Subgroups — #14295606

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11754436	C₂	1	1	yes	maximal, characteristic
2	C₂×#91109	C₂	1	1	yes	maximal, characteristic
3	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×Dic₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90981	C₂	1	1	yes	maximal, characteristic
6	C₃×#64775	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745973	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#3957	—	3	1	no	maximal, Hall
9	C₂×#6817	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	1	yes	characteristic
14	C₃×#4072	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	#91556	—	2	2	no	—
17	C₂×Dic₃×Dic₅	—	2	2	no	—
18	#91428	C₄	1	2	yes	complemented
19	C₄×#1200	—	2	1	no	—
20	#91386	—	2	1	no	—
21	#91340	C₄	1	2	yes	complemented
22	#91109	C₄	1	4	yes	complemented
23	C₅×#815	—	2	1	no	—
24	C₅×C₈×Dic₃	—	2	1	no	—
25	#90981	C₄	1	4	yes	complemented
26	#68728	—	5	1	no	maximal, Hall
27	C₄×#709	—	3	1	no	—
28	C₄×C₅×M₁₆	—	3	1	no	—
29	C₂×#3957	—	3	1	no	—
30	C₂×#3957	—	3	1	no	—
31	C₄²×Dic₅	—	3	1	no	—
32	#64775	—	3	1	no	—
33	#64775	D₃	1	1	yes	characteristic, complemented
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×#1220	—	2	1	no	—
36	C₂²×Dic₁₅	—	2	1	no	—
37	#6817	—	2	1	no	—
38	#6817	—	2	1	no	—
39	#6817	C₂×C₄	1	2	yes	—
40	#6817	C₂×C₄	1	2	yes	—
41	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×D₁₅	—	2	1	no	—
43	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	D₄	1	2	yes	—
45	C₂²×C₃×Dic₅	—	2	1	no	—
46	C₂×#1200	—	2	2	no	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₄×Dic₁₅	—	2	1	no	—
51	C₄×Dic₁₅	C₂×C₄	1	2	yes	complemented
52	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
53	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
54	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
55	C₅×#208	—	2	1	no	—
56	C₅×#208	C₂×C₄	1	2	yes	complemented
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₃×C₂²⋊Dic₅	—	2	1	no	—
59	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
60	C₃×C₄×Dic₅	—	2	1	no	—
61	C₃×C₄×Dic₅	—	2	1	no	—
62	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
63	#6669	—	2	2	no	—
64	#6667	—	2	2	no	—
65	Dic₃×Dic₅	—	2	8	no	—
66	Dic₃×Dic₅	—	2	2	no	—
67	#5522	—	5	1	no	—
68	C₂×#825	—	5	1	no	—
69	Dic₃×M₁₆	D₅	1	1	yes	characteristic, complemented
70	C₄²×Dic₃	—	5	1	no	—
71	C₂×#805	—	5	1	no	—
72	C₃×#339	—	5	1	no	—
73	#4532	—	5	1	no	—
74	C₂×#709	—	3	1	no	—
75	C₂×C₅×M₁₆	—	3	1	no	—
76	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
77	C₂×C₄²×C₅	—	3	1	no	—
78	C₄×C₂²⋊D₅	—	6	2	no	—
79	#4072	C₂×D₃	1	1	yes	characteristic
80	C₂×C₄×Dic₅	—	3	1	no	—
81	C₂×C₄×Dic₅	—	6	2	no	—
