Subgroups — #14417634

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91793	C₂	1	1	yes	maximal, characteristic
2	#11756282	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751234	C₂	1	2	yes	maximal, complemented
5	C₂×#91102	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750811	C₂	1	4	yes	maximal, complemented
7	C₄×Dic₆₀	C₂	1	2	yes	maximal, complemented
8	C₄×D₁₂₀	C₂	1	2	yes	maximal, complemented
9	#10610293	—	3	1	no	maximal, Hall
10	C₂×#6817	C₂²	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
15	C₂×Dic₆₀	C₂²	1	1	yes	characteristic
16	#91793	C₄	1	8	yes	complemented
17	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
18	C₂×#6706	C₂²	1	2	yes	—
19	#91781	—	2	2	no	—
20	C₄⋊C₄×D₁₅	—	2	2	no	—
21	#91770	—	2	4	no	—
22	C₄×D₆₀	C₂²	1	4	yes	—
23	C₄×Dic₃₀	C₂²	1	4	yes	—
24	C₃×C₅×#97	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	#91105	C₂²	1	4	yes	—
27	#91102	C₂²	1	2	yes	—
28	#91102	C₂²	1	2	yes	—
29	#91100	C₂²	1	4	yes	—
30	#78562	—	5	1	no	maximal, Hall
31	C₂×#4050	—	3	1	no	—
32	#65857	—	3	2	no	—
33	C₅×#405	D₃	1	1	yes	characteristic, complemented
34	#65422	—	3	2	no	—
35	C₂×#3950	—	3	1	no	—
36	#64999	—	3	4	no	—
37	C₄×Dic₂₀	—	3	2	no	—
38	C₄×D₄₀	—	3	2	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂×#1220	—	2	2	no	—
41	C₂²×Dic₁₅	—	2	2	no	—
42	#6817	—	2	4	no	—
43	#6817	C₂×C₄	1	8	yes	complemented
44	C₂×D₆₀	C₂³	1	2	yes	—
45	C₂×C₄×D₁₅	—	2	2	no	—
46	C₂×C₄×D₁₅	—	2	4	no	—
47	C₂×Dic₃₀	C₂³	1	2	yes	—
48	C₃×C₅×M₁₆	—	2	2	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
54	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
56	C₃×C₄²×C₅	C₂³	1	2	yes	—
57	#6714	—	2	4	no	—
58	C₄⋊Dic₁₅	—	2	2	no	—
59	C₄⋊Dic₁₅	C₂³	1	4	yes	—
60	#6712	—	2	4	no	—
61	C₄×Dic₁₅	—	2	4	no	—
62	Dic₆₀	C₂×C₄	1	4	yes	complemented
63	D₁₂₀	C₂×C₄	1	4	yes	complemented
64	#6706	C₂×C₄	1	8	yes	complemented
65	C₂×#904	—	5	1	no	—
66	#5523	—	5	2	no	—
67	C₃×#405	D₅	1	1	yes	characteristic, complemented
68	#5133	—	5	2	no	—
69	C₂×#818	—	5	1	no	—
70	#4710	—	5	4	no	—
71	C₄×Dic₁₂	—	5	2	no	—
72	C₄×D₂₄	—	5	2	no	—
73	C₂×#709	—	3	2	no	—
74	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
76	C₅×#117	C₂×D₃	1	1	yes	characteristic
77	C₂×C₄⋊Dic₅	—	3	2	no	—
78	C₂×Dic₂₀	—	3	1	no	—
79	#4050	—	3	8	no	—
80	C₂×D₄₀	—	3	1	no	—
81	C₂×#677	—	3	2	no	—
82	#4038	—	6	2	no	—
83	D₅×C₄⋊C₄	—	6	2	no	—
84	#4027	—	6	4	no	—
85	C₄×D₂₀	—	3	4	no	—
86	C₄×Dic₁₀	—	3	4	no	—
87	C₅×#97	C₂×D₃	1	2	yes	—
88	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
89	#3953	—	3	4	no	—
90	#3950	—	3	2	no	—
91	#3950	—	3	2	no	—
92	#3948	—	3	4	no	—
93	#2951	—	15	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×D₁₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
102	#1220	—	2	8	no	—
103	C₂×Dic₁₅	—	2	2	no	—
104	C₂×Dic₁₅	—	2	4	no	—
105	C₂×Dic₁₅	—	8	2	no	—
106	D₆₀	—	2	2	no	—
107	D₆₀	C₂²×C₄	1	4	yes	—
108	C₄×D₁₅	—	2	8	no	—
109	C₄×D₁₅	—	8	4	no	—
110	Dic₃₀	—	2	2	no	—
111	Dic₃₀	C₂²×C₄	1	4	yes	—
112	C₃×C₅×C₈	—	2	2	no	—
113	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
115	C₂×#235	—	5	2	no	—
