454	C₄×D₄	—	15	1	no	—
455	C₄×D₄	—	15	1	no	—
456	C₄×D₄	—	15	1	no	—
457	C₄×D₄	—	15	1	no	—
458	C₄×D₄	—	15	1	no	—
459	#117	—	15	1	no	—
460	#117	—	15	1	no	—
461	#117	—	15	1	no	—
462	C₂×C₄²	—	5	1	no	—
463	C₂×C₄²	—	15	1	no	—
464	C₂×C₄²	—	15	1	no	—
465	C₄⋊C₈	—	3	1	no	—
466	C₄⋊C₈	—	3	1	no	—
467	C₄⋊C₈	—	5	1	no	—
468	C₄⋊C₈	—	15	1	no	—
469	C₄⋊C₈	—	15	1	no	—
470	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic
471	C₂²⋊C₈	—	5	1	no	—
472	C₂²⋊C₈	—	5	1	no	—
473	C₂²⋊C₈	—	15	1	no	—
474	C₂²⋊C₈	—	15	1	no	—
475	C₂²⋊C₈	—	15	1	no	—
476	C₂²⋊C₈	—	15	1	no	—
477	#97	—	3	1	no	—
478	#97	—	3	1	no	—
479	#97	—	15	1	no	—
480	#97	—	15	1	no	—
481	C₄×C₈	—	3	1	no	—
482	C₄×C₈	—	5	1	no	—
483	C₄×C₈	—	5	1	no	—
484	C₄×C₈	—	15	1	no	—
485	C₄×C₈	—	15	1	no	—
486	C₄×C₈	—	15	1	no	—
487	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
488	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
489	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
490	D₁₅	—	2	2	no	—
491	D₁₅	—	4	1	no	—
492	C₃×D₅	—	4	1	no	—
493	C₂³×C₃	—	5	1	no	—
494	C₂²×D₃	—	5	1	no	—
495	C₂²×D₃	—	5	1	no	—
496	C₂×C₃×C₄	—	5	1	no	—
497	C₂×C₃×C₄	—	5	1	no	—
498	C₂×C₃×C₄	—	5	1	no	—
499	C₂×C₃×C₄	—	10	2	no	—
500	C₂×C₃×C₄	—	10	2	no	—
501	C₂×C₃×C₄	—	10	1	no	—
502	C₂×C₃×C₄	—	10	1	no	—
503	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
506	#67	—	10	2	no	—
507	#67	—	10	2	no	—
508	C₂×Dic₃	—	5	1	no	—
509	C₂×Dic₃	—	5	1	no	—
510	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
511	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
512	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
513	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
514	D₁₂	—	10	2	no	—
515	C₄×D₃	—	5	4	no	—
516	C₄×D₃	—	10	2	no	—
517	C₄×D₃	—	10	2	no	—
518	C₄×D₃	—	10	2	no	—
519	C₄×D₃	—	10	1	no	—
520	C₄×D₃	—	10	1	no	—
521	C₄×D₃	—	10	1	no	—
522	C₄×D₃	—	10	1	no	—
523	Dic₆	—	2	2	no	—
524	C₃×C₈	—	2	1	no	—
525	C₃×C₈	—	2	1	no	—
526	C₃×C₈	—	10	1	no	—
527	C₃×C₈	—	10	1	no	—
528	C₃⋊C₈	—	2	1	no	—
529	C₃⋊C₈	—	5	2	no	—
530	C₃⋊C₈	—	10	1	no	—
531	C₃⋊C₈	#713	1	2	yes	complemented
532	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
533	C₂×D₅	—	2	1	no	—
534	C₂×D₅	—	2	1	no	—
535	C₂×D₅	—	2	1	no	—
536	C₂×D₅	—	3	2	no	—
537	C₂×D₅	—	6	1	no	—
538	C₂×D₅	—	6	1	no	—
539	C₂×D₅	—	6	1	no	—
540	C₂×D₅	—	6	1	no	—
541	C₂×D₅	—	6	1	no	—
542	C₄×C₅	—	2	1	no	—
543	C₄×C₅	—	2	1	no	—
544	C₄×C₅	—	3	2	no	—
545	C₄×C₅	—	6	1	no	—
546	C₄×C₅	—	6	1	no	—
547	C₄×C₅	—	6	1	no	—
548	C₄×C₅	D₃×#41	1	1	yes	characteristic
549	C₄×C₅	D₃×#41	1	1	yes	characteristic
550	Dic₅	—	2	1	no	—