82	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
83	C₄×D₂₀	—	3	2	no	—
84	#4018	—	6	1	no	—
85	C₄²×D₅	—	6	1	no	—
86	C₄×Dic₁₀	—	3	2	no	—
87	C₅×#97	—	6	1	no	—
88	C₄×C₅×C₈	—	6	1	no	—
89	#3957	—	3	4	no	—
90	#3957	—	3	4	no	—
91	C₄×#104	—	15	1	no	Sylow
92	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×D₁₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	#1220	—	2	2	no	—
101	#1220	—	2	2	no	—
102	C₂×Dic₁₅	—	2	4	no	—
103	C₂×Dic₁₅	—	2	1	no	—
104	C₂×Dic₁₅	—	2	2	no	—
105	D₆₀	—	2	1	no	—
106	D₆₀	C₄²	1	2	yes	complemented
107	C₄×D₁₅	—	2	2	no	—
108	C₄×D₁₅	—	2	2	no	—
109	Dic₃₀	—	2	1	no	—
110	Dic₃₀	C₄²	1	2	yes	complemented
111	C₂×C₅×Dic₃	—	2	4	no	—
112	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
113	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
114	C₂×C₃×Dic₅	—	2	4	no	—
115	C₂×C₃×Dic₅	—	2	2	no	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	#1200	—	4	4	no	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₅×C₃⋊C₈	—	2	2	no	—
120	C₂×#235	—	5	1	no	—
121	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
122	C₃×#117	—	5	1	no	—
123	C₂×C₃×C₄²	—	5	1	no	—
124	C₂×C₄×Dic₃	—	5	1	no	—
125	C₂×C₄×Dic₃	—	10	2	no	—
126	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
127	C₂×#208	C₂×D₅	1	1	yes	characteristic
128	#893	—	5	2	no	—
129	#887	—	5	2	no	—
130	#67⋊C₄	—	10	2	no	—
131	#872	—	10	1	no	—
132	C₄²×D₃	—	10	1	no	—
133	#825	—	5	4	no	—
134	#815	—	2	1	no	—
135	C₈×Dic₃	—	2	1	no	—
136	#805	—	5	4	no	—
137	C₂²×C₄×C₅	—	3	2	no	—
138	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
139	C₂×C₂²⋊D₅	—	6	1	no	—
140	C₂²×Dic₅	—	2	1	no	—
141	C₂²×Dic₅	—	6	1	no	—
142	#709	—	3	2	no	—
143	#709	—	3	2	no	—
144	#709	—	6	1	no	—
145	#709	—	6	1	no	—
146	C₂×D₂₀	—	3	1	no	—
147	C₂×C₄×D₅	—	6	1	no	—
148	C₂×C₄×D₅	—	6	2	no	—
149	C₂×Dic₁₀	—	3	1	no	—
150	C₅×M₁₆	—	2	1	no	—
151	C₅×M₁₆	—	3	2	no	—
152	C₅×M₁₆	—	6	1	no	—
153	C₅×M₁₆	C₄×D₃	1	2	yes	complemented
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	6	1	no	—
156	C₄²×C₅	—	3	2	no	—
157	C₄²×C₅	—	3	1	no	—
158	C₄²×C₅	—	3	1	no	—
159	C₂²⋊Dic₅	—	2	1	no	—
160	#685	—	6	2	no	—
161	C₄⋊Dic₅	C₄×D₃	1	2	yes	—
162	#683	—	6	2	no	—
163	C₄×Dic₅	—	2	1	no	—
164	C₄×Dic₅	—	2	1	no	—
165	C₄×Dic₅	—	3	2	no	—
166	C₄×Dic₅	—	6	2	no	—
167	C₄×Dic₅	—	6	8	no	—
168	C₄×Dic₅	—	6	1	no	—
169	C₄×Dic₅	C₄×D₃	1	2	yes	complemented
170	C₄×#41	—	15	1	no	—
171	C₂×#104	—	15	1	no	—
172	C₂×#104	—	15	1	no	—
173	C₄×M₁₆	—	3	1	no	—
174	C₄³	—	15	1	no	—
175	#339	—	5	1	no	—
176	#339	—	15	1	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
181	C₂×D₁₅	—	2	2	no	—
182	C₂×D₁₅	—	4	2	no	—
183	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
