Subgroups — #14411386

Order 1920.

1128 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	C₂²×#6705	C₂	1	1	yes	maximal, characteristic
3	D₁₅×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751223	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751202	C₂	1	1	yes	maximal, characteristic, complemented
7	#11751098	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750809	C₂	1	2	yes	maximal, complemented
9	#11750808	C₂	1	2	yes	maximal, complemented
10	#11750790	C₂	1	2	yes	maximal, complemented
11	C₄×#6705	C₂	1	2	yes	maximal, complemented
12	#10610279	—	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	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	#91815	C₂²	1	1	yes	characteristic
18	C₂×#6710	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
20	M₁₆×D₁₅	C₄	1	8	yes	complemented
21	C₂×#6705	C₄	1	8	yes	complemented
22	C₂×#6705	C₂²	1	1	yes	characteristic
23	C₂×#6705	C₂²	1	2	yes	—
24	C₂×#6705	C₂²	1	1	yes	characteristic
25	C₂×#6705	C₂²	1	1	yes	characteristic
26	C₂×#6705	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₁₅	C₂²	1	2	yes	—
28	#91781	C₄	1	2	yes	—
29	C₄⋊C₄×D₁₅	C₄	1	2	yes	—
30	C₂²⋊C₄×D₁₅	C₄	1	2	yes	—
31	#91766	C₄	1	2	yes	—
32	#91761	C₂²	1	2	yes	—
33	C₄²×D₁₅	C₂²	1	2	yes	—
34	C₃×C₅×#97	C₂²	1	2	yes	complemented
35	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
36	#91099	C₂²	1	2	yes	complemented
37	#91099	C₂²	1	2	yes	complemented
38	C₈×Dic₁₅	C₂²	1	2	yes	complemented
39	C₈×Dic₁₅	C₂²	1	2	yes	complemented
40	#91087	C₂²	1	2	yes	complemented
41	C₄×C₃⋊#168	C₂²	1	2	yes	complemented
42	#78548	—	5	1	no	maximal, Hall
43	C₂×D₅×M₁₆	—	3	1	no	—
44	C₂²×#676	—	3	1	no	—
45	D₅×#117	—	3	1	no	—
46	C₅×#405	D₃	1	1	yes	characteristic, complemented
47	#65411	—	3	1	no	—
48	#65390	—	3	1	no	—
49	#65286	—	3	1	no	—
50	#64997	—	3	2	no	—
51	#64996	—	3	2	no	—
52	#64978	—	3	2	no	—
53	C₄×#676	—	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	4	yes	—
58	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×D₁₅	C₂×C₄	1	4	yes	—
61	C₂×C₄×D₁₅	C₂×C₄	1	4	yes	—
62	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
63	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
70	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₃×C₄²×C₅	C₂³	1	2	yes	—
72	#6719	C₂×C₄	1	2	yes	—
73	#6714	C₂×C₄	1	4	yes	—
74	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
75	#6712	C₂×C₄	1	4	yes	—
76	C₄×Dic₁₅	C₂×C₄	1	4	yes	—
77	C₄×Dic₁₅	C₂³	1	2	yes	—
78	#6710	C₂×C₄	1	4	yes	complemented
79	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
80	C₂×C₃⋊#168	C₂³	1	2	yes	—
81	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
82	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
83	#6705	C₂×C₄	1	4	yes	—
84	#6705	C₂×C₄	1	4	yes	—
85	#6705	C₂×C₄	1	8	yes	—
86	#6705	C₂×C₄	1	4	yes	complemented
87	#6705	C₂×C₄	1	4	yes	complemented
88	C₈×D₁₅	C₂×C₄	1	8	yes	complemented
89	C₂×D₃×M₁₆	—	5	1	no	—
