Subgroups — #14413883

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	#11753835	C₂	1	1	yes	maximal, characteristic
2	#11752365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65706	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751901	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751884	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751883	C₂	1	1	yes	maximal, characteristic
7	#11751883	C₂	1	1	yes	maximal, characteristic
8	#11751873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#6738	C₂	1	1	yes	maximal, characteristic, complemented
10	#11751809	C₂	1	1	yes	maximal, characteristic, complemented
11	#11751799	C₂	1	1	yes	maximal, characteristic, complemented
12	#11751798	C₂	1	1	yes	maximal, characteristic, complemented
13	#11751772	C₂	1	1	yes	maximal, characteristic, complemented
14	#11751770	C₂	1	1	yes	maximal, characteristic, complemented
15	#11751769	C₂	1	1	yes	maximal, characteristic, complemented
16	D₅⋊#433	—	3	1	no	maximal, Hall
17	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
18	C₂×#6738	C₂²	1	1	yes	characteristic
19	C₂×#6738	C₂²	1	1	yes	characteristic
20	C₂×#6738	C₂²	1	1	yes	characteristic
21	C₂×#6738	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×D₁₅	C₄	1	1	yes	characteristic
23	C₅×#892	C₄	1	1	yes	characteristic
24	C₃×#4038	C₂²	1	1	yes	characteristic
25	#91473	C₄	1	1	yes	characteristic
26	#91473	C₄	1	1	yes	characteristic
27	#91437	C₄	1	1	yes	characteristic
28	C₄×#1200	C₂²	1	1	yes	characteristic
29	C₄×#1200	C₂²	1	1	yes	characteristic
30	#91398	C₂²	1	1	yes	characteristic
31	#91398	C₂²	1	1	yes	characteristic
32	#91393	C₄	1	1	yes	characteristic
33	#91393	C₄	1	1	yes	characteristic
34	#91358	C₂²	1	1	yes	characteristic
35	#91338	C₄	1	1	yes	characteristic
36	#91233	C₂²	1	1	yes	characteristic, complemented
37	#91232	C₂²	1	1	yes	characteristic
38	#91232	C₂²	1	1	yes	characteristic
39	#91231	C₂²	1	1	yes	characteristic, complemented
40	C₄⋊(C₃⋊#170)	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₃⋊#170	C₂²	1	1	yes	characteristic, complemented
42	C₃×#4004	C₂²	1	1	yes	characteristic, complemented
43	C₃×#4003	C₂²	1	1	yes	characteristic
44	C₃×#4003	C₂²	1	1	yes	characteristic
45	C₃×#4002	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₄×#170	C₂²	1	1	yes	characteristic, complemented
48	#91177	C₂²	1	1	yes	characteristic, complemented
49	#91177	C₂²	1	1	yes	characteristic, complemented
50	Dic₃⋊#170	C₂²	1	1	yes	characteristic, complemented
51	Dic₃⋊#170	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₃)⋊#170	C₂²	1	1	yes	characteristic
53	(C₂×D₃)⋊#170	C₂²	1	1	yes	characteristic
54	(C₂×D₃)⋊#170	C₂²	1	1	yes	characteristic