116	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
117	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
118	C₃×#117	C₂×D₅	1	1	yes	characteristic
119	C₂×C₄⋊Dic₃	—	5	2	no	—
120	C₂×Dic₁₂	—	5	1	no	—
121	#904	—	5	8	no	—
122	C₂×D₂₄	—	5	1	no	—
123	C₂×#204	—	5	2	no	—
124	#892	—	10	2	no	—
125	D₃×C₄⋊C₄	—	10	2	no	—
126	#67⋊C₄	—	10	4	no	—
127	C₄×D₁₂	—	5	4	no	—
128	C₄×Dic₆	—	5	4	no	—
129	C₃×#97	C₂×D₅	1	2	yes	—
130	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
131	#821	—	5	4	no	—
132	#818	—	5	2	no	—
133	#818	—	5	2	no	—
134	#816	—	5	4	no	—
135	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
136	C₂×C₂²⋊D₅	—	6	2	no	—
137	C₂²×Dic₅	—	6	2	no	—
138	#709	—	3	8	no	—
139	#709	—	6	4	no	—
140	C₂×D₂₀	—	3	2	no	—
141	C₂×C₄×D₅	—	6	2	no	—
142	C₂×C₄×D₅	—	6	4	no	—
143	C₂×Dic₁₀	—	3	2	no	—
144	C₅×M₁₆	—	2	2	no	—
145	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
146	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
147	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
149	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
150	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
152	C₄²×C₅	C₂²×D₃	1	2	yes	—
153	#685	—	6	4	no	—
154	C₄⋊Dic₅	—	3	4	no	—
155	C₄⋊Dic₅	—	6	2	no	—
156	#683	—	6	4	no	—
157	C₄×Dic₅	—	6	4	no	—
158	Dic₂₀	—	3	4	no	—
159	D₄₀	—	3	4	no	—
160	#677	—	3	8	no	—
161	C₂×#135	—	15	1	no	—
162	#520	—	15	2	no	—
163	#440	—	15	4	no	—
164	C₄×Q₁₆	—	15	2	no	—
165	C₄×D₈	—	15	2	no	—
166	C₂×#107	—	15	1	no	—
167	#417	—	15	2	no	—
168	#405	D₁₅	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	2	1	no	—
170	C₂²×C₃×C₅	—	2	1	no	—
171	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
172	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
173	C₂×D₁₅	—	2	4	no	—
174	C₂×D₁₅	—	4	2	no	—
175	C₂×D₁₅	—	4	2	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
179	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
181	Dic₁₅	—	2	4	no	—
182	Dic₁₅	—	4	4	no	—
183	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
184	C₂×#67	—	10	2	no	—
185	C₂²×Dic₃	—	10	2	no	—
186	#235	—	5	8	no	—
187	#235	—	10	4	no	—
188	C₂×D₁₂	—	5	2	no	—
189	C₂×C₄×D₃	—	10	2	no	—
190	C₂×C₄×D₃	—	10	4	no	—
191	C₂×Dic₆	—	5	2	no	—
192	C₃×M₁₆	—	2	2	no	—
193	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
194	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
195	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
196	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
197	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
198	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	D₂₀	1	2	yes	—
200	C₃×C₄²	C₂²×D₅	1	2	yes	—
201	(C₂×D₃)⋊C₄	—	10	4	no	—
202	C₄⋊Dic₃	—	5	4	no	—
203	C₄⋊Dic₃	—	10	2	no	—
204	Dic₃⋊C₄	—	10	4	no	—
205	C₄×Dic₃	—	10	4	no	—
206	Dic₁₂	—	5	4	no	—
207	D₂₄	—	5	4	no	—
208	#204	—	5	8	no	—
209	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
210	C₂²×D₅	—	6	2	no	—
211	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
212	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
213	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
