Subgroups — #14411570

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91267	C₂	1	1	yes	maximal, characteristic
2	C₂×#91266	C₂	1	1	yes	maximal, characteristic
3	#11752667	C₂	1	1	yes	maximal, characteristic
4	C₄×#6705	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64978	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748054	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748053	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
10	Dic₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
11	Dic₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
13	#11746983	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746979	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746975	C₂	1	1	yes	maximal, characteristic, complemented
16	#10610281	—	3	1	no	maximal, Hall
17	C₂×#6771	C₂²	1	1	yes	characteristic
18	C₂×#6705	C₂²	1	1	yes	characteristic
19	C₂×#6705	C₂²	1	1	yes	characteristic
20	C₄²×D₁₅	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×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₃×#4018	C₂²	1	1	yes	characteristic
27	#91442	C₄	1	2	yes	—
28	#91406	C₄	1	2	yes	—
29	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
30	#91396	C₄	1	2	yes	—
31	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
32	#91386	C₂²	1	1	yes	characteristic
33	#91325	C₄	1	2	yes	—
34	C₂×#6650	C₂²	1	1	yes	characteristic
35	C₂×#6649	C₂²	1	1	yes	characteristic
36	C₂×#6648	C₂²	1	1	yes	characteristic
37	C₂×#6648	C₂²	1	1	yes	characteristic
38	C₂×D₃×#168	C₂²	1	1	yes	characteristic
39	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
40	#91267	C₄	1	8	yes	complemented
41	#91266	C₄	1	8	yes	complemented
42	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	#91099	C₂²	1	1	yes	characteristic
44	#91099	C₂²	1	1	yes	characteristic
45	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
46	C₅×#815	C₂²	1	1	yes	characteristic
47	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
48	C₅×#803	C₂²	1	1	yes	characteristic
49	C₃×#3947	C₂²	1	1	yes	characteristic
50	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
51	C₃×#3935	C₂²	1	1	yes	characteristic
52	#90954	C₂²	1	1	yes	characteristic
53	#90954	C₂²	1	1	yes	characteristic
54	#90953	C₂²	1	1	yes	characteristic
55	#90952	C₂²	1	1	yes	characteristic
56	Dic₃×#168	C₂²	1	1	yes	characteristic
57	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
58	#78550	—	5	1	no	maximal, Hall
59	C₂×#4053	—	3	1	no	—
60	C₂×#4047	—	3	1	no	—
61	#65856	—	3	1	no	—
62	C₅×#405	—	3	1	no	—
63	M₁₆×Dic₅	—	3	1	no	—
64	C₂×#3947	—	3	1	no	—
65	#65286	—	3	1	no	—
66	#64997	—	3	1	no	—
67	#64997	—	3	1	no	—
68	D₅×#97	—	3	1	no	—
69	D₅×#97	—	3	1	no	—
70	#64978	—	3	1	no	—
71	#64978	D₃	1	1	yes	characteristic, complemented
72	C₄×#676	—	3	1	no	—