55	(C₂×D₃)⋊#170	C₂²	1	1	yes	characteristic
56	#91169	C₂²	1	1	yes	characteristic, complemented
57	#91169	C₂²	1	1	yes	characteristic, complemented
58	Dic₃×#170	C₂²	1	1	yes	characteristic, complemented
59	Dic₃×#170	C₂²	1	1	yes	characteristic, complemented
60	D₃×#433	—	5	1	no	maximal, Hall
61	D₅×#117	—	3	1	no	—
62	D₅⋊(C₂²⋊C₈)	—	3	1	no	—
63	D₅⋊(C₂²⋊C₈)	—	3	1	no	—
64	#65706	—	3	1	no	—
65	#65706	—	3	1	no	—
66	#65706	—	3	1	no	—
67	#65706	D₃	1	1	yes	characteristic, complemented
68	#65697	—	3	1	no	—
69	#65697	—	3	1	no	—
70	#65697	—	3	1	no	—
71	#65697	—	3	1	no	—
72	D₅⋊(C₄⋊C₈)	—	3	1	no	—
73	D₅⋊(C₄⋊C₈)	—	3	1	no	—
74	#65676	—	3	1	no	—
75	C₄×D₅⋊C₈	—	3	1	no	—
76	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
82	C₂×#1200	C₂×C₄	1	1	yes	characteristic
83	C₂×#1200	C₂×C₄	1	1	yes	characteristic
84	C₂×#1200	C₂³	1	1	yes	characteristic
85	C₂×D₃×Dic₅	C₂³	1	1	yes	characteristic
86	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
87	C₄×D₃×D₅	—	2	2	no	—
88	C₄×D₃×D₅	—	2	2	no	—
89	C₂×C₃⋊#170	C₂³	1	1	yes	characteristic
90	C₂×C₃⋊#170	C₂³	1	1	yes	characteristic
91	C₂×C₃⋊#170	C₂³	1	1	yes	characteristic
92	C₂×C₃⋊#170	C₂³	1	1	yes	characteristic
93	C₂×C₃×#170	C₂³	1	1	yes	characteristic
94	C₂×C₃×#170	C₂³	1	1	yes	characteristic
95	C₂×C₃×#170	C₂³	1	1	yes	characteristic
96	C₂×C₃×#170	C₂³	1	1	yes	characteristic
97	#6738	—	2	2	no	—
98	#6738	—	2	2	no	—
99	#6738	—	2	2	no	—
100	#6738	—	2	2	no	—
101	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
103	#6712	C₂×C₄	1	1	yes	characteristic
104	#6712	C₂×C₄	1	1	yes	characteristic
105	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
108	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
109	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
110	C₃×#685	C₂×C₄	1	1	yes	characteristic
111	C₃×#685	C₂×C₄	1	1	yes	characteristic
112	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
113	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
114	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
115	#6669	C₂×C₄	1	1	yes	characteristic
116	#6669	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
118	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
119	#6665	C₂×C₄	1	1	yes	characteristic
120	#6665	C₂×C₄	1	1	yes	characteristic
121	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
122	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
123	Dic₃×Dic₅	C₂³	1	1	yes	characteristic
124	Dic₃×Dic₅	C₂³	1	1	yes	characteristic
125	D₃×#117	—	5	1	no	—
126	C₃×#433	—	5	1	no	—
127	#5000	—	5	1	no	—
128	#4840	—	5	1	no	—
129	#4840	—	5	1	no	—
130	D₃×C₄⋊C₈	—	5	1	no	—
131	D₃×C₄⋊C₈	—	5	1	no	—
132	D₃×C₂²⋊C₈	—	5	1	no	—
133	D₃×C₂²⋊C₈	—	5	1	no	—
134	#4720	—	5	1	no	—
