Subgroups — #14411404

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91246	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×#676	C₂	1	1	yes	maximal, characteristic
3	D₅×#872	C₂	1	1	yes	maximal, characteristic
4	#11750790	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748055	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748054	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747668	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747665	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747601	C₂	1	1	yes	maximal, characteristic, complemented
12	Dic₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747003	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746981	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746977	C₂	1	1	yes	maximal, characteristic, complemented
16	#10610279	—	3	1	no	maximal, Hall
17	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
18	C₂×#6705	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
20	#91761	C₂²	1	1	yes	characteristic
21	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₅×#872	C₂²	1	1	yes	characteristic
24	C₂×C₃×#676	C₂²	1	1	yes	characteristic
25	C₂×C₃×#676	C₂²	1	1	yes	characteristic
26	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
27	D₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
28	#91402	C₄	1	2	yes	—
29	#91398	C₄	1	2	yes	—
30	D₅×Dic₃⋊C₄	C₄	1	2	yes	—
31	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
32	#91386	C₂²	1	1	yes	characteristic
33	#91371	C₂²	1	1	yes	characteristic
34	C₂×#6651	C₂²	1	1	yes	characteristic
35	C₂×#6650	C₂²	1	1	yes	characteristic
36	C₂×#6649	C₂²	1	1	yes	characteristic
37	C₂×#6649	C₂²	1	1	yes	characteristic
38	C₂×#6648	C₂²	1	1	yes	characteristic
39	C₂×D₃×#168	C₂²	1	1	yes	characteristic
40	#91246	C₄	1	8	yes	complemented
41	D₃×#676	C₄	1	8	yes	complemented
42	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
43	#91099	C₂²	1	1	yes	characteristic, complemented
44	C₈×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
45	#91087	C₂²	1	1	yes	characteristic, complemented
46	C₅×#815	C₂²	1	1	yes	characteristic, complemented
47	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
48	C₅×#803	C₂²	1	1	yes	characteristic, complemented
49	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
50	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
52	#90954	C₂²	1	1	yes	characteristic, complemented
53	#90953	C₂²	1	1	yes	characteristic, complemented
54	#90951	C₂²	1	1	yes	characteristic, complemented
55	Dic₃×#168	C₂²	1	1	yes	characteristic, complemented
56	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	#78514	—	5	1	no	maximal, Hall
59	C₂×D₅×M₁₆	—	3	1	no	—
60	C₂²×#676	—	3	1	no	—
61	D₅×#117	—	3	1	no	—
62	C₅×#405	—	3	1	no	—
63	#65411	—	3	1	no	—
64	#65390	—	3	1	no	—
65	#65286	—	3	1	no	—
66	#64997	—	3	1	no	—
67	#64997	—	3	1	no	—
68	#64996	—	3	1	no	—
69	#64996	—	3	1	no	—
70	#64978	—	3	1	no	—
71	#64978	—	3	1	no	—
72	C₄×#676	—	3	1	no	—
73	C₄×#676	D₃	1	1	yes	characteristic, complemented
74	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
