Subgroups — #16792620

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131640	C₂	1	1	yes	maximal, characteristic
2	#13131640	C₂	1	1	yes	maximal, characteristic
3	#13130050	C₂	1	2	yes	maximal, complemented
4	#13130049	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130044	C₂	1	2	yes	maximal, complemented
6	#13130044	C₂	1	2	yes	maximal, complemented
7	#13130043	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130043	C₂	1	1	yes	maximal, characteristic, complemented
9	#13130032	C₂	1	2	yes	maximal, complemented
10	C₂×#1057⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123258	C₂	1	1	yes	maximal, characteristic
12	C₂×#88161	C₄	1	1	yes	characteristic
13	C₂×#88155	C₄	1	1	yes	characteristic
14	#11719227	C₂²	1	1	yes	characteristic
15	#11719119	C₂²	1	1	yes	characteristic
16	#11719119	C₂²	1	1	yes	characteristic
17	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
18	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
19	#11719074	C₄	1	2	yes	—
20	#11719074	C₄	1	2	yes	—
21	#11719073	C₄	1	2	yes	—
22	#11719073	C₄	1	2	yes	—
23	#11719063	C₄	1	4	yes	—
24	#11719063	C₄	1	4	yes	—
25	#11719049	C₂²	1	2	yes	—
26	#11719049	C₂²	1	2	yes	—
27	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
28	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
29	C₁₃×#405	C₄	1	1	yes	characteristic
30	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
32	#11718658	C₄	1	1	yes	characteristic
33	#11718369	C₄	1	2	yes	—
34	#11718368	C₂²	1	2	yes	—
35	#11718350	C₄	1	2	yes	—
36	C₄×C₈×D₁₃	C₂²	1	2	yes	—
37	#1057⋊C₈	C₂²	1	1	yes	characteristic
38	#1057⋊C₈	C₂²	1	1	yes	characteristic
39	#1057⋊C₈	C₂²	1	1	yes	characteristic
40	#1057⋊C₈	C₂²	1	1	yes	characteristic
41	#1057⋊C₈	C₂²	1	2	yes	—
42	#1057⋊C₈	C₂²	1	2	yes	—
43	#1057⋊C₈	C₂²	1	2	yes	—
44	#1057⋊C₈	C₂²	1	2	yes	—
45	#1057⋊C₈	C₂²	1	2	yes	—
46	#1057⋊C₈	C₂²	1	2	yes	—
47	C₂×#6127	C₂×C₄	1	1	yes	characteristic
48	C₂²×#1057	C₂×C₄	1	2	yes	—
49	C₂²×#1057	C₂×C₄	1	2	yes	—
50	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
51	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
52	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
56	C₂×#6099	C₂×C₄	1	1	yes	characteristic
57	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
58	#88161	—	2	4	no	—
59	#88155	—	2	4	no	—
60	C₂×#6094	C₂×C₄	1	2	yes	—
61	C₂×#6094	C₂×C₄	1	2	yes	—
62	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
64	#88147	C₂×C₄	1	1	yes	characteristic
65	#88147	C₂×C₄	1	1	yes	characteristic
66	#88141	C₂×C₄	1	1	yes	characteristic
67	#88141	C₂×C₄	1	1	yes	characteristic
68	#88135	C₂×C₄	1	2	yes	—
69	#88135	C₂×C₄	1	2	yes	—
70	#88126	C₂×C₄	1	2	yes	—
71	C₄²×D₁₃	C₂³	1	2	yes	—
72	C₂²⋊#1057	C₂×C₄	1	2	yes	—
73	C₂²⋊#1057	C₂×C₄	1	2	yes	—
74	#88112	C₂×C₄	1	4	yes	—
75	#88112	C₂×C₄	1	4	yes	—
76	#88111	C₂×C₄	1	4	yes	—
77	#88111	C₂×C₄	1	4	yes	—
78	C₄⋊#1057	C₂×C₄	1	2	yes	—
79	C₄⋊#1057	C₂×C₄	1	2	yes	—
80	C₄×#1057	C₂×C₄	1	4	yes	—
81	C₄×#1057	C₂×C₄	1	4	yes	—
82	C₄×#1057	C₂×C₄	1	2	yes	—
83	C₄×#1057	C₂×C₄	1	2	yes	—
84	C₄×#1057	C₂³	1	1	yes	characteristic