90	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
91	D₃×#117	—	5	1	no	—
92	C₃×#405	D₅	1	1	yes	characteristic, complemented
93	#5122	—	5	1	no	—
94	#5101	—	5	1	no	—
95	#4997	—	5	1	no	—
96	#4708	—	5	2	no	—
97	#4707	—	5	2	no	—
98	#4689	—	5	2	no	—
99	C₄×ΓL(1,𝔽₂₅)	—	5	2	no	—
100	C₂²×C₄×D₅	—	3	1	no	—
101	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
102	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
103	C₅×#117	C₂×D₃	1	1	yes	characteristic
104	#4072	—	3	1	no	—
105	C₂×#681	—	3	1	no	—
106	C₂²×#168	—	3	1	no	—
107	D₅×M₁₆	—	3	8	no	—
108	C₂×#676	—	3	8	no	—
109	C₂×#676	—	3	1	no	—
110	C₂×#676	—	3	1	no	—
111	C₂×#676	—	3	1	no	—
112	C₂×#676	—	3	1	no	—
113	C₂×#676	—	3	2	no	—
114	C₂×C₈×D₅	—	3	2	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	C₂×D₃	1	2	yes	complemented
122	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
123	#3947	—	3	2	no	—
124	#3947	—	3	2	no	—
125	C₈×Dic₅	—	3	2	no	—
126	C₈×Dic₅	—	3	2	no	—
127	#3935	—	3	2	no	—
128	C₄×#168	—	3	2	no	—
129	#2873	—	15	1	no	Sylow
130	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×D₁₅	—	4	2	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	4	yes	—
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂×Dic₁₅	C₄²	1	4	yes	—
141	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
142	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
144	C₄×D₁₅	—	4	4	no	—
145	C₄×D₁₅	C₄²	1	4	yes	—
146	C₄×D₁₅	C₄²	1	4	yes	—
147	C₄×D₁₅	C₂²×C₄	1	2	yes	—
148	C₄×D₁₅	C₂²×C₄	1	2	yes	—
149	C₄×D₁₅	C₂²×C₄	1	2	yes	—
150	C₄×D₁₅	C₂²×C₄	1	2	yes	—
151	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
152	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
153	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
154	C₃⋊#168	C₂²×C₄	1	4	yes	—
155	C₃⋊#168	C₂²×C₄	1	2	yes	—
156	C₃⋊#168	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	C₂×D₅	1	1	yes	characteristic
160	C₃×#117	C₂×D₅	1	1	yes	characteristic
161	#926	—	5	1	no	—
162	C₂×#208	—	5	1	no	—
163	C₂²×C₃⋊C₈	—	5	1	no	—
164	D₃×M₁₆	—	5	8	no	—
165	C₂×ΓL(1,𝔽₂₅)	—	5	8	no	—
166	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
167	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
168	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
169	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
170	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
171	C₂×D₃×C₈	—	5	2	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	C₂×D₅	1	2	yes	complemented
179	C₃×C₄×C₈	C₂×D₅	1	2	yes	complemented
180	#815	—	5	2	no	—
181	#815	—	5	2	no	—
182	C₈×Dic₃	—	5	2	no	—
183	C₈×Dic₃	—	5	2	no	—
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	C₄×D₃	1	4	yes	complemented
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
201	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
202	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
203	C₄²×C₅	C₂²×D₃	1	2	yes	—
204	C₂²⋊Dic₅	—	3	2	no	—
205	#685	—	3	4	no	—
206	C₄⋊Dic₅	—	3	2	no	—
