Subgroups — D₁₅×#508 #14478262

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅×#135	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751295	C₂	1	2	yes	maximal, complemented
4	#11751020	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₅×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751017	C₂	1	2	yes	maximal, complemented
7	D₁₅×SD₃₂	C₂	1	2	yes	maximal, complemented
8	#11751013	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₅×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#11751005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₆×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#508	—	3	1	no	maximal, Hall
13	#41×D₁₅	—	2	2	no	—
14	C₃×C₅×#135	C₂²	1	2	yes	complemented
15	#91839	—	2	2	no	—
16	#91808	C₂²	1	2	yes	complemented
17	Q₁₆×D₁₅	C₂²	1	2	yes	—
18	#91805	—	2	2	no	—
19	SD₁₆×D₁₅	—	2	2	no	—
20	#91801	C₂²	1	2	yes	complemented
21	D₈×D₁₅	C₂²	1	2	yes	—
22	#91793	C₂²	1	2	yes	complemented
23	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
24	C₃×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
26	C₃×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
28	#91113	C₂²	1	2	yes	complemented
29	#91112	C₂²	1	2	yes	complemented
30	#91111	C₂²	1	2	yes	complemented
31	#91110	C₂²	1	2	yes	complemented
32	C₂×C₃⋊#672	C₂²	1	1	yes	characteristic, complemented
33	Dic₁₂₀	C₂²	1	1	yes	characteristic, complemented
34	#91084	C₂²	1	2	yes	complemented
35	D₂₄₀	C₂²	1	1	yes	characteristic, complemented
36	C₁₆×D₁₅	C₂²	1	1	yes	characteristic
37	C₁₆×D₁₅	C₂²	1	1	yes	characteristic
38	C₁₆×D₁₅	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×D₁₅	C₂²	1	1	yes	characteristic, complemented
40	D₃×#508	—	5	1	no	maximal, Hall
41	D₅×#135	—	3	2	no	—
42	C₅×#508	D₃	1	1	yes	characteristic, complemented
43	#65483	—	3	2	no	—
44	#65208	—	3	1	no	—
45	D₅×Q₃₂	—	3	1	no	—
46	#65205	—	3	2	no	—
47	D₅×SD₃₂	—	3	2	no	—
48	#65201	—	3	1	no	—
49	D₅×D₁₆	—	3	1	no	—
50	#65193	—	3	1	no	—
51	C₂×D₅×C₁₆	—	3	1	no	—
52	C₃×C₅×#41	—	2	2	no	—
53	#6821	—	2	2	no	—
54	Q₈×D₁₅	—	2	2	no	—
55	#6819	—	2	2	no	—
56	#6819	—	4	2	no	—
57	D₄×D₁₅	—	2	2	no	—
58	D₄×D₁₅	—	4	2	no	—
59	#6817	—	2	2	no	—
60	#6817	—	4	2	no	—
61	C₂×C₄×D₁₅	—	4	2	no	—
62	C₂×C₄×D₁₅	D₄	1	1	yes	characteristic
63	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
64	C₃×C₅×SD₁₆	—	2	2	no	—
65	C₃×C₅×D₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	#6718	—	2	2	no	—
68	#6717	—	2	2	no	—
69	#6716	—	2	2	no	—
70	#6715	—	2	2	no	—
71	C₂×C₃⋊#168	D₄	1	1	yes	characteristic
72	Dic₆₀	C₂³	1	2	yes	—
73	D₁₂₀	C₂³	1	2	yes	—