85	C₄×#1057	C₂³	1	1	yes	characteristic
86	C₄×#1057	C₂³	1	2	yes	—
87	C₄×#1057	C₂³	1	2	yes	—
88	C₄×#1057	C₂³	1	1	yes	characteristic
89	C₄×#1057	C₂³	1	1	yes	characteristic
90	C₁₃×#97	C₂×C₄	1	2	yes	—
91	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
92	#88055	C₂×C₄	1	2	yes	—
93	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₁₃	C₂³	1	2	yes	—
98	#88043	C₂×C₄	1	2	yes	—
99	C₄×#1055	C₂×C₄	1	2	yes	—
100	#17320	—	13	1	no	maximal, Sylow
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊D₁₃	C₄²	1	2	yes	—
103	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
105	#6127	M₁₆	1	4	yes	—
106	#6127	M₁₆	1	4	yes	—
107	C₂×D₅₂	C₄²	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
111	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
112	C₂×#1057	—	2	4	no	—
113	C₂×#1057	—	4	2	no	—
114	C₂×#1057	C₂²×C₄	1	2	yes	—
115	C₂×#1057	C₂²×C₄	1	4	yes	—
116	C₂×#1057	C₂²×C₄	1	4	yes	—
117	C₂×#1057	C₂²×C₄	1	2	yes	—
118	C₂×#1057	C₂²×C₄	1	2	yes	—
119	C₂×#1057	C₂²×C₄	1	2	yes	—
120	D₁₃⋊C₈	—	2	8	no	—
121	D₁₃⋊C₈	—	4	4	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
129	C₁₃×C₂²⋊C₄	C₄²	1	2	yes	—
130	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
131	#6103	C₄²	1	2	yes	—
132	#6103	C₄²	1	2	yes	—
133	#6101	C₄²	1	2	yes	—
134	#6101	C₄²	1	2	yes	—
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
139	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
140	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
141	#6099	—	2	2	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	C₂×#1055	C₂²×C₄	1	2	yes	—
145	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
146	#6094	—	2	4	no	—
147	#6094	—	2	4	no	—
148	C₈×D₁₃	—	2	4	no	—
149	C₈×D₁₃	—	2	4	no	—
150	C₈×#41	—	13	1	no	—
151	C₈×#41	—	13	1	no	—
152	C₄×#131	—	13	1	no	—
153	#1452	—	13	1	no	—
154	#1452	—	13	2	no	—
155	#1451	—	13	1	no	—
156	#1451	—	13	1	no	—
157	#1451	—	13	2	no	—
158	#1451	—	13	2	no	—
159	C₂×#322	—	13	1	no	—
160	C₂×#322	—	13	2	no	—
161	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
163	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
168	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
169	C₂²⋊D₁₃	#97	1	8	yes	—
170	C₂×Dic₁₃	—	2	2	no	—
171	C₂×Dic₁₃	—	2	2	no	—
172	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
175	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
177	D₅₂	#97	1	4	yes	—
178	C₄×D₁₃	—	2	4	no	—
179	C₄×D₁₃	—	2	4	no	—
180	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
181	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
182	Dic₂₆	#97	1	4	yes	—
183	#1057	—	2	4	no	—
184	#1057	—	2	2	no	—
185	#1057	—	2	2	no	—
186	#1057	—	2	4	no	—
187	#1057	—	2	2	no	—
188	#1057	#131	1	4	yes	complemented
189	C₈×C₁₃	—	2	1	no	—
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	2	1	no	—
192	#1055	—	2	1	no	—
193	#1055	—	2	2	no	—
194	#1055	—	2	1	no	—
195	C₂×#131	—	13	1	no	—
196	C₂×#131	—	13	1	no	—
197	C₄×#41	—	13	1	no	—
198	C₈×Q₈	—	13	2	no	—
199	C₈×Q₈	—	13	2	no	—
200	C₈×D₄	—	13	4	no	—
201	C₈×D₄	—	13	4	no	—
