Subgroups — #14295539

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91283	C₂	1	1	yes	maximal, characteristic
2	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65421	C₂	1	1	yes	maximal, characteristic
4	#11748624	C₂	1	1	yes	maximal, characteristic
5	#11748326	C₂	1	1	yes	maximal, characteristic, complemented
6	#11746380	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745989	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600691	—	3	1	no	maximal, Hall
9	C₂×C₃×#709	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	#91815	C₂²	1	1	yes	characteristic
12	C₂×#6710	C₂²	1	1	yes	characteristic
13	C₅×#926	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	C₂×#6649	C₄	1	2	yes	complemented
17	#91283	—	2	1	no	—
18	#91283	—	2	1	no	—
19	#91283	—	2	1	no	—
20	#91283	—	2	1	no	—
21	C₂×D₅×C₃⋊C₈	C₄	1	2	yes	complemented
22	C₅×#815	—	2	1	no	—
23	C₅×C₈×Dic₃	—	2	1	no	—
24	C₃×#3956	C₄	1	2	yes	complemented
25	C₃×#3955	C₄	1	2	yes	complemented
26	#90995	C₄	1	4	yes	—
27	#90954	—	2	1	no	—
28	#90951	—	2	1	no	—
29	#70133	—	5	1	no	maximal, Hall
30	C₂×#4047	—	3	1	no	—
31	C₅×#405	—	3	1	no	—
32	#65421	D₃	1	1	yes	characteristic
33	#65390	—	3	1	no	—
34	#65295	—	3	1	no	—
35	#64779	—	3	1	no	—
36	#64753	—	3	1	no	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
39	C₃×#709	—	2	1	no	—
40	C₃×#709	—	2	1	no	—
41	C₃×#709	—	2	1	no	—
42	C₃×#709	—	2	1	no	—
43	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
45	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
46	C₃×C₅×M₁₆	—	2	1	no	—
47	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	#6719	C₂×C₄	1	2	yes	—
50	C₄⋊Dic₁₅	—	2	1	no	—
51	C₄×Dic₁₅	—	2	1	no	—
52	#6710	—	2	1	no	—
53	#6710	—	2	1	no	—
54	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
55	C₅×#217	C₂×C₄	1	2	yes	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
61	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
62	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
63	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
64	C₃×#681	—	2	1	no	—
65	C₃×#681	C₂×C₄	1	2	yes	—
66	C₂×C₃×#168	—	2	1	no	—
67	#6649	—	2	2	no	—
68	#6649	—	2	2	no	—
69	D₅×C₃⋊C₈	—	2	2	no	—
70	D₅×C₃⋊C₈	—	2	2	no	—
71	C₂×#948	—	5	1	no	—
72	C₃×#413	—	5	1	no	—
73	#5240	—	5	1	no	—
74	#5122	—	5	1	no	—
75	#5122	D₅	1	1	yes	characteristic, complemented
76	#4559	—	5	1	no	—
77	#4559	—	5	1	no	—
78	C₂×#709	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₅×C₈	—	3	1	no	—
81	C₅×#117	—	3	1	no	—
82	#4072	—	3	1	no	—
83	C₂×#681	—	3	1	no	—
84	C₂×#681	C₂×D₃	1	1	yes	characteristic
85	#4047	—	6	1	no	—
86	#4047	—	6	1	no	—
87	#4047	—	6	1	no	—
88	#4047	—	6	1	no	—
89	C₂×#676	—	3	2	no	—
90	C₂×C₈×D₅	—	3	2	no	—
91	C₅×#97	—	6	1	no	—
92	C₄×C₅×C₈	—	6	1	no	—
93	#3956	Dic₃	1	2	yes	complemented
94	#3955	Dic₃	1	2	yes	complemented
95	#3947	—	6	1	no	—
96	C₈×Dic₅	—	6	1	no	—
97	#3938	—	3	4	no	—
98	#1757	—	15	1	no	Sylow
99	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₃×D₅	C₄²	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×Dic₁₅	—	2	2	no	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₃×C₂²⋊D₅	—	2	2	no	—
110	C₃×C₂²⋊D₅	—	2	2	no	—
111	C₂×C₃×Dic₅	C₄²	1	2	yes	—
112	C₃×D₂₀	—	2	1	no	—
113	C₃×D₂₀	—	2	1	no	—
