Subgroups — #16018930

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125264	C₂	1	1	yes	maximal, characteristic, complemented
2	#13117108	C₂	1	1	yes	maximal, characteristic, complemented
3	#13117103	C₂	1	1	yes	maximal, characteristic, complemented
4	#13117083	C₂	1	1	yes	maximal, characteristic, complemented
5	#13117079	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116898	C₂	1	2	yes	maximal, complemented
7	#13116891	C₂	1	2	yes	maximal, complemented
8	#13116774	C₂	1	2	yes	maximal, complemented
9	#13116757	C₂	1	2	yes	maximal, complemented
10	#13116639	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	—	2	1	no	—
13	C₂×#88158	—	2	1	no	—
14	C₂×#88158	C₂²	1	2	yes	—
15	#11719182	—	2	1	no	—
16	C₁₃×#499	C₂²	1	1	yes	characteristic
17	C₁₃×#495	C₂²	1	1	yes	characteristic
18	C₁₃×#488	—	2	1	no	—
19	C₁₃×#467	C₂²	1	1	yes	characteristic
20	C₁₃×#466	C₂²	1	1	yes	characteristic
21	C₁₃×#465	—	2	1	no	—
22	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₁₃×SD₁₆	—	2	1	no	—
24	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×#88069	C₂²	1	2	yes	—
27	C₂×#88068	C₂²	1	2	yes	—
28	C₂×#88067	C₂²	1	2	yes	—
29	C₂×#88066	C₂²	1	2	yes	—
30	#11718360	C₂²	1	1	yes	characteristic
31	#11718357	—	2	1	no	—
32	#11718357	C₂²	1	2	yes	—
33	#11718356	C₂²	1	1	yes	characteristic
34	#11718354	—	2	1	no	—
35	C₂²⋊#6090	C₂²	1	2	yes	—
36	#11718084	C₂²	1	2	yes	—
37	#11718084	C₂²	1	2	yes	—
38	#11718083	C₂²	1	2	yes	—
39	#11718083	C₂²	1	2	yes	—
40	C₄⋊#6090	C₂²	1	2	yes	—
41	#11718053	C₂²	1	1	yes	characteristic
42	#11718053	C₂²	1	1	yes	characteristic
43	C₂×#6127	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×SD₁₆	—	2	1	no	—
46	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#126	—	4	1	no	—
50	C₁₃×#125	—	2	1	no	—
51	C₁₃×#124	—	2	1	no	—
52	C₁₃×#123	—	4	1	no	—
53	C₁₃×C₂²⋊Q₈	—	2	1	no	—
54	C₁₃×#121	—	2	1	no	—
55	C₄×Q₈×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	—	4	1	no	—
58	C₁₃×#117	—	4	1	no	—
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	#88184	—	4	1	no	—
61	#88184	—	4	1	no	—
62	C₂×Dic₅₂	—	2	1	no	—
63	C₂×Dic₅₂	C₂³	1	2	yes	—
64	#88158	—	4	2	no	—
65	#88158	—	4	2	no	—
66	#88158	—	4	4	no	—
67	C₂×D₁₀₄	—	2	1	no	—
68	C₂×D₁₀₄	C₂³	1	2	yes	—
69	C₂×#6095	—	2	2	no	—
70	C₂×#6095	—	2	2	no	—
71	#88129	—	2	2	no	—
72	#88128	—	2	1	no	—
73	C₄×D₅₂	—	4	1	no	—
74	C₄×D₅₂	—	4	1	no	—
75	#88123	—	2	1	no	—
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	1	yes	characteristic
78	C₁₃×#106	—	2	1	no	—
79	C₁₃×#103	—	2	1	no	—
80	C₁₃×#103	—	2	1	no	—
81	C₁₃×#102	—	2	1	no	—
82	C₁₃×#102	—	2	1	no	—
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	#88069	—	4	2	no	—
88	#88068	—	4	2	no	—
89	#88067	—	4	2	no	—
90	#88066	—	4	2	no	—
91	C₂×#6090	C₂³	1	2	yes	—
92	C₂×#6090	C₂³	1	2	yes	—
93	#33785	—	13	1	no	maximal, Sylow
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₂²⋊D₁₃	—	4	2	no	—
102	#6127	—	4	4	no	—
103	#6127	—	4	4	no	—
104	C₂×D₅₂	—	2	2	no	—
105	C₂×D₅₂	—	4	1	no	—
106	C₂×D₅₂	—	4	1	no	—
107	C₂×C₄×D₁₃	—	4	2	no	—
108	C₂×Dic₂₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×SD₁₆	—	4	2	no	—
111	C₁₃×D₈	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₂²⋊C₄	—	4	1	no	—
125	C₁₃×C₂²⋊C₄	—	4	1	no	—
126	C₁₃×C₂²⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	4	1	no	—
128	C₁₃×C₂²⋊C₄	—	4	1	no	—
129	C₄²×C₁₃	—	4	1	no	—
130	C₄²×C₁₃	D₈	1	1	yes	characteristic
131	C₄²×C₁₃	D₈	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
134	#6103	—	4	2	no	—
135	#6103	—	4	2	no	—
136	C₄⋊Dic₁₃	—	4	1	no	—