73	C₄×#676	—	3	1	no	—
74	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
75	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
76	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
78	C₂×#1204	C₂×C₄	1	1	yes	characteristic
79	C₂×#1203	C₂×C₄	1	1	yes	characteristic
80	C₂×#1202	C₂×C₄	1	1	yes	characteristic
81	C₂×#1201	C₂×C₄	1	1	yes	characteristic
82	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
83	C₂×D₅×Dic₃	C₂×C₄	1	2	yes	—
84	#6771	C₂×C₄	1	4	yes	—
85	#6771	C₂×C₄	1	4	yes	—
86	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₄×Dic₁₅	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	#6705	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×#685	C₂×C₄	1	2	yes	—
103	C₃×#683	C₂×C₄	1	2	yes	—
104	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
105	C₂×C₃×#168	C₂³	1	1	yes	characteristic
106	C₂×C₃×#168	C₂³	1	1	yes	characteristic
107	C₃×#676	C₂×C₄	1	4	yes	complemented
108	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
109	#6669	C₂×C₄	1	2	yes	—
110	#6667	C₂×C₄	1	2	yes	—
111	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
112	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
113	#6650	C₂×C₄	1	4	yes	complemented
114	#6649	C₂×C₄	1	4	yes	complemented
115	#6648	C₂×C₄	1	4	yes	complemented
116	#6648	C₂×C₄	1	4	yes	complemented
117	D₃×#168	C₂×C₄	1	4	yes	complemented
118	D₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
119	C₂×#907	—	5	1	no	—
120	C₂×#901	—	5	1	no	—
121	#5522	—	5	1	no	—
122	C₃×#405	—	5	1	no	—
123	Dic₃×M₁₆	—	5	1	no	—
124	C₂×#815	—	5	1	no	—
125	#4997	—	5	1	no	—
126	#4708	—	5	1	no	—
127	#4708	—	5	1	no	—
128	D₃×#97	—	5	1	no	—
129	D₃×#97	—	5	1	no	—
130	#4689	—	5	1	no	—
131	#4689	D₅	1	1	yes	characteristic, complemented
132	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
133	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
134	C₂×#709	—	3	1	no	—
135	C₂×C₅×M₁₆	—	3	1	no	—
136	C₂²×C₅×C₈	—	3	1	no	—
137	C₅×#117	—	3	1	no	—
138	C₂×C₄×Dic₅	—	3	1	no	—
139	C₂×#681	—	3	1	no	—
140	C₂²×#168	—	3	1	no	—
141	#4053	—	3	8	no	—
142	#4047	—	3	8	no	—
143	C₂×#676	—	3	1	no	—
144	C₂×#676	—	3	1	no	—
145	C₂×#676	—	3	1	no	—
146	C₂×#676	C₂×D₃	1	1	yes	characteristic
147	C₂×C₈×D₅	—	3	1	no	—
148	C₂×C₈×D₅	—	3	1	no	—
149	C₂×C₈×D₅	—	3	1	no	—
150	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
151	#4039	—	3	2	no	—
152	#4033	—	3	2	no	—
153	#4027	—	3	2	no	—
154	#4027	—	3	2	no	—
155	#4018	—	3	1	no	—
156	#4018	C₂×D₃	1	1	yes	characteristic
157	C₄²×D₅	—	3	1	no	—
158	C₄²×D₅	—	3	1	no	—
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
163	#3947	—	3	1	no	—
164	#3947	—	3	1	no	—
165	#3947	—	3	1	no	—
166	#3947	—	3	1	no	—
167	#3947	—	3	1	no	—
168	#3947	C₂×D₃	1	1	yes	characteristic
169	C₈×Dic₅	—	3	1	no	—
