Subgroups — #16016369

Order 3328.

652 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13127970	C₂	1	1	yes	maximal, characteristic
2	#13123638	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116734	C₂	1	4	yes	maximal, complemented
4	#13116727	C₂	1	4	yes	maximal, complemented
5	#13116610	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116583	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116572	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11718058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#131	—	2	1	no	—
12	C₂×#88158	C₂²	1	1	yes	characteristic
13	C₄×#6127	—	2	1	no	—
14	C₁₃×#444	—	2	2	no	—
15	C₁₃×#444	C₂²	1	4	yes	—
16	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#104	—	2	1	no	—
18	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
19	#11718856	C₂²	1	2	yes	—
20	#11718855	C₄	1	4	yes	complemented
21	#11718854	C₂²	1	2	yes	—
22	#11718840	C₄	1	2	yes	complemented
23	#11718808	C₄	1	2	yes	complemented
24	#11718774	—	2	1	no	—
25	#11718767	C₂²	1	1	yes	characteristic
26	C₂×#88052	C₂²	1	1	yes	characteristic
27	C₂×#88052	C₂²	1	1	yes	characteristic
28	#11718377	C₂²	1	2	yes	complemented
29	#11718372	C₂²	1	2	yes	complemented
30	#11718371	—	2	2	no	—
31	#11718158	C₂²	1	4	yes	—
32	#11718088	C₂²	1	2	yes	complemented
33	#11718087	C₂²	1	2	yes	complemented
34	#11718086	C₂²	1	4	yes	complemented
35	#11718058	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×#6127	—	2	1	no	—
38	C₁₃×#135	—	2	1	no	—
39	C₁₃×#135	—	2	1	no	—
40	C₁₃×#135	C₂×C₄	1	2	yes	complemented
41	C₁₃×#135	C₂³	1	2	yes	—
42	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
43	C₂×C₁₃×SD₁₆	—	2	1	no	—
44	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
45	C₁₃×#131	—	2	4	no	—
46	C₁₃×#131	—	4	2	no	—
47	C₂×C₁₃×M₁₆	—	2	1	no	—
48	C₂×C₁₃×M₁₆	—	4	1	no	—
49	C₂²×C₈×C₁₃	—	4	1	no	—
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₃	—	4	2	no	—
54	#88180	—	2	1	no	—
55	C₂×Dic₅₂	C₂³	1	1	yes	characteristic
56	#88158	—	2	1	no	—
57	#88158	—	2	1	no	—
58	#88158	C₂×C₄	1	2	yes	—
59	#88158	C₂×C₄	1	2	yes	—
60	C₂×D₁₀₄	C₂³	1	1	yes	characteristic
61	C₂×#6095	—	2	1	no	—
62	C₄×D₅₂	—	2	2	no	—
63	#88126	—	4	1	no	—
64	C₄²×D₁₃	—	4	1	no	—
65	C₄×Dic₂₆	—	2	2	no	—
66	C₁₃×#108	—	2	1	no	—
67	C₁₃×#108	C₂³	1	2	yes	—
68	C₁₃×#104	—	2	4	no	—
69	C₁₃×#97	D₄	1	2	yes	—
70	C₁₃×#97	C₂³	1	2	yes	—
71	#88069	C₂×C₄	1	4	yes	complemented
72	#88068	C₂×C₄	1	4	yes	complemented
73	#88067	C₂×C₄	1	4	yes	complemented
74	#88066	C₂×C₄	1	4	yes	complemented
75	#88061	—	2	2	no	—
76	#88058	—	2	1	no	—
77	#88057	C₂³	1	2	yes	—
78	#88056	—	2	2	no	—
79	#88052	—	2	1	no	—
80	#88052	C₂×C₄	1	2	yes	complemented
81	#88052	C₂³	1	2	yes	—
82	#88052	C₂³	1	2	yes	—
83	C₂×#6090	—	2	1	no	—
84	C₂×#6090	C₂×C₄	1	2	yes	complemented
85	#33468	—	13	1	no	maximal, Sylow
86	C₁₃×#41	—	2	2	no	—
87	C₁₃×#41	—	2	2	no	—
88	C₁₃×#41	—	4	1	no	—
89	C₁₃×#41	—	4	1	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	4	1	no	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₃	—	4	1	no	—
97	#6127	—	2	2	no	—