114	C₃×C₄×D₅	—	2	2	no	—
115	C₃×C₄×D₅	—	2	2	no	—
116	C₃×Dic₁₀	—	2	1	no	—
117	C₃×Dic₁₀	—	2	1	no	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₃⋊#168	—	2	2	no	—
120	C₃×#168	—	2	2	no	—
121	C₅×C₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
122	C₅×C₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
123	C₅×C₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
124	C₅×C₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₃×#41	—	5	1	no	—
126	C₂×C₃×M₁₆	—	5	1	no	—
127	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
128	#948	—	10	1	no	—
129	#948	—	10	1	no	—
130	#948	—	10	1	no	—
131	#948	—	10	1	no	—
132	#926	—	5	1	no	—
133	#926	C₂×D₅	1	1	yes	characteristic
134	C₂×#208	—	5	1	no	—
135	C₂×#208	—	5	2	no	—
136	C₂²×C₃⋊C₈	—	5	2	no	—
137	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
138	C₃×#101	—	5	2	no	—
139	C₃×#100	—	5	2	no	—
140	#834	—	5	4	no	—
141	#815	—	2	1	no	—
142	#815	—	10	1	no	—
143	C₈×Dic₃	—	2	1	no	—
144	C₈×Dic₃	—	10	1	no	—
145	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
146	C₂×C₂²⋊D₅	C₄×D₃	1	2	yes	—
147	#709	—	2	1	no	—
148	#709	—	2	1	no	—
149	#709	—	2	1	no	—
150	#709	—	2	1	no	—
151	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
152	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
153	C₂×Dic₁₀	C₂×Dic₃	1	1	yes	characteristic
154	C₅×M₁₆	—	2	1	no	—
155	C₅×M₁₆	C₂×Dic₃	1	2	yes	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	3	1	no	—
158	C₂×C₅×C₈	—	3	1	no	—
159	C₂×C₅×C₈	—	3	1	no	—
160	C₂×C₅×C₈	—	3	1	no	—
161	C₂×C₅×C₈	—	3	1	no	—
162	C₂×C₅×C₈	—	3	1	no	—
163	C₅×C₄⋊C₄	—	6	1	no	—
164	C₅×C₂²⋊C₄	—	3	2	no	—
165	C₄²×C₅	—	6	1	no	—
166	C₂²⋊Dic₅	—	3	2	no	—
167	C₄⋊Dic₅	—	6	1	no	—
168	C₄×Dic₅	—	6	1	no	—
169	#681	—	2	1	no	—
170	#681	—	6	1	no	—
171	#681	—	6	1	no	—
172	#681	C₂×Dic₃	1	2	yes	—
173	C₂×#168	—	2	1	no	—
174	C₂×#168	—	3	2	no	—
175	#676	—	6	2	no	—
176	#676	—	6	2	no	—
177	C₈×D₅	—	6	2	no	—
178	C₈×D₅	—	6	2	no	—
179	C₂×#131	—	15	1	no	—
180	#413	—	5	1	no	—
181	#410	—	15	1	no	—
182	#405	—	3	1	no	—
183	#405	—	15	1	no	—
184	#344	—	15	1	no	—
185	#344	—	15	1	no	—
186	C₂²×C₃×C₅	—	4	1	no	—
187	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
190	C₂×C₃×D₅	—	2	2	no	—
191	C₂×C₃×D₅	—	4	2	no	—
192	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₃×C₄×C₅	#117	1	1	yes	characteristic
194	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
196	Dic₁₅	—	4	2	no	—
197	C₃×Dic₅	—	2	2	no	—
198	C₅×Dic₃	—	4	2	no	—
199	C₃×#41	—	10	1	no	—
200	C₃×#41	—	10	1	no	—
201	C₃×#41	—	10	1	no	—
202	C₃×#41	—	10	1	no	—
203	C₂×C₃×Q₈	—	5	1	no	—
204	C₂×C₃×D₄	—	5	2	no	—
205	C₂×C₃×D₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	2	no	—
207	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
208	C₃×M₁₆	—	2	1	no	—
209	C₃×M₁₆	—	5	2	no	—
210	C₃×M₁₆	—	10	1	no	—
211	C₃×M₁₆	C₄×D₅	1	2	yes	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	10	1	no	—
214	#217	—	5	2	no	—
215	#217	C₄×D₅	1	2	yes	—
216	C₄⋊Dic₃	—	2	1	no	—
217	C₄⋊Dic₃	—	10	1	no	—
218	C₄×Dic₃	—	2	1	no	—
219	C₄×Dic₃	—	10	1	no	—
220	#208	—	10	1	no	—
221	#208	—	10	1	no	—
222	#208	—	10	2	no	—
223	#208	—	10	2	no	—
224	C₂×C₃⋊C₈	—	5	2	no	—
225	C₂×C₃⋊C₈	—	10	2	no	—
226	C₂×C₃⋊C₈	—	10	2	no	—