170	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
171	#3935	—	3	1	no	—
172	#3935	C₂×D₃	1	1	yes	characteristic
173	C₄×#168	—	3	1	no	—
174	C₄×#168	—	3	1	no	—
175	#2875	—	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×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
180	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
182	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
183	C₄×D₁₅	—	4	2	no	—
184	C₄×D₁₅	C₂²×C₄	1	2	yes	—
185	C₄×D₁₅	C₂²×C₄	1	2	yes	—
186	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
187	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
188	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
189	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
190	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
191	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
192	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
193	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
194	#1204	C₄²	1	4	yes	—
195	#1203	C₄²	1	4	yes	—
196	#1202	C₄²	1	4	yes	—
197	#1201	C₄²	1	4	yes	—
198	D₃×Dic₅	—	4	2	no	—
199	D₅×Dic₃	—	4	2	no	—
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	C₂×#235	—	5	1	no	—
209	C₂×C₃×M₁₆	—	5	1	no	—
210	C₂²×C₃×C₈	—	5	1	no	—
211	C₃×#117	—	5	1	no	—
212	C₂×C₄×Dic₃	—	5	1	no	—
213	C₂×#208	—	5	1	no	—
214	C₂²×C₃⋊C₈	—	5	1	no	—
215	#907	—	5	8	no	—
216	#901	—	5	8	no	—
217	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
218	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
219	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
220	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
221	C₂×D₃×C₈	—	5	1	no	—
222	C₂×D₃×C₈	—	5	1	no	—
223	C₂×D₃×C₈	—	5	1	no	—
224	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
225	#893	—	5	2	no	—
226	#887	—	5	2	no	—
227	#67⋊C₄	—	5	2	no	—
228	#67⋊C₄	—	5	2	no	—
229	#872	—	5	1	no	—
230	#872	C₂×D₅	1	1	yes	characteristic
231	C₄²×D₃	—	5	1	no	—
232	C₄²×D₃	—	5	1	no	—
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
237	#815	—	5	1	no	—
238	#815	—	5	1	no	—
239	#815	—	5	1	no	—
240	#815	—	5	1	no	—
241	#815	—	5	1	no	—
242	#815	C₂×D₅	1	1	yes	characteristic
243	C₈×Dic₃	—	5	1	no	—
244	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
245	#803	—	5	1	no	—
246	#803	C₂×D₅	1	1	yes	characteristic
247	C₄×C₃⋊C₈	—	5	1	no	—
248	C₄×C₃⋊C₈	—	5	1	no	—
249	C₂²×C₄×C₅	—	3	1	no	—
250	C₂×C₂²⋊D₅	—	3	1	no	—
251	C₂×C₂²⋊D₅	—	3	1	no	—
252	C₂²×Dic₅	—	3	2	no	—
253	#709	—	3	4	no	—
254	#709	—	3	4	no	—
255	C₂×D₂₀	—	3	1	no	—
256	C₂×C₄×D₅	—	3	1	no	—
257	C₂×C₄×D₅	—	3	2	no	—
258	C₂×C₄×D₅	—	3	2	no	—
259	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
260	C₂×Dic₁₀	—	3	1	no	—
261	C₅×M₁₆	—	3	4	no	—
262	C₂×C₅×C₈	—	3	1	no	—
263	C₂×C₅×C₈	—	3	1	no	—
264	C₂×C₅×C₈	—	3	4	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	2	no	—
