Subgroups — #14411332

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₁₅	C₂	1	1	yes	maximal, characteristic
2	#11754461	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6648	C₂	1	1	yes	maximal, characteristic
4	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748323	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748318	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748054	C₂	1	2	yes	maximal, complemented
9	#11748053	C₂	1	2	yes	maximal, complemented
10	#11747603	C₂	1	2	yes	maximal, complemented
11	C₈×#1200	C₂	1	2	yes	maximal, complemented
12	D₅×#405	—	3	1	no	maximal, Hall
13	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×#6710	C₂²	1	1	yes	characteristic
16	M₁₆×D₁₅	C₄	1	8	yes	complemented
17	C₂×#6705	C₂²	1	2	yes	—
18	C₂×C₈×D₁₅	C₂²	1	2	yes	—
19	C₅×#926	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×#4072	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	#91561	C₄	1	2	yes	—
24	#91532	C₄	1	2	yes	—
25	#91437	C₄	1	2	yes	—
26	C₄×#1200	C₂²	1	2	yes	—
27	#91386	C₂²	1	2	yes	—
28	#91347	C₄	1	2	yes	—
29	C₂×#6648	C₄	1	8	yes	complemented
30	C₂×#6648	C₂²	1	1	yes	characteristic
31	C₂×#6648	C₂²	1	1	yes	characteristic
32	C₂×#6648	C₂²	1	1	yes	characteristic
33	C₂×#6648	C₂²	1	1	yes	characteristic
34	C₅×#815	C₂²	1	2	yes	complemented
35	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
36	C₃×#3947	C₂²	1	2	yes	complemented
37	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
38	#90953	C₂²	1	2	yes	complemented
39	#90952	C₂²	1	2	yes	complemented
40	Dic₃×#168	C₂²	1	2	yes	complemented
41	Dic₅×C₃⋊C₈	C₂²	1	2	yes	complemented
42	D₃×#405	—	5	1	no	maximal, Hall
43	C₂×D₅×M₁₆	—	3	1	no	—
44	C₂²×C₈×D₅	—	3	1	no	—
45	D₅×#117	—	3	1	no	—
46	C₅×#405	—	3	1	no	—
47	#65411	D₃	1	1	yes	characteristic, complemented
48	#65390	—	3	1	no	—
49	#65286	—	3	1	no	—
50	#64997	—	3	2	no	—
51	D₅×#97	—	3	2	no	—
52	#64978	—	3	2	no	—
53	C₄×C₈×D₅	—	3	2	no	—
54	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂×C₄	1	4	yes	—
60	C₂×C₄×D₁₅	C₂×C₄	1	4	yes	—
61	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
62	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
63	C₂×#1200	C₂×C₄	1	4	yes	—
64	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	#6710	C₂×C₄	1	4	yes	complemented
67	C₂×C₃⋊#168	C₂³	1	2	yes	—
68	#6705	C₂×C₄	1	8	yes	complemented
69	C₈×D₁₅	C₂×C₄	1	8	yes	—
70	C₅×#217	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
72	C₄×C₅×Dic₃	C₂³	1	2	yes	—
73	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
74	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
76	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
