Subgroups — #14438624

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91758	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65811	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748369	C₂	1	4	yes	maximal, complemented
5	#11746920	C₂	1	2	yes	maximal, complemented
6	#11746893	C₂	1	4	yes	maximal, complemented
7	#11746890	C₂	1	2	yes	maximal, complemented
8	#10610259	—	3	1	no	maximal, Hall
9	C₂²×Dic₃₀	—	2	1	no	—
10	C₂×C₃×#709	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	—	2	1	no	—
13	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
14	#91758	—	2	1	no	—
15	#91758	—	2	1	no	—
16	#91758	C₂²	1	2	yes	—
17	#91758	C₂²	1	2	yes	—
18	C₂×C₅×#208	C₂²	1	2	yes	—
19	C₃×#4076	—	2	1	no	—
20	C₃×#4076	—	2	1	no	—
21	C₃×#4021	C₂²	1	2	yes	—
22	C₃×#4020	C₂²	1	1	yes	characteristic
23	C₃×C₄×D₂₀	—	2	1	no	—
24	C₃×C₄×D₂₀	—	2	1	no	—
25	C₃×#4015	C₂²	1	1	yes	characteristic
26	C₅×#803	C₂²	1	2	yes	—
27	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
28	#90971	C₂²	1	8	yes	—
29	#90965	C₂²	1	8	yes	—
30	#83283	—	5	1	no	maximal, Hall
31	#65811	D₃	1	1	yes	characteristic
32	C₂×#4015	—	3	1	no	—
33	C₄×C₅×M₁₆	—	3	1	no	—
34	#65422	—	3	4	no	—
35	#65003	—	3	4	no	—
36	#64983	—	3	2	no	—
37	#64970	—	3	2	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×Dic₁₅	—	2	2	no	—
42	C₂×Dic₃₀	—	2	2	no	—
43	C₂×Dic₃₀	—	2	2	no	—
44	C₂×Dic₃₀	—	4	4	no	—
45	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
46	C₃×#709	—	2	8	no	—
47	C₂×C₃×D₂₀	—	2	1	no	—
48	C₂×C₃×D₂₀	—	2	1	no	—
49	C₂×C₃×D₂₀	C₂³	1	2	yes	—
50	C₂×C₃×C₄×D₅	—	2	2	no	—
51	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₄⋊Dic₁₅	—	2	2	no	—
57	C₄⋊Dic₁₅	—	2	2	no	—
58	C₄⋊Dic₁₅	—	2	2	no	—
59	C₄⋊Dic₁₅	C₂³	1	4	yes	—
60	C₅×#208	—	2	4	no	—
61	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
62	C₃×#685	—	2	2	no	—
63	C₃×#685	—	2	2	no	—
64	C₃×C₄⋊Dic₅	—	2	1	no	—
65	C₃×C₄⋊Dic₅	—	2	1	no	—
66	C₃×#532	—	5	1	no	—
67	C₂×#869	—	5	1	no	—
68	#5232	—	5	4	no	—
69	#5079	—	5	2	no	—
70	#5070	—	5	2	no	—
71	#5055	—	5	4	no	—
72	C₄×#208	D₅	1	1	yes	characteristic, complemented
73	C₂×#709	C₂×D₃	1	2	yes	—
74	C₂²×Dic₁₀	—	6	1	no	—
75	C₂×C₅×M₁₆	—	3	2	no	—
76	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
77	#4076	—	2	1	no	—
78	#4076	—	2	1	no	—
79	C₂×C₄⋊Dic₅	—	3	2	no	—
80	C₂×C₄⋊Dic₅	—	6	1	no	—
81	#4021	C₂×D₃	1	2	yes	—
82	#4020	C₂×D₃	1	1	yes	characteristic
83	C₄×D₂₀	—	2	1	no	—
84	C₄×D₂₀	—	2	1	no	—
85	#4015	—	3	2	no	—
86	#4015	—	3	2	no	—
87	#4015	—	6	1	no	—
88	#4015	—	6	1	no	—
89	#4015	C₂×D₃	1	1	yes	characteristic
90	C₅×#97	—	3	2	no	—
91	C₄×C₅×C₈	—	3	2	no	—
92	#3953	—	3	8	no	—
93	#3948	—	3	8	no	—
94	#3141	—	15	1	no	Sylow
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×D₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂×Dic₁₅	—	2	4	no	—
107	C₂×Dic₁₅	—	4	4	no	—
108	Dic₃₀	—	4	4	no	—