268	C₅×C₂²⋊C₄	—	3	2	no	—
269	C₄²×C₅	—	3	1	no	—
270	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
271	#685	—	3	2	no	—
272	#685	C₄×D₃	1	2	yes	—
273	#683	—	3	2	no	—
274	#683	C₄×D₃	1	2	yes	—
275	C₄×Dic₅	—	3	2	no	—
276	C₄×Dic₅	—	3	1	no	—
277	C₄×Dic₅	—	3	2	no	—
278	C₄×Dic₅	—	3	2	no	—
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	C₄×D₃	1	4	yes	complemented
290	C₈×D₅	—	3	4	no	—
291	C₈×D₅	—	3	4	no	—
292	C₈×D₅	—	3	4	no	—
293	C₈×D₅	C₄×D₃	1	4	yes	complemented
294	C₂×#131	—	15	1	no	—
295	C₂×#131	—	15	1	no	—
296	C₄×#41	—	15	1	no	—
297	#405	—	3	1	no	—
298	#405	—	5	1	no	—
299	#405	—	15	1	no	—
300	#405	—	15	1	no	—
301	#405	—	15	1	no	—
302	#405	—	15	1	no	—
303	C₄×M₁₆	—	15	1	no	—
304	C₄×M₁₆	—	15	1	no	—
305	C₄×M₁₆	—	15	1	no	—
306	C₂×#97	—	15	1	no	—
307	C₂×#97	—	15	1	no	—
308	C₂×#97	—	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	C₃×C₄×C₅	—	2	2	no	—
317	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
318	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
319	Dic₁₅	—	2	2	no	—
320	Dic₁₅	C₂×C₄²	1	2	yes	—
321	C₃×Dic₅	—	2	2	no	—
322	C₃×Dic₅	C₂×C₄²	1	2	yes	—
323	C₅×Dic₃	—	2	2	no	—
324	C₅×Dic₃	C₂×C₄²	1	2	yes	—
325	C₂²×C₃×C₄	—	5	1	no	—
326	C₂×#67	—	5	1	no	—
327	C₂×#67	—	5	1	no	—
328	C₂²×Dic₃	—	5	2	no	—
329	#235	—	5	4	no	—
330	#235	—	5	4	no	—
331	C₂×D₁₂	—	5	1	no	—
332	C₂×C₄×D₃	—	5	1	no	—
333	C₂×C₄×D₃	—	5	2	no	—
334	C₂×C₄×D₃	—	5	2	no	—
335	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
336	C₂×Dic₆	—	5	1	no	—
337	C₃×M₁₆	—	5	4	no	—
338	C₂×C₃×C₈	—	5	1	no	—
339	C₂×C₃×C₈	—	5	1	no	—
340	C₂×C₃×C₈	—	5	4	no	—
341	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
342	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
343	C₃×C₄⋊C₄	—	5	2	no	—
344	C₃×C₂²⋊C₄	—	5	2	no	—
345	C₃×C₄²	—	5	1	no	—
346	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
347	(C₂×D₃)⋊C₄	—	5	2	no	—
348	(C₂×D₃)⋊C₄	C₄×D₅	1	2	yes	—
349	Dic₃⋊C₄	—	5	2	no	—
350	Dic₃⋊C₄	C₄×D₅	1	2	yes	—
351	C₄×Dic₃	—	5	2	no	—
352	C₄×Dic₃	—	5	1	no	—
353	C₄×Dic₃	—	5	2	no	—
354	C₄×Dic₃	—	5	2	no	—
355	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
356	#208	—	5	4	no	—
357	C₂×C₃⋊C₈	—	5	1	no	—
358	C₂×C₃⋊C₈	—	5	1	no	—
359	C₂×C₃⋊C₈	—	5	4	no	—
360	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
361	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
362	ΓL(1,𝔽₂₅)	—	5	4	no	—
363	ΓL(1,𝔽₂₅)	—	5	4	no	—
364	ΓL(1,𝔽₂₅)	—	5	4	no	—
365	ΓL(1,𝔽₂₅)	C₄×D₅	1	4	yes	complemented
366	D₃×C₈	—	5	4	no	—
367	D₃×C₈	—	5	4	no	—
368	D₃×C₈	—	5	4	no	—
369	D₃×C₈	C₄×D₅	1	4	yes	complemented
370	C₂³×C₅	—	3	1	no	—
371	C₂²×D₅	—	3	1	no	—
372	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
373	C₂×C₄×C₅	—	3	1	no	—
374	C₂×C₄×C₅	—	3	2	no	—
375	C₂×C₄×C₅	—	3	2	no	—
376	C₂×C₄×C₅	—	3	2	no	—
