Subgroups — #14415924

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756236	C₂	1	1	yes	maximal, characteristic
2	C₂×#91291	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748350	C₂	1	2	yes	maximal, complemented
6	#11747009	C₂	1	2	yes	maximal, complemented
7	#11746989	C₂	1	4	yes	maximal, complemented
8	#11746988	C₂	1	2	yes	maximal, complemented
9	#10610735	—	3	1	no	maximal, Hall
10	C₂×#6817	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	#91819	C₄	1	2	yes	—
13	#91819	C₄	1	2	yes	—
14	#91764	C₄	1	2	yes	—
15	#91763	C₄	1	1	yes	characteristic
16	C₄×D₆₀	C₂²	1	2	yes	—
17	C₄×D₆₀	C₂²	1	2	yes	—
18	#91758	C₄	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
20	C₂×C₃×#681	C₂²	1	1	yes	characteristic
21	C₂×C₃×#681	C₂²	1	1	yes	characteristic
22	C₂×#6651	C₂²	1	4	yes	—
23	#91291	—	2	8	no	—
24	C₂×#6648	C₂²	1	4	yes	—
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
27	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₃×#3935	C₂²	1	2	yes	—
29	C₃×C₄×#168	C₂²	1	2	yes	—
30	#90957	C₂²	1	4	yes	—
31	#90957	C₂²	1	4	yes	—
32	#78522	—	5	1	no	maximal, Hall
33	C₂×#4047	—	3	2	no	—
34	#65811	—	3	1	no	—
35	C₂×C₅×C₄⋊C₈	—	3	1	no	—
36	#65399	—	3	2	no	—
37	C₄×#681	D₃	1	1	yes	characteristic, complemented
38	#65127	—	3	2	no	—
39	#65125	—	3	4	no	—
40	#65123	—	3	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×#1220	C₂×C₄	1	4	yes	—
45	#6817	—	2	4	no	—
46	#6817	—	2	4	no	—
47	C₂×D₆₀	C₂×C₄	1	2	yes	—
48	C₂×D₆₀	C₂×C₄	1	2	yes	—
49	C₂×D₆₀	C₂×C₄	1	2	yes	—
50	C₂×C₄×D₁₅	C₂³	1	4	yes	—
51	C₂×Dic₃₀	C₂×C₄	1	2	yes	—
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
56	#6714	C₂×C₄	1	4	yes	—
57	#6714	C₂×C₄	1	4	yes	—
58	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
59	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	—	2	4	no	—
61	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
62	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
63	C₃×#681	—	2	2	no	—
64	C₃×#681	D₄	1	4	yes	complemented
65	C₂×C₃×#168	C₂³	1	2	yes	—
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	#6651	—	2	8	no	—
68	#6648	—	2	8	no	—
69	C₂×#907	—	5	2	no	—
70	#5477	—	5	1	no	—
71	C₃×C₄×M₁₆	—	5	1	no	—
72	#5129	—	5	2	no	—
73	C₂×C₄⋊(C₃⋊C₈)	D₅	1	1	yes	characteristic, complemented
74	#4706	—	5	4	no	—
75	#4688	—	5	2	no	—
76	C₈×D₁₂	—	5	2	no	—
77	C₂×#709	—	3	2	no	—
78	C₂²×C₅×C₈	—	3	2	no	—
79	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
80	#4076	—	3	2	no	—
81	#4076	—	3	2	no	—
82	C₂×#681	C₂×D₃	1	1	yes	characteristic
83	C₂×#681	C₂×D₃	1	1	yes	characteristic
84	#4047	—	6	8	no	—
85	C₂×#676	—	3	4	no	—
86	C₂×C₈×D₅	—	3	4	no	—
87	#4021	—	3	2	no	—
88	#4020	—	3	1	no	—
89	C₄×D₂₀	—	3	2	no	—
90	C₄×D₂₀	—	3	2	no	—
91	#4015	—	3	1	no	—
92	C₅×C₄⋊C₈	—	3	1	no	—
93	C₅×C₄⋊C₈	—	3	2	no	—
94	C₅×C₄⋊C₈	—	3	1	no	—
95	#3952	—	3	4	no	—
96	#3952	—	3	4	no	—
97	#3935	C₂×D₃	1	2	yes	—
98	C₄×#168	C₂×D₃	1	2	yes	—
99	#2935	—	15	1	no	Sylow