109	Dic₃₀	—	4	4	no	—
110	C₃×C₂²⋊D₅	—	4	4	no	—
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₃×D₂₀	—	2	4	no	—
113	C₃×D₂₀	—	4	2	no	—
114	C₃×D₂₀	—	4	2	no	—
115	C₃×C₄×D₅	—	4	4	no	—
116	C₃×Dic₁₀	—	2	4	no	—
117	C₅×C₃⋊C₈	—	2	4	no	—
118	C₂×C₃×#41	—	5	2	no	—
119	C₂²×Dic₆	—	10	1	no	—
120	C₃×C₄⋊Q₈	—	5	1	no	—
121	C₃×#127	—	5	1	no	—
122	C₃×#124	—	5	2	no	—
123	C₃×#121	—	10	1	no	—
124	C₃×#121	—	10	1	no	—
125	C₃×C₄×D₄	—	10	1	no	—
126	C₃×C₄×D₄	—	10	1	no	—
127	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
128	C₂×C₄⋊Dic₃	—	5	2	no	—
129	C₂×C₄⋊Dic₃	—	10	1	no	—
130	C₂×#208	C₂×D₅	1	2	yes	—
131	#869	—	5	2	no	—
132	#869	—	5	2	no	—
133	#869	—	10	1	no	—
134	#869	—	10	1	no	—
135	#835	—	5	8	no	—
136	#832	—	5	8	no	—
137	#803	C₂×D₅	1	2	yes	—
138	C₄×C₃⋊C₈	C₂×D₅	1	2	yes	—
139	C₂²×C₄×C₅	#67	1	1	yes	characteristic
140	C₂²×C₄×C₅	#67	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
142	C₂×C₂²⋊D₅	—	2	2	no	—
143	C₂²×Dic₅	—	6	2	no	—
144	#709	—	2	8	no	—
145	C₂×D₂₀	—	2	1	no	—
146	C₂×D₂₀	—	2	1	no	—
147	C₂×D₂₀	C₂²×D₃	1	2	yes	—
148	C₂×C₄×D₅	—	2	2	no	—
149	C₂×Dic₁₀	—	6	2	no	—
150	C₂×Dic₁₀	—	6	2	no	—
151	C₂×Dic₁₀	—	12	4	no	—
152	C₂×Dic₁₀	C₂²×D₃	1	2	yes	—
153	C₅×M₁₆	—	6	4	no	—
154	C₂×C₅×C₈	—	3	4	no	—
155	C₄²×C₅	#67	1	1	yes	characteristic
156	C₄²×C₅	#67	1	1	yes	characteristic
157	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
159	#685	—	2	2	no	—
160	#685	—	2	2	no	—
161	C₄⋊Dic₅	—	2	1	no	—
162	C₄⋊Dic₅	—	2	1	no	—
163	C₄⋊Dic₅	—	3	4	no	—
164	C₄⋊Dic₅	—	6	2	no	—
165	C₄⋊Dic₅	—	6	2	no	—
166	C₄⋊Dic₅	—	6	2	no	—
167	#532	—	5	1	no	—
168	C₂×C₄⋊Q₈	—	15	1	no	—
169	#489	—	15	4	no	—
170	#487	—	15	2	no	—
171	#486	—	15	2	no	—
172	#417	—	15	4	no	—
173	C₄×M₁₆	—	3	1	no	—
174	C₂²×C₃×C₅	—	2	1	no	—
175	C₂²×C₃×C₅	—	2	1	no	—
176	C₂²×C₃×C₅	#124	1	2	yes	—
177	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₃×D₅	—	4	2	no	—
179	C₂×C₃×D₅	—	4	2	no	—
180	C₂×C₃×D₅	—	4	2	no	—
181	C₃×C₄×C₅	—	2	1	no	—
182	C₃×C₄×C₅	—	2	1	no	—
183	C₃×C₄×C₅	#124	1	2	yes	—
184	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
185	C₃×C₄×C₅	#137	1	2	yes	—
186	C₃×C₄×C₅	C₂×#41	1	2	yes	—
187	Dic₁₅	—	4	4	no	—
188	C₃×Dic₅	—	4	2	no	—
189	C₃×#41	—	10	8	no	—
190	C₂×C₃×Q₈	—	5	2	no	—
191	C₂×C₃×D₄	—	5	2	no	—
192	C₂×C₃×D₄	—	10	2	no	—
193	C₂×C₃×D₄	—	10	1	no	—
194	C₂×C₃×D₄	—	10	1	no	—
195	C₂²×C₃×C₄	—	10	2	no	—
196	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
197	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
199	C₂²×Dic₃	—	10	2	no	—
200	C₂×Dic₆	—	10	2	no	—
201	C₂×Dic₆	—	10	2	no	—
202	C₂×Dic₆	—	20	4	no	—
203	C₃×C₄⋊C₄	—	10	1	no	—
204	C₃×C₄⋊C₄	—	10	1	no	—
205	C₃×C₂²⋊C₄	—	10	2	no	—
206	C₃×C₂²⋊C₄	—	10	2	no	—
207	C₃×C₄²	D₂₀	1	1	yes	characteristic
208	C₃×C₄²	D₂₀	1	1	yes	characteristic
209	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