214	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
215	C₂×C₄×C₅	#235	1	2	yes	—
216	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
217	C₂²⋊D₅	—	6	8	no	—
218	C₂×Dic₅	—	6	2	no	—
219	C₂×Dic₅	—	6	4	no	—
220	C₂×Dic₅	—	24	2	no	—
221	D₂₀	—	3	4	no	—
222	D₂₀	—	6	2	no	—
223	C₄×D₅	—	6	8	no	—
224	C₄×D₅	—	24	4	no	—
225	Dic₁₀	—	3	4	no	—
226	Dic₁₀	—	6	2	no	—
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
229	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
230	C₂×#41	—	15	2	no	—
231	#135	—	15	8	no	—
232	C₂×Q₁₆	—	15	1	no	—
233	C₂×SD₁₆	—	15	2	no	—
234	C₂×D₈	—	15	1	no	—
235	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
236	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
237	C₄×Q₈	—	15	4	no	—
238	C₄×D₄	—	15	4	no	—
239	C₄×D₄	—	30	4	no	—
240	#117	—	30	2	no	—
241	#117	C₂×D₁₅	1	1	yes	characteristic
242	C₂×C₄⋊C₄	—	15	2	no	—
243	C₂×C₄⋊C₄	—	30	2	no	—
244	#107	—	15	2	no	—
245	#107	—	15	2	no	—
246	#103	—	15	4	no	—
247	#102	—	15	4	no	—
248	#97	C₂×D₁₅	1	2	yes	—
249	C₄×C₈	C₂×D₁₅	1	2	yes	—
250	C₂×C₃×C₅	—	2	2	no	—
251	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂×C₃×C₅	#576	1	1	yes	characteristic
253	C₂×C₃×C₅	#578	1	1	yes	characteristic
254	D₁₅	—	4	4	no	—
255	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
256	C₂²×D₃	—	10	2	no	—
257	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
258	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
259	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
260	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
261	C₂×C₃×C₄	#709	1	2	yes	—
262	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
263	#67	—	10	8	no	—
264	C₂×Dic₃	—	10	2	no	—
265	C₂×Dic₃	—	10	4	no	—
266	C₂×Dic₃	—	40	2	no	—
267	D₁₂	—	5	4	no	—
268	D₁₂	—	10	2	no	—
269	C₄×D₃	—	10	8	no	—
270	C₄×D₃	—	40	4	no	—
271	Dic₆	—	5	4	no	—
272	Dic₆	—	10	2	no	—
273	C₃×C₈	—	2	2	no	—
274	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
275	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	C₄×D₁₂	1	2	yes	—
279	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
280	C₂×D₅	—	6	4	no	—
281	C₂×D₅	—	12	2	no	—
282	C₂×D₅	—	12	2	no	—
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	C₄×D₁₂	1	2	yes	—
286	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
287	C₄×C₅	C₂×#235	1	1	yes	characteristic
288	Dic₅	—	6	4	no	—
289	Dic₅	—	12	4	no	—
290	#41	—	15	8	no	—
291	#41	—	30	4	no	—
292	C₂×Q₈	—	15	2	no	—
293	C₂×D₄	—	15	2	no	—
294	C₂×D₄	—	30	2	no	—
295	C₂²×C₄	—	30	2	no	—
296	C₂²×C₄	—	30	2	no	—
297	C₂²×C₄	—	30	4	no	—
298	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
299	Q₁₆	—	15	4	no	—
300	SD₁₆	—	15	8	no	—
301	D₈	—	15	4	no	—
302	M₁₆	—	2	2	no	—
303	C₂×C₈	C₄×D₁₅	1	4	yes	complemented
304	C₂×C₈	C₂²×D₁₅	1	2	yes	—
305	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
306	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
307	C₄⋊C₄	—	15	4	no	—
308	C₄⋊C₄	—	30	2	no	—
309	C₄⋊C₄	—	30	4	no	—
310	C₄⋊C₄	D₆₀	1	1	yes	characteristic
311	C₄⋊C₄	D₆₀	1	1	yes	characteristic
312	C₂²⋊C₄	—	30	4	no	—