74	#6706	—	2	2	no	—
75	C₈×D₁₅	D₄	1	1	yes	characteristic
76	C₈×D₁₅	D₄	1	1	yes	characteristic
77	C₈×D₁₅	C₂³	1	1	yes	characteristic
78	C₈×D₁₅	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
81	C₃⋊#672	C₂³	1	1	yes	characteristic
82	C₃⋊#672	C₂³	1	1	yes	characteristic
83	D₃×#135	—	5	2	no	—
84	C₃×#508	D₅	1	1	yes	characteristic, complemented
85	#5194	—	5	2	no	—
86	#4919	—	5	1	no	—
87	D₃×Q₃₂	—	5	1	no	—
88	#4916	—	5	2	no	—
89	D₃×SD₃₂	—	5	2	no	—
90	#4912	—	5	1	no	—
91	D₃×D₁₆	—	5	1	no	—
92	#4904	—	5	1	no	—
93	C₂×D₃×C₁₆	—	5	1	no	—
94	D₅×#41	—	6	2	no	—
95	C₅×#135	C₂×D₃	1	2	yes	complemented
96	#4096	—	6	2	no	—
97	#4065	—	3	2	no	—
98	D₅×Q₁₆	—	3	2	no	—
99	#4062	—	6	2	no	—
100	D₅×SD₁₆	—	6	2	no	—
101	#4058	—	3	2	no	—
102	D₅×D₈	—	3	2	no	—
103	#4050	—	3	2	no	—
104	C₂×C₈×D₅	—	3	1	no	—
105	C₅×Q₃₂	C₂×D₃	1	1	yes	characteristic, complemented
106	C₅×SD₃₂	C₂×D₃	1	2	yes	complemented
107	C₅×D₁₆	C₂×D₃	1	1	yes	characteristic, complemented
108	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
109	#3961	—	3	2	no	—
110	#3960	—	3	2	no	—
111	#3959	—	3	2	no	—
112	#3958	—	3	2	no	—
113	C₂×#672	—	3	1	no	—
114	Dic₄₀	—	3	1	no	—
115	#3932	—	3	2	no	—
116	D₈₀	—	3	1	no	—
117	D₅×C₁₆	—	3	1	no	—
118	D₅×C₁₆	—	3	1	no	—
119	D₅×C₁₆	—	3	1	no	—
120	D₅×C₁₆	—	3	1	no	—
121	C₂×#508	—	15	1	no	Sylow
122	C₂²×D₁₅	—	4	2	no	—
123	C₂²×D₁₅	D₈	1	1	yes	characteristic
124	C₃×C₅×Q₈	—	2	2	no	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₃×C₅×D₄	—	4	2	no	—
127	C₂×C₃×C₄×C₅	—	4	2	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	#1220	—	4	2	no	—
130	#1220	—	4	2	no	—
131	#1220	—	4	2	no	—
132	C₂×Dic₁₅	—	4	2	no	—
133	C₂×Dic₁₅	D₈	1	1	yes	characteristic
134	D₆₀	—	2	2	no	—
135	D₆₀	—	4	2	no	—
136	C₄×D₁₅	—	4	2	no	—
137	C₄×D₁₅	—	4	2	no	—
138	C₄×D₁₅	—	4	2	no	—
139	C₄×D₁₅	D₈	1	1	yes	characteristic
140	C₄×D₁₅	D₈	1	1	yes	characteristic
141	C₄×D₁₅	C₂×D₄	1	1	yes	characteristic
142	C₄×D₁₅	C₂×D₄	1	1	yes	characteristic
143	Dic₃₀	—	2	2	no	—
144	Dic₃₀	—	4	2	no	—
145	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
146	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
147	C₃⋊#168	C₂×D₄	1	1	yes	characteristic
148	C₃⋊#168	C₂×D₄	1	1	yes	characteristic
149	D₃×#41	—	10	2	no	—
150	C₃×#135	C₂×D₅	1	2	yes	complemented
151	#950	—	10	2	no	—
152	#919	—	5	2	no	—
153	D₃×Q₁₆	—	5	2	no	—
154	#916	—	10	2	no	—
155	D₃×SD₁₆	—	10	2	no	—
156	#912	—	5	2	no	—
157	D₃×D₈	—	5	2	no	—
158	#904	—	5	2	no	—
159	C₂×D₃×C₈	—	5	1	no	—
160	C₃×Q₃₂	C₂×D₅	1	1	yes	characteristic, complemented
161	C₃×SD₃₂	C₂×D₅	1	2	yes	complemented
