Subgroups — #14281898

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5580	C₂	1	1	yes	maximal, characteristic
2	#11746876	C₂	1	1	yes	maximal, characteristic, complemented
3	#11746853	C₂	1	1	yes	maximal, characteristic, complemented
4	#11746356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Q₈⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745837	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745836	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602543	—	3	1	no	maximal, Hall
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₅×#947	C₄	1	1	yes	characteristic
11	C₅×#946	C₄	1	1	yes	characteristic
12	C₅×#898	—	2	1	no	—
13	C₅×#895	C₄	1	1	yes	characteristic
14	C₅×#894	—	2	1	no	—
15	C₅×#890	C₄	1	1	yes	characteristic
16	C₄×C₅×D₁₂	—	2	1	no	—
17	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₅×#872	—	2	1	no	—
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
21	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
22	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
23	C₃×C₄×#168	C₂²	1	1	yes	characteristic
24	Dic₃⋊#168	—	2	1	no	—
25	(C₂×D₃)⋊#168	—	2	1	no	—
26	(C₂×D₃)⋊#168	—	2	1	no	—
27	Dic₃×#168	—	2	1	no	—
28	#68233	—	5	1	no	maximal, Hall
29	C₅×#529	—	3	1	no	—
30	#65214	—	3	1	no	—
31	#65214	—	3	1	no	—
32	Q₈⋊#168	—	3	1	no	—
33	Q₈⋊#168	D₃	1	1	yes	characteristic, complemented
34	D₄⋊#168	—	3	1	no	—
35	D₄⋊#168	—	3	1	no	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
43	C₃×C₅×C₄⋊C₄	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	—	2	1	no	—
46	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₃⋊#168	—	2	1	no	—
48	C₂×C₃⋊#168	—	2	1	no	—
49	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×C₄⋊Dic₃	—	2	1	no	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₅×Dic₃⋊C₄	—	2	1	no	—
58	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₂×C₃×#168	—	2	1	no	—
62	C₂×C₃×#168	—	2	1	no	—
63	#5580	D₅	1	1	yes	characteristic
64	#4833	—	5	1	no	—
65	#4685	—	5	1	no	—
66	C₃×Q₈⋊C₈	—	5	1	no	—
67	#4535	—	5	1	no	—
68	#4483	—	5	1	no	—
69	#4459	—	5	1	no	—
70	C₅×#126	—	6	1	no	—
71	C₅×#125	—	3	1	no	—
72	C₅×#124	—	3	1	no	—
73	C₅×#123	—	6	1	no	—
74	C₅×C₂²⋊Q₈	—	3	1	no	—
75	C₅×#121	—	3	1	no	—
76	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₄×C₅×D₄	—	3	1	no	—
78	C₄×C₅×D₄	—	6	1	no	—
79	C₅×#117	—	6	1	no	—
80	C₂×C₄²×C₅	—	3	1	no	—
81	C₂²⋊#168	—	6	1	no	—
82	C₂²⋊#168	—	6	1	no	—
83	C₄⋊#168	—	3	1	no	—
84	C₄⋊#168	—	6	1	no	—
85	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
86	C₄×#168	—	3	1	no	—
87	C₄×#168	—	6	1	no	—
88	C₄×#168	C₂×D₃	1	1	yes	characteristic
89	#1482	—	15	1	no	Sylow
90	C₂²×C₅×D₃	—	2	1	no	—
91	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	2	1	no	—
93	C₃×C₅×Q₈	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
99	C₂×C₅×Dic₃	—	2	1	no	—
100	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₅×D₁₂	—	2	1	no	—
104	C₅×D₁₂	—	2	1	no	—
105	C₅×D₁₂	—	4	2	no	—
106	C₄×C₅×D₃	—	2	1	no	—
107	C₄×C₅×D₃	—	2	1	no	—
108	C₄×C₅×D₃	—	2	1	no	—
109	C₄×C₅×D₃	—	2	1	no	—
110	C₄×C₅×D₃	—	4	1	no	—
111	C₄×C₅×D₃	—	4	1	no	—