76	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
78	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
79	C₂×#1200	C₂×C₄	1	1	yes	characteristic
80	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₂×D₅×Dic₃	C₂×C₄	1	2	yes	—
82	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₄×D₃×D₅	C₂×C₄	1	4	yes	—
84	C₄×D₃×D₅	C₂×C₄	1	4	yes	—
85	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
88	#6714	C₂×C₄	1	2	yes	—
89	#6712	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	4	yes	complemented
94	C₈×D₁₅	C₂×C₄	1	4	yes	complemented
95	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
96	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
97	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	complemented
101	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
102	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
103	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
104	C₂×C₃×#168	C₂³	1	1	yes	characteristic
105	C₂×C₃×#168	C₂³	1	1	yes	characteristic
106	C₃×#676	C₂×C₄	1	4	yes	—
107	C₃×#676	C₂×C₄	1	4	yes	—
108	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
109	#6669	C₂×C₄	1	2	yes	—
110	#6667	C₂×C₄	1	2	yes	—
111	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
112	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
113	#6651	C₂×C₄	1	4	yes	complemented
114	#6650	C₂×C₄	1	4	yes	complemented
115	#6649	C₂×C₄	1	4	yes	—
116	#6649	C₂×C₄	1	4	yes	—
117	#6648	C₂×C₄	1	4	yes	complemented
118	D₃×#168	C₂×C₄	1	4	yes	complemented
119	C₂×D₃×M₁₆	—	5	1	no	—
120	C₂×D₃×M₁₆	—	5	1	no	—
121	C₂×#872	—	5	1	no	—
122	C₃×C₄×M₁₆	—	5	1	no	—
123	Dic₃×M₁₆	—	5	1	no	—
124	Dic₃×M₁₆	—	5	1	no	—
125	C₄×#208	—	5	1	no	—
126	#4708	—	5	1	no	—
127	#4708	—	5	1	no	—
128	#4708	—	5	1	no	—
129	#4708	—	5	1	no	—
130	#4689	—	5	1	no	—
131	#4689	—	5	1	no	—
132	#4689	—	5	1	no	—
133	#4689	D₅	1	1	yes	characteristic, complemented
134	C₂²×C₄×D₅	—	3	1	no	—
135	C₂×C₅×M₁₆	—	3	1	no	—
136	C₂²×C₅×C₈	—	3	1	no	—
137	C₅×#117	—	3	1	no	—
138	#4072	—	3	1	no	—
139	C₂×#681	—	3	1	no	—
140	C₂²×#168	—	3	1	no	—
141	D₅×M₁₆	—	3	8	no	—
142	C₂×#676	—	3	1	no	—
143	C₂×#676	—	3	1	no	—
144	C₂×#676	—	3	1	no	—
145	C₂×#676	—	3	1	no	—
146	C₂×#676	—	3	8	no	—
147	C₂×#676	C₂×D₃	1	1	yes	characteristic
148	C₂×#676	C₂×D₃	1	1	yes	characteristic
149	C₂×C₈×D₅	—	3	1	no	—
150	C₂×C₈×D₅	—	3	1	no	—
151	#4038	—	3	2	no	—
152	D₅×C₄⋊C₄	—	3	2	no	—
153	D₅×C₂²⋊C₄	—	3	2	no	—
154	#4023	—	3	2	no	—
155	#4018	—	3	1	no	—
156	#4018	—	3	1	no	—
157	C₄²×D₅	—	3	1	no	—
158	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
159	C₅×#97	—	3	1	no	—
160	C₅×#97	—	3	1	no	—
161	C₄×C₅×C₈	—	3	1	no	—
162	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
163	#3947	—	3	1	no	—
164	#3947	—	3	1	no	—
165	#3947	C₂×D₃	1	1	yes	characteristic, complemented
166	#3947	C₂×D₃	1	1	yes	characteristic, complemented
167	C₈×Dic₅	—	3	1	no	—
168	C₈×Dic₅	—	3	1	no	—
169	C₈×Dic₅	—	3	1	no	—
170	C₈×Dic₅	—	3	1	no	—
171	#3935	—	3	1	no	—
172	#3935	—	3	1	no	—
173	C₄×#168	—	3	1	no	—
174	C₄×#168	C₂×D₃	1	1	yes	characteristic, complemented