135	#4720	—	5	1	no	—
136	#4709	—	5	1	no	—
137	D₃×#97	—	5	1	no	—
138	#4690	—	5	1	no	—
139	C₄×D₃×C₈	—	5	1	no	—
140	C₂²×C₄×D₅	—	3	1	no	—
141	C₂×D₅⋊C₈	—	3	1	no	—
142	C₂×D₅⋊C₈	—	3	1	no	—
143	C₂×D₅⋊C₈	—	3	1	no	—
144	C₂×D₅⋊C₈	—	3	1	no	—
145	C₅×#117	—	3	1	no	—
146	#4072	—	3	1	no	—
147	#4038	—	3	1	no	—
148	#4038	C₂×D₃	1	1	yes	characteristic
149	D₅×C₄⋊C₄	—	3	1	no	—
150	D₅×C₄⋊C₄	—	3	1	no	—
151	D₅×C₂²⋊C₄	—	3	1	no	—
152	D₅×C₂²⋊C₄	—	3	1	no	—
153	#4023	—	3	1	no	—
154	#4023	—	3	1	no	—
155	#4018	—	3	1	no	—
156	#4018	—	3	1	no	—
157	C₄²×D₅	—	3	1	no	—
158	C₄²×D₅	—	3	1	no	—
159	C₂²⋊#170	—	3	1	no	—
160	C₂²⋊#170	—	3	1	no	—
161	C₂²⋊#170	—	3	1	no	—
162	C₂²⋊#170	—	3	1	no	—
163	#4004	—	3	1	no	—
164	#4004	—	3	1	no	—
165	#4004	—	3	1	no	—
166	#4004	C₂×D₃	1	1	yes	characteristic, complemented
167	#4003	—	3	1	no	—
168	#4003	—	3	1	no	—
169	#4003	C₂×D₃	1	1	yes	characteristic
170	#4003	C₂×D₃	1	1	yes	characteristic
171	#4002	—	3	1	no	—
172	#4002	—	3	1	no	—
173	#4002	—	3	1	no	—
174	#4002	C₂×D₃	1	1	yes	characteristic, complemented
175	C₄⋊#170	—	3	1	no	—
176	C₄⋊#170	—	3	1	no	—
177	C₄⋊#170	—	3	1	no	—
178	C₄⋊#170	C₂×D₃	1	1	yes	characteristic, complemented
179	C₄×#170	—	3	1	no	—
180	C₄×#170	—	3	1	no	—
181	C₄×#170	—	3	1	no	—
182	C₄×#170	C₂×D₃	1	1	yes	characteristic, complemented
183	C₂×#433	—	15	1	no	Sylow
184	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×D₃×D₅	—	2	2	no	—
188	C₂×D₃×D₅	—	2	2	no	—
189	C₂×D₃×D₅	—	2	2	no	—
190	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
194	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
195	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
196	C₄×D₁₅	—	2	2	no	—
197	C₄×D₁₅	—	2	2	no	—
198	C₄×D₁₅	—	2	2	no	—
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	C₄×C₅×D₃	—	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	C₂⁴	1	1	yes	characteristic
206	C₃×C₄×D₅	—	2	1	no	—
207	C₃×C₄×D₅	—	2	1	no	—
208	#1200	—	2	2	no	—
209	#1200	—	2	2	no	—
210	#1200	#41	1	2	yes	—
211	#1200	#41	1	2	yes	—
212	D₃×Dic₅	—	2	1	no	—
213	D₃×Dic₅	—	2	1	no	—
214	D₅×Dic₃	—	2	2	no	—
215	C₃⋊#170	—	2	1	no	—
216	C₃⋊#170	—	2	1	no	—
217	C₃⋊#170	—	2	1	no	—
218	C₃⋊#170	—	2	1	no	—
219	C₃×#170	—	2	1	no	—
220	C₃×#170	—	2	1	no	—
221	C₃×#170	—	2	1	no	—
222	C₃×#170	—	2	1	no	—
223	C₂²×C₄×D₃	—	5	1	no	—
224	C₃×#117	—	5	1	no	—
225	#926	—	5	1	no	—
226	C₂×D₃×C₈	—	5	1	no	—
227	C₂×D₃×C₈	—	5	1	no	—
228	C₂×D₃×C₈	—	5	1	no	—
229	C₂×D₃×C₈	—	5	1	no	—
230	#892	—	5	1	no	—
231	#892	AGL(1,𝔽₅)	1	1	yes	characteristic
232	D₃×C₄⋊C₄	—	5	1	no	—
233	D₃×C₄⋊C₄	—	5	1	no	—
234	D₃×C₂²⋊C₄	—	5	1	no	—
235	D₃×C₂²⋊C₄	—	5	1	no	—
236	#877	—	5	1	no	—
237	#877	—	5	1	no	—
238	#872	—	5	1	no	—
239	#872	—	5	1	no	—
240	C₄²×D₃	—	5	1	no	—