202	C₈×D₄	—	13	2	no	—
203	C₈×D₄	—	13	2	no	—
204	#431	—	13	2	no	—
205	#431	—	13	2	no	—
206	#431	—	13	1	no	—
207	#431	—	13	1	no	—
208	#405	—	13	1	no	—
209	#405	—	13	2	no	—
210	#405	—	13	2	no	—
211	#405	#261	1	1	yes	characteristic
212	C₄×M₁₆	—	13	1	no	—
213	C₄×M₁₆	—	13	2	no	—
214	C₂×C₄×C₈	—	13	2	no	—
215	C₂×C₄×C₈	—	13	2	no	—
216	C₂×C₄×C₈	—	13	1	no	—
217	C₂×C₄×C₈	—	13	1	no	—
218	C₂×C₄×C₈	—	13	1	no	—
219	C₂×C₄×C₈	—	13	2	no	—
220	#322	—	13	1	no	—
221	#322	—	13	1	no	—
222	#322	—	13	1	no	—
223	#322	—	13	2	no	—
224	#322	—	13	2	no	—
225	#322	—	13	1	no	—
226	#322	—	13	2	no	—
227	#322	—	13	2	no	—
228	#322	—	13	2	no	—
229	#322	—	13	2	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	C₂×#97	1	2	yes	—
233	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
234	C₂×D₁₃	—	2	2	no	—
235	C₂×D₁₃	—	2	2	no	—
236	C₂×D₁₃	C₂×#97	1	4	yes	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	C₂×#97	1	2	yes	—
240	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
241	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
242	Dic₁₃	—	2	1	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	C₂×#97	1	4	yes	—
245	Dic₁₃	C₂×#131	1	2	yes	—
246	Dic₁₃	#568	1	2	yes	—
247	C₂×#41	—	13	1	no	—
248	#131	—	26	4	no	—
249	#131	—	26	4	no	—
250	C₂×M₁₆	—	13	1	no	—
251	C₂×M₁₆	—	13	2	no	—
252	C₂×M₁₆	—	13	2	no	—
253	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
254	C₂²×C₈	—	13	4	no	—
255	C₂²×C₈	—	13	2	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	4	no	—
258	C₂²×C₈	—	13	2	no	—
259	C₂²×C₈	—	13	2	no	—
260	C₂²×C₈	—	13	2	no	—
261	C₂²×C₈	C₂×#261	1	1	yes	characteristic
262	C₄×Q₈	—	13	1	no	—
263	C₄×Q₈	—	13	1	no	—
264	C₄×D₄	—	13	1	no	—
265	C₄×D₄	—	13	1	no	—
266	C₄×D₄	—	13	2	no	—
267	C₄×D₄	—	13	2	no	—
268	#117	—	13	2	no	—
269	#117	C₂×#261	1	1	yes	characteristic
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	2	no	—
272	C₄⋊C₈	—	13	2	no	—
273	C₄⋊C₈	—	13	2	no	—
274	C₄⋊C₈	—	13	4	no	—
275	C₄⋊C₈	—	13	4	no	—
276	C₂²⋊C₈	—	13	4	no	—
277	C₂²⋊C₈	—	13	4	no	—
278	C₂²⋊C₈	—	13	2	no	—
279	C₂²⋊C₈	—	13	2	no	—
280	#97	—	13	2	no	—
281	#97	—	13	2	no	—
282	#97	C₂×#261	1	2	yes	—
283	C₄×C₈	—	13	4	no	—
284	C₄×C₈	—	13	2	no	—
285	C₄×C₈	—	13	4	no	—
286	C₄×C₈	—	13	2	no	—
287	C₄×C₈	—	13	1	no	—
288	C₄×C₈	—	13	1	no	—
289	C₄×C₈	—	13	2	no	—
290	C₄×C₈	—	13	2	no	—
291	C₄×C₈	—	13	1	no	—
292	C₄×C₈	—	13	1	no	—
293	C₄×C₈	—	13	1	no	—
294	C₄×C₈	—	13	1	no	—
295	C₄×C₈	—	13	2	no	—
296	C₄×C₈	—	13	1	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	2	no	—
299	C₄×C₈	C₂×#261	1	2	yes	—
300	C₂×C₁₃	—	2	2	no	—
301	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
302	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
303	C₂×C₁₃	#2875	1	1	yes	characteristic
304	D₁₃	—	2	4	no	—
305	#41	—	13	4	no	—
306	#41	—	13	4	no	—
307	C₂×Q₈	—	13	1	no	—
308	C₂×D₄	—	13	2	no	—
309	C₂×D₄	—	13	1	no	—
310	C₂²×C₄	—	13	2	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	2	no	—
314	C₂²×C₄	—	13	2	no	—
315	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
316	M₁₆	—	2	2	no	—
317	M₁₆	—	26	4	no	—