227	C₂×C₃⋊C₈	C₄×D₅	1	1	yes	characteristic
228	C₂×C₃⋊C₈	C₄×D₅	1	1	yes	characteristic
229	C₂×C₃⋊C₈	D₂₀	1	1	yes	characteristic
230	C₂×C₃⋊C₈	D₂₀	1	1	yes	characteristic
231	C₂×C₃⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
232	C₂×C₃⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
233	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂²×D₅	C₄×Dic₃	1	2	yes	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅	#237	1	1	yes	characteristic
240	C₂×C₄×C₅	#237	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
242	C₂²⋊D₅	—	2	2	no	—
243	C₂²⋊D₅	—	2	2	no	—
244	C₂×Dic₅	—	6	2	no	—
245	C₂×Dic₅	C₄×Dic₃	1	2	yes	—
246	D₂₀	—	2	1	no	—
247	D₂₀	—	2	1	no	—
248	C₄×D₅	—	2	2	no	—
249	C₄×D₅	—	2	2	no	—
250	Dic₁₀	—	2	1	no	—
251	Dic₁₀	—	2	1	no	—
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	—	3	1	no	—
254	C₅×C₈	—	3	1	no	—
255	C₅×C₈	—	3	1	no	—
256	C₅×C₈	—	3	1	no	—
257	#168	—	2	2	no	—
258	#168	—	6	2	no	—
259	C₂×#41	—	5	1	no	—
260	#131	—	30	1	no	—
261	#131	—	30	1	no	—
262	#131	—	30	1	no	—
263	#131	—	30	1	no	—
264	C₂×M₁₆	—	5	1	no	—
265	C₂×M₁₆	—	15	2	no	—
266	C₂×M₁₆	—	15	1	no	—
267	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
268	C₂²×C₈	—	3	1	no	—
269	C₂²×C₈	—	15	2	no	—
270	#117	—	3	1	no	—
271	#117	—	15	1	no	—
272	#101	—	5	2	no	—
273	#100	—	5	2	no	—
274	#99	—	15	4	no	—
275	#97	—	6	1	no	—
276	#97	—	30	1	no	—
277	C₄×C₈	—	6	1	no	—
278	C₄×C₈	—	30	1	no	—
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
283	C₃×D₅	—	4	2	no	—
284	C₂³×C₃	—	5	2	no	—
285	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
286	C₃×Q₈	—	10	1	no	—
287	C₃×Q₈	—	10	1	no	—
288	C₃×D₄	—	10	2	no	—
289	C₃×D₄	—	10	2	no	—
290	C₃×D₄	—	10	1	no	—
291	C₃×D₄	—	10	1	no	—
292	C₂×C₃×C₄	—	5	2	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	—	10	2	no	—
295	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
298	C₂×C₃×C₄	#709	1	1	yes	characteristic
299	C₂×C₃×C₄	#709	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	—	10	2	no	—
303	C₃×C₈	—	2	2	no	—
304	C₃×C₈	—	10	2	no	—
305	C₃⋊C₈	—	10	2	no	—
306	C₃⋊C₈	#685	1	1	yes	characteristic
307	C₃⋊C₈	#685	1	1	yes	characteristic
308	C₃⋊C₈	#685	1	1	yes	characteristic
309	C₃⋊C₈	#685	1	1	yes	characteristic
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
312	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
313	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
314	C₂×D₅	—	2	2	no	—
315	C₂×D₅	—	4	2	no	—
316	C₄×C₅	—	12	2	no	—
317	C₄×C₅	#877	1	1	yes	characteristic
318	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
319	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
320	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
321	Dic₅	—	2	2	no	—
322	Dic₅	—	12	2	no	—
323	#41	—	10	1	no	—
324	#41	—	10	1	no	—
325	#41	—	10	1	no	—
326	#41	—	10	1	no	—
327	C₂×Q₈	—	5	1	no	—
328	C₂×D₄	—	5	2	no	—
329	C₂×D₄	—	5	1	no	—
330	C₂²×C₄	—	5	2	no	—
331	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
332	M₁₆	—	2	1	no	—
333	M₁₆	—	5	2	no	—
334	M₁₆	—	10	1	no	—
335	M₁₆	—	30	2	no	—
336	M₁₆	—	30	2	no	—
337	M₁₆	—	30	1	no	—
338	M₁₆	—	30	1	no	—
339	M₁₆	D₅×Dic₃	1	2	yes	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	3	1	no	—
342	C₂×C₈	—	3	1	no	—
343	C₂×C₈	—	3	1	no	—
344	C₂×C₈	—	3	1	no	—
