Subgroups — #14478315

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	#11754105	C₂	1	2	yes	maximal, complemented
2	D₁₅×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4919	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65208	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748304	C₂	1	2	yes	maximal, complemented
6	#11748301	C₂	1	2	yes	maximal, complemented
7	#11748292	C₂	1	2	yes	maximal, complemented
8	#11746835	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746832	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746822	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#508	—	3	1	no	maximal, Hall
13	#92034	—	2	2	no	—
14	Q₁₆×D₁₅	C₂²	1	2	yes	—
15	C₅×#919	C₂²	1	2	yes	complemented
16	C₃×#4065	C₂²	1	2	yes	complemented
17	#91517	—	2	2	no	—
18	#91514	—	2	2	no	—
19	#91505	—	2	2	no	—
20	#91273	C₂²	1	2	yes	complemented
21	#91270	C₂²	1	2	yes	complemented
22	#91256	C₂²	1	2	yes	—
23	D₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₃×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
25	#91113	C₂²	1	2	yes	complemented
26	Dic₁₂₀	C₂²	1	1	yes	characteristic, complemented
27	C₁₆×D₁₅	C₂²	1	1	yes	characteristic
28	C₅×#828	C₂²	1	2	yes	complemented
29	C₅×D₄₈	C₂²	1	1	yes	characteristic, complemented
30	C₅×D₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×#3960	C₂²	1	2	yes	complemented
32	C₃×D₈₀	C₂²	1	1	yes	characteristic, complemented
33	C₃×D₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
34	#90944	C₂²	1	2	yes	complemented
35	#90942	C₂²	1	2	yes	complemented
36	#90937	C₂²	1	2	yes	complemented
37	#90933	C₂²	1	1	yes	characteristic
38	D₃×#672	C₂²	1	1	yes	characteristic, complemented
39	D₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	D₃×#508	—	5	1	no	maximal, Hall
41	D₅×#135	—	3	2	no	—
42	C₅×#508	—	3	1	no	—
43	#65483	—	3	2	no	—
44	#65208	D₃	1	1	yes	characteristic, complemented
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	Q₈×D₁₅	—	2	2	no	—
53	C₅×#239	—	2	2	no	—
54	C₃×#713	—	2	2	no	—
55	#6777	—	2	2	no	—
56	#6777	—	4	2	no	—
57	C₄×D₃×D₅	—	4	2	no	—
58	C₄×D₃×D₅	D₄	1	1	yes	characteristic
59	#6772	—	2	2	no	—
60	#6772	—	4	2	no	—
61	#6765	—	2	2	no	—
62	#6765	—	4	2	no	—
63	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
64	#6718	—	2	2	no	—
65	Dic₆₀	C₂³	1	2	yes	—
66	C₈×D₁₅	C₂³	1	1	yes	characteristic
67	C₅×#215	—	2	2	no	—
68	C₅×D₂₄	C₂³	1	2	yes	—
69	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
70	C₃×#688	—	2	2	no	—
71	C₃×D₄₀	C₂³	1	2	yes	—
72	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
73	#6659	—	2	2	no	—
74	#6657	—	2	2	no	—
75	#6652	—	2	2	no	—
76	#6648	D₄	1	1	yes	characteristic
77	D₃×#168	D₄	1	1	yes	characteristic
78	D₅×C₃⋊C₈	D₄	1	1	yes	characteristic
79	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₃⋊#672	C₂³	1	1	yes	characteristic
81	C₃×#672	C₂³	1	1	yes	characteristic
82	C₅×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
83	D₃×#135	—	5	2	no	—
84	C₃×#508	—	5	1	no	—
85	#5194	—	5	2	no	—
86	#4919	D₅	1	1	yes	characteristic, complemented
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	—	3	2	no	—
96	#4096	—	6	2	no	—
97	#4065	C₂×D₃	1	2	yes	complemented
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	—	3	2	no	—