241	C₄²×D₃	—	5	1	no	—
242	C₃×C₄⋊C₈	—	5	1	no	—
243	C₃×C₄⋊C₈	—	5	1	no	—
244	C₃×C₂²⋊C₈	—	5	1	no	—
245	C₃×C₂²⋊C₈	—	5	1	no	—
246	C₃×#97	—	5	1	no	—
247	C₃×C₄×C₈	—	5	1	no	—
248	#830	—	5	1	no	—
249	#830	—	5	1	no	—
250	(C₂×D₃)⋊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	#815	—	5	1	no	—
255	#815	—	5	1	no	—
256	Dic₃⋊C₈	—	5	1	no	—
257	Dic₃⋊C₈	—	5	1	no	—
258	Dic₃⋊C₈	—	5	1	no	—
259	Dic₃⋊C₈	—	5	1	no	—
260	C₈×Dic₃	—	5	1	no	—
261	C₈×Dic₃	—	5	1	no	—
262	C₄⋊(C₃⋊C₈)	—	5	1	no	—
263	C₄⋊(C₃⋊C₈)	—	5	1	no	—
264	#803	—	5	1	no	—
265	C₄×C₃⋊C₈	—	5	1	no	—
266	C₂³×D₅	—	3	1	no	—
267	C₂²×C₄×C₅	—	3	1	no	—
268	C₂²×Dic₅	—	3	1	no	—
269	C₂×C₄×D₅	—	3	1	no	—
270	C₂×C₄×D₅	—	3	1	no	—
271	C₂×C₄×D₅	—	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	—	6	2	no	—
277	C₂×C₄×D₅	—	6	2	no	—
278	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
279	C₂×#170	—	3	1	no	—
280	C₂×#170	—	3	1	no	—
281	C₂×#170	—	3	1	no	—
282	C₂×#170	—	3	1	no	—
283	C₂×#170	C₂²×D₃	1	1	yes	characteristic
284	C₂×#170	C₂²×D₃	1	1	yes	characteristic
285	C₂×#170	C₂²×D₃	1	1	yes	characteristic
286	C₂×#170	C₂²×D₃	1	1	yes	characteristic
287	D₅⋊C₈	—	6	2	no	—
288	D₅⋊C₈	—	6	2	no	—
289	D₅⋊C₈	—	6	2	no	—
290	D₅⋊C₈	—	6	2	no	—
291	C₅×C₄⋊C₄	—	3	1	no	—
292	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
293	C₅×C₂²⋊C₄	—	3	1	no	—
294	C₅×C₂²⋊C₄	—	3	1	no	—
295	C₄²×C₅	—	3	1	no	—
296	C₄²×C₅	—	3	1	no	—
297	C₂²⋊Dic₅	—	3	1	no	—
298	C₂²⋊Dic₅	—	3	1	no	—
299	#685	—	3	1	no	—
300	#685	—	3	1	no	—
301	#685	C₄×D₃	1	1	yes	characteristic
302	#685	C₄×D₃	1	1	yes	characteristic
303	C₄⋊Dic₅	—	3	1	no	—
304	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
305	#683	—	3	1	no	—
306	#683	—	3	1	no	—
307	#683	—	3	1	no	—
308	#683	—	3	1	no	—
309	C₄×Dic₅	—	3	1	no	—
310	C₄×Dic₅	—	3	1	no	—
311	C₄×Dic₅	—	3	1	no	—
312	C₄×Dic₅	—	3	1	no	—
313	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
314	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
315	C₂×#117	—	15	1	no	—
316	#433	—	5	1	no	—
317	#433	—	15	1	no	—
318	#433	—	15	1	no	—
319	#433	—	15	1	no	—
320	#433	—	15	1	no	—
321	#433	—	15	1	no	—
322	#433	—	15	1	no	—
323	#433	—	15	1	no	—
324	C₂×C₄⋊C₈	—	15	1	no	—
325	C₂×C₄⋊C₈	—	15	1	no	—
326	C₂×C₂²⋊C₈	—	15	1	no	—
327	C₂×C₂²⋊C₈	—	15	1	no	—
328	C₂×#97	—	15	1	no	—
329	C₂×C₄×C₈	—	15	1	no	—
330	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
331	C₂×D₁₅	#117	1	2	yes	—
332	C₂×D₁₅	#131	1	2	yes	—
333	C₂×D₁₅	#131	1	2	yes	—
334	C₂×C₅×D₃	—	2	1	no	—
335	C₂×C₅×D₃	—	2	1	no	—
336	C₂×C₅×D₃	—	2	1	no	—
337	C₂×C₃×D₅	—	2	1	no	—
338	C₂×C₃×D₅	—	2	1	no	—
339	C₂×C₃×D₅	—	2	1	no	—
340	D₃×D₅	—	4	4	no	—
341	C₃×C₄×C₅	—	2	1	no	—
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	—	2	1	no	—
344	Dic₁₅	—	2	1	no	—