207	#683	—	3	4	no	—
208	C₄×Dic₅	—	3	4	no	—
209	C₄×Dic₅	—	3	2	no	—
210	#681	—	3	4	no	—
211	C₂×#168	—	3	4	no	—
212	C₂×#168	—	3	1	no	—
213	C₂×#168	—	3	2	no	—
214	C₂×#168	—	3	1	no	—
215	#676	—	3	4	no	—
216	#676	—	3	4	no	—
217	#676	—	3	8	no	—
218	#676	—	3	4	no	—
219	#676	—	3	4	no	—
220	C₈×D₅	—	3	8	no	—
221	C₂²×M₁₆	—	15	1	no	—
222	C₂²×M₁₆	—	15	1	no	—
223	C₂×#117	—	15	1	no	—
224	#405	—	15	1	no	—
225	#405	—	15	1	no	—
226	#405	—	15	1	no	—
227	#405	—	15	2	no	—
228	#405	—	15	2	no	—
229	#405	D₁₅	1	1	yes	characteristic, complemented
230	C₄×M₁₆	—	15	2	no	—
231	C₄×M₁₆	—	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	2	no	—
237	C₂×D₁₅	—	4	4	no	—
238	C₂×D₁₅	C₂×C₄²	1	2	yes	—
239	C₂×D₁₅	C₂×C₄²	1	2	yes	—
240	C₃×C₄×C₅	—	2	4	no	—
241	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
244	Dic₁₅	—	2	4	no	—
245	Dic₁₅	C₂×C₄²	1	2	yes	—
246	Dic₁₅	C₂×C₄²	1	2	yes	—
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	C₄×D₅	1	4	yes	complemented
259	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
261	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
262	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
263	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
264	C₃×C₄²	C₂²×D₅	1	2	yes	—
265	#217	—	5	2	no	—
266	(C₂×D₃)⋊C₄	—	5	4	no	—
267	C₄⋊Dic₃	—	5	2	no	—
268	Dic₃⋊C₄	—	5	4	no	—
269	C₄×Dic₃	—	5	4	no	—
270	C₄×Dic₃	—	5	2	no	—
271	#208	—	5	4	no	—
272	C₂×C₃⋊C₈	—	5	4	no	—
273	C₂×C₃⋊C₈	—	5	1	no	—
274	C₂×C₃⋊C₈	—	5	2	no	—
275	C₂×C₃⋊C₈	—	5	1	no	—
276	ΓL(1,𝔽₂₅)	—	5	4	no	—
277	ΓL(1,𝔽₂₅)	—	5	4	no	—
278	ΓL(1,𝔽₂₅)	—	5	8	no	—
279	ΓL(1,𝔽₂₅)	—	5	4	no	—
280	ΓL(1,𝔽₂₅)	—	5	4	no	—
281	D₃×C₈	—	5	8	no	—
282	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
283	C₂²×D₅	—	3	1	no	—
284	C₂²×D₅	—	3	1	no	—
285	C₂²×D₅	—	3	4	no	—
286	C₂²×D₅	—	12	2	no	—
287	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
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	—	3	4	no	—
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	—	12	4	no	—
303	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
304	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
305	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
306	#168	—	3	4	no	—
307	#168	—	3	2	no	—
308	#168	—	3	2	no	—
309	C₂³×C₄	—	15	1	no	—
310	C₂×M₁₆	—	15	1	no	—
311	C₂×M₁₆	—	15	8	no	—
312	C₂×M₁₆	—	15	8	no	—
313	C₂×M₁₆	—	15	1	no	—
314	C₂×M₁₆	—	15	2	no	—
315	C₂×M₁₆	—	15	1	no	—
316	C₂×M₁₆	—	15	1	no	—
317	C₂×M₁₆	—	15	1	no	—
318	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
319	C₂²×C₈	—	15	1	no	—
320	C₂²×C₈	—	15	2	no	—
321	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
322	#117	—	15	1	no	—
323	#117	—	15	2	no	—
324	#117	—	15	2	no	—
325	#117	—	15	2	no	—
326	#117	C₂×D₁₅	1	1	yes	characteristic
327	C₂×C₄⋊C₄	—	15	2	no	—
328	C₂×C₂²⋊C₄	—	15	2	no	—
329	C₂×C₄²	—	15	2	no	—
330	#97	—	15	2	no	—
331	#97	—	15	2	no	—
332	#97	—	15	2	no	—
333	#97	C₂×D₁₅	1	2	yes	complemented