551	Dic₅	—	6	1	no	—
552	Dic₅	—	6	1	no	—
553	Dic₅	#901	1	2	yes	—
554	Dic₅	D₃×M₁₆	1	2	yes	—
555	#41	—	30	4	no	—
556	C₂×Q₈	—	3	1	no	—
557	C₂×D₄	—	15	1	no	—
558	C₂×D₄	—	15	1	no	—
559	C₂×D₄	—	15	1	no	—
560	C₂²×C₄	—	5	1	no	—
561	C₂²×C₄	—	5	1	no	—
562	C₂²×C₄	—	5	1	no	—
563	C₂²×C₄	—	15	1	no	—
564	C₂²×C₄	—	15	1	no	—
565	C₂²×C₄	—	15	1	no	—
566	C₂²×C₄	—	15	1	no	—
567	C₂²×C₄	—	15	1	no	—
568	C₂²×C₄	—	15	1	no	—
569	M₁₆	—	30	2	no	—
570	M₁₆	—	30	2	no	—
571	M₁₆	—	30	2	no	—
572	M₁₆	—	30	2	no	—
573	C₂×C₈	—	3	1	no	—
574	C₂×C₈	—	3	1	no	—
575	C₂×C₈	—	5	1	no	—
576	C₂×C₈	—	5	1	no	—
577	C₂×C₈	—	15	1	no	—
578	C₂×C₈	—	15	1	no	—
579	C₂×C₈	—	30	2	no	—
580	C₂×C₈	—	30	2	no	—
581	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
582	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
583	C₄⋊C₄	—	3	1	no	—
584	C₄⋊C₄	—	3	1	no	—
585	C₄⋊C₄	—	3	1	no	—
586	C₄⋊C₄	—	15	1	no	—
587	C₄⋊C₄	—	15	1	no	—
588	C₄⋊C₄	—	15	1	no	—
589	C₂²⋊C₄	—	15	1	no	—
590	C₂²⋊C₄	—	15	1	no	—
591	C₂²⋊C₄	—	15	1	no	—
592	C₂²⋊C₄	—	15	1	no	—
593	C₂²⋊C₄	—	15	1	no	—
594	C₂²⋊C₄	—	15	1	no	—
595	C₄²	—	3	1	no	—
596	C₄²	—	3	1	no	—
597	C₄²	—	5	1	no	—
598	C₄²	—	5	1	no	—
599	C₄²	—	5	1	no	—
600	C₄²	—	15	1	no	—
601	C₄²	—	15	1	no	—
602	C₄²	—	15	1	no	—
603	C₄²	—	15	1	no	—
604	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
605	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
606	C₂²×C₃	—	10	1	no	—
607	C₂²×C₃	—	10	1	no	—
608	C₂²×C₃	—	10	1	no	—
609	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
610	C₂×D₃	—	5	2	no	—
611	C₂×D₃	—	10	1	no	—
612	C₂×D₃	—	10	1	no	—
613	C₂×D₃	—	10	1	no	—
614	C₂×D₃	—	10	1	no	—
615	C₂×D₃	—	10	1	no	—
616	C₃×C₄	—	2	1	no	—
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	5	2	no	—
619	C₃×C₄	—	5	2	no	—
620	C₃×C₄	—	10	1	no	—
621	C₃×C₄	C₂×#713	1	1	yes	characteristic
622	C₃×C₄	D₅×#41	1	1	yes	characteristic
623	Dic₃	—	2	1	no	—
624	Dic₃	—	2	1	no	—
625	Dic₃	—	2	1	no	—
626	Dic₃	—	10	1	no	—
627	Dic₃	—	10	1	no	—
628	Dic₃	D₅×M₁₆	1	2	yes	—
629	C₂×C₅	#5522	1	1	yes	characteristic
630	C₂×C₅	C₂×#901	1	1	yes	characteristic
631	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
632	D₅	—	4	1	no	—
633	D₅	—	6	2	no	—
634	D₅	—	12	1	no	—
635	C₂³	—	5	1	no	—
636	C₂³	—	15	1	no	—
637	C₂³	—	15	1	no	—
638	Q₈	—	6	2	no	—
639	D₄	—	30	2	no	—
640	D₄	—	30	2	no	—
641	D₄	—	30	2	no	—
642	C₂×C₄	—	3	1	no	—
643	C₂×C₄	—	3	1	no	—
644	C₂×C₄	—	3	1	no	—
645	C₂×C₄	—	3	1	no	—
646	C₂×C₄	—	5	1	no	—
647	C₂×C₄	—	5	1	no	—
648	C₂×C₄	—	5	1	no	—
649	C₂×C₄	—	10	2	no	—
650	C₂×C₄	—	10	2	no	—
651	C₂×C₄	—	10	1	no	—