345	Dic₁₅	—	2	1	no	—
346	Dic₁₅	—	2	1	no	—
347	C₃×Dic₅	—	2	1	no	—
348	C₃×Dic₅	—	2	1	no	—
349	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
350	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	—	2	1	no	—
353	C₅×Dic₃	#117	1	2	yes	—
354	C₂³×D₃	—	5	1	no	—
355	C₂²×C₃×C₄	—	5	1	no	—
356	C₂²×Dic₃	—	5	1	no	—
357	C₂×C₄×D₃	—	5	1	no	—
358	C₂×C₄×D₃	—	5	1	no	—
359	C₂×C₄×D₃	—	5	1	no	—
360	C₂×C₄×D₃	—	5	1	no	—
361	C₂×C₄×D₃	—	5	1	no	—
362	C₂×C₄×D₃	—	5	1	no	—
363	C₂×C₄×D₃	—	5	1	no	—
364	C₂×C₄×D₃	—	10	2	no	—
365	C₂×C₄×D₃	—	10	2	no	—
366	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₂×C₃×C₈	—	5	1	no	—
368	C₂×C₃×C₈	—	5	1	no	—
369	C₂×C₃×C₈	—	5	1	no	—
370	C₂×C₃×C₈	—	5	1	no	—
371	C₃×C₄⋊C₄	—	5	1	no	—
372	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₃×C₂²⋊C₄	—	5	1	no	—
374	C₃×C₂²⋊C₄	—	5	1	no	—
375	C₃×C₄²	—	5	1	no	—
376	C₃×C₄²	—	5	1	no	—
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	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
382	(C₂×D₃)⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₄⋊Dic₃	—	5	1	no	—
384	C₄⋊Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
385	Dic₃⋊C₄	—	5	1	no	—
386	Dic₃⋊C₄	—	5	1	no	—
387	Dic₃⋊C₄	—	5	1	no	—
388	Dic₃⋊C₄	—	5	1	no	—
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	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
394	C₄×Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
395	C₂×C₃⋊C₈	—	5	1	no	—
396	C₂×C₃⋊C₈	—	5	1	no	—
397	C₂×C₃⋊C₈	—	5	1	no	—
398	C₂×C₃⋊C₈	—	5	1	no	—
399	D₃×C₈	—	10	2	no	—
400	D₃×C₈	—	10	2	no	—
401	D₃×C₈	—	10	2	no	—
402	D₃×C₈	—	10	2	no	—
403	C₂³×C₅	—	3	1	no	—
404	C₂²×D₅	—	3	1	no	—
405	C₂²×D₅	—	6	2	no	—
406	C₂²×D₅	—	6	2	no	—
407	C₂²×D₅	—	6	2	no	—
408	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
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	—	6	2	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	C₂×C₄×D₃	1	1	yes	characteristic
416	C₂×Dic₅	—	3	1	no	—
417	C₂×Dic₅	—	3	1	no	—
418	C₂×Dic₅	—	3	1	no	—
419	C₂×Dic₅	—	6	1	no	—
420	C₂×Dic₅	—	6	1	no	—
421	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
422	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
423	C₂×Dic₅	C₂³×D₃	1	1	yes	characteristic
424	C₄×D₅	—	2	1	no	—
425	C₄×D₅	—	2	1	no	—
426	C₄×D₅	—	3	2	no	—
427	C₄×D₅	—	3	2	no	—
428	C₄×D₅	—	6	2	no	—
429	C₄×D₅	—	6	2	no	—
430	C₄×D₅	—	6	2	no	—
431	C₄×D₅	—	6	2	no	—
432	C₄×D₅	—	6	2	no	—
433	C₄×D₅	—	6	2	no	—
434	#170	—	2	1	no	—
435	#170	—	2	1	no	—
436	#170	—	2	1	no	—
437	#170	—	2	1	no	—
438	#170	—	6	1	no	—
439	#170	—	6	1	no	—
440	#170	—	6	1	no	—
441	#170	—	6	1	no	—
442	C₂³×C₄	—	15	1	no	—
443	C₂²×C₈	—	15	1	no	—
444	C₂²×C₈	—	15	1	no	—
445	C₂²×C₈	—	15	1	no	—
446	C₂²×C₈	—	15	1	no	—