107	C₅×D₁₆	—	3	1	no	—
108	C₂×C₅×C₁₆	—	3	1	no	—
109	#3961	—	3	2	no	—
110	#3960	C₂×D₃	1	2	yes	complemented
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	C₂×D₃	1	1	yes	characteristic, complemented
117	D₅×C₁₆	—	3	1	no	—
118	D₅×C₁₆	—	3	1	no	—
119	D₅×C₁₆	—	3	1	no	—
120	D₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
121	C₂×#508	—	15	1	no	Sylow
122	C₂×D₃×D₅	—	4	2	no	—
123	C₂×D₃×D₅	D₈	1	1	yes	characteristic
124	C₃×C₅×Q₈	—	2	2	no	—
125	C₄×D₁₅	—	4	2	no	—
126	C₄×D₁₅	C₂×D₄	1	1	yes	characteristic
127	Dic₃₀	—	2	2	no	—
128	Dic₃₀	—	4	2	no	—
129	C₅×D₁₂	—	2	2	no	—
130	C₅×D₁₂	—	4	2	no	—
131	C₄×C₅×D₃	—	4	2	no	—
132	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
133	C₃×D₂₀	—	2	2	no	—
134	C₃×D₂₀	—	4	2	no	—
135	C₃×C₄×D₅	—	4	2	no	—
136	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
137	#1201	—	4	2	no	—
138	#1201	—	4	2	no	—
139	#1201	—	4	2	no	—
140	#1200	D₈	1	1	yes	characteristic
141	D₃×Dic₅	—	4	2	no	—
142	D₃×Dic₅	D₈	1	1	yes	characteristic
143	D₅×Dic₃	—	4	2	no	—
144	D₅×Dic₃	D₈	1	1	yes	characteristic
145	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
146	C₃⋊#168	C₂×D₄	1	1	yes	characteristic
147	C₃×#168	C₂×D₄	1	1	yes	characteristic
148	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
149	D₃×#41	—	10	2	no	—
150	C₃×#135	—	5	2	no	—
151	#950	—	10	2	no	—
152	#919	C₂×D₅	1	2	yes	complemented
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	—	5	2	no	—
162	C₃×D₁₆	—	5	1	no	—
163	C₂×C₃×C₁₆	—	5	1	no	—
164	#829	—	5	2	no	—
165	#828	C₂×D₅	1	2	yes	complemented
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	C₂×D₅	1	1	yes	characteristic, complemented
172	D₃×C₁₆	—	5	1	no	—
173	D₃×C₁₆	—	5	1	no	—
174	D₃×C₁₆	—	5	1	no	—
175	D₃×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
176	C₅×#41	—	6	2	no	—
177	#713	—	2	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	—	6	2	no	—
189	C₅×D₈	—	3	2	no	—
190	C₂×C₅×C₈	—	3	1	no	—
191	#689	—	6	2	no	—
192	#688	—	2	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	C₂²×D₃	1	2	yes	—
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	C₂²×D₃	1	1	yes	characteristic
203	C₅×C₁₆	—	3	1	no	—
204	C₅×C₁₆	C₂²×D₃	1	1	yes	characteristic
205	#672	—	3	1	no	—
206	#672	C₂²×D₃	1	1	yes	characteristic
207	C₂×#135	—	15	2	no	—
208	#508	—	3	1	no	—
209	#508	—	5	1	no	—
210	#508	—	15	1	no	—
211	#508	—	15	1	no	—
212	#508	—	15	2	no	—
213	#508	—	15	2	no	—
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	C₂×D₁₅	C₂×D₈	1	1	yes	characteristic
219	C₂×C₅×D₃	—	4	2	no	—
220	C₂×C₅×D₃	C₂×D₈	1	1	yes	characteristic
221	C₂×C₃×D₅	—	4	2	no	—
222	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
223	D₃×D₅	—	2	2	no	—
224	D₃×D₅	—	8	4	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
227	Dic₁₅	—	4	2	no	—
228	Dic₁₅	C₂×D₈	1	1	yes	characteristic
229	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
230	C₅×Dic₃	C₂×D₈	1	1	yes	characteristic
231	C₃×#41	—	10	2	no	—
232	#239	—	2	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	—	10	2	no	—
244	C₃×D₈	—	5	2	no	—
245	C₂×C₃×C₈	—	5	1	no	—
246	#216	—	10	2	no	—
247	#215	—	2	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	C₂²×D₅	1	2	yes	—