184	C₃×C₄×C₅	#117	1	1	yes	characteristic
185	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
187	Dic₁₅	—	2	4	no	—
188	Dic₁₅	—	2	2	no	—
189	C₃×Dic₅	—	2	4	no	—
190	C₃×Dic₅	—	4	2	no	—
191	C₅×Dic₃	—	2	2	no	—
192	C₅×Dic₃	#104	1	4	yes	complemented
193	C₂²×C₃×C₄	—	10	1	no	—
194	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
195	C₂×#67	—	10	1	no	—
196	C₂²×Dic₃	—	10	1	no	—
197	C₂²×Dic₃	D₂₀	1	2	yes	—
198	#235	—	5	2	no	—
199	#235	—	5	2	no	—
200	#235	—	10	1	no	—
201	#235	—	10	1	no	—
202	C₂×D₁₂	—	5	1	no	—
203	C₂×C₄×D₃	—	10	1	no	—
204	C₂×C₄×D₃	—	10	2	no	—
205	C₂×Dic₆	—	5	1	no	—
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	C₄×D₅	1	2	yes	complemented
208	C₂×C₃×C₈	—	2	1	no	—
209	C₃×C₄⋊C₄	—	5	2	no	—
210	C₃×C₂²⋊C₄	—	10	1	no	—
211	C₃×C₄²	—	5	2	no	—
212	C₃×C₄²	—	10	1	no	—
213	C₃×C₄²	—	10	1	no	—
214	(C₂×D₃)⋊C₄	—	10	2	no	—
215	Dic₃⋊C₄	—	10	2	no	—
216	C₄×Dic₃	—	5	2	no	—
217	C₄×Dic₃	—	10	8	no	—
218	C₄×Dic₃	—	10	1	no	—
219	C₄×Dic₃	—	10	2	no	—
220	C₄×Dic₃	C₄×D₅	1	2	yes	—
221	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
222	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
223	#208	—	2	1	no	—
224	#208	C₄×D₅	1	2	yes	complemented
225	C₂×C₃⋊C₈	—	2	1	no	—
226	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
227	C₂²×D₅	—	6	1	no	—
228	C₂×C₄×C₅	—	3	2	no	—
229	C₂×C₄×C₅	—	3	2	no	—
230	C₂×C₄×C₅	—	6	4	no	—
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	D₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	#237	1	1	yes	characteristic
236	C₂×C₄×C₅	#239	1	1	yes	characteristic
237	C₂²⋊D₅	—	6	2	no	—
238	C₂²⋊D₅	—	6	2	no	—
239	C₂×Dic₅	—	2	4	no	—
240	C₂×Dic₅	—	2	2	no	—
241	C₂×Dic₅	—	2	2	no	—
242	C₂×Dic₅	—	6	4	no	—
243	C₂×Dic₅	—	6	1	no	—
244	C₂×Dic₅	—	6	2	no	—
245	D₂₀	—	3	2	no	—
246	D₂₀	—	6	1	no	—
247	C₄×D₅	—	6	2	no	—
248	C₄×D₅	—	6	2	no	—
249	C₄×D₅	—	12	4	no	—
250	Dic₁₀	—	3	2	no	—
251	Dic₁₀	—	6	1	no	—
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	—	6	2	no	—
254	C₂×#41	—	15	1	no	—
255	C₂×M₁₆	—	3	1	no	—
256	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
257	C₄×Q₈	—	15	2	no	—
258	C₄×D₄	—	15	2	no	—
259	C₄×D₄	—	30	2	no	—
260	#117	—	5	1	no	—
261	#117	—	30	1	no	—
262	C₂×C₄²	—	3	1	no	—
263	C₂×C₄²	—	5	1	no	—
264	C₂×C₄²	—	15	1	no	—
265	C₂×C₄²	—	30	1	no	—
266	C₂×C₄²	—	30	2	no	—
267	#104	—	15	4	no	—
268	#104	—	15	4	no	—
269	#97	—	6	1	no	—
270	C₄×C₈	—	6	1	no	—
271	C₂×C₃×C₅	—	2	1	no	—
272	C₂×C₃×C₅	—	2	1	no	—
273	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×#104	1	2	yes	—
275	D₁₅	—	4	2	no	—
276	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
277	C₂²×D₃	—	10	1	no	—
278	C₂×C₃×C₄	—	10	4	no	—
279	C₂×C₃×C₄	—	10	2	no	—
280	C₂×C₃×C₄	—	10	2	no	—