345	C₂×C₈	—	3	1	no	—
346	C₂×C₈	—	3	1	no	—
347	C₂×C₈	—	10	1	no	—
348	C₂×C₈	—	15	2	no	—
349	C₂×C₈	—	30	2	no	—
350	C₂×C₈	—	30	2	no	—
351	C₄⋊C₄	—	6	1	no	—
352	C₄⋊C₄	—	30	1	no	—
353	C₂²⋊C₄	—	3	2	no	—
354	C₂²⋊C₄	—	15	2	no	—
355	C₄²	—	6	1	no	—
356	C₄²	—	30	1	no	—
357	C₃×C₅	#1757	1	1	yes	characteristic, complemented, Hall
358	C₂²×C₃	—	4	1	no	—
359	C₂²×C₃	—	10	2	no	—
360	C₂²×C₃	—	20	2	no	—
361	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
362	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
363	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
364	C₃×C₄	—	10	2	no	—
365	C₃×C₄	#4018	1	1	yes	characteristic
366	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
367	C₃×C₄	C₂×#685	1	1	yes	characteristic
368	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
369	Dic₃	—	4	2	no	—
370	Dic₃	—	20	2	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	2	1	no	—
373	C₂×C₅	—	2	1	no	—
374	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
375	D₅	—	4	2	no	—
376	C₂³	—	5	2	no	—
377	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
378	Q₈	—	10	1	no	—
379	Q₈	—	10	1	no	—
380	D₄	—	10	2	no	—
381	D₄	—	10	2	no	—
382	D₄	—	10	1	no	—
383	D₄	—	10	1	no	—
384	C₂×C₄	—	5	2	no	—
385	C₂×C₄	—	6	2	no	—
386	C₂×C₄	—	10	2	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	30	2	no	—
389	C₂×C₄	#6765	1	1	yes	characteristic
390	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
391	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
392	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
393	C₂×C₄	#6779	1	1	yes	characteristic
394	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	3	1	no	—
397	C₈	—	3	1	no	—
398	C₈	—	3	1	no	—
399	C₈	—	3	1	no	—
400	C₈	—	10	2	no	—
401	C₈	—	30	2	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	—	20	2	no	—
406	C₂×C₃	C₄×#685	1	1	yes	characteristic
407	C₅	#70133	1	1	yes	characteristic, complemented, Sylow
408	C₂²	—	4	1	no	—
409	C₂²	—	10	2	no	—
410	C₂²	—	20	2	no	—
411	C₂²	C₄×D₅×Dic₃	1	1	yes	characteristic
412	C₂²	#91395	1	1	yes	characteristic
413	C₂²	#91441	1	1	yes	characteristic
414	C₄	—	10	2	no	—
415	C₄	—	12	2	no	—
416	C₄	—	60	2	no	—
417	C₄	#91393	1	1	yes	characteristic
418	C₄	Dic₃×D₂₀	1	1	yes	characteristic
419	C₄	D₃×#685	1	1	yes	characteristic
420	C₄	Dic₃×C₂²⋊D₅	1	1	yes	characteristic
421	C₃	#10600691	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	20	2	no	—
426	C₂	Dic₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃×#685
commutator	C₂²×C₃×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂×C₃×C₅	C₄×C₂²⋊C₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1757
LCS	G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×#5122	C₂	semidirect
5. #11748326	C₂	semidirect
6. #11746380	C₂	semidirect
7. #11745989	C₂	semidirect
16. C₂×#6649	C₄	semidirect
21. C₂×D₅×C₃⋊C₈	C₄	semidirect
24. C₃×#3956	C₄	semidirect
25. C₃×#3955	C₄	semidirect
75. #5122	D₅	semidirect
93. #3956	Dic₃	semidirect
94. #3955	Dic₃	semidirect
357. C₃×C₅	#1757	semidirect
407. C₅	#70133	semidirect
421. C₃	#10600691	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91283	2
C₅×#5122	2
C₃×#65421	2
#11748624	2
#11748326	2
#11746380	2
#11745989	2
#10600691	3
#70133	5