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	C₂²×D₅	1	1	yes	characteristic
258	C₃×C₁₆	—	5	1	no	—
259	C₃×C₁₆	C₂²×D₅	1	1	yes	characteristic
260	C₃⋊C₁₆	—	5	1	no	—
261	C₃⋊C₁₆	C₂²×D₅	1	1	yes	characteristic
262	C₂²×D₅	—	3	1	no	—
263	C₂²×D₅	—	12	2	no	—
264	C₅×Q₈	—	2	2	no	—
265	C₅×D₄	—	6	2	no	—
266	C₅×D₄	—	12	2	no	—
267	C₂×C₄×C₅	—	3	1	no	—
268	C₂×C₄×C₅	—	12	2	no	—
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	—	2	2	no	—
275	D₂₀	—	4	2	no	—
276	C₄×D₅	—	3	1	no	—
277	C₄×D₅	—	3	1	no	—
278	C₄×D₅	—	3	1	no	—
279	C₄×D₅	—	4	2	no	—
280	C₄×D₅	—	12	2	no	—
281	C₄×D₅	—	12	2	no	—
282	C₄×D₅	D₃×D₄	1	1	yes	characteristic
283	Dic₁₀	—	6	2	no	—
284	Dic₁₀	—	12	2	no	—
285	C₅×C₈	—	3	1	no	—
286	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
287	#168	—	3	1	no	—
288	#168	D₃×D₄	1	1	yes	characteristic
289	C₂×#41	—	30	2	no	—
290	#135	—	3	2	no	—
291	#135	—	5	2	no	—
292	#135	—	15	2	no	—
293	#135	—	15	2	no	—
294	#135	—	30	2	no	—
295	#135	—	30	2	no	—
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	D₃×D₅	1	1	yes	characteristic, complemented
303	SD₃₂	—	3	2	no	—
304	SD₃₂	—	5	2	no	—
305	SD₃₂	—	15	2	no	—
306	SD₃₂	—	15	2	no	—
307	D₁₆	—	3	1	no	—
308	D₁₆	—	5	1	no	—
309	D₁₆	—	15	2	no	—
310	C₂×C₁₆	—	3	1	no	—
311	C₂×C₁₆	—	5	1	no	—
312	C₂×C₁₆	—	15	1	no	—
313	C₂×C₁₆	—	15	1	no	—
314	C₂×C₁₆	—	15	1	no	—
315	C₂×C₁₆	—	15	1	no	—
316	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
317	D₁₅	#508	1	2	yes	complemented
318	C₃×D₅	—	2	1	no	—
319	C₃×D₅	—	8	2	no	—
320	C₅×D₃	—	2	1	no	—
321	C₅×D₃	—	8	2	no	—
322	C₂²×D₃	—	5	1	no	—
323	C₂²×D₃	—	20	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×D₄	—	10	2	no	—
326	C₃×D₄	—	20	2	no	—
327	C₂×C₃×C₄	—	5	1	no	—
328	C₂×C₃×C₄	—	20	2	no	—
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	—	2	2	no	—
335	D₁₂	—	4	2	no	—
336	C₄×D₃	—	4	2	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	D₄×D₅	1	1	yes	characteristic
343	Dic₆	—	10	2	no	—
344	Dic₆	—	20	2	no	—
345	C₃×C₈	—	5	1	no	—
346	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
347	C₃⋊C₈	—	5	1	no	—
348	C₃⋊C₈	D₄×D₅	1	1	yes	characteristic
349	C₂²×C₅	—	3	1	no	—
350	C₂²×C₅	—	12	2	no	—
351	C₂×D₅	—	3	1	no	—
352	C₂×D₅	—	4	2	no	—
353	C₂×D₅	—	6	2	no	—
354	C₂×D₅	—	24	4	no	—
355	C₂×D₅	D₃×D₈	1	1	yes	characteristic
356	C₄×C₅	—	3	1	no	—
357	C₄×C₅	—	4	2	no	—
358	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
359	Dic₅	—	3	1	no	—
360	Dic₅	—	12	2	no	—
361	Dic₅	D₃×D₈	1	1	yes	characteristic
362	#41	—	6	2	no	—
363	#41	—	10	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	C₂×D₃×D₅	1	2	yes	—
376	SD₁₆	—	6	2	no	—
377	SD₁₆	—	10	2	no	—
378	SD₁₆	—	30	2	no	—
379	SD₁₆	—	30	2	no	—
380	D₈	—	3	2	no	—
381	D₈	—	5	2	no	—
382	D₈	—	30	2	no	—
383	C₂×C₈	—	3	1	no	—
384	C₂×C₈	—	5	1	no	—
385	C₂×C₈	—	15	1	no	—
386	C₂×C₈	—	15	1	no	—
387	C₂×C₈	—	15	1	no	—
388	C₂×C₈	—	15	1	no	—
389	C₁₆	—	3	1	no	—
390	C₁₆	—	5	1	no	—
391	C₁₆	—	15	1	no	—
392	C₁₆	C₂×D₃×D₅	1	1	yes	characteristic
393	C₃×C₅	C₂×#508	1	1	yes	characteristic, complemented, Hall
394	C₂²×C₃	—	5	1	no	—
395	C₂²×C₃	—	20	2	no	—
396	C₂×D₃	—	4	2	no	—
397	C₂×D₃	—	5	1	no	—
398	C₂×D₃	—	10	2	no	—
399	C₂×D₃	—	40	4	no	—
400	C₂×D₃	D₅×D₈	1	1	yes	characteristic
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	5	1	no	—