77	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
78	C₃×C₄×Dic₅	C₂³	1	2	yes	—
79	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	#6669	C₂×C₄	1	4	yes	—
83	#6667	C₂×C₄	1	4	yes	—
84	Dic₃×Dic₅	C₂×C₄	1	4	yes	—
85	#6648	C₂×C₄	1	4	yes	—
86	#6648	C₂×C₄	1	4	yes	—
87	#6648	C₂×C₄	1	4	yes	complemented
88	#6648	C₂×C₄	1	4	yes	complemented
89	C₂×D₃×M₁₆	—	5	1	no	—
90	C₂²×D₃×C₈	—	5	1	no	—
91	D₃×#117	—	5	1	no	—
92	C₃×#405	—	5	1	no	—
93	#5122	D₅	1	1	yes	characteristic, complemented
94	#5101	—	5	1	no	—
95	#4997	—	5	1	no	—
96	#4708	—	5	2	no	—
97	D₃×#97	—	5	2	no	—
98	#4689	—	5	2	no	—
99	C₄×D₃×C₈	—	5	2	no	—
100	C₂²×C₄×D₅	—	3	1	no	—
101	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
102	C₂²×C₅×C₈	—	3	1	no	—
103	C₅×#117	—	3	1	no	—
104	#4072	C₂×D₃	1	1	yes	characteristic
105	C₂×#681	—	3	1	no	—
106	C₂²×#168	C₂×D₃	1	1	yes	characteristic
107	D₅×M₁₆	—	3	8	no	—
108	C₂×#676	—	3	2	no	—
109	C₂×C₈×D₅	—	3	2	no	—
110	C₂×C₈×D₅	—	3	8	no	—
111	C₂×C₈×D₅	—	3	1	no	—
112	C₂×C₈×D₅	—	3	1	no	—
113	C₂×C₈×D₅	—	3	1	no	—
114	C₂×C₈×D₅	—	3	1	no	—
115	#4038	—	3	2	no	—
116	D₅×C₄⋊C₄	—	3	2	no	—
117	D₅×C₂²⋊C₄	—	3	2	no	—
118	#4023	—	3	2	no	—
119	#4018	—	3	2	no	—
120	C₄²×D₅	—	3	2	no	—
121	C₅×#97	—	3	2	no	—
122	C₄×C₅×C₈	—	3	2	no	—
123	#3947	—	3	2	no	—
124	#3947	C₂×D₃	1	2	yes	complemented
125	C₈×Dic₅	—	3	2	no	—
126	C₈×Dic₅	C₂×D₃	1	2	yes	complemented
127	#3935	—	3	2	no	—
128	C₄×#168	—	3	2	no	—
129	C₂×#405	—	15	1	no	Sylow
130	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×D₁₅	—	2	4	no	—
132	C₂²×D₁₅	C₄²	1	4	yes	—
133	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₂×Dic₁₅	C₄²	1	4	yes	—
140	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
142	C₄×D₁₅	C₄²	1	4	yes	—
143	C₄×D₁₅	C₄²	1	4	yes	—
144	C₄×D₁₅	C₂²×C₄	1	2	yes	—
145	C₄×D₁₅	C₂²×C₄	1	2	yes	—
146	C₄×D₁₅	C₂²×C₄	1	2	yes	—
147	C₄×D₁₅	C₂²×C₄	1	2	yes	—
148	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
149	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
150	#1200	—	2	8	no	—
151	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
152	C₃⋊#168	C₂²×C₄	1	4	yes	—
153	C₃×#168	C₂²×C₄	1	2	yes	—
154	C₃×#168	C₂²×C₄	1	2	yes	—
155	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
156	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×D₃	—	5	1	no	—
158	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
159	C₂²×C₃×C₈	—	5	1	no	—
160	C₃×#117	—	5	1	no	—
161	#926	C₂×D₅	1	1	yes	characteristic
162	C₂×#208	—	5	1	no	—
163	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
164	D₃×M₁₆	—	5	8	no	—
165	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
166	C₂×D₃×C₈	—	5	2	no	—
167	C₂×D₃×C₈	—	5	8	no	—
168	C₂×D₃×C₈	—	5	1	no	—
169	C₂×D₃×C₈	—	5	1	no	—
