Subgroups — #12068342

Order 1280.

666 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611023	C₂	1	1	yes	maximal, characteristic
2	#10610745	C₂	1	1	yes	maximal, characteristic
3	C₄×#4053	C₂	1	1	yes	maximal, characteristic
4	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601538	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64700	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600643	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599364	C₂	1	2	yes	maximal, complemented
9	#10599363	C₂	1	2	yes	maximal, complemented
10	#10599324	C₂	1	2	yes	maximal, complemented
11	#10599322	C₂	1	2	yes	maximal, complemented
12	C₂×#4053	C₄	1	1	yes	characteristic
13	C₂×#4053	C₄	1	1	yes	characteristic
14	C₄×#709	C₂²	1	1	yes	characteristic
15	C₅×#431	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	#65411	C₄	1	1	yes	characteristic
19	#65411	C₄	1	1	yes	characteristic
20	#65400	—	2	2	no	—
21	#65214	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
23	C₂×C₄×#168	C₂²	1	1	yes	characteristic
24	#65127	—	2	1	no	—
25	#65126	C₂²	1	2	yes	—
26	#65126	C₂²	1	2	yes	—
27	#65124	C₂²	1	2	yes	—
28	#65124	C₂²	1	2	yes	—
29	#65120	—	2	1	no	—
30	#65019	—	2	2	no	—
31	#64997	C₄	1	2	yes	—
32	#64997	C₄	1	2	yes	—
33	#64977	—	2	1	no	—
34	C₄×#676	C₂²	1	2	yes	—
35	C₄×C₈×D₅	C₂²	1	2	yes	—
36	#64968	—	2	1	no	—
37	C₅×#335	C₂²	1	2	yes	—
38	C₅×#334	C₂²	1	2	yes	—
39	#64700	C₂²	1	1	yes	characteristic
40	#64700	C₂²	1	1	yes	characteristic
41	#64700	C₂²	1	2	yes	—
42	#64700	C₂²	1	2	yes	—
43	#64699	C₂²	1	1	yes	characteristic
44	#64699	C₂²	1	1	yes	characteristic
45	#64678	C₂²	1	2	yes	—
46	#64677	C₂²	1	2	yes	—
47	#17798	—	5	1	no	maximal, Sylow
48	C₂×#709	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅×C₈	—	2	1	no	—
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₄×C₂²⋊D₅	D₄	1	2	yes	—
54	C₄×C₂²⋊D₅	Q₈	1	2	yes	—
55	#4072	C₂×C₄	1	1	yes	characteristic
56	C₂²×#168	—	2	1	no	—
57	C₂²×#168	C₂×C₄	1	1	yes	characteristic
58	C₂²×#168	C₂×C₄	1	1	yes	characteristic
59	#4053	—	2	4	no	—
60	#4053	—	2	4	no	—
61	C₂×#676	—	2	2	no	—
62	C₂×#676	—	2	2	no	—
63	C₂×#676	C₂×C₄	1	2	yes	—
64	C₂×#676	C₂×C₄	1	2	yes	—
65	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
67	C₄×D₂₀	D₄	1	1	yes	characteristic
68	C₄×D₂₀	Q₈	1	1	yes	characteristic
69	#4018	C₂×C₄	1	2	yes	—
70	C₄²×D₅	C₂³	1	2	yes	—
71	C₄×Dic₁₀	D₄	1	1	yes	characteristic
72	C₄×Dic₁₀	Q₈	1	1	yes	characteristic
73	C₅×C₄⋊C₈	—	2	1	no	—
74	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₅×C₄⋊C₈	C₂³	1	2	yes	—
76	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₅×C₂²⋊C₈	—	2	1	no	—
78	C₅×#97	C₂×C₄	1	2	yes	—
79	C₄×C₅×C₈	—	2	1	no	—
80	C₄×C₅×C₈	C₂³	1	2	yes	—
81	C₂²⋊#168	—	2	1	no	—
82	#3952	—	2	2	no	—
83	#3952	—	2	2	no	—
84	#3947	—	2	2	no	—
85	#3947	—	2	2	no	—
86	#3947	C₂×C₄	1	2	yes	—
87	#3947	C₂×C₄	1	2	yes	—
88	#3946	—	2	2	no	—
89	#3946	—	2	2	no	—
90	C₈×Dic₅	C₂×C₄	1	2	yes	—
91	C₈×Dic₅	C₂×C₄	1	2	yes	—
92	C₄⋊#168	—	2	1	no	—
93	C₄⋊#168	C₂³	1	1	yes	characteristic
94	C₄⋊#168	C₂³	1	2	yes	—
95	C₄⋊#168	C₂³	1	1	yes	characteristic
