Subgroups — #15752652

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117234	C₂	1	1	yes	maximal, characteristic
2	#13117234	C₂	1	1	yes	maximal, characteristic
3	#13112690	C₂	1	4	yes	maximal
4	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×#432	—	2	1	no	—
7	C₁₃×#432	C₄	1	2	yes	complemented
8	C₁₃×#431	—	2	1	no	—
9	C₁₃×#431	C₄	1	2	yes	complemented
10	C₁₃×#423	—	2	1	no	—
11	C₁₃×#407	C₂²	1	2	yes	—
12	C₄×C₁₃×M₁₆	—	2	1	no	—
13	#11718873	—	2	1	no	—
14	#11718873	—	2	1	no	—
15	#11718872	—	2	1	no	—
16	#11718872	C₂²	1	2	yes	—
17	C₄×C₂²⋊Dic₁₃	—	2	1	no	—
18	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
19	#11718598	—	2	1	no	—
20	#11718598	—	2	1	no	—
21	#11718597	—	2	1	no	—
22	#11718597	C₄	1	2	yes	complemented
23	C₄×C₄⋊Dic₁₃	—	2	1	no	—
24	C₄×C₄⋊Dic₁₃	C₄	1	2	yes	complemented
25	#11718593	C₄	1	2	yes	complemented
26	#11718593	C₄	1	2	yes	complemented
27	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₁₃×M₁₆	—	2	2	no	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
43	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
44	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
45	C₂×C₄⋊Dic₁₃	—	2	2	no	—
46	C₂×C₄⋊Dic₁₃	—	2	2	no	—
47	C₂×C₄×Dic₁₃	—	2	2	no	—
48	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
49	C₁₃×C₄⋊C₈	—	2	2	no	—
50	C₁₃×C₄⋊C₈	—	2	2	no	—
51	C₁₃×C₂²⋊C₈	—	2	2	no	—
52	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
53	C₁₃×#97	—	2	2	no	—
54	C₄×C₈×C₁₃	—	2	2	no	—
55	#88071	—	2	2	no	—
56	#88071	—	2	2	no	—
57	#88071	—	2	2	no	—
58	#88071	—	2	2	no	—
59	#88071	—	2	2	no	—
60	#88071	—	2	2	no	—
61	#88071	—	2	2	no	—
62	#88071	C₂×C₄	1	4	yes	—
63	#7944	—	13	1	no	maximal, Sylow
64	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	—	4	2	no	—
66	C₂²×C₄×C₁₃	—	4	2	no	—
67	C₂²×C₄×C₁₃	—	4	2	no	—
68	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
86	C₂²×Dic₁₃	—	2	4	no	—
87	C₂²×Dic₁₃	—	2	4	no	—
88	C₁₃×M₁₆	—	4	4	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₄²×C₁₃	C₄²	1	1	yes	characteristic
91	C₄²×C₁₃	C₄²	1	1	yes	characteristic
92	C₄²×C₁₃	C₄²	1	1	yes	characteristic
93	C₄²×C₁₃	C₄²	1	1	yes	characteristic
94	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂²⋊Dic₁₃	—	4	4	no	—
107	C₂²⋊Dic₁₃	—	4	4	no	—
108	C₄⋊Dic₁₃	—	4	4	no	—
109	C₄⋊Dic₁₃	—	4	4	no	—
110	C₄×Dic₁₃	—	4	4	no	—
111	C₄×Dic₁₃	—	4	4	no	—
112	#2920	D₁₃	1	1	yes	characteristic
113	#2283	—	13	1	no	—
114	#2283	—	13	1	no	—
115	#1284	—	13	4	no	—
116	C₂³×C₁₃	—	2	2	no	—
117	C₂³×C₁₃	—	2	2	no	—
118	C₂³×C₁₃	—	4	1	no	—
119	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₃	—	2	2	no	—
123	C₂×C₄×C₁₃	—	2	2	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	2	no	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	4	1	no	—
130	C₂×C₄×C₁₃	—	4	1	no	—
131	C₂×C₄×C₁₃	—	4	1	no	—
132	C₂×C₄×C₁₃	—	4	1	no	—
133	C₂×C₄×C₁₃	—	4	1	no	—
134	C₂×C₄×C₁₃	—	4	1	no	—
135	C₂×C₄×C₁₃	—	4	1	no	—
136	C₂×C₄×C₁₃	—	4	1	no	—
137	C₂×C₄×C₁₃	—	4	1	no	—
138	C₂×C₄×C₁₃	—	4	1	no	—
139	C₂×C₄×C₁₃	—	4	1	no	—
140	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×Dic₁₃	—	4	4	no	—
153	C₂×Dic₁₃	—	4	4	no	—
154	C₂×Dic₁₃	—	4	4	no	—
155	C₂×Dic₁₃	—	4	4	no	—
156	C₂×Dic₁₃	—	4	4	no	—
157	C₂×Dic₁₃	—	4	4	no	—