652	C₂×C₄	—	10	1	no	—
653	C₂×C₄	—	15	4	no	—
654	C₂×C₄	—	15	1	no	—
655	C₂×C₄	—	15	1	no	—
656	C₂×C₄	—	30	2	no	—
657	C₂×C₄	—	30	2	no	—
658	C₂×C₄	—	30	2	no	—
659	C₂×C₄	—	30	1	no	—
660	C₂×C₄	—	30	1	no	—
661	C₂×C₄	—	30	1	no	—
662	C₂×C₄	—	30	1	no	—
663	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
664	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
666	C₈	—	2	1	no	—
667	C₈	—	2	1	no	—
668	C₈	—	3	2	no	—
669	C₈	—	6	1	no	—
670	C₈	—	10	1	no	—
671	C₈	—	10	1	no	—
672	C₈	—	15	2	no	—
673	C₈	—	30	1	no	—
674	C₂×C₃	—	20	1	no	—
675	C₂×C₃	C₄×#713	1	1	yes	characteristic
676	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
677	C₂×C₃	D₅×#131	1	1	yes	characteristic
678	D₃	—	10	2	no	—
679	D₃	—	20	1	no	—
680	C₅	#79278	1	1	yes	characteristic, complemented, Sylow
681	C₂²	—	10	1	no	—
682	C₂²	—	10	1	no	—
683	C₂²	—	10	1	no	—
684	C₂²	—	15	2	no	—
685	C₂²	—	30	1	no	—
686	C₂²	—	30	1	no	—
687	C₂²	—	30	1	no	—
688	C₂²	—	30	1	no	—
689	C₂²	—	30	1	no	—
690	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	3	2	no	—
694	C₄	—	5	2	no	—
695	C₄	—	5	2	no	—
696	C₄	—	6	1	no	—
697	C₄	—	6	1	no	—
698	C₄	—	6	1	no	—
699	C₄	—	10	1	no	—
700	C₄	—	30	1	no	—
701	C₄	—	30	1	no	—
702	C₄	#92024	1	1	yes	characteristic
703	C₄	D₃×#713	1	1	yes	characteristic
704	C₃	#10611669	1	1	yes	characteristic, complemented, Sylow
705	C₂	—	20	1	no	—
706	C₂	—	30	2	no	—
707	C₂	—	60	1	no	—
708	C₂	#11753403	1	1	yes	characteristic
709	C₂	D₅×#901	1	1	yes	characteristic
710	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	C₂×#6773	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄⋊C₈	D₃×D₅
hypocenter	C₃×C₅	#2965
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. #11750937	C₂	semidirect
3. C₅×#4828	C₂	semidirect
4. C₃×#65122	C₂	semidirect
5. #11747728	C₂	semidirect
6. #11747726	C₂	semidirect
7. #11747718	C₂	semidirect
8. #11747716	C₂	semidirect
9. #11747592	C₂	semidirect
10. #11747583	C₂	semidirect
11. #11747583	C₂	semidirect
12. C₈×#1200	C₂	semidirect
13. #11747003	C₂	semidirect
14. #11746995	C₂	semidirect
15. #11746858	C₂	semidirect
69. #65122	D₃	semidirect
132. #4828	D₅	semidirect
215. #1200	M₁₆	semidirect
219. C₃⋊#168	#41	semidirect
223. C₅×C₃⋊C₈	#41	semidirect
531. C₃⋊C₈	#713	semidirect
605. C₃×C₅	#2965	semidirect
680. C₅	#79278	semidirect
704. C₃	#10611669	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6773	2
#11750937	2
C₅×#4828	2
C₃×#65122	2
#11747728	2
#11747726	2
#11747718	2
#11747716	2
#11747592	2
#11747583	2
C₈×#1200	2
#11747003	2
#11746995	2
#11746858	2
#10611669	3
#79278	5