334	C₄×C₈	—	15	2	no	—
335	C₄×C₈	—	15	2	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	C₂×D₁₅	1	2	yes	complemented
338	C₂×C₃×C₅	—	2	2	no	—
339	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
340	C₂×C₃×C₅	#568	1	2	yes	—
341	D₁₅	—	2	2	no	—
342	D₁₅	—	2	2	no	—
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	—	20	2	no	—
348	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
349	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
350	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
351	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
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	—	5	4	no	—
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	—	20	4	no	—
364	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
365	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
366	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
367	C₃⋊C₈	—	5	4	no	—
368	C₃⋊C₈	—	5	2	no	—
369	C₃⋊C₈	—	5	2	no	—
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	2	no	—
375	C₂×D₅	—	6	2	no	—
376	C₂×D₅	—	6	2	no	—
377	C₂×D₅	—	12	4	no	—
378	C₄×C₅	—	2	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	—	3	2	no	—
383	Dic₅	—	3	2	no	—
384	Dic₅	—	6	4	no	—
385	C₂⁴	—	15	1	no	—
386	C₂²×C₄	—	15	1	no	—
387	C₂²×C₄	—	15	1	no	—
388	C₂²×C₄	—	15	1	no	—
389	C₂²×C₄	—	15	4	no	—
390	C₂²×C₄	—	15	4	no	—
391	C₂²×C₄	—	15	1	no	—
392	C₂²×C₄	—	15	1	no	—
393	C₂²×C₄	—	15	4	no	—
394	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
395	M₁₆	—	15	4	no	—
396	M₁₆	—	15	8	no	—
397	M₁₆	—	15	4	no	—
398	M₁₆	—	15	4	no	—
399	M₁₆	—	15	4	no	—
400	M₁₆	—	15	4	no	—
401	M₁₆	C₄×D₁₅	1	4	yes	complemented
402	C₂×C₈	—	15	4	no	—
403	C₂×C₈	—	15	1	no	—
404	C₂×C₈	—	15	2	no	—
405	C₂×C₈	—	15	1	no	—
406	C₂×C₈	—	15	8	no	—
407	C₂×C₈	C₄×D₁₅	1	4	yes	complemented
408	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
409	C₂×C₈	C₂²×D₁₅	1	2	yes	—
410	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
411	C₄⋊C₄	—	15	4	no	—
412	C₄⋊C₄	—	15	2	no	—
413	C₄⋊C₄	C₄×D₁₅	1	2	yes	—
414	C₂²⋊C₄	—	15	2	no	—
415	C₂²⋊C₄	—	15	4	no	—
416	C₂²⋊C₄	C₄×D₁₅	1	2	yes	—
417	C₄²	—	15	4	no	—
418	C₄²	—	15	2	no	—
419	C₄²	C₂²×D₁₅	1	2	yes	—
420	C₃×C₅	#2873	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	2	no	—
426	C₂×D₃	—	10	2	no	—
427	C₂×D₃	—	10	2	no	—
428	C₂×D₃	—	20	4	no	—
429	C₃×C₄	—	2	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	—	5	2	no	—
434	Dic₃	—	5	2	no	—
435	Dic₃	—	10	4	no	—
436	C₂×C₅	—	2	2	no	—
437	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
438	C₂×C₅	#5750	1	2	yes	—
439	D₅	—	6	2	no	—
440	D₅	—	6	2	no	—
441	C₂³	—	15	1	no	—
442	C₂³	—	15	1	no	—
443	C₂³	—	15	4	no	—
444	C₂³	—	60	2	no	—
445	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
446	C₂×C₄	—	15	4	no	—
447	C₂×C₄	—	15	1	no	—
448	C₂×C₄	—	15	1	no	—
449	C₂×C₄	—	15	4	no	—
450	C₂×C₄	—	15	4	no	—
451	C₂×C₄	—	15	2	no	—
452	C₂×C₄	—	15	2	no	—
453	C₂×C₄	—	15	2	no	—