313	C₂²⋊C₄	D₆₀	1	2	yes	—
314	C₄²	—	30	4	no	—
315	C₄²	C₂²×D₁₅	1	2	yes	—
316	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	C₄×D₂₀	1	2	yes	—
320	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
321	C₂×D₃	—	10	4	no	—
322	C₂×D₃	—	20	2	no	—
323	C₂×D₃	—	20	2	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	C₄×D₂₀	1	2	yes	—
327	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
328	C₃×C₄	C₂×#709	1	1	yes	characteristic
329	Dic₃	—	10	4	no	—
330	Dic₃	—	20	4	no	—
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
333	C₂×C₅	#5752	1	1	yes	characteristic
334	C₂×C₅	#5753	1	1	yes	characteristic
335	D₅	—	12	4	no	—
336	C₂³	—	30	2	no	—
337	C₂³	C₂×D₆₀	1	1	yes	characteristic
338	Q₈	—	15	4	no	—
339	Q₈	—	30	2	no	—
340	D₄	—	15	4	no	—
341	D₄	—	30	8	no	—
342	D₄	—	30	2	no	—
343	C₂×C₄	—	30	2	no	—
344	C₂×C₄	—	30	8	no	—
345	C₂×C₄	—	30	4	no	—
346	C₂×C₄	—	120	4	no	—
347	C₂×C₄	—	120	2	no	—
348	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
349	C₂×C₄	C₂×D₆₀	1	2	yes	—
350	C₂×C₄	C₂×D₆₀	1	2	yes	—
351	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
352	C₂×C₄	#6817	1	2	yes	—
353	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	C₂×C₄×D₁₅	1	2	yes	—
356	C₈	C₂×C₄×D₁₅	1	2	yes	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
359	C₂×C₃	#66086	1	1	yes	characteristic
360	C₂×C₃	#66087	1	1	yes	characteristic
361	D₃	—	20	4	no	—
362	C₅	#78562	1	1	yes	characteristic, complemented, Sylow
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	30	4	no	—
366	C₂²	—	60	2	no	—
367	C₂²	—	60	2	no	—
368	C₂²	C₄×D₆₀	1	2	yes	—
369	C₂²	C₂²×D₆₀	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	30	4	no	—
373	C₄	—	60	4	no	—
374	C₄	C₄×D₆₀	1	2	yes	—
375	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
376	C₄	C₂×#6817	1	1	yes	characteristic
377	C₃	#10610293	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	2	2	no	—
379	C₂	—	60	4	no	—
380	C₂	C₂×C₄×D₆₀	1	1	yes	characteristic
381	C₂	#11756511	1	1	yes	characteristic
382	C₂	#11756512	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₆₀
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×#91793	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#405	D₁₅
hypocenter	C₃×C₅	#2951
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #11756282	C₂	semidirect
3. C₃×C₅×#405	C₂	semidirect
4. #11751234	C₂	semidirect
5. C₂×#91102	C₂	semidirect
6. #11750811	C₂	semidirect
7. C₄×Dic₆₀	C₂	semidirect
8. C₄×D₁₂₀	C₂	semidirect
16. #91793	C₄	semidirect
33. C₅×#405	D₃	semidirect
43. #6817	C₂×C₄	semidirect
49. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
62. Dic₆₀	C₂×C₄	semidirect
63. D₁₂₀	C₂×C₄	semidirect
64. #6706	C₂×C₄	semidirect
67. C₃×#405	D₅	semidirect
145. C₂×C₅×C₈	C₄×D₃	semidirect
168. #405	D₁₅	semidirect
193. C₂×C₃×C₈	C₄×D₅	semidirect
303. C₂×C₈	C₄×D₁₅	semidirect
316. C₃×C₅	#2951	semidirect
362. C₅	#78562	semidirect
377. C₃	#10610293	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91793	2
#11756282	2
C₃×C₅×#405	2
#11751234	2
C₂×#91102	2
#11750811	2
C₄×Dic₆₀	2
C₄×D₁₂₀	2
#10610293	3
#78562	5