100	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×D₁₅	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	#1220	—	2	8	no	—
113	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
114	D₆₀	—	2	4	no	—
115	D₆₀	—	2	4	no	—
116	D₆₀	—	4	2	no	—
117	C₄×D₁₅	—	2	4	no	—
118	C₄×D₁₅	—	2	4	no	—
119	Dic₃₀	—	2	4	no	—
120	C₃×#168	—	2	2	no	—
121	C₃×#168	C₂×D₄	1	4	yes	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	—	2	2	no	—
124	C₂×#235	—	5	2	no	—
125	C₂×C₃×M₁₆	—	5	1	no	—
126	C₂×C₃×M₁₆	—	5	1	no	—
127	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
128	#930	—	5	2	no	—
129	#930	—	5	2	no	—
130	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
131	#907	—	10	8	no	—
132	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
133	C₂×D₃×C₈	—	5	4	no	—
134	#875	—	5	2	no	—
135	#874	—	5	1	no	—
136	C₄×D₁₂	—	5	2	no	—
137	C₄×D₁₂	—	5	2	no	—
138	#869	—	5	1	no	—
139	C₃×#97	—	5	2	no	—
140	C₃×C₄×C₈	—	5	2	no	—
141	(C₂×D₃)⋊C₈	—	5	4	no	—
142	(C₂×D₃)⋊C₈	—	5	4	no	—
143	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
144	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
145	C₄⋊(C₃⋊C₈)	C₂×D₅	1	2	yes	—
146	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	—	3	4	no	—
150	#709	—	6	4	no	—
151	#709	—	6	4	no	—
152	C₂×D₂₀	—	3	2	no	—
153	C₂×D₂₀	—	3	2	no	—
154	C₂×D₂₀	—	3	2	no	—
155	C₂×C₄×D₅	—	3	4	no	—
156	C₂×Dic₁₀	—	3	2	no	—
157	C₂×C₅×C₈	—	3	2	no	—
158	C₂×C₅×C₈	—	3	2	no	—
159	C₂×C₅×C₈	—	6	4	no	—
160	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
161	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
162	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
164	#685	—	3	4	no	—
165	#685	—	3	4	no	—
166	C₄⋊Dic₅	—	3	2	no	—
167	C₄⋊Dic₅	—	3	2	no	—
168	#681	—	2	2	no	—
169	#681	D₁₂	1	4	yes	complemented
170	C₂×#168	C₂²×D₃	1	2	yes	—
171	C₂×#168	C₂²×D₃	1	2	yes	—
172	#676	—	6	8	no	—
173	C₈×D₅	—	6	8	no	—
174	C₂×#131	—	15	2	no	—
175	#532	—	15	1	no	—
176	#436	—	15	2	no	—
177	#435	—	15	4	no	—
178	C₈×D₄	—	15	2	no	—
179	C₂×C₄⋊C₈	—	3	1	no	—
180	#408	—	15	2	no	—
181	C₄×M₁₆	—	5	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×D₁₅	—	2	4	no	—
187	C₂×D₁₅	—	2	4	no	—
188	C₂×D₁₅	—	2	4	no	—
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
193	C₃×C₄×C₅	#131	1	2	yes	complemented
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
196	Dic₁₅	—	2	4	no	—
197	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
200	C₂×#67	—	5	4	no	—
201	#235	—	10	4	no	—
202	#235	—	10	4	no	—
203	C₂×D₁₂	—	5	2	no	—
204	C₂×D₁₂	—	5	2	no	—
205	C₂×D₁₂	—	5	2	no	—
206	C₂×C₄×D₃	—	5	4	no	—
207	C₂×Dic₆	—	5	2	no	—
208	C₃×M₁₆	—	5	4	no	—
209	C₃×M₁₆	—	10	2	no	—
210	C₂×C₃×C₈	—	5	2	no	—
211	C₂×C₃×C₈	—	5	2	no	—
212	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
213	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
214	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
215	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	—	5	4	no	—
217	(C₂×D₃)⋊C₄	—	5	4	no	—
218	C₄⋊Dic₃	—	5	2	no	—
219	C₄⋊Dic₃	—	5	2	no	—
220	C₂×C₃⋊C₈	—	2	4	no	—