454	C₂×C₄	—	15	2	no	—
455	C₂×C₄	—	15	4	no	—
456	C₂×C₄	—	60	4	no	—
457	C₂×C₄	C₂×C₄×D₁₅	1	4	yes	—
458	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
459	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
460	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
461	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
462	C₈	—	15	2	no	—
463	C₈	—	15	2	no	—
464	C₈	—	15	4	no	—
465	C₈	C₂×C₄×D₁₅	1	4	yes	—
466	C₈	C₂×C₄×D₁₅	1	2	yes	—
467	C₈	C₂×C₄×D₁₅	1	2	yes	—
468	C₂×C₃	—	2	2	no	—
469	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
470	C₂×C₃	#66084	1	2	yes	—
471	D₃	—	10	2	no	—
472	D₃	—	10	2	no	—
473	C₅	#78548	1	1	yes	characteristic, complemented, Sylow
474	C₂²	—	2	2	no	—
475	C₂²	—	15	2	no	—
476	C₂²	—	15	2	no	—
477	C₂²	—	30	2	no	—
478	C₂²	—	30	2	no	—
479	C₂²	—	60	4	no	—
480	C₂²	C₄²×D₁₅	1	2	yes	—
481	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	15	2	no	—
484	C₄	—	15	2	no	—
485	C₄	—	30	4	no	—
486	C₄	C₄²×D₁₅	1	2	yes	—
487	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
488	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
489	C₃	#10610279	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	2	2	no	—
491	C₂	—	30	2	no	—
492	C₂	—	30	2	no	—
493	C₂	C₂×C₄²×D₁₅	1	1	yes	characteristic
494	C₂	#11756509	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×D₁₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#405	D₁₅
hypocenter	C₃×C₅	#2873
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#405	C₂	semidirect
5. #11751223	C₂	semidirect
6. #11751202	C₂	semidirect
7. #11751098	C₂	semidirect
8. #11750809	C₂	semidirect
9. #11750808	C₂	semidirect
10. #11750790	C₂	semidirect
11. C₄×#6705	C₂	semidirect
20. M₁₆×D₁₅	C₄	semidirect
21. C₂×#6705	C₄	semidirect
34. C₃×C₅×#97	C₂²	semidirect
35. C₃×C₄×C₅×C₈	C₂²	semidirect
36. #91099	C₂²	semidirect
37. #91099	C₂²	semidirect
38. C₈×Dic₁₅	C₂²	semidirect
39. C₈×Dic₁₅	C₂²	semidirect
40. #91087	C₂²	semidirect
41. C₄×C₃⋊#168	C₂²	semidirect
46. C₅×#405	D₃	semidirect
64. C₃×C₅×M₁₆	C₂×C₄	semidirect
65. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
78. #6710	C₂×C₄	semidirect
79. C₂×C₃⋊#168	C₂×C₄	semidirect
86. #6705	C₂×C₄	semidirect
87. #6705	C₂×C₄	semidirect
88. C₈×D₁₅	C₂×C₄	semidirect
92. C₃×#405	D₅	semidirect
121. C₅×#97	C₂×D₃	semidirect
122. C₄×C₅×C₈	C₂×D₃	semidirect
178. C₃×#97	C₂×D₅	semidirect
179. C₃×C₄×C₈	C₂×D₅	semidirect
196. C₅×M₁₆	C₄×D₃	semidirect
197. C₂×C₅×C₈	C₄×D₃	semidirect
229. #405	D₁₅	semidirect
257. C₃×M₁₆	C₄×D₅	semidirect
258. C₂×C₃×C₈	C₄×D₅	semidirect
333. #97	C₂×D₁₅	semidirect
337. C₄×C₈	C₂×D₁₅	semidirect
401. M₁₆	C₄×D₁₅	semidirect
407. C₂×C₈	C₄×D₁₅	semidirect
420. C₃×C₅	#2873	semidirect
473. C₅	#78548	semidirect
489. 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×M₁₆×D₁₅	2
C₂²×#6705	2
D₁₅×#117	2
C₃×C₅×#405	2
#11751223	2
#11751202	2
#11751098	2
#11750809	2
#11750808	2
#11750790	2
C₄×#6705	2
#10610279	3
#78548	5