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	#709	1	1	yes	characteristic
285	C₂×C₃×C₄	#709	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
287	#67	—	10	2	no	—
288	#67	—	10	2	no	—
289	C₂×Dic₃	—	2	4	no	—
290	C₂×Dic₃	—	10	4	no	—
291	C₂×Dic₃	—	10	2	no	—
292	C₂×Dic₃	—	10	1	no	—
293	C₂×Dic₃	#685	1	2	yes	—
294	C₂×Dic₃	#685	1	2	yes	—
295	D₁₂	—	5	2	no	—
296	D₁₂	—	10	1	no	—
297	C₄×D₃	—	10	2	no	—
298	C₄×D₃	—	10	2	no	—
299	C₄×D₃	—	20	4	no	—
300	Dic₆	—	5	2	no	—
301	Dic₆	—	10	1	no	—
302	C₃×C₈	—	2	2	no	—
303	C₃⋊C₈	—	2	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
306	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
307	C₂²×C₅	#893	1	1	yes	characteristic
308	C₂×D₅	—	6	2	no	—
309	C₂×D₅	—	12	2	no	—
310	C₄×C₅	—	3	4	no	—
311	C₄×C₅	—	6	2	no	—
312	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
313	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
314	C₄×C₅	#892	1	1	yes	characteristic
315	C₄×C₅	#893	1	1	yes	characteristic
316	Dic₅	—	2	4	no	—
317	Dic₅	—	4	2	no	—
318	Dic₅	—	6	4	no	—
319	Dic₅	—	6	2	no	—
320	#41	—	15	2	no	—
321	#41	—	15	2	no	—
322	#41	—	30	1	no	—
323	#41	—	30	1	no	—
324	C₂×Q₈	—	15	1	no	—
325	C₂×D₄	—	15	1	no	—
326	C₂×D₄	—	30	1	no	—
327	C₂²×C₄	—	3	2	no	—
328	C₂²×C₄	—	10	1	no	—
329	C₂²×C₄	—	30	2	no	—
330	C₂²×C₄	—	30	1	no	—
331	C₂²×C₄	—	30	1	no	—
332	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
333	M₁₆	—	2	1	no	—
334	M₁₆	—	3	2	no	—
335	M₁₆	—	6	1	no	—
336	M₁₆	#1200	1	2	yes	complemented
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	6	1	no	—
339	C₄⋊C₄	—	5	2	no	—
340	C₄⋊C₄	—	30	2	no	—
341	C₂²⋊C₄	—	10	1	no	—
342	C₂²⋊C₄	—	30	2	no	—
343	C₄²	—	3	2	no	—
344	C₄²	—	3	1	no	—
345	C₄²	—	3	1	no	—
346	C₄²	—	5	2	no	—
347	C₄²	—	10	1	no	—
348	C₄²	—	10	1	no	—
349	C₄²	—	15	2	no	—
350	C₄²	—	30	2	no	—
351	C₄²	—	30	8	no	—
352	C₄²	—	30	1	no	—
353	C₃×C₅	C₄×#104	1	1	yes	characteristic, complemented, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
356	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
357	C₂²×C₃	C₂×#685	1	1	yes	characteristic
358	C₂×D₃	—	10	2	no	—
359	C₂×D₃	—	20	2	no	—
360	C₃×C₄	—	10	4	no	—
361	C₃×C₄	—	20	2	no	—
362	C₃×C₄	C₄²×D₅	1	1	yes	characteristic
363	C₃×C₄	#4018	1	1	yes	characteristic
364	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
365	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
366	Dic₃	—	2	2	no	—
367	Dic₃	—	10	4	no	—
368	Dic₃	—	10	2	no	—
369	Dic₃	#3957	1	4	yes	complemented
370	C₂×C₅	—	2	1	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	#4666	1	1	yes	characteristic
373	C₂×C₅	D₃×#104	1	2	yes	—
374	D₅	—	12	2	no	—
375	C₂³	—	30	1	no	—
376	C₂³	D₃×D₂₀	1	1	yes	characteristic