112	C₄×C₅×D₃	—	4	1	no	—
113	C₃⋊#168	—	4	1	no	—
114	C₃⋊#168	—	4	1	no	—
115	C₃×#168	—	4	1	no	—
116	C₃×#168	—	4	1	no	—
117	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
118	#947	Dic₅	1	1	yes	characteristic
119	#946	Dic₅	1	1	yes	characteristic
120	#898	—	2	1	no	—
121	#895	Dic₅	1	1	yes	characteristic
122	#894	—	2	1	no	—
123	#890	Dic₅	1	1	yes	characteristic
124	C₄×D₁₂	—	2	1	no	—
125	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
126	#872	—	2	1	no	—
127	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
128	C₃×C₄⋊C₈	—	5	1	no	—
129	C₃×C₄×C₈	—	5	1	no	—
130	(C₂×D₃)⋊C₈	—	10	1	no	—
131	(C₂×D₃)⋊C₈	—	10	1	no	—
132	Dic₃⋊C₈	—	10	1	no	—
133	C₈×Dic₃	—	10	1	no	—
134	C₄⋊(C₃⋊C₈)	—	5	1	no	—
135	C₄×C₃⋊C₈	—	5	1	no	—
136	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
137	C₂×C₅×D₄	—	3	1	no	—
138	C₂×C₅×D₄	—	6	1	no	—
139	C₂²×C₄×C₅	—	3	1	no	—
140	C₂²×C₄×C₅	—	3	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	6	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	3	1	no	—
145	C₅×C₄⋊C₄	—	6	1	no	—
146	C₅×C₄⋊C₄	—	6	1	no	—
147	C₅×C₄⋊C₄	—	6	1	no	—
148	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
149	C₅×C₂²⋊C₄	—	6	1	no	—
150	C₅×C₂²⋊C₄	—	6	1	no	—
151	C₅×C₂²⋊C₄	—	6	1	no	—
152	C₅×C₂²⋊C₄	—	6	1	no	—
153	C₅×C₂²⋊C₄	—	6	1	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	—	3	1	no	—
156	C₄²×C₅	—	3	1	no	—
157	C₄²×C₅	—	3	1	no	—
158	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₂×#168	—	2	1	no	—
160	C₂×#168	—	2	1	no	—
161	C₂×#168	—	6	1	no	—
162	C₂×#168	—	6	1	no	—
163	#529	—	3	1	no	—
164	#431	—	15	1	no	—
165	#431	—	15	1	no	—
166	Q₈⋊C₈	—	5	1	no	—
167	Q₈⋊C₈	—	15	1	no	—
168	D₄⋊C₈	—	15	1	no	—
169	D₄⋊C₈	—	15	1	no	—
170	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₅×D₃	—	2	1	no	—
172	C₂×C₅×D₃	—	2	1	no	—
173	C₂×C₅×D₃	—	2	1	no	—
174	C₂×C₅×D₃	—	4	1	no	—
175	C₂×C₅×D₃	—	4	1	no	—
176	C₂×C₅×D₃	—	4	1	no	—
177	C₃×C₄×C₅	—	2	1	no	—
178	C₃×C₄×C₅	—	4	1	no	—
179	C₃×C₄×C₅	—	4	1	no	—
180	C₃×C₄×C₅	#131	1	1	yes	characteristic
181	C₃×C₄×C₅	#131	1	1	yes	characteristic
182	C₃×C₄×C₅	#135	1	1	yes	characteristic
183	C₃×C₄×C₅	#135	1	1	yes	characteristic
184	C₅×Dic₃	—	2	1	no	—
185	C₅×Dic₃	—	2	1	no	—
186	C₅×Dic₃	—	2	1	no	—
187	C₅×Dic₃	—	4	1	no	—
188	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
189	C₂×D₁₂	—	2	1	no	—
190	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	1	no	—
192	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
193	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
194	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
195	C₂×C₃×C₈	—	10	1	no	—
196	C₂×C₃×C₈	—	10	1	no	—
197	C₃×C₄⋊C₄	—	2	1	no	—
198	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
201	(C₂×D₃)⋊C₄	—	2	1	no	—
202	(C₂×D₃)⋊C₄	—	2	1	no	—
203	(C₂×D₃)⋊C₄	—	2	1	no	—
204	(C₂×D₃)⋊C₄	—	2	1	no	—
205	(C₂×D₃)⋊C₄	—	2	1	no	—
206	C₄⋊Dic₃	—	2	1	no	—
207	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
208	Dic₃⋊C₄	—	2	1	no	—
209	Dic₃⋊C₄	—	2	1	no	—
210	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
211	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