221	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
222	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
223	ΓL(1,𝔽₂₅)	—	10	8	no	—
224	D₃×C₈	—	10	8	no	—
225	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
226	C₂²×D₅	—	3	4	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
235	C₂×C₄×C₅	#235	1	2	yes	—
236	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
237	C₂²⋊D₅	—	6	8	no	—
238	C₂×Dic₅	—	3	4	no	—
239	D₂₀	—	6	4	no	—
240	D₂₀	—	6	4	no	—
241	D₂₀	—	12	2	no	—
242	C₄×D₅	—	6	4	no	—
243	C₄×D₅	—	6	4	no	—
244	Dic₁₀	—	6	4	no	—
245	C₅×C₈	—	6	2	no	—
246	C₅×C₈	—	6	2	no	—
247	#168	—	2	2	no	—
248	#168	C₂×D₁₂	1	4	yes	—
249	C₂×#41	—	15	2	no	—
250	#131	—	30	8	no	—
251	C₂×M₁₆	—	5	1	no	—
252	C₂×M₁₆	—	5	1	no	—
253	C₂×M₁₆	—	15	4	no	—
254	C₂²×C₈	—	3	2	no	—
255	C₂²×C₈	—	15	4	no	—
256	C₄⋊Q₈	—	15	1	no	—
257	#127	—	15	1	no	—
258	#124	—	15	2	no	—
259	#121	—	15	2	no	—
260	#121	—	15	2	no	—
261	C₄×D₄	—	15	2	no	—
262	C₄×D₄	—	15	2	no	—
263	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
264	C₄⋊C₈	—	3	1	no	—
265	C₄⋊C₈	—	3	2	no	—
266	C₄⋊C₈	—	3	1	no	—
267	C₂²⋊C₈	—	15	4	no	—
268	C₂²⋊C₈	—	15	4	no	—
269	#97	—	5	2	no	—
270	C₄×C₈	—	5	2	no	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
274	C₂×C₃×C₅	#568	1	1	yes	characteristic
275	D₁₅	—	4	4	no	—
276	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
277	C₂²×D₃	—	5	4	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
286	C₂×C₃×C₄	#713	1	2	yes	—
287	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
288	#67	—	10	8	no	—
289	C₂×Dic₃	—	5	4	no	—
290	D₁₂	—	10	4	no	—
291	D₁₂	—	10	4	no	—
292	D₁₂	—	20	2	no	—
293	C₄×D₃	—	10	4	no	—
294	C₄×D₃	—	10	4	no	—
295	Dic₆	—	10	4	no	—
296	C₃×C₈	—	5	4	no	—
297	C₃×C₈	—	10	2	no	—
298	C₃⋊C₈	—	2	2	no	—
299	C₃⋊C₈	—	2	2	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	C₄×D₁₂	1	2	yes	—
303	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
304	C₂×D₅	—	6	4	no	—
305	C₂×D₅	—	6	4	no	—
306	C₂×D₅	—	6	4	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	C₄×D₁₂	1	2	yes	—
311	C₄×C₅	#907	1	2	yes	complemented
312	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
313	C₄×C₅	C₂×#235	1	1	yes	characteristic
314	Dic₅	—	6	4	no	—
315	#41	—	30	4	no	—
316	#41	—	30	4	no	—
317	C₂×Q₈	—	15	2	no	—
318	C₂×D₄	—	15	4	no	—
319	C₂×D₄	—	15	2	no	—
320	C₂×D₄	—	15	2	no	—
321	C₂×D₄	—	15	2	no	—
322	C₂²×C₄	—	15	4	no	—
323	C₂²×C₄	#1200	1	1	yes	characteristic
324	C₂²×C₄	#1200	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
326	M₁₆	—	5	4	no	—
327	M₁₆	—	10	2	no	—
328	M₁₆	—	30	8	no	—
329	C₂×C₈	—	3	2	no	—
330	C₂×C₈	—	3	2	no	—
331	C₂×C₈	—	5	2	no	—
332	C₂×C₈	—	5	2	no	—
333	C₂×C₈	—	6	4	no	—
334	C₂×C₈	—	30	8	no	—
335	C₄⋊C₄	—	15	2	no	—
336	C₄⋊C₄	—	15	2	no	—
337	C₂²⋊C₄	—	15	4	no	—
338	C₂²⋊C₄	—	15	4	no	—
339	C₄²	#1200	1	1	yes	characteristic
340	C₄²	#1200	1	1	yes	characteristic
341	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
342	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