377	Q₈	—	15	2	no	—
378	Q₈	—	30	1	no	—
379	D₄	—	15	2	no	—
380	D₄	—	30	2	no	—
381	D₄	—	30	2	no	—
382	D₄	—	30	1	no	—
383	C₂×C₄	—	3	2	no	—
384	C₂×C₄	—	3	2	no	—
385	C₂×C₄	—	6	4	no	—
386	C₂×C₄	—	10	4	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	10	2	no	—
389	C₂×C₄	—	30	4	no	—
390	C₂×C₄	—	30	2	no	—
391	C₂×C₄	—	30	1	no	—
392	C₂×C₄	—	30	2	no	—
393	C₂×C₄	—	30	2	no	—
394	C₂×C₄	—	60	4	no	—
395	C₂×C₄	#6769	1	1	yes	characteristic
396	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
397	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
398	C₂×C₄	#6779	1	1	yes	characteristic
399	C₂×C₄	C₂×#1200	1	1	yes	characteristic
400	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	6	2	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	C₄×#685	1	1	yes	characteristic
406	C₂×C₃	C₂×#3957	1	2	yes	—
407	D₃	—	20	2	no	—
408	C₅	#68728	1	1	yes	characteristic, complemented, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	30	2	no	—
411	C₂²	—	60	2	no	—
412	C₂²	#91395	1	1	yes	characteristic
413	C₂²	#91428	1	1	yes	characteristic
414	C₂²	D₃×#685	1	1	yes	characteristic
415	C₄	—	3	4	no	—
416	C₄	—	6	2	no	—
417	C₄	—	10	4	no	—
418	C₄	—	20	2	no	—
419	C₄	—	30	4	no	—
420	C₄	—	30	2	no	—
421	C₄	C₄×#1200	1	1	yes	characteristic
422	C₄	#91403	1	1	yes	characteristic
423	C₄	#91446	1	1	yes	characteristic
424	C₄	#91556	1	1	yes	characteristic
425	C₃	C₄×#3957	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	60	2	no	—
429	C₂	D₃×#3957	1	2	yes	—
430	C₂	#11748881	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×#6817	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	C₄×#104
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₅×Dic₃×M₁₆	C₂	semidirect
4. C₄×Dic₃×Dic₅	C₂	semidirect
6. C₃×#64775	C₂	semidirect
7. #11745973	C₂	semidirect
18. #91428	C₄	semidirect
21. #91340	C₄	semidirect
22. #91109	C₄	semidirect
25. #90981	C₄	semidirect
33. #64775	D₃	semidirect
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
51. C₄×Dic₁₅	C₂×C₄	semidirect
56. C₅×#208	C₂×C₄	semidirect
62. C₃×C₄×Dic₅	C₂×C₄	semidirect
69. Dic₃×M₁₆	D₅	semidirect
106. D₆₀	C₄²	semidirect
110. Dic₃₀	C₄²	semidirect
153. C₅×M₁₆	C₄×D₃	semidirect
169. C₄×Dic₅	C₄×D₃	semidirect
192. C₅×Dic₃	#104	semidirect
207. C₃×M₁₆	C₄×D₅	semidirect
224. #208	C₄×D₅	semidirect
336. M₁₆	#1200	semidirect
353. C₃×C₅	C₄×#104	semidirect
369. Dic₃	#3957	semidirect
408. C₅	#68728	semidirect
425. C₃	C₄×#3957	semidirect

Maximal subgroups

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

subgroup	index
#11754436	2
C₂×#91109	2
C₅×Dic₃×M₁₆	2
C₄×Dic₃×Dic₅	2
C₂×#90981	2
C₃×#64775	2
#11745973	2
C₄×#3957	3
#68728	5