162	C₃×D₁₆	C₂×D₅	1	1	yes	characteristic, complemented
163	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
164	#829	—	5	2	no	—
165	#828	—	5	2	no	—
166	#827	—	5	2	no	—
167	#826	—	5	2	no	—
168	C₂×C₃⋊C₁₆	—	5	1	no	—
169	Dic₂₄	—	5	1	no	—
170	#800	—	5	2	no	—
171	D₄₈	—	5	1	no	—
172	D₃×C₁₆	—	5	1	no	—
173	D₃×C₁₆	—	5	1	no	—
174	D₃×C₁₆	—	5	1	no	—
175	D₃×C₁₆	—	5	1	no	—
176	C₅×#41	—	2	2	no	—
177	#713	—	6	2	no	—
178	Q₈×D₅	—	6	2	no	—
179	#711	—	6	2	no	—
180	#711	—	12	2	no	—
181	D₄×D₅	—	6	2	no	—
182	D₄×D₅	—	12	2	no	—
183	#709	—	6	2	no	—
184	#709	—	12	2	no	—
185	C₂×C₄×D₅	—	3	1	no	—
186	C₂×C₄×D₅	—	12	2	no	—
187	C₅×Q₁₆	C₂²×D₃	1	2	yes	—
188	C₅×SD₁₆	—	2	2	no	—
189	C₅×D₈	C₂²×D₃	1	2	yes	—
190	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
191	#689	—	6	2	no	—
192	#688	—	6	2	no	—
193	#687	—	6	2	no	—
194	#686	—	6	2	no	—
195	C₂×#168	—	3	1	no	—
196	Dic₂₀	—	3	2	no	—
197	D₄₀	—	3	2	no	—
198	#677	—	6	2	no	—
199	C₈×D₅	—	3	1	no	—
200	C₈×D₅	—	3	1	no	—
201	C₈×D₅	—	3	1	no	—
202	C₈×D₅	—	3	1	no	—
203	C₅×C₁₆	C₂²×D₃	1	1	yes	characteristic
204	C₅×C₁₆	C₂²×D₃	1	1	yes	characteristic
205	#672	—	3	1	no	—
206	#672	—	3	1	no	—
207	C₂×#135	—	15	2	no	—
208	#508	—	15	2	no	—
209	#508	—	15	1	no	—
210	#508	—	15	2	no	—
211	#508	—	15	1	no	—
212	#508	—	15	1	no	—
213	#508	D₁₅	1	1	yes	characteristic, direct product factor
214	C₂×Q₃₂	—	15	1	no	—
215	C₂×SD₃₂	—	15	2	no	—
216	C₂×D₁₆	—	15	1	no	—
217	C₂²×C₁₆	—	15	1	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
220	C₂×D₁₅	—	2	2	no	—
221	C₂×D₁₅	—	4	2	no	—
222	C₂×D₁₅	—	8	4	no	—
223	C₂×D₁₅	C₂×D₈	1	1	yes	characteristic
224	C₂×D₁₅	C₂×D₈	1	1	yes	characteristic
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
227	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
228	Dic₁₅	—	4	2	no	—
229	Dic₁₅	C₂×D₈	1	1	yes	characteristic
230	Dic₁₅	C₂×D₈	1	1	yes	characteristic
231	C₃×#41	—	2	2	no	—
232	#239	—	10	2	no	—
233	D₃×Q₈	—	10	2	no	—
234	#237	—	10	2	no	—
235	#237	—	20	2	no	—
236	D₃×D₄	—	10	2	no	—
237	D₃×D₄	—	20	2	no	—
238	#235	—	10	2	no	—
239	#235	—	20	2	no	—
240	C₂×C₄×D₃	—	5	1	no	—
241	C₂×C₄×D₃	—	20	2	no	—
242	C₃×Q₁₆	C₂²×D₅	1	2	yes	—
243	C₃×SD₁₆	—	2	2	no	—
244	C₃×D₈	C₂²×D₅	1	2	yes	—
245	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
246	#216	—	10	2	no	—
247	#215	—	10	2	no	—
248	#214	—	10	2	no	—
249	#213	—	10	2	no	—
250	C₂×C₃⋊C₈	—	5	1	no	—
251	Dic₁₂	—	5	2	no	—
252	D₂₄	—	5	2	no	—
253	#204	—	10	2	no	—
254	D₃×C₈	—	5	1	no	—
255	D₃×C₈	—	5	1	no	—
256	D₃×C₈	—	5	1	no	—
257	D₃×C₈	—	5	1	no	—
258	C₃×C₁₆	C₂²×D₅	1	1	yes	characteristic
259	C₃×C₁₆	C₂²×D₅	1	1	yes	characteristic