343	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	#4039	1	2	yes	—
347	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
348	C₂×D₃	—	10	4	no	—
349	C₂×D₃	—	10	4	no	—
350	C₂×D₃	—	10	4	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	#4039	1	2	yes	—
355	C₃×C₄	#4047	1	2	yes	complemented
356	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
357	C₃×C₄	C₂×#713	1	1	yes	characteristic
358	Dic₃	—	10	4	no	—
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
361	C₂×C₅	C₂×#907	1	1	yes	characteristic
362	C₂×C₅	#5745	1	1	yes	characteristic
363	D₅	—	12	4	no	—
364	C₂³	—	15	4	no	—
365	C₂³	C₂×#1200	1	1	yes	characteristic
366	Q₈	—	30	4	no	—
367	D₄	—	30	8	no	—
368	D₄	—	30	4	no	—
369	D₄	—	30	4	no	—
370	D₄	—	60	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	15	4	no	—
374	C₂×C₄	—	30	4	no	—
375	C₂×C₄	—	30	4	no	—
376	C₂×C₄	#6773	1	2	yes	—
377	C₂×C₄	D₅×D₁₂	1	2	yes	—
378	C₂×C₄	C₂×#1200	1	1	yes	characteristic
379	C₂×C₄	C₂×#1200	1	1	yes	characteristic
380	C₂×C₄	C₂×#1200	1	1	yes	characteristic
381	C₂×C₄	C₂×#1200	1	1	yes	characteristic
382	C₂×C₄	C₂×#1200	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
384	C₈	—	5	4	no	—
385	C₈	—	6	2	no	—
386	C₈	—	6	2	no	—
387	C₈	—	10	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	C₂×#4039	1	1	yes	characteristic
390	C₂×C₃	C₂×#4047	1	1	yes	characteristic
391	C₂×C₃	#66079	1	1	yes	characteristic
392	D₃	—	20	4	no	—
393	C₅	#78522	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	30	4	no	—
397	C₂²	—	30	4	no	—
398	C₂²	—	30	4	no	—
399	C₂²	#91418	1	2	yes	—
400	C₂²	C₂²×#1200	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	30	4	no	—
405	C₄	#91291	1	2	yes	complemented
406	C₄	#91418	1	2	yes	—
407	C₄	C₂×#6773	1	1	yes	characteristic
408	C₄	C₂×D₅×D₁₂	1	1	yes	characteristic
409	C₃	#10610735	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	60	4	no	—
412	C₂	C₂×#91291	1	1	yes	characteristic
413	C₂	#11754130	1	1	yes	characteristic
414	C₂	C₂×#91418	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
prime radical	#11756236	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#2935
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#91291	C₂	semidirect
3. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
4. C₃×C₄×#681	C₂	semidirect
5. #11748350	C₂	semidirect
6. #11747009	C₂	semidirect
7. #11746989	C₂	semidirect
8. #11746988	C₂	semidirect
37. C₄×#681	D₃	semidirect
64. C₃×#681	D₄	semidirect
73. C₂×C₄⋊(C₃⋊C₈)	D₅	semidirect
169. #681	D₁₂	semidirect
193. C₃×C₄×C₅	#131	semidirect
311. C₄×C₅	#907	semidirect
343. C₃×C₅	#2935	semidirect
355. C₃×C₄	#4047	semidirect
393. C₅	#78522	semidirect
405. C₄	#91291	semidirect
409. C₃	#10610735	semidirect

Maximal subgroups

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

subgroup	index
#11756236	2
C₂×#91291	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₃×C₄×#681	2
#11748350	2
#11747009	2
#11746989	2
#11746988	2
#10610735	3
#78522	5