318	M₁₆	—	26	4	no	—
319	M₁₆	—	26	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	13	2	no	—
322	C₂×C₈	—	13	2	no	—
323	C₂×C₈	—	13	2	no	—
324	C₂×C₈	—	13	4	no	—
325	C₂×C₈	—	13	2	no	—
326	C₂×C₈	—	13	4	no	—
327	C₂×C₈	—	13	1	no	—
328	C₂×C₈	—	13	1	no	—
329	C₂×C₈	—	13	2	no	—
330	C₂×C₈	—	26	4	no	—
331	C₂×C₈	—	26	4	no	—
332	C₂×C₈	—	26	8	no	—
333	C₂×C₈	—	26	4	no	—
334	C₂×C₈	—	26	2	no	—
335	C₂×C₈	—	52	4	no	—
336	C₂×C₈	—	52	2	no	—
337	C₂×C₈	C₂²×#261	1	1	yes	characteristic
338	C₂×C₈	C₂²×#261	1	1	yes	characteristic
339	C₂×C₈	C₂²×#261	1	2	yes	—
340	C₄⋊C₄	—	13	2	no	—
341	C₄⋊C₄	—	13	2	no	—
342	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
343	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
344	C₂²⋊C₄	—	13	2	no	—
345	C₂²⋊C₄	—	13	2	no	—
346	C₂²⋊C₄	C₄×#261	1	2	yes	—
347	C₄²	—	13	2	no	—
348	C₄²	—	13	2	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	13	1	no	—
353	C₄²	C₂²×#261	1	2	yes	—
354	C₁₃	#17320	1	1	yes	characteristic, complemented, Sylow
355	C₂³	—	13	2	no	—
356	C₂³	C₂×C₄×#261	1	1	yes	characteristic
357	Q₈	—	13	4	no	—
358	D₄	—	13	8	no	—
359	D₄	—	13	4	no	—
360	C₂×C₄	—	13	1	no	—
361	C₂×C₄	—	13	1	no	—
362	C₂×C₄	—	13	2	no	—
363	C₂×C₄	—	13	4	no	—
364	C₂×C₄	—	13	4	no	—
365	C₂×C₄	—	13	1	no	—
366	C₂×C₄	—	13	1	no	—
367	C₂×C₄	—	26	4	no	—
368	C₂×C₄	—	26	4	no	—
369	C₂×C₄	—	26	2	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
372	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
373	C₂×C₄	C₂×C₄×#261	1	2	yes	—
374	C₂×C₄	C₂×C₄×#261	1	2	yes	—
375	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
376	C₂×C₄	C₂³×#261	1	1	yes	characteristic
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	2	no	—
380	C₈	—	13	4	no	—
381	C₈	—	26	4	no	—
382	C₈	—	26	2	no	—
383	C₈	—	26	2	no	—
384	C₈	—	26	4	no	—
385	C₈	—	26	2	no	—
386	C₈	—	26	1	no	—
387	C₈	—	26	2	no	—
388	C₈	—	26	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	13	4	no	—
392	C₂²	—	26	2	no	—
393	C₂²	—	26	2	no	—
394	C₂²	#11719047	1	2	yes	—
395	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	13	4	no	—
399	C₄	—	13	2	no	—
400	C₄	—	13	2	no	—
401	C₄	—	26	1	no	—
402	C₄	—	26	1	no	—
403	C₄	#11719047	1	2	yes	—
404	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
405	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	26	4	no	—
408	C₂	C₂×#11719047	1	1	yes	characteristic
409	C₂	#131×#261	1	1	yes	characteristic
410	C₂	#13131406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#405	C₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#17320
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #13130050	C₂	semidirect
4. #13130049	C₂	semidirect
5. #13130044	C₂	semidirect
6. #13130044	C₂	semidirect
7. #13130043	C₂	semidirect
8. #13130043	C₂	semidirect
9. #13130032	C₂	semidirect
10. C₂×#1057⋊C₈	C₂	semidirect
188. #1057	#131	semidirect
354. C₁₃	#17320	semidirect

Maximal subgroups

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

subgroup	index
#13131640	2
#13130050	2
#13130049	2
#13130044	2
#13130043	2
#13130032	2
C₂×#1057⋊C₈	2
#13123258	2
#17320	13