170	C₂×D₃×C₈	—	5	1	no	—
171	C₂×D₃×C₈	—	5	1	no	—
172	#892	—	5	2	no	—
173	D₃×C₄⋊C₄	—	5	2	no	—
174	D₃×C₂²⋊C₄	—	5	2	no	—
175	#877	—	5	2	no	—
176	#872	—	5	2	no	—
177	C₄²×D₃	—	5	2	no	—
178	C₃×#97	—	5	2	no	—
179	C₃×C₄×C₈	—	5	2	no	—
180	#815	—	5	2	no	—
181	#815	C₂×D₅	1	2	yes	complemented
182	C₈×Dic₃	—	5	2	no	—
183	C₈×Dic₃	C₂×D₅	1	2	yes	complemented
184	#803	—	5	2	no	—
185	C₄×C₃⋊C₈	—	5	2	no	—
186	C₂³×D₅	—	3	1	no	—
187	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
188	C₂²×Dic₅	—	3	1	no	—
189	C₂×C₄×D₅	—	3	1	no	—
190	C₂×C₄×D₅	—	3	1	no	—
191	C₂×C₄×D₅	—	3	4	no	—
192	C₂×C₄×D₅	—	3	4	no	—
193	C₂×C₄×D₅	—	3	1	no	—
194	C₂×C₄×D₅	—	3	1	no	—
195	C₂×C₄×D₅	—	3	4	no	—
196	C₅×M₁₆	C₄×D₃	1	4	yes	complemented
197	C₂×C₅×C₈	—	3	4	no	—
198	C₂×C₅×C₈	—	3	1	no	—
199	C₂×C₅×C₈	—	3	1	no	—
200	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
201	C₅×C₄⋊C₄	—	3	2	no	—
202	C₅×C₂²⋊C₄	—	3	2	no	—
203	C₄²×C₅	—	3	2	no	—
204	C₂²⋊Dic₅	C₄×D₃	1	2	yes	—
205	#685	—	3	4	no	—
206	C₄⋊Dic₅	C₄×D₃	1	2	yes	—
207	#683	—	3	4	no	—
208	C₄×Dic₅	—	3	4	no	—
209	C₄×Dic₅	C₂²×D₃	1	2	yes	—
210	#681	—	3	4	no	—
211	C₂×#168	—	3	2	no	—
212	C₂×#168	C₄×D₃	1	4	yes	complemented
213	C₂×#168	C₂²×D₃	1	1	yes	characteristic
214	C₂×#168	C₂²×D₃	1	1	yes	characteristic
215	#676	—	3	8	no	—
216	C₈×D₅	—	3	8	no	—
217	C₈×D₅	—	3	4	no	—
218	C₈×D₅	—	3	4	no	—
219	C₈×D₅	—	3	4	no	—
220	C₈×D₅	—	3	4	no	—
221	C₂²×M₁₆	—	15	1	no	—
222	C₂³×C₈	—	15	1	no	—
223	C₂×#117	—	15	1	no	—
224	#405	—	3	1	no	—
225	#405	—	5	1	no	—
226	#405	—	15	2	no	—
227	#405	—	15	2	no	—
228	#405	—	15	1	no	—
229	#405	—	15	1	no	—
230	C₂×#97	—	15	2	no	—
231	C₂×C₄×C₈	—	15	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
234	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×D₁₅	—	2	2	no	—
236	C₂×D₁₅	—	2	8	no	—
237	C₂×D₁₅	C₂×C₄²	1	2	yes	—
238	C₂×D₁₅	C₂×C₄²	1	2	yes	—
239	C₂×D₁₅	#131	1	4	yes	—
240	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
241	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	Dic₁₅	C₂×C₄²	1	2	yes	—
244	Dic₁₅	C₂×C₄²	1	2	yes	—
245	C₃×Dic₅	—	2	4	no	—
246	C₅×Dic₃	—	2	4	no	—
247	C₂³×D₃	—	5	1	no	—
248	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
249	C₂²×Dic₃	—	5	1	no	—
250	C₂×C₄×D₃	—	5	1	no	—
251	C₂×C₄×D₃	—	5	1	no	—
252	C₂×C₄×D₃	—	5	4	no	—
253	C₂×C₄×D₃	—	5	4	no	—
254	C₂×C₄×D₃	—	5	1	no	—
255	C₂×C₄×D₃	—	5	1	no	—
256	C₂×C₄×D₃	—	5	4	no	—
257	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
258	C₂×C₃×C₈	—	5	4	no	—
259	C₂×C₃×C₈	—	5	1	no	—
260	C₂×C₃×C₈	—	5	1	no	—
261	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
262	C₃×C₄⋊C₄	—	5	2	no	—
263	C₃×C₂²⋊C₄	—	5	2	no	—
264	C₃×C₄²	—	5	2	no	—
265	#217	C₄×D₅	1	2	yes	—
266	(C₂×D₃)⋊C₄	—	5	4	no	—