175	#2873	—	15	1	no	Sylow
176	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
179	C₂×D₃×D₅	—	4	2	no	—
180	C₂×D₃×D₅	C₄²	1	4	yes	—
181	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
182	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
183	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
184	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
185	C₄×D₁₅	C₂²×C₄	1	2	yes	—
186	C₄×D₁₅	C₂²×C₄	1	2	yes	—
187	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
188	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
189	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
190	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
191	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
192	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
193	C₃×C₄×D₅	—	4	2	no	—
194	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
195	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
196	#1200	C₄²	1	4	yes	—
197	D₃×Dic₅	C₄²	1	4	yes	—
198	D₅×Dic₃	—	4	2	no	—
199	D₅×Dic₃	C₄²	1	4	yes	—
200	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
201	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
202	C₃⋊#168	C₂²×C₄	1	2	yes	—
203	C₃⋊#168	C₂²×C₄	1	2	yes	—
204	C₃×#168	C₂²×C₄	1	2	yes	—
205	C₃×#168	C₂²×C₄	1	2	yes	—
206	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
207	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
208	C₂²×C₄×D₃	—	5	1	no	—
209	C₂×C₃×M₁₆	—	5	1	no	—
210	C₂×C₃×M₁₆	—	5	1	no	—
211	C₂×C₃×C₄²	—	5	1	no	—
212	C₂×(C₂×D₃)⋊C₄	—	5	2	no	—
213	C₂×Dic₃⋊C₄	—	5	2	no	—
214	C₂×C₄×Dic₃	—	5	1	no	—
215	C₂×#208	—	5	1	no	—
216	C₂×#208	—	5	1	no	—
217	D₃×M₁₆	—	5	8	no	—
218	D₃×M₁₆	—	5	8	no	—
219	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
220	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
221	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
222	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
223	C₂×D₃×C₈	—	5	1	no	—
224	C₂×D₃×C₈	—	5	1	no	—
225	C₂×D₃×C₈	—	5	1	no	—
226	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
227	#872	—	5	1	no	—
228	#872	—	5	1	no	—
229	#872	—	5	2	no	—
230	#872	—	5	2	no	—
231	#872	—	5	1	no	—
232	#872	C₂×D₅	1	1	yes	characteristic
233	C₃×#97	—	5	1	no	—
234	C₃×#97	—	5	1	no	—
235	C₃×C₄×C₈	—	5	1	no	—
236	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
237	#815	—	5	1	no	—
238	#815	—	5	1	no	—
239	#815	—	5	1	no	—
240	#815	C₂×D₅	1	1	yes	characteristic, complemented
241	C₈×Dic₃	—	5	1	no	—
242	C₈×Dic₃	—	5	1	no	—
243	C₈×Dic₃	—	5	1	no	—
244	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
245	#803	—	5	1	no	—
246	#803	C₂×D₅	1	1	yes	characteristic, complemented
247	C₄×C₃⋊C₈	—	5	1	no	—
248	C₄×C₃⋊C₈	—	5	1	no	—
249	C₂³×D₅	—	3	1	no	—
250	C₂²×C₄×C₅	—	3	1	no	—
251	C₂²×Dic₅	—	3	1	no	—
252	C₂×C₄×D₅	—	3	1	no	—
253	C₂×C₄×D₅	—	3	1	no	—
254	C₂×C₄×D₅	—	3	1	no	—
255	C₂×C₄×D₅	—	3	4	no	—
256	C₂×C₄×D₅	—	3	4	no	—
257	C₂×C₄×D₅	—	3	2	no	—
258	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
259	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
260	C₅×M₁₆	—	3	4	no	—
261	C₂×C₅×C₈	—	3	1	no	—