210	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
211	C₄⋊Dic₃	—	5	4	no	—
212	C₄⋊Dic₃	—	10	2	no	—
213	C₄⋊Dic₃	—	10	2	no	—
214	C₄⋊Dic₃	—	10	2	no	—
215	#208	—	2	4	no	—
216	C₂×C₃⋊C₈	C₂²×D₅	1	4	yes	—
217	C₂³×C₅	C₂×#67	1	1	yes	characteristic
218	C₂²×D₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	#237	1	4	yes	—
222	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
228	C₂²⋊D₅	—	4	4	no	—
229	C₂×Dic₅	—	2	2	no	—
230	C₂×Dic₅	—	6	4	no	—
231	C₂×Dic₅	—	12	4	no	—
232	D₂₀	—	2	4	no	—
233	D₂₀	—	4	2	no	—
234	D₂₀	—	4	2	no	—
235	C₄×D₅	—	4	4	no	—
236	Dic₁₀	—	2	4	no	—
237	Dic₁₀	—	12	4	no	—
238	Dic₁₀	—	12	4	no	—
239	C₅×C₈	—	6	4	no	—
240	C₂×#41	—	5	2	no	—
241	C₂²×Q₈	—	30	1	no	—
242	C₂×M₁₆	—	3	2	no	—
243	C₄⋊Q₈	—	5	1	no	—
244	C₄⋊Q₈	—	15	2	no	—
245	C₄⋊Q₈	—	15	2	no	—
246	C₄⋊Q₈	—	30	1	no	—
247	C₄⋊Q₈	—	30	1	no	—
248	#127	—	5	1	no	—
249	#124	—	5	2	no	—
250	#121	—	10	1	no	—
251	#121	—	10	1	no	—
252	C₄×D₄	—	10	1	no	—
253	C₄×D₄	—	10	1	no	—
254	C₂×C₄⋊C₄	—	15	2	no	—
255	C₂×C₄⋊C₄	—	30	1	no	—
256	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
257	#103	—	15	8	no	—
258	#102	—	15	8	no	—
259	#97	—	3	2	no	—
260	C₄×C₈	—	3	2	no	—
261	C₂×C₃×C₅	—	2	2	no	—
262	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
263	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
265	C₃×D₅	—	8	2	no	—
266	C₂³×C₃	—	10	2	no	—
267	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
268	C₃×Q₈	—	10	4	no	—
269	C₃×D₄	—	10	4	no	—
270	C₃×D₄	—	20	4	no	—
271	C₃×D₄	—	20	2	no	—
272	C₃×D₄	—	20	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	20	4	no	—
277	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
282	C₂×C₃×C₄	#709	1	4	yes	—
283	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
284	C₂×Dic₃	—	10	4	no	—
285	C₂×Dic₃	—	20	4	no	—
286	Dic₆	—	20	4	no	—
287	Dic₆	—	20	4	no	—
288	C₃⋊C₈	—	2	4	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	#936	1	2	yes	—
292	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
293	C₂×D₅	—	4	2	no	—
294	C₂×D₅	—	4	2	no	—
295	C₂×D₅	—	4	2	no	—
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	#936	1	2	yes	—
299	C₄×C₅	#949	1	2	yes	—
300	C₄×C₅	#951	1	2	yes	—
301	C₄×C₅	C₂×#237	1	2	yes	—
302	Dic₅	—	4	2	no	—
303	Dic₅	—	12	4	no	—
304	#41	—	10	8	no	—
305	C₂×Q₈	—	5	2	no	—
306	C₂×Q₈	—	30	2	no	—
307	C₂×Q₈	—	30	2	no	—
308	C₂×Q₈	—	60	4	no	—
309	C₂×D₄	—	5	2	no	—
310	C₂×D₄	—	10	2	no	—
311	C₂×D₄	—	10	1	no	—
312	C₂×D₄	—	10	1	no	—
313	C₂²×C₄	—	10	2	no	—
314	C₂²×C₄	—	30	2	no	—
315	C₂²×C₄	#1202	1	1	yes	characteristic
316	C₂²×C₄	#1202	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
318	M₁₆	—	6	4	no	—
319	C₂×C₈	—	3	4	no	—
320	C₄⋊C₄	—	10	1	no	—
321	C₄⋊C₄	—	10	1	no	—
322	C₄⋊C₄	—	15	4	no	—
323	C₄⋊C₄	—	30	2	no	—
324	C₄⋊C₄	—	30	2	no	—
325	C₄⋊C₄	—	30	2	no	—
326	C₂²⋊C₄	—	10	2	no	—
327	C₂²⋊C₄	—	10	2	no	—
328	C₄²	#1202	1	1	yes	characteristic