377	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
378	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
379	C₂²⋊D₅	—	3	4	no	—
380	C₂²⋊D₅	—	3	4	no	—
381	C₂×Dic₅	—	3	1	no	—
382	C₂×Dic₅	—	3	2	no	—
383	C₂×Dic₅	—	12	2	no	—
384	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
385	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
386	D₂₀	—	3	4	no	—
387	C₄×D₅	—	3	2	no	—
388	C₄×D₅	—	3	2	no	—
389	C₄×D₅	—	12	2	no	—
390	C₄×D₅	—	12	2	no	—
391	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
392	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
393	Dic₁₀	—	3	4	no	—
394	C₅×C₈	—	3	2	no	—
395	C₅×C₈	—	3	2	no	—
396	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
397	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
398	#168	—	3	2	no	—
399	#168	—	3	2	no	—
400	#168	C₂×C₄×D₃	1	2	yes	—
401	#168	C₂×C₄×D₃	1	2	yes	—
402	C₂×#41	—	15	1	no	—
403	#131	—	15	8	no	—
404	#131	—	15	8	no	—
405	C₂×M₁₆	—	3	1	no	—
406	C₂×M₁₆	—	5	1	no	—
407	C₂×M₁₆	—	15	1	no	—
408	C₂×M₁₆	—	15	1	no	—
409	C₂×M₁₆	—	15	1	no	—
410	C₂×M₁₆	—	15	1	no	—
411	C₂²×C₈	—	3	1	no	—
412	C₂²×C₈	—	5	1	no	—
413	C₂²×C₈	—	15	1	no	—
414	C₂²×C₈	—	15	1	no	—
415	C₂²×C₈	—	15	1	no	—
416	C₂²×C₈	—	15	1	no	—
417	C₄×Q₈	—	15	2	no	—
418	C₄×D₄	—	15	2	no	—
419	C₄×D₄	—	15	2	no	—
420	C₄×D₄	—	15	2	no	—
421	#117	—	3	1	no	—
422	#117	—	5	1	no	—
423	#117	—	15	1	no	—
424	C₂×C₄²	—	15	1	no	—
425	C₂×C₄²	—	15	1	no	—
426	C₂×C₄²	—	15	1	no	—
427	#97	—	3	1	no	—
428	#97	—	3	1	no	—
429	#97	—	5	1	no	—
430	#97	—	5	1	no	—
431	#97	—	15	1	no	—
432	#97	—	15	1	no	—
433	#97	—	15	1	no	—
434	#97	—	15	1	no	—
435	#97	—	15	1	no	—
436	#97	—	15	1	no	—
437	C₄×C₈	—	3	1	no	—
438	C₄×C₈	—	5	1	no	—
439	C₄×C₈	—	15	1	no	—
440	C₄×C₈	—	15	1	no	—
441	C₄×C₈	—	15	1	no	—
442	C₄×C₈	D₃×D₅	1	1	yes	characteristic
443	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
444	C₂×C₃×C₅	#568	1	2	yes	—
445	D₁₅	—	2	2	no	—
446	C₃×D₅	—	2	2	no	—
447	C₅×D₃	—	2	2	no	—
448	C₂³×C₃	—	5	1	no	—
449	C₂²×D₃	—	5	1	no	—
450	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
451	C₂×C₃×C₄	—	5	1	no	—
452	C₂×C₃×C₄	—	5	2	no	—
453	C₂×C₃×C₄	—	5	2	no	—
454	C₂×C₃×C₄	—	5	2	no	—
455	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
456	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
457	#67	—	5	4	no	—
458	#67	—	5	4	no	—
459	C₂×Dic₃	—	5	1	no	—
460	C₂×Dic₃	—	5	2	no	—
461	C₂×Dic₃	—	20	2	no	—
462	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
463	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
464	D₁₂	—	5	4	no	—
465	C₄×D₃	—	5	2	no	—
466	C₄×D₃	—	5	2	no	—
467	C₄×D₃	—	20	2	no	—
468	C₄×D₃	—	20	2	no	—
469	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
470	C₄×D₃	C₂×C₄×D₅	1	2	yes	—
471	Dic₆	—	5	4	no	—
472	C₃×C₈	—	5	2	no	—
473	C₃×C₈	—	5	2	no	—