447	#117	—	3	1	no	—
448	#117	—	5	1	no	—
449	#117	—	15	1	no	—
450	#117	—	15	1	no	—
451	#117	—	15	1	no	—
452	#117	—	15	1	no	—
453	#117	—	15	1	no	—
454	#117	—	15	1	no	—
455	C₂×C₄⋊C₄	—	15	1	no	—
456	C₂×C₄⋊C₄	—	15	1	no	—
457	C₂×C₂²⋊C₄	—	15	1	no	—
458	C₂×C₂²⋊C₄	—	15	1	no	—
459	C₂×C₄²	—	15	1	no	—
460	C₂×C₄²	—	15	1	no	—
461	C₄⋊C₈	—	5	1	no	—
462	C₄⋊C₈	—	5	1	no	—
463	C₄⋊C₈	—	15	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	C₂²⋊C₈	—	5	1	no	—
470	C₂²⋊C₈	—	5	1	no	—
471	C₂²⋊C₈	—	15	1	no	—
472	C₂²⋊C₈	—	15	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	—	5	1	no	—
478	#97	—	15	1	no	—
479	#97	—	15	1	no	—
480	#97	—	15	1	no	—
481	C₄×C₈	—	5	1	no	—
482	C₄×C₈	—	15	1	no	—
483	C₄×C₈	—	15	1	no	—
484	C₄×C₈	—	15	1	no	—
485	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
486	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
487	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
488	D₁₅	#433	1	4	yes	complemented
489	C₃×D₅	—	4	1	no	—
490	C₅×D₃	—	4	1	no	—
491	C₂³×C₃	—	5	1	no	—
492	C₂²×D₃	—	5	1	no	—
493	C₂²×D₃	—	10	2	no	—
494	C₂²×D₃	—	10	2	no	—
495	C₂²×D₃	—	10	2	no	—
496	C₂²×D₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
497	C₂×C₃×C₄	—	5	1	no	—
498	C₂×C₃×C₄	—	5	1	no	—
499	C₂×C₃×C₄	—	5	1	no	—
500	C₂×C₃×C₄	—	10	1	no	—
501	C₂×C₃×C₄	—	10	1	no	—
502	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
503	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
505	C₂×Dic₃	—	5	1	no	—
506	C₂×Dic₃	—	5	1	no	—
507	C₂×Dic₃	—	5	1	no	—
508	C₂×Dic₃	—	10	2	no	—
509	C₂×Dic₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
510	C₂×Dic₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
511	C₂×Dic₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
512	C₄×D₃	—	2	2	no	—
513	C₄×D₃	—	5	2	no	—
514	C₄×D₃	—	5	2	no	—
515	C₄×D₃	—	10	2	no	—
516	C₄×D₃	—	10	2	no	—
517	C₄×D₃	—	10	2	no	—
518	C₄×D₃	—	10	2	no	—
519	C₄×D₃	—	10	2	no	—
520	C₄×D₃	—	10	1	no	—
521	C₄×D₃	—	10	1	no	—
522	C₃×C₈	—	10	1	no	—
523	C₃×C₈	—	10	1	no	—
524	C₃×C₈	—	10	1	no	—
525	C₃×C₈	—	10	1	no	—
526	C₃⋊C₈	—	10	1	no	—
527	C₃⋊C₈	—	10	1	no	—
528	C₃⋊C₈	—	10	1	no	—
529	C₃⋊C₈	—	10	1	no	—
530	C₂²×C₅	—	6	1	no	—
531	C₂²×C₅	—	6	1	no	—
532	C₂²×C₅	—	6	1	no	—
533	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
534	C₂×D₅	—	2	1	no	—
535	C₂×D₅	—	2	1	no	—
536	C₂×D₅	—	2	1	no	—
537	C₂×D₅	—	3	2	no	—
538	C₂×D₅	—	3	2	no	—
539	C₂×D₅	—	3	2	no	—
540	C₂×D₅	—	12	4	no	—
541	C₄×C₅	—	2	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	Dic₅	—	2	1	no	—
548	Dic₅	—	2	1	no	—
549	Dic₅	—	6	1	no	—
550	Dic₅	—	6	1	no	—
551	Dic₅	—	6	1	no	—
552	Dic₅	D₃×#41	1	1	yes	characteristic
553	Dic₅	D₃×#41	1	1	yes	characteristic
554	C₂⁴	—	15	1	no	—