98	#6127	—	2	2	no	—
99	#6127	—	4	1	no	—
100	#6127	—	4	1	no	—
101	C₂×D₅₂	—	2	1	no	—
102	C₂×C₄×D₁₃	—	4	1	no	—
103	C₂×C₄×D₁₃	—	4	2	no	—
104	C₂×Dic₂₆	—	2	1	no	—
105	C₁₃×Q₁₆	—	2	1	no	—
106	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	—
107	C₁₃×SD₁₆	—	2	2	no	—
108	C₁₃×SD₁₆	—	2	2	no	—
109	C₁₃×D₈	—	2	1	no	—
110	C₁₃×D₈	C₂²×C₄	1	2	yes	—
111	C₁₃×M₁₆	—	2	2	no	—
112	C₁₃×M₁₆	—	4	4	no	—
113	C₁₃×M₁₆	—	4	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	4	4	no	—
117	C₂×C₈×C₁₃	—	4	1	no	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
123	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₄²×C₁₃	—	2	1	no	—
126	C₄²×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²⋊Dic₁₃	—	4	1	no	—
128	#6103	—	4	2	no	—
129	C₄⋊Dic₁₃	—	2	2	no	—
130	#6101	—	4	2	no	—
131	C₄×Dic₁₃	—	4	2	no	—
132	C₄×Dic₁₃	—	4	1	no	—
133	Dic₅₂	—	2	1	no	—
134	Dic₅₂	C₂²×C₄	1	2	yes	—
135	D₁₀₄	—	2	1	no	—
136	D₁₀₄	C₂²×C₄	1	2	yes	—
137	#6095	—	2	2	no	—
138	#6095	—	2	2	no	—
139	#6090	—	2	2	no	—
140	#6090	C₂²×C₄	1	4	yes	—
141	#3414	—	13	1	no	—
142	C₂×#444	D₁₃	1	1	yes	characteristic, complemented
143	#2943	—	13	1	no	—
144	AGL(1,ℤ/16)	—	13	4	no	—
145	#2180	—	13	4	no	—
146	#2155	—	13	1	no	—
147	#2148	—	13	1	no	—
148	#2145	—	13	1	no	—
149	C₂×#347	—	13	1	no	—
150	C₂³×C₁₃	—	4	1	no	—
151	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂²×D₁₃	—	4	1	no	—
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	4	1	no	—
155	D₄×C₁₃	—	2	2	no	—
156	D₄×C₁₃	—	4	2	no	—
157	D₄×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	8	1	no	—
164	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₂²⋊D₁₃	—	4	2	no	—
171	C₂²⋊D₁₃	—	4	2	no	—
172	C₂×Dic₁₃	—	4	1	no	—
173	C₂×Dic₁₃	—	4	2	no	—
174	D₅₂	—	2	2	no	—
175	D₅₂	—	4	1	no	—
176	C₄×D₁₃	—	4	2	no	—
177	C₄×D₁₃	—	4	2	no	—
178	C₄×D₁₃	—	8	4	no	—
179	Dic₂₆	—	2	2	no	—
180	Dic₂₆	—	4	1	no	—
181	C₈×C₁₃	—	2	2	no	—
182	C₈×C₁₃	—	4	2	no	—
183	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×#135	—	13	1	no	—
188	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
189	C₂×#131	—	2	1	no	—
190	C₄×#41	—	26	1	no	—
191	#510	—	13	2	no	—
192	#510	—	13	2	no	—
193	#509	—	13	2	no	—
194	#509	—	13	2	no	—
195	#508	—	13	4	no	—
196	C₂×M₃₂	—	13	1	no	—
197	C₂×M₃₂	—	13	1	no	—
198	#444	—	2	2	no	—
199	#444	C₂×D₁₃	1	4	yes	—
200	#442	—	13	2	no	—
201	#441	—	13	2	no	—
202	#440	—	26	2	no	—
203	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
204	#427	—	13	1	no	—
205	C₂×#104	—	2	1	no	—
206	#416	—	26	1	no	—
207	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
208	#365	—	13	4	no	—
209	#362	—	13	2	no	—
210	#361	—	13	2	no	—
211	#360	—	13	4	no	—
212	#347	—	13	4	no	—
213	C₂²×C₁₃	—	4	1	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	#442	1	1	yes	characteristic
217	C₂²×C₁₃	#442	1	1	yes	characteristic
218	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂×D₁₃	—	4	2	no	—
220	C₂×D₁₃	—	8	2	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	#442	1	1	yes	characteristic
224	C₄×C₁₃	#442	1	1	yes	characteristic