267	C₄⋊Dic₃	C₄×D₅	1	2	yes	—
268	Dic₃⋊C₄	—	5	4	no	—
269	C₄×Dic₃	—	5	4	no	—
270	C₄×Dic₃	C₂²×D₅	1	2	yes	—
271	#208	—	5	4	no	—
272	C₂×C₃⋊C₈	—	5	2	no	—
273	C₂×C₃⋊C₈	C₄×D₅	1	4	yes	complemented
274	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
275	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
276	ΓL(1,𝔽₂₅)	—	5	8	no	—
277	D₃×C₈	—	5	8	no	—
278	D₃×C₈	—	5	4	no	—
279	D₃×C₈	—	5	4	no	—
280	D₃×C₈	—	5	4	no	—
281	D₃×C₈	—	5	4	no	—
282	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
283	C₂²×D₅	—	3	1	no	—
284	C₂²×D₅	—	3	4	no	—
285	C₂²×D₅	—	3	1	no	—
286	C₂²×D₅	—	6	4	no	—
287	C₂×C₄×C₅	—	3	4	no	—
288	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
290	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
291	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
292	C₂×Dic₅	—	3	4	no	—
293	C₂×Dic₅	—	3	1	no	—
294	C₂×Dic₅	—	3	1	no	—
295	C₂×Dic₅	C₂×C₄×D₃	1	4	yes	—
296	C₄×D₅	—	3	4	no	—
297	C₄×D₅	—	3	4	no	—
298	C₄×D₅	—	3	2	no	—
299	C₄×D₅	—	3	2	no	—
300	C₄×D₅	—	3	2	no	—
301	C₄×D₅	—	3	2	no	—
302	C₄×D₅	—	6	8	no	—
303	C₅×C₈	—	3	2	no	—
304	C₅×C₈	—	3	2	no	—
305	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
306	#168	—	3	4	no	—
307	#168	C₂×C₄×D₃	1	2	yes	—
308	#168	C₂×C₄×D₃	1	2	yes	—
309	C₂³×C₄	—	15	1	no	—
310	C₂×M₁₆	—	15	1	no	—
311	C₂×M₁₆	—	15	8	no	—
312	C₂×M₁₆	—	15	2	no	—
313	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
314	C₂²×C₈	—	3	1	no	—
315	C₂²×C₈	—	5	1	no	—
316	C₂²×C₈	—	15	1	no	—
317	C₂²×C₈	—	15	1	no	—
318	C₂²×C₈	—	15	1	no	—
319	C₂²×C₈	—	15	1	no	—
320	C₂²×C₈	—	15	8	no	—
321	C₂²×C₈	—	15	2	no	—
322	#117	—	3	1	no	—
323	#117	—	5	1	no	—
324	#117	—	15	2	no	—
325	#117	—	15	2	no	—
326	#117	—	15	2	no	—
327	C₂×C₄⋊C₄	—	15	2	no	—
328	C₂×C₂²⋊C₄	—	15	2	no	—
329	C₂×C₄²	—	15	2	no	—
330	#97	—	3	2	no	—
331	#97	—	5	2	no	—
332	#97	—	15	2	no	—
333	#97	—	15	2	no	—
334	C₄×C₈	—	3	2	no	—
335	C₄×C₈	—	5	2	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	2	no	—
338	C₂×C₃×C₅	—	2	2	no	—
339	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂×#131	1	2	yes	—
341	D₁₅	—	2	2	no	—
342	D₁₅	#405	1	4	yes	complemented
343	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂²×D₃	—	5	1	no	—
345	C₂²×D₃	—	5	1	no	—
346	C₂²×D₃	—	5	4	no	—
347	C₂²×D₃	—	10	4	no	—
348	C₂×C₃×C₄	—	5	4	no	—
349	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
350	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
352	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
353	C₂×Dic₃	—	5	1	no	—
354	C₂×Dic₃	—	5	1	no	—
355	C₂×Dic₃	—	5	4	no	—
356	C₂×Dic₃	C₂×C₄×D₅	1	4	yes	—
357	C₄×D₃	—	5	2	no	—
358	C₄×D₃	—	5	2	no	—
359	C₄×D₃	—	5	2	no	—
360	C₄×D₃	—	5	2	no	—
361	C₄×D₃	—	5	4	no	—