212	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
213	C₂×C₃⋊C₈	—	10	1	no	—
214	C₂×C₃⋊C₈	—	10	1	no	—
215	C₂³×C₅	—	3	1	no	—
216	C₂³×C₅	—	6	1	no	—
217	C₅×Q₈	—	2	1	no	—
218	C₅×Q₈	—	2	1	no	—
219	C₅×D₄	—	6	1	no	—
220	C₅×D₄	—	6	1	no	—
221	C₅×D₄	—	12	2	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	3	1	no	—
225	C₂×C₄×C₅	—	3	1	no	—
226	C₂×C₄×C₅	—	3	1	no	—
227	C₂×C₄×C₅	—	6	1	no	—
228	C₂×C₄×C₅	—	6	1	no	—
229	C₂×C₄×C₅	—	6	1	no	—
230	C₂×C₄×C₅	—	6	1	no	—
231	C₂×C₄×C₅	—	6	1	no	—
232	C₂×C₄×C₅	—	12	1	no	—
233	C₂×C₄×C₅	—	12	1	no	—
234	C₂×C₄×C₅	—	12	1	no	—
235	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
236	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
238	#168	—	4	1	no	—
239	#168	—	4	1	no	—
240	#168	—	12	1	no	—
241	#168	—	12	1	no	—
242	#126	—	6	1	no	—
243	#125	—	3	1	no	—
244	#124	—	3	1	no	—
245	#123	—	6	1	no	—
246	C₂²⋊Q₈	—	3	1	no	—
247	#121	—	3	1	no	—
248	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
249	C₄×D₄	—	3	1	no	—
250	C₄×D₄	—	6	1	no	—
251	#117	—	6	1	no	—
252	C₂×C₄²	—	3	1	no	—
253	C₄⋊C₈	—	5	1	no	—
254	C₄⋊C₈	—	15	1	no	—
255	C₄⋊C₈	—	30	1	no	—
256	C₂²⋊C₈	—	30	1	no	—
257	C₂²⋊C₈	—	30	1	no	—
258	C₄×C₈	—	5	1	no	—
259	C₄×C₈	—	15	1	no	—
260	C₄×C₈	—	30	1	no	—
261	C₂×C₃×C₅	#408	1	1	yes	characteristic
262	C₂×C₃×C₅	#416	1	1	yes	characteristic
263	C₂×C₃×C₅	#421	1	1	yes	characteristic
264	C₅×D₃	—	4	1	no	—
265	C₅×D₃	—	8	1	no	—
266	C₂²×D₃	—	2	1	no	—
267	C₂²×D₃	C₂²⋊Dic₅	1	1	yes	characteristic
268	C₃×Q₈	—	2	1	no	—
269	C₃×Q₈	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
275	C₂×Dic₃	—	2	1	no	—
276	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
277	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
278	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
279	D₁₂	—	2	1	no	—
280	D₁₂	—	2	1	no	—
281	D₁₂	—	4	2	no	—
282	C₄×D₃	—	2	1	no	—
283	C₄×D₃	—	2	1	no	—
284	C₄×D₃	—	2	1	no	—
285	C₄×D₃	—	2	1	no	—
286	C₄×D₃	—	4	1	no	—
287	C₄×D₃	—	4	1	no	—
288	C₄×D₃	—	4	1	no	—
289	C₃×C₈	—	20	1	no	—
290	C₃×C₈	—	20	1	no	—
291	C₃⋊C₈	—	20	1	no	—
292	C₃⋊C₈	—	20	1	no	—
293	C₂²×C₅	—	6	1	no	—
294	C₂²×C₅	—	6	1	no	—
295	C₂²×C₅	—	6	1	no	—
296	C₂²×C₅	—	12	1	no	—
297	C₂²×C₅	—	12	1	no	—
298	C₂²×C₅	—	12	1	no	—
299	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	4	1	no	—
302	C₄×C₅	—	4	1	no	—
303	C₄×C₅	—	6	1	no	—
304	C₄×C₅	—	6	1	no	—
305	C₄×C₅	—	6	1	no	—
306	C₄×C₅	—	12	1	no	—
307	C₄×C₅	#901	1	1	yes	characteristic
308	C₄×C₅	#907	1	1	yes	characteristic
309	C₄×C₅	#916	1	1	yes	characteristic
310	C₄×C₅	#919	1	1	yes	characteristic
311	C₂×Q₈	D₃×Dic₅	1	1	yes	characteristic
312	C₂×D₄	—	3	1	no	—
313	C₂×D₄	—	6	1	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	3	1	no	—
316	C₂²×C₄	—	3	1	no	—
317	C₂²×C₄	—	6	1	no	—
318	C₂×C₈	—	10	1	no	—
319	C₂×C₈	—	10	1	no	—
320	C₂×C₈	—	30	1	no	—
321	C₂×C₈	—	30	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	3	1	no	—
324	C₄⋊C₄	—	6	1	no	—
325	C₄⋊C₄	—	6	1	no	—
326	C₄⋊C₄	—	6	1	no	—
327	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
328	C₂²⋊C₄	—	6	1	no	—
329	C₂²⋊C₄	—	6	1	no	—
330	C₂²⋊C₄	—	6	1	no	—
331	C₂²⋊C₄	—	6	1	no	—