225	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	Dic₁₃	—	4	2	no	—
228	Dic₁₃	—	8	2	no	—
229	C₂×#41	—	2	1	no	—
230	C₂×#41	—	26	1	no	—
231	#135	—	2	1	no	—
232	#135	—	2	1	no	—
233	#135	—	13	2	no	—
234	#135	—	13	2	no	—
235	#135	—	26	1	no	—
236	#135	—	26	1	no	—
237	#135	C₄×D₁₃	1	2	yes	complemented
238	#135	C₂²×D₁₃	1	2	yes	—
239	C₂×Q₁₆	—	13	1	no	—
240	C₂×Q₁₆	C₄×D₁₃	1	1	yes	characteristic, complemented
241	C₂×SD₁₆	—	2	1	no	—
242	C₂×SD₁₆	—	26	1	no	—
243	C₂×D₈	—	13	1	no	—
244	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic, complemented
245	#131	—	2	4	no	—
246	#131	—	4	2	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	4	1	no	—
249	C₂²×C₈	—	4	1	no	—
250	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
252	C₄×Q₈	—	26	2	no	—
253	C₄×D₄	—	26	2	no	—
254	C₄×D₄	—	52	2	no	—
255	#117	—	26	1	no	—
256	#117	—	52	1	no	—
257	C₂×C₄²	—	52	1	no	—
258	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
259	Q₃₂	—	13	4	no	—
260	SD₃₂	—	13	4	no	—
261	SD₃₂	—	13	4	no	—
262	D₁₆	—	13	4	no	—
263	M₃₂	—	13	2	no	—
264	M₃₂	—	13	2	no	—
265	M₃₂	—	13	2	no	—
266	M₃₂	—	26	1	no	—
267	C₂×C₁₆	—	13	2	no	—
268	C₂×C₁₆	—	26	1	no	—
269	#108	—	2	1	no	—
270	#108	C₂²×D₁₃	1	2	yes	—
271	#107	—	26	1	no	—
272	#106	—	13	2	no	—
273	#104	—	2	4	no	—
274	#103	—	26	2	no	—
275	#102	—	26	2	no	—
276	#97	C₂²⋊D₁₃	1	2	yes	—
277	#97	C₂²×D₁₃	1	2	yes	—
278	C₂×C₁₃	—	2	1	no	—
279	C₂×C₁₃	—	2	1	no	—
280	C₂×C₁₃	—	2	1	no	—
281	C₂×C₁₃	—	8	2	no	—
282	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
283	D₁₃	—	8	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	4	1	no	—
287	#41	—	4	1	no	—
288	#41	—	26	2	no	—
289	#41	—	26	2	no	—
290	#41	—	52	1	no	—
291	#41	—	52	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	26	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	26	1	no	—
297	C₂×D₄	—	52	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	52	2	no	—
301	C₂²×C₄	—	52	1	no	—
302	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
303	Q₁₆	—	2	1	no	—
304	Q₁₆	—	13	2	no	—
305	Q₁₆	—	26	1	no	—
306	Q₁₆	C₂×C₄×D₁₃	1	2	yes	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	26	2	no	—
310	SD₁₆	—	26	2	no	—
311	D₈	—	2	1	no	—
312	D₈	—	13	2	no	—
313	D₈	—	26	1	no	—
314	D₈	C₂×C₄×D₁₃	1	2	yes	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	4	4	no	—
317	M₁₆	—	4	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	4	4	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
323	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
324	C₂×C₈	#6127	1	1	yes	characteristic
325	C₂×C₈	#6127	1	1	yes	characteristic
326	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
327	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
328	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
329	C₄⋊C₄	—	26	2	no	—
330	C₄⋊C₄	—	52	2	no	—
331	C₂²⋊C₄	—	52	2	no	—
332	C₂²⋊C₄	—	52	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	52	2	no	—
335	C₄²	—	52	1	no	—
336	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
337	C₁₆	—	13	4	no	—
338	C₁₆	—	26	2	no	—
339	C₁₃	#33468	1	1	yes	characteristic, complemented, Sylow