474	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
475	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
476	C₃⋊C₈	—	5	2	no	—
477	C₃⋊C₈	—	5	2	no	—
478	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
479	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
480	C₂²×C₅	—	3	2	no	—
481	C₂²×C₅	—	6	2	no	—
482	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
483	C₂×D₅	—	2	2	no	—
484	C₂×D₅	—	3	2	no	—
485	C₂×D₅	—	6	2	no	—
486	C₂×D₅	C₄²×D₃	1	2	yes	—
487	C₄×C₅	—	2	2	no	—
488	C₄×C₅	—	3	2	no	—
489	C₄×C₅	—	6	2	no	—
490	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
491	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
492	Dic₅	—	2	2	no	—
493	Dic₅	—	3	2	no	—
494	Dic₅	—	6	2	no	—
495	Dic₅	C₄²×D₃	1	2	yes	—
496	#41	—	15	4	no	—
497	#41	—	15	4	no	—
498	C₂×Q₈	—	15	1	no	—
499	C₂×D₄	—	15	1	no	—
500	C₂×D₄	—	15	1	no	—
501	C₂×D₄	—	15	1	no	—
502	C₂²×C₄	—	3	1	no	—
503	C₂²×C₄	—	5	1	no	—
504	C₂²×C₄	—	15	2	no	—
505	C₂²×C₄	—	15	2	no	—
506	C₂²×C₄	—	15	1	no	—
507	C₂²×C₄	—	15	2	no	—
508	M₁₆	—	3	4	no	—
509	M₁₆	—	5	4	no	—
510	M₁₆	—	15	4	no	—
511	M₁₆	—	15	4	no	—
512	M₁₆	—	15	4	no	—
513	M₁₆	—	15	4	no	—
514	C₂×C₈	—	3	1	no	—
515	C₂×C₈	—	3	1	no	—
516	C₂×C₈	—	3	4	no	—
517	C₂×C₈	—	5	1	no	—
518	C₂×C₈	—	5	1	no	—
519	C₂×C₈	—	5	4	no	—
520	C₂×C₈	—	15	4	no	—
521	C₂×C₈	—	15	4	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	C₂×D₃×D₅	1	1	yes	characteristic
527	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
528	C₄⋊C₄	—	3	2	no	—
529	C₄⋊C₄	—	5	2	no	—
530	C₄⋊C₄	—	15	2	no	—
531	C₂²⋊C₄	—	3	2	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	—	15	2	no	—
534	C₄²	—	3	1	no	—
535	C₄²	—	5	1	no	—
536	C₄²	—	15	2	no	—
537	C₄²	—	15	2	no	—
538	C₄²	—	15	2	no	—
539	C₄²	—	15	1	no	—
540	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
541	C₃×C₅	#2875	1	1	yes	characteristic, complemented, Hall
542	C₂²×C₃	—	5	2	no	—
543	C₂²×C₃	—	10	2	no	—
544	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
545	C₂×D₃	—	2	2	no	—
546	C₂×D₃	—	5	2	no	—
547	C₂×D₃	—	10	2	no	—
548	C₂×D₃	C₄²×D₅	1	2	yes	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	5	2	no	—
551	C₃×C₄	—	10	2	no	—
552	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
553	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
554	Dic₃	—	2	2	no	—
555	Dic₃	—	5	2	no	—
556	Dic₃	—	10	2	no	—
557	Dic₃	C₄²×D₅	1	2	yes	—
558	C₂×C₅	—	6	2	no	—
559	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
560	C₂×C₅	#5750	1	2	yes	—
561	D₅	—	2	2	no	—
562	D₅	—	6	2	no	—
563	C₂³	—	3	1	no	—
564	C₂³	—	5	1	no	—
565	C₂³	—	15	1	no	—
566	Q₈	—	15	4	no	—
567	D₄	—	15	4	no	—
568	D₄	—	15	4	no	—
569	D₄	—	15	4	no	—
570	C₂×C₄	—	3	1	no	—
571	C₂×C₄	—	3	2	no	—
572	C₂×C₄	—	3	2	no	—
573	C₂×C₄	—	3	2	no	—
574	C₂×C₄	—	5	1	no	—
575	C₂×C₄	—	5	2	no	—