362	C₄×D₃	—	5	4	no	—
363	C₄×D₃	—	10	8	no	—
364	C₃×C₈	—	5	2	no	—
365	C₃×C₈	—	5	2	no	—
366	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
367	C₃⋊C₈	—	5	4	no	—
368	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
369	C₃⋊C₈	C₂×C₄×D₅	1	2	yes	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	C₄²×D₃	1	2	yes	—
372	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
373	C₂×D₅	—	3	2	no	—
374	C₂×D₅	—	3	4	no	—
375	C₂×D₅	—	3	2	no	—
376	C₂×D₅	—	6	8	no	—
377	C₂×D₅	—	6	2	no	—
378	C₄×C₅	—	6	4	no	—
379	C₄×C₅	C₄²×D₃	1	2	yes	—
380	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
381	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
382	Dic₅	—	2	4	no	—
383	Dic₅	—	3	2	no	—
384	Dic₅	—	3	2	no	—
385	C₂⁴	—	15	1	no	—
386	C₂²×C₄	—	15	4	no	—
387	C₂²×C₄	—	15	1	no	—
388	C₂²×C₄	—	15	1	no	—
389	C₂²×C₄	—	15	1	no	—
390	C₂²×C₄	—	15	4	no	—
391	C₂²×C₄	—	15	4	no	—
392	C₂²×C₄	—	15	1	no	—
393	C₂²×C₄	—	15	1	no	—
394	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
395	M₁₆	—	15	4	no	—
396	M₁₆	—	15	8	no	—
397	M₁₆	#1200	1	4	yes	complemented
398	C₂×C₈	—	3	4	no	—
399	C₂×C₈	—	3	1	no	—
400	C₂×C₈	—	3	1	no	—
401	C₂×C₈	—	5	4	no	—
402	C₂×C₈	—	5	1	no	—
403	C₂×C₈	—	5	1	no	—
404	C₂×C₈	—	15	4	no	—
405	C₂×C₈	—	15	4	no	—
406	C₂×C₈	—	15	4	no	—
407	C₂×C₈	—	15	4	no	—
408	C₂×C₈	—	15	2	no	—
409	C₂×C₈	—	15	8	no	—
410	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
411	C₄⋊C₄	—	3	2	no	—
412	C₄⋊C₄	—	5	2	no	—
413	C₄⋊C₄	—	15	4	no	—
414	C₂²⋊C₄	—	3	2	no	—
415	C₂²⋊C₄	—	5	2	no	—
416	C₂²⋊C₄	—	15	4	no	—
417	C₄²	—	3	2	no	—
418	C₄²	—	5	2	no	—
419	C₄²	—	15	4	no	—
420	C₃×C₅	C₂×#405	1	1	yes	characteristic, complemented, Hall
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	C₄²×D₅	1	2	yes	—
423	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
424	C₂×D₃	—	5	2	no	—
425	C₂×D₃	—	5	4	no	—
426	C₂×D₃	—	5	2	no	—
427	C₂×D₃	—	10	8	no	—
428	C₂×D₃	—	10	2	no	—
429	C₃×C₄	—	10	4	no	—
430	C₃×C₄	C₄²×D₅	1	2	yes	—
431	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
432	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
433	Dic₃	—	2	4	no	—
434	Dic₃	—	5	2	no	—
435	Dic₃	—	5	2	no	—
436	C₂×C₅	—	2	2	no	—
437	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
438	C₂×C₅	D₃×#131	1	2	yes	—
439	D₅	—	3	4	no	—
440	D₅	—	6	2	no	—
441	C₂³	—	15	1	no	—
442	C₂³	—	15	4	no	—
443	C₂³	—	15	1	no	—
444	C₂³	—	30	4	no	—
445	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
446	C₂×C₄	—	3	4	no	—
447	C₂×C₄	—	5	4	no	—
448	C₂×C₄	—	15	4	no	—
449	C₂×C₄	—	15	1	no	—
450	C₂×C₄	—	15	1	no	—
451	C₂×C₄	—	15	4	no	—
452	C₂×C₄	—	15	4	no	—
453	C₂×C₄	—	15	2	no	—
454	C₂×C₄	—	15	2	no	—
455	C₂×C₄	—	15	2	no	—
456	C₂×C₄	—	15	2	no	—