96	C₄×#168	—	2	1	no	—
97	C₄×#168	C₂×C₄	1	1	yes	characteristic
98	C₄×#168	C₂×C₄	1	1	yes	characteristic
99	C₄×#168	C₂³	1	1	yes	characteristic
100	C₄×#168	C₂³	1	1	yes	characteristic
101	#2989	—	5	1	no	—
102	#2989	—	5	1	no	—
103	C₄×#131	—	5	1	no	—
104	#1569	—	5	2	no	—
105	#1569	—	5	2	no	—
106	#1568	—	5	2	no	—
107	#1566	—	5	2	no	—
108	#1565	—	5	1	no	—
109	#1565	D₅	1	1	yes	characteristic, complemented
110	#1564	—	5	1	no	—
111	C₂×#334	—	5	1	no	—
112	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₂²⋊D₅	C₄⋊C₄	1	2	yes	—
116	#709	—	2	2	no	—
117	#709	—	2	2	no	—
118	C₂×D₂₀	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₅	C₂×D₄	1	2	yes	—
121	C₂×C₄×D₅	C₂×Q₈	1	2	yes	—
122	C₂×Dic₁₀	C₄⋊C₄	1	1	yes	characteristic
123	C₅×M₁₆	—	2	2	no	—
124	C₅×M₁₆	M₁₆	1	4	yes	complemented
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	8	1	no	—
129	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
131	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
134	C₄²×C₅	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₅	C₄⋊C₄	1	2	yes	—
136	#685	C₄⋊C₄	1	2	yes	—
137	#685	C₄⋊C₄	1	2	yes	—
138	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
139	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
140	#683	C₄⋊C₄	1	2	yes	—
141	#683	C₄⋊C₄	1	2	yes	—
142	C₄×Dic₅	C₂²×C₄	1	2	yes	—
143	C₄×Dic₅	C₂×D₄	1	2	yes	—
144	C₄×Dic₅	C₂×Q₈	1	2	yes	—
145	C₂×#168	—	2	2	no	—
146	C₂×#168	—	2	1	no	—
147	C₂×#168	—	2	1	no	—
148	C₂×#168	—	2	2	no	—
149	C₂×#168	—	8	1	no	—
150	C₂×#168	M₁₆	1	4	yes	complemented
151	C₂×#168	C₂²×C₄	1	1	yes	characteristic
152	C₂×#168	C₂²×C₄	1	1	yes	characteristic
153	C₂×#168	C₂²×C₄	1	1	yes	characteristic
154	C₂×#168	C₂²×C₄	1	1	yes	characteristic
155	#676	—	2	4	no	—
156	#676	—	2	4	no	—
157	#676	—	8	2	no	—
158	#676	—	8	2	no	—
159	C₈×D₅	—	2	4	no	—
160	C₈×D₅	—	2	4	no	—
161	C₂×#131	—	5	1	no	—
162	C₂×#131	—	5	1	no	—
163	C₄×#41	—	5	1	no	—
164	#446	—	10	1	no	—
165	#446	—	10	1	no	—
166	#436	—	10	1	no	—
167	#436	—	10	1	no	—
168	#435	—	10	2	no	—
169	#435	—	10	2	no	—
170	#432	—	5	2	no	—
171	#432	—	5	2	no	—
172	#431	—	5	1	no	—
173	#431	C₂×D₅	1	1	yes	characteristic
174	#423	—	5	2	no	—
175	#423	—	5	2	no	—
176	C₂×C₄⋊C₈	—	5	1	no	—
177	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
178	#405	—	5	1	no	—
179	#405	—	5	1	no	—
180	#405	—	5	2	no	—
181	#405	—	5	2	no	—
182	C₄×M₁₆	—	5	2	no	—
183	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
184	C₂×C₄×C₈	—	5	1	no	—
185	C₂×C₄×C₈	—	5	2	no	—
186	#335	—	5	1	no	—
187	#335	—	5	1	no	—
188	#335	—	5	2	no	—
189	#335	C₂×D₅	1	2	yes	—
190	#334	—	5	2	no	—
191	#334	—	5	2	no	—
192	#334	—	5	1	no	—
193	#334	—	5	1	no	—
194	#334	—	5	2	no	—
195	#334	C₂×D₅	1	2	yes	—
196	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂²×D₅	C₂×C₄⋊C₄	1	2	yes	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
205	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
206	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
209	C₂²⋊D₅	—	2	4	no	—
210	C₂×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
212	C₂×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