576	C₂×C₄	—	5	2	no	—
577	C₂×C₄	—	5	2	no	—
578	C₂×C₄	—	15	1	no	—
579	C₂×C₄	—	15	2	no	—
580	C₂×C₄	—	15	2	no	—
581	C₂×C₄	—	15	2	no	—
582	C₂×C₄	—	60	2	no	—
583	C₂×C₄	—	60	2	no	—
584	C₂×C₄	—	60	2	no	—
585	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
586	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
587	C₈	—	3	2	no	—
588	C₈	—	3	2	no	—
589	C₈	—	5	2	no	—
590	C₈	—	5	2	no	—
591	C₈	—	15	2	no	—
592	C₈	—	15	2	no	—
593	C₈	C₄×D₃×D₅	1	2	yes	—
594	C₈	C₄×D₃×D₅	1	2	yes	—
595	C₂×C₃	—	10	2	no	—
596	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
597	C₂×C₃	#66084	1	2	yes	—
598	D₃	—	2	2	no	—
599	D₃	—	10	2	no	—
600	C₅	#78550	1	1	yes	characteristic, complemented, Sylow
601	C₂²	—	3	2	no	—
602	C₂²	—	5	2	no	—
603	C₂²	—	6	2	no	—
604	C₂²	—	10	2	no	—
605	C₂²	—	15	2	no	—
606	C₂²	—	30	2	no	—
607	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
608	C₄	—	2	2	no	—
609	C₄	—	3	2	no	—
610	C₄	—	5	2	no	—
611	C₄	—	6	2	no	—
612	C₄	—	10	2	no	—
613	C₄	—	15	2	no	—
614	C₄	—	30	2	no	—
615	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
616	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
617	C₃	#10610281	1	1	yes	characteristic, complemented, Sylow
618	C₂	—	6	2	no	—
619	C₂	—	10	2	no	—
620	C₂	—	30	2	no	—
621	C₂	C₄²×D₃×D₅	1	1	yes	characteristic
622	C₂	#11753953	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	C₂×#6771	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2875
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. C₄×#6705	C₂	semidirect
5. C₅×#4689	C₂	semidirect
6. C₃×#64978	C₂	semidirect
7. #11748054	C₂	semidirect
8. #11748053	C₂	semidirect
9. D₃×#3947	C₂	semidirect
10. Dic₃×#676	C₂	semidirect
11. Dic₅×ΓL(1,𝔽₂₅)	C₂	semidirect
12. D₅×#815	C₂	semidirect
13. #11746983	C₂	semidirect
14. #11746979	C₂	semidirect
15. #11746975	C₂	semidirect
40. #91267	C₄	semidirect
41. #91266	C₄	semidirect
71. #64978	D₃	semidirect
93. #6705	C₂×C₄	semidirect
94. #6705	C₂×C₄	semidirect
100. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
101. C₅×D₃×C₈	C₂×C₄	semidirect
107. C₃×#676	C₂×C₄	semidirect
108. C₃×C₈×D₅	C₂×C₄	semidirect
113. #6650	C₂×C₄	semidirect
114. #6649	C₂×C₄	semidirect
115. #6648	C₂×C₄	semidirect
116. #6648	C₂×C₄	semidirect
117. D₃×#168	C₂×C₄	semidirect
118. D₅×C₃⋊C₈	C₂×C₄	semidirect
131. #4689	D₅	semidirect
289. #676	C₄×D₃	semidirect
293. C₈×D₅	C₄×D₃	semidirect
365. ΓL(1,𝔽₂₅)	C₄×D₅	semidirect
369. D₃×C₈	C₄×D₅	semidirect
541. C₃×C₅	#2875	semidirect
600. C₅	#78550	semidirect
617. C₃	#10610281	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91267	2
C₂×#91266	2
#11752667	2
C₄×#6705	2
C₅×#4689	2
C₃×#64978	2
#11748054	2
#11748053	2
D₃×#3947	2
Dic₃×#676	2
Dic₅×ΓL(1,𝔽₂₅)	2
D₅×#815	2
#11746983	2
#11746979	2
#11746975	2
#10610281	3
#78550	5