260	C₃⋊C₁₆	—	5	1	no	—
261	C₃⋊C₁₆	—	5	1	no	—
262	C₂²×D₅	—	3	1	no	—
263	C₂²×D₅	—	12	2	no	—
264	C₅×Q₈	—	2	2	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	—	4	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
269	C₂²⋊D₅	—	12	2	no	—
270	C₂²⋊D₅	—	12	2	no	—
271	C₂²⋊D₅	—	12	2	no	—
272	C₂×Dic₅	—	3	1	no	—
273	C₂×Dic₅	—	12	2	no	—
274	D₂₀	—	6	2	no	—
275	D₂₀	—	12	2	no	—
276	C₄×D₅	—	3	1	no	—
277	C₄×D₅	—	3	1	no	—
278	C₄×D₅	—	3	1	no	—
279	C₄×D₅	—	3	1	no	—
280	C₄×D₅	—	12	2	no	—
281	C₄×D₅	—	12	2	no	—
282	C₄×D₅	—	12	2	no	—
283	Dic₁₀	—	6	2	no	—
284	Dic₁₀	—	12	2	no	—
285	C₅×C₈	D₃×D₄	1	1	yes	characteristic
286	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
287	#168	—	3	1	no	—
288	#168	—	3	1	no	—
289	C₂×#41	—	30	2	no	—
290	#135	—	15	2	no	—
291	#135	—	15	2	no	—
292	#135	—	15	2	no	—
293	#135	—	30	2	no	—
294	#135	—	30	2	no	—
295	#135	C₂×D₁₅	1	2	yes	complemented
296	C₂×Q₁₆	—	15	2	no	—
297	C₂×SD₁₆	—	30	2	no	—
298	C₂×D₈	—	15	2	no	—
299	C₂²×C₈	—	15	1	no	—
300	Q₃₂	—	15	2	no	—
301	Q₃₂	—	15	1	no	—
302	Q₃₂	C₂×D₁₅	1	1	yes	characteristic, complemented
303	SD₃₂	—	15	2	no	—
304	SD₃₂	—	15	2	no	—
305	SD₃₂	—	15	2	no	—
306	SD₃₂	C₂×D₁₅	1	2	yes	complemented
307	D₁₆	—	15	2	no	—
308	D₁₆	—	15	1	no	—
309	D₁₆	C₂×D₁₅	1	1	yes	characteristic, complemented
310	C₂×C₁₆	—	15	1	no	—
311	C₂×C₁₆	—	15	1	no	—
312	C₂×C₁₆	—	15	1	no	—
313	C₂×C₁₆	—	15	1	no	—
314	C₂×C₁₆	—	15	1	no	—
315	C₂×C₁₆	C₂×D₁₅	1	1	yes	characteristic, complemented
316	C₂×C₃×C₅	—	2	1	no	—
317	C₂×C₃×C₅	—	8	2	no	—
318	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
319	D₁₅	—	2	1	no	—
320	D₁₅	—	8	2	no	—
321	D₁₅	#508	1	2	yes	direct product factor
322	C₂²×D₃	—	5	1	no	—
323	C₂²×D₃	—	20	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×D₄	—	2	2	no	—
326	C₃×D₄	—	4	2	no	—
327	C₂×C₃×C₄	—	4	2	no	—
328	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
329	#67	—	20	2	no	—
330	#67	—	20	2	no	—
331	#67	—	20	2	no	—
332	C₂×Dic₃	—	5	1	no	—
333	C₂×Dic₃	—	20	2	no	—
334	D₁₂	—	10	2	no	—
335	D₁₂	—	20	2	no	—
336	C₄×D₃	—	5	1	no	—
337	C₄×D₃	—	5	1	no	—
338	C₄×D₃	—	5	1	no	—
339	C₄×D₃	—	5	1	no	—
340	C₄×D₃	—	20	2	no	—
341	C₄×D₃	—	20	2	no	—
342	C₄×D₃	—	20	2	no	—
343	Dic₆	—	10	2	no	—
344	Dic₆	—	20	2	no	—
345	C₃×C₈	D₄×D₅	1	1	yes	characteristic
346	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
347	C₃⋊C₈	—	5	1	no	—
348	C₃⋊C₈	—	5	1	no	—
349	C₂²×C₅	—	4	2	no	—
350	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
351	C₂×D₅	—	3	1	no	—
352	C₂×D₅	—	3	1	no	—
353	C₂×D₅	—	6	2	no	—
354	C₂×D₅	—	12	2	no	—