213	D₂₀	—	2	2	no	—
214	C₄×D₅	—	2	2	no	—
215	C₄×D₅	—	2	2	no	—
216	C₄×D₅	—	2	2	no	—
217	C₄×D₅	—	2	2	no	—
218	C₄×D₅	—	4	2	no	—
219	Dic₁₀	—	2	2	no	—
220	C₅×C₈	—	2	2	no	—
221	C₅×C₈	—	4	1	no	—
222	C₅×C₈	—	4	2	no	—
223	C₅×C₈	—	4	1	no	—
224	C₅×C₈	C₂×M₁₆	1	4	yes	—
225	#168	—	2	1	no	—
226	#168	—	2	1	no	—
227	#168	—	4	1	no	—
228	#168	—	4	2	no	—
229	#168	—	4	1	no	—
230	#168	C₂×M₁₆	1	2	yes	—
231	#168	C₂×M₁₆	1	2	yes	—
232	C₂×#41	—	5	1	no	—
233	#131	—	10	4	no	—
234	#131	—	10	4	no	—
235	C₂×M₁₆	—	5	2	no	—
236	C₂×M₁₆	—	5	2	no	—
237	C₂×M₁₆	—	10	2	no	—
238	C₂×M₁₆	—	10	2	no	—
239	C₂×M₁₆	C₄×D₅	1	1	yes	characteristic
240	C₂×M₁₆	C₄×D₅	1	1	yes	characteristic
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	5	1	no	—
243	C₂²×C₈	—	5	1	no	—
244	C₂²×C₈	—	5	2	no	—
245	C₂²×C₈	—	5	2	no	—
246	C₂²×C₈	—	10	1	no	—
247	C₄×Q₈	—	5	1	no	—
248	C₄×Q₈	—	5	1	no	—
249	C₄×D₄	—	5	2	no	—
250	C₄×D₄	—	5	2	no	—
251	C₄×D₄	—	5	1	no	—
252	C₄×D₄	—	5	1	no	—
253	#117	—	5	1	no	—
254	#117	—	5	2	no	—
255	C₂×C₄²	—	5	2	no	—
256	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	5	2	no	—
259	C₄⋊C₈	—	5	1	no	—
260	C₄⋊C₈	—	5	1	no	—
261	C₄⋊C₈	—	10	2	no	—
262	C₄⋊C₈	—	10	2	no	—
263	C₄⋊C₈	—	10	1	no	—
264	C₄⋊C₈	C₂²×D₅	1	2	yes	—
265	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
266	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
267	C₂²⋊C₈	—	2	1	no	—
268	C₂²⋊C₈	—	10	2	no	—
269	C₂²⋊C₈	—	10	2	no	—
270	C₂²⋊C₈	—	10	1	no	—
271	#97	—	5	2	no	—
272	#97	—	5	2	no	—
273	#97	—	10	2	no	—
274	#97	—	10	2	no	—
275	#97	C₄×D₅	1	2	yes	—
276	C₄×C₈	—	2	1	no	—
277	C₄×C₈	—	5	2	no	—
278	C₄×C₈	—	5	2	no	—
279	C₄×C₈	—	5	1	no	—
280	C₄×C₈	—	5	1	no	—
281	C₄×C₈	—	5	1	no	—
282	C₄×C₈	—	5	1	no	—
283	C₄×C₈	—	10	1	no	—
284	C₄×C₈	C₂²×D₅	1	2	yes	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	#423	1	2	yes	—
288	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
289	C₂×D₅	—	2	2	no	—
290	C₂×D₅	—	2	2	no	—
291	C₂×D₅	—	2	2	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	2	1	no	—
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	#423	1	2	yes	—
296	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
297	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
298	C₄×C₅	#577	1	1	yes	characteristic
299	C₄×C₅	#577	1	1	yes	characteristic
300	Dic₅	—	2	2	no	—
301	Dic₅	—	2	2	no	—
302	Dic₅	—	2	2	no	—
303	#41	—	10	2	no	—
304	#41	—	10	2	no	—
305	C₂×Q₈	—	5	1	no	—
306	C₂×D₄	—	5	2	no	—
307	C₂×D₄	—	5	1	no	—
308	C₂²×C₄	—	5	2	no	—
309	C₂²×C₄	—	5	2	no	—
310	C₂²×C₄	—	5	2	no	—
311	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
312	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
313	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
314	M₁₆	—	2	2	no	—
315	M₁₆	—	10	4	no	—
316	M₁₆	—	10	4	no	—
317	M₁₆	—	40	2	no	—
318	M₁₆	—	40	2	no	—
319	M₁₆	#676	1	4	yes	complemented
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	5	1	no	—
324	C₂×C₈	—	5	1	no	—
325	C₂×C₈	—	5	4	no	—
326	C₂×C₈	—	5	1	no	—
327	C₂×C₈	—	5	1	no	—
328	C₂×C₈	—	8	1	no	—
329	C₂×C₈	—	10	4	no	—
330	C₂×C₈	—	10	2	no	—
331	C₂×C₈	—	10	4	no	—