555	C₂²×C₄	—	3	1	no	—
556	C₂²×C₄	—	5	1	no	—
557	C₂²×C₄	—	15	1	no	—
558	C₂²×C₄	—	15	1	no	—
559	C₂²×C₄	—	15	1	no	—
560	C₂²×C₄	—	15	1	no	—
561	C₂²×C₄	—	15	1	no	—
562	C₂²×C₄	—	15	1	no	—
563	C₂²×C₄	—	15	1	no	—
564	C₂²×C₄	—	15	1	no	—
565	C₂²×C₄	—	30	2	no	—
566	C₂²×C₄	—	30	2	no	—
567	C₂×C₈	—	5	1	no	—
568	C₂×C₈	—	5	1	no	—
569	C₂×C₈	—	5	1	no	—
570	C₂×C₈	—	5	1	no	—
571	C₂×C₈	—	15	1	no	—
572	C₂×C₈	—	15	1	no	—
573	C₂×C₈	—	15	1	no	—
574	C₂×C₈	—	15	1	no	—
575	C₂×C₈	—	30	2	no	—
576	C₂×C₈	—	30	2	no	—
577	C₂×C₈	—	30	2	no	—
578	C₂×C₈	—	30	2	no	—
579	C₄⋊C₄	—	3	1	no	—
580	C₄⋊C₄	—	5	1	no	—
581	C₄⋊C₄	—	15	1	no	—
582	C₄⋊C₄	—	15	1	no	—
583	C₄⋊C₄	—	15	1	no	—
584	C₄⋊C₄	—	15	1	no	—
585	C₄⋊C₄	—	15	1	no	—
586	C₄⋊C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
587	C₂²⋊C₄	—	3	1	no	—
588	C₂²⋊C₄	—	3	1	no	—
589	C₂²⋊C₄	—	5	1	no	—
590	C₂²⋊C₄	—	5	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	—	15	1	no	—
600	C₄²	—	15	1	no	—
601	C₄²	—	15	1	no	—
602	C₄²	—	15	1	no	—
603	C₃×C₅	C₂×#433	1	1	yes	characteristic, complemented, Hall
604	C₂²×C₃	—	10	1	no	—
605	C₂²×C₃	—	10	1	no	—
606	C₂²×C₃	—	10	1	no	—
607	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
608	C₂×D₃	—	2	1	no	—
609	C₂×D₃	—	2	1	no	—
610	C₂×D₃	—	2	1	no	—
611	C₂×D₃	—	5	2	no	—
612	C₂×D₃	—	5	2	no	—
613	C₂×D₃	—	5	2	no	—
614	C₂×D₃	—	20	4	no	—
615	C₃×C₄	—	2	1	no	—
616	C₃×C₄	—	2	1	no	—
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	5	1	no	—
619	C₃×C₄	—	5	1	no	—
620	C₃×C₄	—	10	1	no	—
621	C₃×C₄	—	10	1	no	—
622	Dic₃	—	2	1	no	—
623	Dic₃	—	2	1	no	—
624	Dic₃	—	10	1	no	—
625	Dic₃	—	10	1	no	—
626	Dic₃	—	10	1	no	—
627	Dic₃	#4130	1	2	yes	—
628	C₂×C₅	—	12	1	no	—
629	C₂×C₅	D₃×#117	1	1	yes	characteristic
630	C₂×C₅	D₃×#131	1	1	yes	characteristic
631	C₂×C₅	D₃×#131	1	1	yes	characteristic
632	D₅	—	3	4	no	—
633	D₅	—	4	1	no	—
634	C₂³	—	3	1	no	—
635	C₂³	—	5	1	no	—
636	C₂³	—	15	1	no	—
637	C₂³	—	30	2	no	—
638	C₂³	—	30	2	no	—
639	C₂³	—	30	2	no	—
640	C₂×C₄	—	3	1	no	—
641	C₂×C₄	—	3	1	no	—
642	C₂×C₄	—	3	1	no	—
643	C₂×C₄	—	5	1	no	—
644	C₂×C₄	—	5	1	no	—
645	C₂×C₄	—	5	1	no	—
646	C₂×C₄	—	6	2	no	—
647	C₂×C₄	—	10	1	no	—
648	C₂×C₄	—	10	1	no	—
649	C₂×C₄	—	15	2	no	—
650	C₂×C₄	—	15	2	no	—
651	C₂×C₄	—	15	1	no	—
652	C₂×C₄	—	15	1	no	—
653	C₂×C₄	—	15	1	no	—
654	C₂×C₄	—	30	2	no	—
655	C₂×C₄	—	30	2	no	—
656	C₂×C₄	—	30	2	no	—
657	C₂×C₄	—	30	2	no	—
658	C₂×C₄	—	30	1	no	—
659	C₂×C₄	—	30	1	no	—
660	C₂×C₄	—	30	2	no	—
661	C₂×C₄	—	30	2	no	—
662	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
663	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
664	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
665	C₈	—	10	1	no	—
666	C₈	—	10	1	no	—
667	C₈	—	10	1	no	—
668	C₈	—	10	1	no	—
669	C₈	—	30	1	no	—