262	C₂×C₅×C₈	—	3	1	no	—
263	C₂×C₅×C₈	—	3	4	no	—
264	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
265	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
266	C₅×C₄⋊C₄	—	3	2	no	—
267	C₅×C₂²⋊C₄	—	3	2	no	—
268	C₄²×C₅	—	3	1	no	—
269	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
270	C₂²⋊Dic₅	—	3	2	no	—
271	#685	—	3	2	no	—
272	#685	—	3	2	no	—
273	C₄⋊Dic₅	—	3	2	no	—
274	#683	—	3	2	no	—
275	#683	—	3	2	no	—
276	C₄×Dic₅	—	3	1	no	—
277	C₄×Dic₅	—	3	2	no	—
278	C₄×Dic₅	C₄×D₃	1	2	yes	—
279	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
280	#681	—	3	4	no	—
281	C₂×#168	—	3	1	no	—
282	C₂×#168	—	3	1	no	—
283	C₂×#168	—	3	4	no	—
284	C₂×#168	C₂²×D₃	1	1	yes	characteristic
285	C₂×#168	C₂²×D₃	1	1	yes	characteristic
286	#676	—	3	4	no	—
287	#676	—	3	4	no	—
288	#676	—	3	4	no	—
289	#676	—	3	4	no	—
290	#676	C₄×D₃	1	4	yes	—
291	#676	C₄×D₃	1	4	yes	—
292	C₈×D₅	—	3	4	no	—
293	C₈×D₅	—	3	4	no	—
294	C₂²×M₁₆	—	15	1	no	—
295	C₂²×M₁₆	—	15	1	no	—
296	C₂×#117	—	15	1	no	—
297	#405	—	3	1	no	—
298	#405	—	15	1	no	—
299	#405	—	15	1	no	—
300	#405	—	15	1	no	—
301	#405	—	15	1	no	—
302	#405	—	15	1	no	—
303	#405	—	15	1	no	—
304	#405	—	15	1	no	—
305	C₄×M₁₆	—	5	1	no	—
306	C₄×M₁₆	—	15	1	no	—
307	C₄×M₁₆	—	15	1	no	—
308	C₄×M₁₆	—	15	1	no	—
309	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
310	C₂×D₁₅	—	2	2	no	—
311	C₂×D₁₅	C₂×C₄²	1	2	yes	—
312	C₂×C₅×D₃	—	2	2	no	—
313	C₂×C₅×D₃	C₂×C₄²	1	2	yes	—
314	C₂×C₃×D₅	—	2	2	no	—
315	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
316	D₃×D₅	—	4	4	no	—
317	C₃×C₄×C₅	—	2	2	no	—
318	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
319	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
320	Dic₁₅	—	2	2	no	—
321	Dic₁₅	C₂×C₄²	1	2	yes	—
322	C₃×Dic₅	—	2	2	no	—
323	C₃×Dic₅	C₂×C₄²	1	2	yes	—
324	C₅×Dic₃	—	2	2	no	—
325	C₅×Dic₃	C₂×C₄²	1	2	yes	—
326	C₂³×D₃	—	5	1	no	—
327	C₂²×C₃×C₄	—	5	1	no	—
328	C₂²×C₃×C₄	—	5	2	no	—
329	C₂²×Dic₃	—	5	1	no	—
330	C₂²×Dic₃	—	5	2	no	—
331	C₂×C₄×D₃	—	5	1	no	—
332	C₂×C₄×D₃	—	5	1	no	—
333	C₂×C₄×D₃	—	5	1	no	—
334	C₂×C₄×D₃	—	5	4	no	—
335	C₂×C₄×D₃	—	5	4	no	—
336	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
337	C₃×M₁₆	—	5	4	no	—
338	C₃×M₁₆	—	5	4	no	—
339	C₂×C₃×C₈	—	5	1	no	—
340	C₂×C₃×C₈	—	5	1	no	—
341	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
342	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
343	C₃×C₄²	—	5	2	no	—
344	C₃×C₄²	—	5	1	no	—
345	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
346	(C₂×D₃)⋊C₄	—	5	2	no	—
347	(C₂×D₃)⋊C₄	—	5	2	no	—
348	(C₂×D₃)⋊C₄	—	5	2	no	—
349	(C₂×D₃)⋊C₄	C₄×D₅	1	2	yes	—
350	Dic₃⋊C₄	—	5	2	no	—
351	Dic₃⋊C₄	—	5	2	no	—
352	Dic₃⋊C₄	—	5	2	no	—
353	Dic₃⋊C₄	C₄×D₅	1	2	yes	—
354	C₄×Dic₃	—	5	1	no	—
355	C₄×Dic₃	—	5	2	no	—
356	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
357	#208	—	5	4	no	—
358	#208	—	5	4	no	—
359	C₂×C₃⋊C₈	—	5	1	no	—
360	C₂×C₃⋊C₈	—	5	1	no	—
361	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
362	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
363	ΓL(1,𝔽₂₅)	—	5	4	no	—
364	ΓL(1,𝔽₂₅)	—	5	4	no	—
365	ΓL(1,𝔽₂₅)	—	5	4	no	—