457	C₂×C₄	—	30	8	no	—
458	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
459	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
460	C₂×C₄	C₂×#1200	1	2	yes	—
461	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
462	C₈	—	3	2	no	—
463	C₈	—	3	2	no	—
464	C₈	—	5	2	no	—
465	C₈	—	5	2	no	—
466	C₈	—	15	4	no	—
467	C₈	C₂×#1200	1	4	yes	—
468	C₂×C₃	—	2	2	no	—
469	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
470	C₂×C₃	D₅×#131	1	2	yes	—
471	D₃	—	5	4	no	—
472	D₃	—	10	2	no	—
473	C₅	D₃×#405	1	1	yes	characteristic, complemented, Sylow
474	C₂²	—	2	2	no	—
475	C₂²	—	15	4	no	—
476	C₂²	—	15	2	no	—
477	C₂²	—	15	2	no	—
478	C₂²	—	30	8	no	—
479	C₂²	—	30	2	no	—
480	C₂²	C₄×#1200	1	2	yes	—
481	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
482	C₄	—	6	4	no	—
483	C₄	—	10	4	no	—
484	C₄	—	15	2	no	—
485	C₄	—	15	2	no	—
486	C₄	C₄×#1200	1	2	yes	—
487	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
488	C₄	C₂²×#1200	1	1	yes	characteristic
489	C₃	D₅×#405	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	2	2	no	—
491	C₂	—	15	4	no	—
492	C₂	—	30	2	no	—
493	C₂	#11754017	1	2	yes	—
494	C₂	C₂×C₄×#1200	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×D₁₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	C₂×#405
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₅×#5122	C₂	semidirect
5. C₃×#65411	C₂	semidirect
6. #11748323	C₂	semidirect
7. #11748318	C₂	semidirect
8. #11748054	C₂	semidirect
9. #11748053	C₂	semidirect
10. #11747603	C₂	semidirect
11. C₈×#1200	C₂	semidirect
16. M₁₆×D₁₅	C₄	semidirect
29. C₂×#6648	C₄	semidirect
34. C₅×#815	C₂²	semidirect
35. C₅×C₈×Dic₃	C₂²	semidirect
36. C₃×#3947	C₂²	semidirect
37. C₃×C₈×Dic₅	C₂²	semidirect
38. #90953	C₂²	semidirect
39. #90952	C₂²	semidirect
40. Dic₃×#168	C₂²	semidirect
41. Dic₅×C₃⋊C₈	C₂²	semidirect
47. #65411	D₃	semidirect
64. C₃×C₅×M₁₆	C₂×C₄	semidirect
66. #6710	C₂×C₄	semidirect
68. #6705	C₂×C₄	semidirect
73. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
79. C₂×C₃×#168	C₂×C₄	semidirect
87. #6648	C₂×C₄	semidirect
88. #6648	C₂×C₄	semidirect
93. #5122	D₅	semidirect
124. #3947	C₂×D₃	semidirect
126. C₈×Dic₅	C₂×D₃	semidirect
181. #815	C₂×D₅	semidirect
183. C₈×Dic₃	C₂×D₅	semidirect
196. C₅×M₁₆	C₄×D₃	semidirect
212. C₂×#168	C₄×D₃	semidirect
257. C₃×M₁₆	C₄×D₅	semidirect
273. C₂×C₃⋊C₈	C₄×D₅	semidirect
342. D₁₅	#405	semidirect
397. M₁₆	#1200	semidirect
420. C₃×C₅	C₂×#405	semidirect
473. C₅	D₃×#405	semidirect
489. C₃	D₅×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₁₅	2
#11754461	2
C₂²×#6648	2
C₅×#5122	2
C₃×#65411	2
#11748323	2
#11748318	2
#11748054	2
#11748053	2
#11747603	2
C₈×#1200	2
D₅×#405	3
D₃×#405	5