332	C₂×C₈	—	10	1	no	—
333	C₂×C₈	—	10	1	no	—
334	C₂×C₈	—	10	2	no	—
335	C₂×C₈	—	40	1	no	—
336	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
337	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
338	C₄⋊C₄	—	5	2	no	—
339	C₄⋊C₄	—	5	2	no	—
340	C₄⋊C₄	—	5	1	no	—
341	C₄⋊C₄	—	5	1	no	—
342	C₂²⋊C₄	—	5	2	no	—
343	C₂²⋊C₄	—	5	2	no	—
344	C₂²⋊C₄	—	5	2	no	—
345	C₄²	—	5	2	no	—
346	C₄²	—	5	2	no	—
347	C₄²	—	5	2	no	—
348	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
349	C₄²	D₄×D₅	1	1	yes	characteristic
350	C₄²	Q₈×D₅	1	1	yes	characteristic
351	C₄²	C₂³×D₅	1	1	yes	characteristic
352	C₂×C₅	—	2	2	no	—
353	C₂×C₅	C₂×#423	1	1	yes	characteristic
354	C₂×C₅	#2912	1	1	yes	characteristic
355	C₂×C₅	#2916	1	1	yes	characteristic
356	D₅	—	4	2	no	—
357	C₂³	—	5	2	no	—
358	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
359	Q₈	—	10	2	no	—
360	D₄	—	10	4	no	—
361	D₄	—	10	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	5	2	no	—
366	C₂×C₄	—	5	2	no	—
367	C₂×C₄	—	5	2	no	—
368	C₂×C₄	—	10	2	no	—
369	C₂×C₄	—	10	2	no	—
370	C₂×C₄	—	10	2	no	—
371	C₂×C₄	—	10	2	no	—
372	C₂×C₄	—	20	2	no	—
373	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
374	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
375	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
376	C₂×C₄	C₂×#676	1	2	yes	—
377	C₂×C₄	D₅×M₁₆	1	2	yes	—
378	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
380	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	5	2	no	—
386	C₈	—	5	2	no	—
387	C₈	—	10	1	no	—
388	C₈	—	10	1	no	—
389	C₈	—	20	1	no	—
390	C₈	—	20	2	no	—
391	C₈	—	20	1	no	—
392	C₈	C₂×#676	1	4	yes	—
393	C₅	#17798	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	10	2	no	—
397	C₂²	—	10	2	no	—
398	C₂²	—	10	2	no	—
399	C₂²	#65126	1	2	yes	—
400	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	10	2	no	—
405	C₄	—	10	2	no	—
406	C₄	—	10	2	no	—
407	C₄	#65126	1	2	yes	—
408	C₄	C₂²×#676	1	1	yes	characteristic
409	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
410	C₄	#66109	1	1	yes	characteristic
411	C₄	#66112	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	20	2	no	—
414	C₂	C₂×#65126	1	1	yes	characteristic
415	C₂	#10610940	1	1	yes	characteristic
416	C₂	#10610991	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1565	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×#709	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1565	D₅
hypocenter	C₅	#17798
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. C₅×#1565	C₂	semidirect
5. #10601538	C₂	semidirect
6. C₂×#64700	C₂	semidirect
7. #10600643	C₂	semidirect
8. #10599364	C₂	semidirect
9. #10599363	C₂	semidirect
10. #10599324	C₂	semidirect
11. #10599322	C₂	semidirect
109. #1565	D₅	semidirect
124. C₅×M₁₆	M₁₆	semidirect
150. C₂×#168	M₁₆	semidirect
319. M₁₆	#676	semidirect
393. C₅	#17798	semidirect

Maximal subgroups

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

subgroup	index
#10611023	2
#10610745	2
C₄×#4053	2
C₅×#1565	2
#10601538	2
C₂×#64700	2
#10600643	2
#10599364	2
#10599363	2
#10599324	2
#10599322	2
#17798	5