158	C₈×C₁₃	—	4	4	no	—
159	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
160	#432	—	2	1	no	—
161	#432	Dic₁₃	1	2	yes	complemented
162	#431	—	2	1	no	—
163	#431	Dic₁₃	1	2	yes	complemented
164	#423	—	2	1	no	—
165	#407	C₂×D₁₃	1	2	yes	—
166	C₄×M₁₆	—	2	1	no	—
167	#383	—	26	1	no	—
168	#383	—	26	1	no	—
169	#382	—	13	2	no	—
170	#382	—	26	1	no	—
171	#381	—	13	2	no	—
172	#381	—	26	1	no	—
173	#380	—	26	1	no	—
174	#380	—	26	1	no	—
175	C₄×C₄⋊C₄	—	13	2	no	—
176	C₄×C₄⋊C₄	—	26	1	no	—
177	C₄×C₂²⋊C₄	—	13	2	no	—
178	C₄×C₂²⋊C₄	—	26	1	no	—
179	#376	—	13	2	no	—
180	#376	—	13	2	no	—
181	C₂²×C₁₃	—	2	1	no	—
182	C₂²×C₁₃	—	2	1	no	—
183	C₂²×C₁₃	—	2	1	no	—
184	C₂²×C₁₃	—	2	1	no	—
185	C₂²×C₁₃	—	2	1	no	—
186	C₂²×C₁₃	—	2	1	no	—
187	C₂²×C₁₃	—	2	1	no	—
188	C₂²×C₁₃	—	4	4	no	—
189	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
190	C₂²×C₁₃	#410	1	2	yes	—
191	C₂²×C₁₃	#421	1	2	yes	—
192	C₄×C₁₃	—	2	1	no	—
193	C₄×C₁₃	—	2	1	no	—
194	C₄×C₁₃	—	2	1	no	—
195	C₄×C₁₃	—	2	1	no	—
196	C₄×C₁₃	—	2	1	no	—
197	C₄×C₁₃	—	2	1	no	—
198	C₄×C₁₃	—	2	1	no	—
199	C₄×C₁₃	—	2	1	no	—
200	C₄×C₁₃	—	2	1	no	—
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	—	2	1	no	—
203	C₄×C₁₃	H(3,ℤ/4)	1	2	yes	—
204	Dic₁₃	—	8	4	no	—
205	Dic₁₃	—	8	4	no	—
206	C₂³×C₄	D₅₂	1	1	yes	characteristic
207	C₂³×C₄	D₅₂	1	1	yes	characteristic
208	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
209	C₂×M₁₆	—	2	2	no	—
210	C₂×C₄⋊C₄	—	26	2	no	—
211	C₂×C₄⋊C₄	—	26	2	no	—
212	C₂×C₂²⋊C₄	—	26	2	no	—
213	C₂×C₂²⋊C₄	—	26	2	no	—
214	C₂×C₄²	—	13	4	no	—
215	C₂×C₄²	—	26	2	no	—
216	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
217	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
218	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
219	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
220	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
221	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
222	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
223	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
224	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
225	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
226	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
227	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₂²⋊C₈	—	2	2	no	—
231	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
232	#97	—	2	2	no	—
233	C₄×C₈	—	2	2	no	—
234	#95	—	13	4	no	—
235	#95	—	26	2	no	—
236	#95	—	26	2	no	—
237	#95	—	26	2	no	—
238	#95	—	26	2	no	—
239	#95	—	26	2	no	—
240	#95	—	26	2	no	—
241	#95	—	26	2	no	—
242	C₂×C₁₃	—	2	2	no	—
243	C₂×C₁₃	—	2	2	no	—
244	C₂×C₁₃	—	4	1	no	—
245	C₂×C₁₃	C₂×H(3,ℤ/4)	1	1	yes	characteristic
246	C₂×C₁₃	#1733	1	1	yes	characteristic
247	C₂×C₁₃	#1740	1	1	yes	characteristic
248	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	26	4	no	—
253	C₂²×C₄	—	26	4	no	—
254	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
257	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
258	C₂²×C₄	#6103	1	1	yes	characteristic
259	C₂²×C₄	#6103	1	1	yes	characteristic
260	C₂²×C₄	#6103	1	1	yes	characteristic
261	C₂²×C₄	#6103	1	1	yes	characteristic
262	C₂²×C₄	#6103	1	1	yes	characteristic