332	C₂²⋊C₄	—	6	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	3	1	no	—
335	C₄²	—	3	1	no	—
336	C₄²	—	3	1	no	—
337	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
338	C₃×C₅	#1482	1	1	yes	characteristic, complemented, Hall
339	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
340	C₂×D₃	—	2	1	no	—
341	C₂×D₃	—	2	1	no	—
342	C₂×D₃	—	2	1	no	—
343	C₂×D₃	—	4	1	no	—
344	C₂×D₃	—	4	1	no	—
345	C₂×D₃	—	4	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	4	1	no	—
348	C₃×C₄	—	4	1	no	—
349	C₃×C₄	#4094	1	1	yes	characteristic
350	C₃×C₄	#4094	1	1	yes	characteristic
351	C₃×C₄	#4096	1	1	yes	characteristic
352	C₃×C₄	#4096	1	1	yes	characteristic
353	Dic₃	—	2	1	no	—
354	Dic₃	—	2	1	no	—
355	Dic₃	—	2	1	no	—
356	Dic₃	—	4	1	no	—
357	C₂×C₅	—	12	1	no	—
358	C₂×C₅	—	24	1	no	—
359	C₂×C₅	#4727	1	1	yes	characteristic
360	C₂×C₅	#4804	1	1	yes	characteristic
361	C₂×C₅	#4821	1	1	yes	characteristic
362	C₂³	—	3	1	no	—
363	C₂³	—	6	1	no	—
364	Q₈	—	2	1	no	—
365	Q₈	—	2	1	no	—
366	D₄	—	6	1	no	—
367	D₄	—	6	1	no	—
368	D₄	—	12	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	3	1	no	—
373	C₂×C₄	—	3	1	no	—
374	C₂×C₄	—	6	1	no	—
375	C₂×C₄	—	6	1	no	—
376	C₂×C₄	—	6	1	no	—
377	C₂×C₄	—	6	1	no	—
378	C₂×C₄	—	6	1	no	—
379	C₂×C₄	—	12	1	no	—
380	C₂×C₄	—	12	1	no	—
381	C₂×C₄	—	12	1	no	—
382	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
383	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
384	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
385	C₈	—	20	1	no	—
386	C₈	—	20	1	no	—
387	C₈	—	60	1	no	—
388	C₈	—	60	1	no	—
389	C₂×C₃	#65522	1	1	yes	characteristic
390	C₂×C₃	#65523	1	1	yes	characteristic
391	C₂×C₃	#65525	1	1	yes	characteristic
392	D₃	—	4	1	no	—
393	D₃	—	8	1	no	—
394	C₅	#68233	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	6	1	no	—
396	C₂²	—	6	1	no	—
397	C₂²	—	6	1	no	—
398	C₂²	—	12	1	no	—
399	C₂²	—	12	1	no	—
400	C₂²	—	12	1	no	—
401	C₂²	D₃×C₂²⋊Dic₅	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	6	1	no	—
406	C₄	—	6	1	no	—
407	C₄	—	6	1	no	—
408	C₄	—	12	1	no	—
409	C₄	#91286	1	1	yes	characteristic
410	C₄	#91288	1	1	yes	characteristic
411	C₄	#91517	1	1	yes	characteristic
412	C₄	#91519	1	1	yes	characteristic
413	C₃	#10602543	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	12	1	no	—
415	C₂	—	24	1	no	—
416	C₂	#11748490	1	1	yes	characteristic
417	C₂	#11749211	1	1	yes	characteristic
418	C₂	#11749429	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₃×C₄×C₅×Q₈	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#895	C₄
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	#1482
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #11746876	C₂	semidirect
3. #11746853	C₂	semidirect
4. #11746356	C₂	semidirect
5. C₃×Q₈⋊#168	C₂	semidirect
6. #11745837	C₂	semidirect
7. #11745836	C₂	semidirect
33. Q₈⋊#168	D₃	semidirect
338. C₃×C₅	#1482	semidirect
394. C₅	#68233	semidirect
413. C₃	#10602543	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5580	2
#11746876	2
#11746853	2
#11746356	2
C₃×Q₈⋊#168	2
#11745837	2
#11745836	2
#10602543	3
#68233	5