329	C₄²	#1202	1	1	yes	characteristic
330	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
331	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
332	C₃×C₅	#3141	1	1	yes	characteristic, complemented, Hall
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	—	2	1	no	—
335	C₂²×C₃	—	20	2	no	—
336	C₂²×C₃	—	20	2	no	—
337	C₂²×C₃	—	20	2	no	—
338	C₂²×C₃	#4021	1	2	yes	—
339	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	20	2	no	—
343	C₃×C₄	#4021	1	2	yes	—
344	C₃×C₄	#4054	1	2	yes	—
345	C₃×C₄	#4055	1	2	yes	—
346	C₃×C₄	C₂×#709	1	2	yes	—
347	Dic₃	—	20	4	no	—
348	C₂×C₅	—	2	2	no	—
349	C₂×C₅	C₂×#936	1	1	yes	characteristic
350	C₂×C₅	C₂×#949	1	1	yes	characteristic
351	C₂×C₅	C₂×#951	1	1	yes	characteristic
352	D₅	—	8	2	no	—
353	C₂³	—	10	2	no	—
354	C₂³	C₂×#1202	1	1	yes	characteristic
355	Q₈	—	10	4	no	—
356	Q₈	—	60	4	no	—
357	Q₈	—	60	4	no	—
358	D₄	—	10	4	no	—
359	D₄	—	20	4	no	—
360	D₄	—	20	2	no	—
361	D₄	—	20	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	10	2	no	—
365	C₂×C₄	—	20	4	no	—
366	C₂×C₄	—	30	4	no	—
367	C₂×C₄	—	60	4	no	—
368	C₂×C₄	#6765	1	4	yes	—
369	C₂×C₄	C₂×#1202	1	1	yes	characteristic
370	C₂×C₄	C₂×#1202	1	1	yes	characteristic
371	C₂×C₄	C₂×#1202	1	1	yes	characteristic
372	C₂×C₄	C₂×#1202	1	1	yes	characteristic
373	C₂×C₄	C₂×#1202	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
375	C₈	—	6	4	no	—
376	C₂×C₃	—	2	2	no	—
377	C₂×C₃	—	40	2	no	—
378	C₂×C₃	C₂×#4021	1	1	yes	characteristic
379	C₂×C₃	C₂×#4054	1	1	yes	characteristic
380	C₂×C₃	C₂×#4055	1	1	yes	characteristic
381	C₅	#83283	1	1	yes	characteristic, complemented, Sylow
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	20	2	no	—
385	C₂²	—	20	2	no	—
386	C₂²	—	20	2	no	—
387	C₂²	#91364	1	2	yes	—
388	C₂²	C₂²×#1202	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	20	2	no	—
392	C₄	—	60	4	no	—
393	C₄	#91301	1	2	yes	—
394	C₄	#91313	1	2	yes	—
395	C₄	#91364	1	2	yes	—
396	C₄	C₂×#6765	1	2	yes	—
397	C₃	#10610259	1	1	yes	characteristic, complemented, Sylow
398	C₂	—	2	2	no	—
399	C₂	—	40	2	no	—
400	C₂	C₂×#91301	1	1	yes	characteristic
401	C₂	C₂×#91313	1	1	yes	characteristic
402	C₂	C₂×#91364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#1202
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#65811	C₂
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#3141
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#91758	C₂	semidirect
3. C₄×C₅×#208	C₂	semidirect
4. #11748369	C₂	semidirect
5. #11746920	C₂	semidirect
6. #11746893	C₂	semidirect
7. #11746890	C₂	semidirect
72. C₄×#208	D₅	semidirect
332. C₃×C₅	#3141	semidirect
381. C₅	#83283	semidirect
397. C₃	#10610259	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91758	2
C₃×#65811	2
C₄×C₅×#208	2
#11748369	2
#11746920	2
#11746893	2
#11746890	2
#10610259	3
#83283	5