340	C₂³	—	4	1	no	—
341	C₂³	—	52	1	no	—
342	C₂³	#88203	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	4	1	no	—
345	Q₈	—	26	2	no	—
346	Q₈	—	52	1	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	26	2	no	—
352	D₄	—	52	2	no	—
353	D₄	—	52	2	no	—
354	D₄	—	52	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	52	1	no	—
361	C₂×C₄	—	52	2	no	—
362	C₂×C₄	—	52	2	no	—
363	C₂×C₄	—	52	2	no	—
364	C₂×C₄	—	104	4	no	—
365	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
366	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
367	C₂×C₄	#88186	1	1	yes	characteristic
368	C₂×C₄	#88186	1	1	yes	characteristic
369	C₂×C₄	#88203	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
371	C₈	—	2	2	no	—
372	C₈	—	4	2	no	—
373	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
374	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
375	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
376	C₈	C₂×#6127	1	1	yes	characteristic
377	C₂²	—	4	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	52	2	no	—
381	C₂²	—	104	2	no	—
382	C₂²	#11718675	1	1	yes	characteristic
383	C₂²	#11718675	1	1	yes	characteristic
384	C₂²	C₂×#88203	1	1	yes	characteristic
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	52	2	no	—
388	C₄	—	104	2	no	—
389	C₄	#11718675	1	1	yes	characteristic
390	C₄	#11718675	1	1	yes	characteristic
391	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
392	C₄	C₂×#88186	1	1	yes	characteristic
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	8	2	no	—
397	C₂	—	104	2	no	—
398	C₂	C₂×#11718675	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718675
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#444	C₂
socle	C₂×C₁₃	C₂×#442
prime radical	#13127970	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#444	D₁₃
hypocenter	C₁₃	#33468
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. #13123638	C₂	semidirect
3. #13116734	C₂	semidirect
4. #13116727	C₂	semidirect
5. #13116610	C₂	semidirect
6. #13116583	C₂	semidirect
7. #13116572	C₂	semidirect
8. C₂×#11718058	C₂	semidirect
9. C₂×C₁₃×#444	C₂	semidirect
20. #11718855	C₄	semidirect
22. #11718840	C₄	semidirect
23. #11718808	C₄	semidirect
28. #11718377	C₂²	semidirect
29. #11718372	C₂²	semidirect
32. #11718088	C₂²	semidirect
33. #11718087	C₂²	semidirect
34. #11718086	C₂²	semidirect
35. #11718058	C₂²	semidirect
40. C₁₃×#135	C₂×C₄	semidirect
42. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
44. C₂×C₁₃×D₈	C₂×C₄	semidirect
71. #88069	C₂×C₄	semidirect
72. #88068	C₂×C₄	semidirect
73. #88067	C₂×C₄	semidirect
74. #88066	C₂×C₄	semidirect
80. #88052	C₂×C₄	semidirect
84. C₂×#6090	C₂×C₄	semidirect
142. C₂×#444	D₁₃	semidirect
237. #135	C₄×D₁₃	semidirect
240. C₂×Q₁₆	C₄×D₁₃	semidirect
244. C₂×D₈	C₄×D₁₃	semidirect
339. C₁₃	#33468	semidirect

Maximal subgroups

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

subgroup	index
#13127970	2
#13123638	2
#13116734	2
#13116727	2
#13116610	2
#13116583	2
#13116572	2
C₂×#11718058	2
C₂×C₁₃×#444	2
#33468	13