670	C₈	—	30	1	no	—
671	C₈	—	30	1	no	—
672	C₈	—	30	1	no	—
673	C₂×C₃	—	20	1	no	—
674	C₂×C₃	C₂×#4130	1	1	yes	characteristic
675	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
676	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
677	D₃	—	4	1	no	—
678	D₃	—	5	4	no	—
679	C₅	D₃×#433	1	1	yes	characteristic, complemented, Sylow
680	C₂²	—	6	1	no	—
681	C₂²	—	6	1	no	—
682	C₂²	—	6	1	no	—
683	C₂²	—	10	1	no	—
684	C₂²	—	10	1	no	—
685	C₂²	—	10	1	no	—
686	C₂²	—	15	2	no	—
687	C₂²	—	15	2	no	—
688	C₂²	—	15	2	no	—
689	C₂²	—	60	4	no	—
690	C₂²	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	3	2	no	—
695	C₄	—	5	1	no	—
696	C₄	—	5	1	no	—
697	C₄	—	6	1	no	—
698	C₄	—	6	1	no	—
699	C₄	—	10	1	no	—
700	C₄	—	10	1	no	—
701	C₄	—	30	1	no	—
702	C₄	—	30	1	no	—
703	C₄	—	30	1	no	—
704	C₃	D₅⋊#433	1	1	yes	characteristic, complemented, Sylow
705	C₂	—	12	1	no	—
706	C₂	—	15	4	no	—
707	C₂	—	20	1	no	—
708	C₂	D₃×#4130	1	1	yes	characteristic
709	C₂	#11756840	1	1	yes	characteristic
710	C₂	#11756849	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×AGL(1,𝔽₅)
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×C₄⋊C₄	C₂×C₄
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₂×C₃×Dic₅	C₂⁴
hypercenter	C₄⋊C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#433
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #11752365	C₂	semidirect
3. C₃×#65706	C₂	semidirect
4. #11751901	C₂	semidirect
5. #11751884	C₂	semidirect
8. #11751873	C₂	semidirect
9. C₄×#6738	C₂	semidirect
10. #11751809	C₂	semidirect
11. #11751799	C₂	semidirect
12. #11751798	C₂	semidirect
13. #11751772	C₂	semidirect
14. #11751770	C₂	semidirect
15. #11751769	C₂	semidirect
36. #91233	C₂²	semidirect
39. #91231	C₂²	semidirect
40. C₄⋊(C₃⋊#170)	C₂²	semidirect
41. C₄×C₃⋊#170	C₂²	semidirect
42. C₃×#4004	C₂²	semidirect
45. C₃×#4002	C₂²	semidirect
46. C₃×C₄⋊#170	C₂²	semidirect
47. C₃×C₄×#170	C₂²	semidirect
48. #91177	C₂²	semidirect
49. #91177	C₂²	semidirect
50. Dic₃⋊#170	C₂²	semidirect
51. Dic₃⋊#170	C₂²	semidirect
56. #91169	C₂²	semidirect
57. #91169	C₂²	semidirect
58. Dic₃×#170	C₂²	semidirect
59. Dic₃×#170	C₂²	semidirect
67. #65706	D₃	semidirect
166. #4004	C₂×D₃	semidirect
174. #4002	C₂×D₃	semidirect
178. C₄⋊#170	C₂×D₃	semidirect
182. C₄×#170	C₂×D₃	semidirect
488. D₁₅	#433	semidirect
603. C₃×C₅	C₂×#433	semidirect
679. C₅	D₃×#433	semidirect
704. C₃	D₅⋊#433	semidirect

Maximal subgroups

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

subgroup	index
#11753835	2
#11752365	2
C₃×#65706	2
#11751901	2
#11751884	2
#11751883	2
#11751873	2
C₄×#6738	2
#11751809	2
#11751799	2
#11751798	2
#11751772	2
#11751770	2
#11751769	2
D₅⋊#433	3
D₃×#433	5