366	ΓL(1,𝔽₂₅)	C₄×D₅	1	4	yes	complemented
367	D₃×C₈	—	5	4	no	—
368	D₃×C₈	—	5	4	no	—
369	D₃×C₈	—	5	4	no	—
370	D₃×C₈	C₄×D₅	1	4	yes	complemented
371	C₂³×C₅	—	3	1	no	—
372	C₂²×D₅	—	3	1	no	—
373	C₂²×D₅	—	3	4	no	—
374	C₂²×D₅	—	12	2	no	—
375	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
376	C₂×C₄×C₅	—	3	1	no	—
377	C₂×C₄×C₅	—	3	2	no	—
378	C₂×C₄×C₅	—	3	2	no	—
379	C₂×C₄×C₅	—	3	2	no	—
380	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
381	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
382	C₂×Dic₅	—	3	1	no	—
383	C₂×Dic₅	—	3	4	no	—
384	C₂×Dic₅	—	3	2	no	—
385	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
386	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
387	C₄×D₅	—	3	4	no	—
388	C₄×D₅	—	3	2	no	—
389	C₄×D₅	—	3	2	no	—
390	C₄×D₅	—	3	4	no	—
391	C₄×D₅	—	4	2	no	—
392	C₄×D₅	—	12	2	no	—
393	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
394	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
395	C₅×C₈	—	3	2	no	—
396	C₅×C₈	—	3	2	no	—
397	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
398	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
399	#168	—	3	2	no	—
400	#168	—	3	2	no	—
401	#168	C₂×C₄×D₃	1	2	yes	—
402	#168	C₂×C₄×D₃	1	2	yes	—
403	C₂³×C₄	—	15	1	no	—
404	C₂×M₁₆	—	3	1	no	—
405	C₂×M₁₆	—	5	1	no	—
406	C₂×M₁₆	—	5	1	no	—
407	C₂×M₁₆	—	15	1	no	—
408	C₂×M₁₆	—	15	8	no	—
409	C₂×M₁₆	—	15	1	no	—
410	C₂×M₁₆	—	15	1	no	—
411	C₂×M₁₆	—	15	1	no	—
412	C₂×M₁₆	—	15	8	no	—
413	C₂×M₁₆	—	15	1	no	—
414	C₂²×C₈	—	3	1	no	—
415	C₂²×C₈	—	15	1	no	—
416	C₂²×C₈	—	15	1	no	—
417	C₂²×C₈	—	15	1	no	—
418	#117	—	3	1	no	—
419	#117	—	15	1	no	—
420	#117	—	15	2	no	—
421	#117	—	15	2	no	—
422	#117	—	15	1	no	—
423	#117	—	15	1	no	—
424	C₂×C₄⋊C₄	—	15	2	no	—
425	C₂×C₂²⋊C₄	—	15	2	no	—
426	C₂×C₄²	—	5	1	no	—
427	C₂×C₄²	—	15	1	no	—
428	#97	—	3	1	no	—
429	#97	—	3	1	no	—
430	#97	—	5	1	no	—
431	#97	—	5	1	no	—
432	#97	—	15	1	no	—
433	#97	—	15	1	no	—
434	#97	—	15	1	no	—
435	#97	—	15	1	no	—
436	C₄×C₈	—	3	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	D₃×D₅	1	1	yes	characteristic, complemented
444	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
445	C₂×C₃×C₅	#568	1	2	yes	—
446	D₁₅	—	2	2	no	—
447	C₃×D₅	—	2	2	no	—
448	C₅×D₃	—	2	2	no	—
449	C₂³×C₃	—	5	1	no	—
450	C₂²×D₃	—	5	1	no	—
451	C₂²×D₃	—	5	4	no	—
452	C₂²×D₃	—	20	2	no	—
453	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
454	C₂×C₃×C₄	—	5	1	no	—
455	C₂×C₃×C₄	—	5	2	no	—
456	C₂×C₃×C₄	—	5	2	no	—
457	C₂×C₃×C₄	—	5	2	no	—
458	C₂×C₃×C₄	—	20	2	no	—
459	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
460	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
461	C₂×Dic₃	—	5	1	no	—
462	C₂×Dic₃	—	5	4	no	—
463	C₂×Dic₃	—	5	2	no	—
464	C₂×Dic₃	—	20	2	no	—
465	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
466	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
467	C₄×D₃	—	5	4	no	—
468	C₄×D₃	—	5	2	no	—
469	C₄×D₃	—	5	2	no	—
470	C₄×D₃	—	5	4	no	—
471	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
472	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
473	C₃×C₈	—	5	2	no	—
474	C₃×C₈	—	5	2	no	—