355	C₂×D₅	—	24	4	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	D₃×D₈	1	1	yes	characteristic
358	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
359	Dic₅	—	3	1	no	—
360	Dic₅	—	3	1	no	—
361	Dic₅	—	12	2	no	—
362	#41	—	2	2	no	—
363	#41	—	30	2	no	—
364	#41	—	30	2	no	—
365	#41	—	30	2	no	—
366	#41	—	60	2	no	—
367	#41	—	60	2	no	—
368	C₂×Q₈	—	30	2	no	—
369	C₂×D₄	—	30	2	no	—
370	C₂×D₄	—	60	2	no	—
371	C₂²×C₄	—	15	1	no	—
372	C₂²×C₄	—	60	2	no	—
373	Q₁₆	—	15	2	no	—
374	Q₁₆	—	30	2	no	—
375	Q₁₆	C₂²×D₁₅	1	2	yes	—
376	SD₁₆	—	2	2	no	—
377	SD₁₆	—	30	2	no	—
378	SD₁₆	—	30	2	no	—
379	SD₁₆	—	30	2	no	—
380	D₈	—	15	2	no	—
381	D₈	—	30	2	no	—
382	D₈	C₂²×D₁₅	1	2	yes	—
383	C₂×C₈	—	15	1	no	—
384	C₂×C₈	—	15	1	no	—
385	C₂×C₈	—	15	1	no	—
386	C₂×C₈	—	15	1	no	—
387	C₂×C₈	—	15	1	no	—
388	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
389	C₁₆	—	15	1	no	—
390	C₁₆	—	15	1	no	—
391	C₁₆	C₂²×D₁₅	1	1	yes	characteristic
392	C₁₆	C₂²×D₁₅	1	1	yes	characteristic
393	C₃×C₅	C₂×#508	1	1	yes	characteristic, complemented, Hall
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
396	C₂×D₃	—	5	1	no	—
397	C₂×D₃	—	5	1	no	—
398	C₂×D₃	—	10	2	no	—
399	C₂×D₃	—	20	2	no	—
400	C₂×D₃	—	40	4	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	D₅×D₈	1	1	yes	characteristic
403	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
404	Dic₃	—	5	1	no	—
405	Dic₃	—	5	1	no	—
406	Dic₃	—	20	2	no	—
407	C₂×C₅	—	2	1	no	—
408	C₂×C₅	—	8	2	no	—
409	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
410	D₅	—	3	2	no	—
411	D₅	—	6	1	no	—
412	D₅	—	24	2	no	—
413	C₂³	—	15	1	no	—
414	C₂³	—	60	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	30	2	no	—
417	Q₈	—	60	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	30	2	no	—
421	D₄	—	60	2	no	—
422	D₄	—	60	2	no	—
423	D₄	—	60	2	no	—
424	D₄	—	60	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	15	1	no	—
427	C₂×C₄	—	15	1	no	—
428	C₂×C₄	—	15	1	no	—
429	C₂×C₄	—	15	1	no	—
430	C₂×C₄	—	15	1	no	—
431	C₂×C₄	—	60	2	no	—
432	C₂×C₄	—	60	2	no	—
433	C₂×C₄	—	60	2	no	—
434	C₂×C₄	—	60	2	no	—
435	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
436	C₈	—	15	1	no	—
437	C₈	—	15	1	no	—
438	C₈	D₄×D₁₅	1	1	yes	characteristic
439	C₈	C₂³×D₁₅	1	1	yes	characteristic
440	C₂×C₃	—	2	1	no	—
441	C₂×C₃	—	8	2	no	—
442	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
443	D₃	—	5	2	no	—
444	D₃	—	10	1	no	—
445	D₃	—	40	2	no	—
446	C₅	D₃×#508	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	4	2	no	—
448	C₂²	—	15	1	no	—
449	C₂²	—	15	1	no	—
450	C₂²	—	30	2	no	—
451	C₂²	—	60	2	no	—
452	C₂²	—	120	4	no	—