403	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
404	Dic₃	—	5	1	no	—
405	Dic₃	—	20	2	no	—
406	Dic₃	D₅×D₈	1	1	yes	characteristic
407	C₂×C₅	—	6	1	no	—
408	C₂×C₅	—	24	2	no	—
409	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
410	D₅	—	2	1	no	—
411	D₅	—	3	2	no	—
412	D₅	—	8	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	—	6	2	no	—
419	D₄	—	10	2	no	—
420	D₄	—	12	2	no	—
421	D₄	—	20	2	no	—
422	D₄	—	60	2	no	—
423	D₄	—	60	2	no	—
424	D₄	—	60	2	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	5	1	no	—
427	C₂×C₄	—	12	2	no	—
428	C₂×C₄	—	15	1	no	—
429	C₂×C₄	—	15	1	no	—
430	C₂×C₄	—	15	1	no	—
431	C₂×C₄	—	15	1	no	—
432	C₂×C₄	—	20	2	no	—
433	C₂×C₄	—	60	2	no	—
434	C₂×C₄	—	60	2	no	—
435	C₂×C₄	—	60	2	no	—
436	C₈	—	3	1	no	—
437	C₈	—	5	1	no	—
438	C₈	—	15	1	no	—
439	C₈	C₂²×D₃×D₅	1	1	yes	characteristic
440	C₂×C₃	—	10	1	no	—
441	C₂×C₃	—	40	2	no	—
442	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
443	D₃	—	2	1	no	—
444	D₃	—	5	2	no	—
445	D₃	—	8	2	no	—
446	C₅	D₃×#508	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	3	1	no	—
448	C₂²	—	5	1	no	—
449	C₂²	—	12	2	no	—
450	C₂²	—	15	1	no	—
451	C₂²	—	20	2	no	—
452	C₂²	—	30	2	no	—
453	C₂²	—	120	4	no	—
454	C₄	—	3	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	5	1	no	—
457	C₄	—	15	1	no	—
458	C₄	—	60	2	no	—
459	C₄	D₃×D₄×D₅	1	1	yes	characteristic
460	C₃	D₅×#508	1	1	yes	characteristic, complemented, Sylow
461	C₂	—	6	1	no	—
462	C₂	—	10	1	no	—
463	C₂	—	15	2	no	—
464	C₂	—	24	2	no	—
465	C₂	—	40	2	no	—
466	C₂	D₃×D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×D₅×D₈
commutator, cosocle	C₃×C₅×C₈	C₂⁴
Frattini	C₈	C₂²×D₃×D₅
Fitting	C₃×C₅×Q₃₂	C₂²
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	Q₃₂	D₃×D₅
hypocenter	C₃×C₅	C₂×#508
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #11754105	C₂	semidirect
2. D₁₅×Q₃₂	C₂	semidirect
3. C₅×#4919	C₂	semidirect
4. C₃×#65208	C₂	semidirect
5. #11748304	C₂	semidirect
6. #11748301	C₂	semidirect
7. #11748292	C₂	semidirect
8. #11746835	C₂	semidirect
9. #11746832	C₂	semidirect
10. #11746822	C₂	semidirect
11. D₃×D₅×C₁₆	C₂	semidirect
15. C₅×#919	C₂²	semidirect
16. C₃×#4065	C₂²	semidirect
20. #91273	C₂²	semidirect
21. #91270	C₂²	semidirect
24. C₃×C₅×Q₃₂	C₂²	semidirect
25. #91113	C₂²	semidirect
26. Dic₁₂₀	C₂²	semidirect
28. C₅×#828	C₂²	semidirect
29. C₅×D₄₈	C₂²	semidirect
30. C₅×D₃×C₁₆	C₂²	semidirect
31. C₃×#3960	C₂²	semidirect
32. C₃×D₈₀	C₂²	semidirect
33. C₃×D₅×C₁₆	C₂²	semidirect
34. #90944	C₂²	semidirect
35. #90942	C₂²	semidirect
36. #90937	C₂²	semidirect
38. D₃×#672	C₂²	semidirect
39. D₅×C₃⋊C₁₆	C₂²	semidirect
44. #65208	D₃	semidirect
86. #4919	D₅	semidirect
97. #4065	C₂×D₃	semidirect
105. C₅×Q₃₂	C₂×D₃	semidirect
110. #3960	C₂×D₃	semidirect
116. D₈₀	C₂×D₃	semidirect
120. D₅×C₁₆	C₂×D₃	semidirect
152. #919	C₂×D₅	semidirect
160. C₃×Q₃₂	C₂×D₅	semidirect
165. #828	C₂×D₅	semidirect
171. D₄₈	C₂×D₅	semidirect
175. D₃×C₁₆	C₂×D₅	semidirect
302. Q₃₂	D₃×D₅	semidirect
317. D₁₅	#508	semidirect
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
#11754105	2
D₁₅×Q₃₂	2
C₅×#4919	2
C₃×#65208	2
#11748304	2
#11748301	2
#11748292	2
#11746835	2
#11746832	2
#11746822	2
D₃×D₅×C₁₆	2
D₅×#508	3
D₃×#508	5