475	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
476	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
477	C₃⋊C₈	—	5	2	no	—
478	C₃⋊C₈	—	5	2	no	—
479	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
480	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
481	C₂²×C₅	—	3	2	no	—
482	C₂²×C₅	—	6	2	no	—
483	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
484	C₂×D₅	—	2	2	no	—
485	C₂×D₅	—	3	2	no	—
486	C₂×D₅	—	6	2	no	—
487	C₂×D₅	—	12	4	no	—
488	C₂×D₅	C₄²×D₃	1	2	yes	—
489	C₄×C₅	—	2	2	no	—
490	C₄×C₅	—	3	2	no	—
491	C₄×C₅	—	6	2	no	—
492	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
493	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
494	Dic₅	—	2	2	no	—
495	Dic₅	—	3	2	no	—
496	Dic₅	—	6	2	no	—
497	Dic₅	C₄²×D₃	1	2	yes	—
498	C₂⁴	—	15	1	no	—
499	C₂²×C₄	—	3	1	no	—
500	C₂²×C₄	—	5	1	no	—
501	C₂²×C₄	—	5	2	no	—
502	C₂²×C₄	—	15	1	no	—
503	C₂²×C₄	—	15	4	no	—
504	C₂²×C₄	—	15	4	no	—
505	C₂²×C₄	—	15	1	no	—
506	C₂²×C₄	—	15	2	no	—
507	C₂²×C₄	—	15	1	no	—
508	C₂²×C₄	—	15	1	no	—
509	M₁₆	—	3	4	no	—
510	M₁₆	—	5	4	no	—
511	M₁₆	—	5	4	no	—
512	M₁₆	—	15	4	no	—
513	M₁₆	—	15	4	no	—
514	M₁₆	—	15	4	no	—
515	M₁₆	—	15	4	no	—
516	M₁₆	—	15	4	no	—
517	C₂×C₈	—	3	1	no	—
518	C₂×C₈	—	3	1	no	—
519	C₂×C₈	—	3	4	no	—
520	C₂×C₈	—	5	1	no	—
521	C₂×C₈	—	5	1	no	—
522	C₂×C₈	—	15	4	no	—
523	C₂×C₈	—	15	4	no	—
524	C₂×C₈	—	15	1	no	—
525	C₂×C₈	—	15	1	no	—
526	C₂×C₈	—	15	4	no	—
527	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
528	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
529	C₄⋊C₄	—	3	2	no	—
530	C₄⋊C₄	—	15	2	no	—
531	C₄⋊C₄	—	15	2	no	—
532	C₄⋊C₄	—	15	2	no	—
533	C₂²⋊C₄	—	3	2	no	—
534	C₂²⋊C₄	—	15	2	no	—
535	C₂²⋊C₄	—	15	2	no	—
536	C₂²⋊C₄	—	15	2	no	—
537	C₄²	—	3	1	no	—
538	C₄²	—	5	2	no	—
539	C₄²	—	5	1	no	—
540	C₄²	—	15	2	no	—
541	C₄²	—	15	1	no	—
542	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
543	C₃×C₅	#2873	1	1	yes	characteristic, complemented, Hall
544	C₂²×C₃	—	5	2	no	—
545	C₂²×C₃	—	10	2	no	—
546	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
547	C₂×D₃	—	2	2	no	—
548	C₂×D₃	—	5	2	no	—
549	C₂×D₃	—	10	2	no	—
550	C₂×D₃	—	20	4	no	—
551	C₂×D₃	C₄²×D₅	1	2	yes	—
552	C₃×C₄	—	2	2	no	—
553	C₃×C₄	—	5	2	no	—
554	C₃×C₄	—	10	2	no	—
555	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
556	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
557	Dic₃	—	2	2	no	—
558	Dic₃	—	5	2	no	—
559	Dic₃	—	10	2	no	—
560	Dic₃	C₄²×D₅	1	2	yes	—
561	C₂×C₅	—	6	2	no	—
562	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
563	C₂×C₅	#5745	1	2	yes	—
564	D₅	—	2	2	no	—
565	D₅	—	6	2	no	—
566	C₂³	—	3	1	no	—
567	C₂³	—	5	1	no	—
568	C₂³	—	15	4	no	—
569	C₂³	—	15	1	no	—
570	C₂³	—	60	2	no	—
571	C₂×C₄	—	3	1	no	—
572	C₂×C₄	—	3	2	no	—
573	C₂×C₄	—	3	2	no	—
574	C₂×C₄	—	3	2	no	—
575	C₂×C₄	—	5	1	no	—
576	C₂×C₄	—	5	2	no	—
577	C₂×C₄	—	5	2	no	—
578	C₂×C₄	—	5	2	no	—
579	C₂×C₄	—	15	4	no	—
580	C₂×C₄	—	15	4	no	—
581	C₂×C₄	—	15	4	no	—
582	C₂×C₄	—	15	1	no	—
583	C₂×C₄	—	15	2	no	—
584	C₂×C₄	—	15	2	no	—
585	C₂×C₄	—	15	2	no	—
586	C₂×C₄	—	20	2	no	—
587	C₂×C₄	—	60	2	no	—