453	C₂²	D₈×D₁₅	1	1	yes	characteristic
454	C₄	—	4	2	no	—
455	C₄	—	15	1	no	—
456	C₄	—	15	1	no	—
457	C₄	—	60	2	no	—
458	C₄	D₈×D₁₅	1	1	yes	characteristic
459	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
460	C₃	D₅×#508	1	1	yes	characteristic, complemented, Sylow
461	C₂	—	2	1	no	—
462	C₂	—	8	2	no	—
463	C₂	—	15	2	no	—
464	C₂	—	30	1	no	—
465	C₂	—	120	2	no	—
466	C₂	C₂×D₈×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₁₅
commutator, cosocle	C₃×C₅×C₈	C₂⁴
Frattini	C₈	C₂³×D₁₅
Fitting	C₃×C₅×#508	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	#508	D₁₅
hypocenter	C₃×C₅	C₂×#508
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

Complements

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

N	H ≅ G/N	type
1. D₁₅×#135	C₂	semidirect
2. C₃×C₅×#508	C₂	semidirect
3. #11751295	C₂	semidirect
4. #11751020	C₂	semidirect
5. D₁₅×Q₃₂	C₂	semidirect
6. #11751017	C₂	semidirect
7. D₁₅×SD₃₂	C₂	semidirect
8. #11751013	C₂	semidirect
9. D₁₅×D₁₆	C₂	semidirect
10. #11751005	C₂	semidirect
11. C₂×C₁₆×D₁₅	C₂	semidirect
14. C₃×C₅×#135	C₂²	semidirect
16. #91808	C₂²	semidirect
20. #91801	C₂²	semidirect
22. #91793	C₂²	semidirect
24. C₃×C₅×Q₃₂	C₂²	semidirect
25. C₃×C₅×SD₃₂	C₂²	semidirect
26. C₃×C₅×D₁₆	C₂²	semidirect
27. C₂×C₃×C₅×C₁₆	C₂²	semidirect
28. #91113	C₂²	semidirect
29. #91112	C₂²	semidirect
30. #91111	C₂²	semidirect
31. #91110	C₂²	semidirect
32. C₂×C₃⋊#672	C₂²	semidirect
33. Dic₁₂₀	C₂²	semidirect
34. #91084	C₂²	semidirect
35. D₂₄₀	C₂²	semidirect
38. C₁₆×D₁₅	C₂²	semidirect
39. C₁₆×D₁₅	C₂²	semidirect
42. C₅×#508	D₃	semidirect
84. C₃×#508	D₅	semidirect
95. C₅×#135	C₂×D₃	semidirect
105. C₅×Q₃₂	C₂×D₃	semidirect
106. C₅×SD₃₂	C₂×D₃	semidirect
107. C₅×D₁₆	C₂×D₃	semidirect
108. C₂×C₅×C₁₆	C₂×D₃	semidirect
150. C₃×#135	C₂×D₅	semidirect
160. C₃×Q₃₂	C₂×D₅	semidirect
161. C₃×SD₃₂	C₂×D₅	semidirect
162. C₃×D₁₆	C₂×D₅	semidirect
163. C₂×C₃×C₁₆	C₂×D₅	semidirect
213. #508	D₁₅	direct (N × H)
295. #135	C₂×D₁₅	semidirect
302. Q₃₂	C₂×D₁₅	semidirect
306. SD₃₂	C₂×D₁₅	semidirect
309. D₁₆	C₂×D₁₅	semidirect
315. C₂×C₁₆	C₂×D₁₅	semidirect
321. D₁₅	#508	direct (N × H)
393. C₃×C₅	C₂×#508	semidirect
446. C₅	D₃×#508	semidirect
460. C₃	D₅×#508	semidirect

Maximal subgroups

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

subgroup	index
D₁₅×#135	2
C₃×C₅×#508	2
#11751295	2
#11751020	2
D₁₅×Q₃₂	2
#11751017	2
D₁₅×SD₃₂	2
#11751013	2
D₁₅×D₁₆	2
#11751005	2
C₂×C₁₆×D₁₅	2
D₅×#508	3
D₃×#508	5

Subgroups — D15×#508 #14478262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×#508 #14478262