263	C₂²×C₄	#6103	1	1	yes	characteristic
264	C₂²×C₄	#6103	1	1	yes	characteristic
265	C₂²×C₄	#6103	1	1	yes	characteristic
266	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
272	M₁₆	—	4	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₄⋊C₄	—	52	4	no	—
275	C₄⋊C₄	—	52	4	no	—
276	C₂²⋊C₄	—	52	4	no	—
277	C₂²⋊C₄	—	52	4	no	—
278	C₄²	—	52	4	no	—
279	C₄²	—	52	4	no	—
280	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
281	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
282	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
283	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
284	C₄²	#6101	1	1	yes	characteristic
285	C₄²	#6101	1	1	yes	characteristic
286	C₄²	#6101	1	1	yes	characteristic
287	C₄²	#6101	1	1	yes	characteristic
288	C₄²	#6101	1	1	yes	characteristic
289	C₄²	#6101	1	1	yes	characteristic
290	C₄²	#6101	1	1	yes	characteristic
291	C₄²	#6101	1	1	yes	characteristic
292	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
293	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
294	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
295	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
296	C₁₃	#7944	1	1	yes	characteristic, complemented, Sylow
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	4	1	no	—
300	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
301	C₂³	C₂×#6103	1	1	yes	characteristic
302	C₂³	C₂×#6103	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	52	4	no	—
322	C₂×C₄	—	52	4	no	—
323	C₂×C₄	—	52	4	no	—
324	C₂×C₄	—	52	4	no	—
325	C₂×C₄	—	52	4	no	—
326	C₂×C₄	—	52	4	no	—
327	C₂×C₄	#88071	1	1	yes	characteristic
328	C₂×C₄	#88071	1	1	yes	characteristic
329	C₂×C₄	#88071	1	1	yes	characteristic
330	C₂×C₄	#88071	1	1	yes	characteristic
331	C₂×C₄	#88071	1	1	yes	characteristic
332	C₂×C₄	#88071	1	1	yes	characteristic
333	C₂×C₄	#88071	1	1	yes	characteristic
334	C₂×C₄	#88071	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
336	C₂×C₄	C₂×#6101	1	1	yes	characteristic
337	C₂×C₄	C₂×#6101	1	1	yes	characteristic
338	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
339	C₈	—	4	4	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	4	no	—
348	C₂²	#11718667	1	2	yes	—
349	C₂²	#11718800	1	2	yes	—
350	C₂²	C₂×#88071	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	104	4	no	—
363	C₄	—	104	4	no	—
364	C₄	#11718149	1	2	yes	—
365	C₂	—	2	2	no	—
366	C₂	—	2	2	no	—
367	C₂	—	4	1	no	—
368	C₂	C₂×#11718149	1	1	yes	characteristic
369	C₂	#13114547	1	1	yes	characteristic
370	C₂	#13114568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88071
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₁₃×#2920	C₂
socle	C₂²×C₁₃	C₂×#95
prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#7944
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
7. C₁₃×#432	C₄	semidirect
9. C₁₃×#431	C₄	semidirect
22. #11718597	C₄	semidirect
24. C₄×C₄⋊Dic₁₃	C₄	semidirect
25. #11718593	C₄	semidirect
26. #11718593	C₄	semidirect
161. #432	Dic₁₃	semidirect
163. #431	Dic₁₃	semidirect
296. C₁₃	#7944	semidirect

Maximal subgroups

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

subgroup	index
#13117234	2
#13112690	2
C₁₃×#2920	2
#7944	13