588	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
589	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
590	C₈	—	3	2	no	—
591	C₈	—	3	2	no	—
592	C₈	—	5	2	no	—
593	C₈	—	5	2	no	—
594	C₈	—	15	2	no	—
595	C₈	—	15	2	no	—
596	C₈	C₄×D₃×D₅	1	2	yes	—
597	C₈	C₄×D₃×D₅	1	2	yes	—
598	C₂×C₃	—	10	2	no	—
599	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
600	C₂×C₃	#66084	1	2	yes	—
601	D₃	—	2	2	no	—
602	D₃	—	10	2	no	—
603	C₅	#78514	1	1	yes	characteristic, complemented, Sylow
604	C₂²	—	3	2	no	—
605	C₂²	—	5	2	no	—
606	C₂²	—	6	2	no	—
607	C₂²	—	10	2	no	—
608	C₂²	—	15	2	no	—
609	C₂²	—	30	2	no	—
610	C₂²	—	60	4	no	—
611	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
612	C₄	—	2	2	no	—
613	C₄	—	3	2	no	—
614	C₄	—	5	2	no	—
615	C₄	—	6	2	no	—
616	C₄	—	10	2	no	—
617	C₄	—	15	2	no	—
618	C₄	—	30	2	no	—
619	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
620	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
621	C₃	#10610279	1	1	yes	characteristic, complemented, Sylow
622	C₂	—	6	2	no	—
623	C₂	—	10	2	no	—
624	C₂	—	30	2	no	—
625	C₂	C₄²×D₃×D₅	1	1	yes	characteristic
626	C₂	#11753949	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2873
LCS	G ▷ C₂×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
4. #11750790	C₂	semidirect
5. C₅×#4689	C₂	semidirect
6. C₃×C₄×#676	C₂	semidirect
7. #11748055	C₂	semidirect
8. #11748054	C₂	semidirect
9. #11747668	C₂	semidirect
10. #11747665	C₂	semidirect
11. #11747601	C₂	semidirect
12. Dic₃×#676	C₂	semidirect
13. #11747003	C₂	semidirect
14. #11746981	C₂	semidirect
15. #11746977	C₂	semidirect
40. #91246	C₄	semidirect
41. D₃×#676	C₄	semidirect
42. C₃×C₄×C₅×C₈	C₂²	semidirect
43. #91099	C₂²	semidirect
44. C₈×Dic₁₅	C₂²	semidirect
45. #91087	C₂²	semidirect
46. C₅×#815	C₂²	semidirect
47. C₅×C₈×Dic₃	C₂²	semidirect
48. C₅×#803	C₂²	semidirect
49. C₃×#3947	C₂²	semidirect
50. C₃×#3947	C₂²	semidirect
51. C₃×C₄×#168	C₂²	semidirect
52. #90954	C₂²	semidirect
53. #90953	C₂²	semidirect
54. #90951	C₂²	semidirect
55. Dic₃×#168	C₂²	semidirect
56. Dic₅×C₃⋊C₈	C₂²	semidirect
57. Dic₅×C₃⋊C₈	C₂²	semidirect
73. C₄×#676	D₃	semidirect
93. #6705	C₂×C₄	semidirect
94. C₈×D₁₅	C₂×C₄	semidirect
100. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
101. C₅×D₃×C₈	C₂×C₄	semidirect
113. #6651	C₂×C₄	semidirect
114. #6650	C₂×C₄	semidirect
117. #6648	C₂×C₄	semidirect
118. D₃×#168	C₂×C₄	semidirect
133. #4689	D₅	semidirect
162. C₄×C₅×C₈	C₂×D₃	semidirect
165. #3947	C₂×D₃	semidirect
166. #3947	C₂×D₃	semidirect
174. C₄×#168	C₂×D₃	semidirect
236. C₃×C₄×C₈	C₂×D₅	semidirect
240. #815	C₂×D₅	semidirect
244. C₈×Dic₃	C₂×D₅	semidirect
246. #803	C₂×D₅	semidirect
366. ΓL(1,𝔽₂₅)	C₄×D₅	semidirect
370. D₃×C₈	C₄×D₅	semidirect
443. C₄×C₈	D₃×D₅	semidirect
543. C₃×C₅	#2873	semidirect
603. C₅	#78514	semidirect
621. C₃	#10610279	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91246	2
C₂×D₃×#676	2
D₅×#872	2
#11750790	2
C₅×#4689	2
C₃×C₄×#676	2
#11748055	2
#11748054	2
#11747668	2
#11747665	2
#11747601	2
Dic₃×#676	2
#11747003	2
#11746981	2
#11746977	2
#10610279	3
#78514	5