137	C₄⋊Dic₁₃	—	4	1	no	—
138	Dic₅₂	—	2	2	no	—
139	Dic₅₂	—	2	2	no	—
140	Dic₅₂	—	4	2	no	—
141	D₁₀₄	—	2	2	no	—
142	D₁₀₄	—	2	2	no	—
143	D₁₀₄	—	4	2	no	—
144	#6095	—	4	4	no	—
145	#6095	—	4	4	no	—
146	#6090	—	2	2	no	—
147	#6090	—	2	2	no	—
148	#3168	D₁₃	1	1	yes	characteristic, complemented
149	#3147	—	13	1	no	—
150	#2251	—	13	1	no	—
151	#2250	—	13	1	no	—
152	#2245	—	13	1	no	—
153	#2244	—	13	1	no	—
154	#2211	—	13	2	no	—
155	#2210	—	13	2	no	—
156	#2189	—	13	2	no	—
157	#2186	—	13	2	no	—
158	#2163	—	13	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
161	C₂²×D₁₃	—	4	2	no	—
162	Q₈×C₁₃	—	4	1	no	—
163	Q₈×C₁₃	—	4	1	no	—
164	D₄×C₁₃	—	4	1	no	—
165	D₄×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	8	2	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	8	2	no	—
175	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₂²⋊D₁₃	—	8	4	no	—
182	C₂×Dic₁₃	—	4	2	no	—
183	D₅₂	—	4	2	no	—
184	D₅₂	—	4	2	no	—
185	D₅₂	—	8	2	no	—
186	D₅₂	—	8	2	no	—
187	C₄×D₁₃	—	8	4	no	—
188	Dic₂₆	—	4	2	no	—
189	Dic₂₆	—	4	2	no	—
190	C₈×C₁₃	—	2	1	no	—
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
193	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
194	C₂×#135	—	13	2	no	—
195	C₂×#135	—	26	1	no	—
196	#532	—	26	1	no	—
197	#529	—	2	1	no	—
198	C₂×Q₃₂	—	13	2	no	—
199	C₂×SD₃₂	—	13	2	no	—
200	C₂×SD₃₂	—	13	2	no	—
201	C₂×D₁₆	—	13	2	no	—
202	#499	C₂×D₁₃	1	1	yes	characteristic
203	#495	—	13	2	no	—
204	#495	—	26	1	no	—
205	#495	C₂×D₁₃	1	1	yes	characteristic
206	#494	—	13	1	no	—
207	#493	—	13	1	no	—
208	#492	—	26	1	no	—
209	#488	—	2	1	no	—
210	#467	C₂×D₁₃	1	1	yes	characteristic
211	#466	C₂×D₁₃	1	1	yes	characteristic
212	#465	—	2	1	no	—
213	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
214	C₄×SD₁₆	—	2	1	no	—
215	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
217	C₄⋊C₁₆	—	13	2	no	—
218	#358	—	13	2	no	—
219	#358	—	13	2	no	—
220	#357	—	13	2	no	—
221	#357	—	13	2	no	—
222	C₂²⋊C₁₆	—	13	2	no	—
223	#346	—	13	1	no	—
224	#346	—	13	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	—	8	1	no	—
230	C₂²×C₁₃	—	8	1	no	—
231	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
232	C₂×D₁₃	—	8	2	no	—
233	C₂×D₁₃	—	8	2	no	—
234	C₂×D₁₃	—	8	2	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	8	1	no	—
241	C₄×C₁₃	—	8	1	no	—
242	C₄×C₁₃	—	8	1	no	—
243	C₄×C₁₃	#535	1	1	yes	characteristic
244	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	Dic₁₃	—	8	2	no	—
246	C₂×#41	—	26	2	no	—
247	#135	—	52	2	no	—
248	#135	—	52	2	no	—
249	#135	—	52	4	no	—
250	C₂×Q₁₆	—	13	2	no	—
251	C₂×Q₁₆	—	26	1	no	—
252	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
253	C₂×SD₁₆	—	2	1	no	—
254	C₂×SD₁₆	—	26	2	no	—
255	C₂×SD₁₆	—	26	2	no	—
256	C₂×D₈	—	13	2	no	—
257	C₂×D₈	—	26	1	no	—
258	C₂×D₈	C₂²×D₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
261	C₄⋊Q₈	—	26	1	no	—
262	#127	—	26	1	no	—
263	#126	—	4	1	no	—
264	#125	—	2	1	no	—
265	#124	—	2	1	no	—
266	#124	—	26	2	no	—
267	#123	—	4	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	#121	—	2	1	no	—
270	#121	—	52	1	no	—
271	#121	—	52	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	4	1	no	—
275	C₄×D₄	—	52	1	no	—
276	C₄×D₄	—	52	1	no	—
277	#117	—	4	1	no	—
278	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
279	Q₃₂	—	52	2	no	—
280	SD₃₂	—	52	2	no	—
281	SD₃₂	—	52	2	no	—
282	D₁₆	—	52	2	no	—
283	C₂×C₁₆	—	13	2	no	—
284	C₂×C₁₆	—	13	2	no	—
285	#107	C₂²×D₁₃	1	1	yes	characteristic
286	#107	C₂²×D₁₃	1	1	yes	characteristic
287	#106	—	2	1	no	—
288	#103	—	2	1	no	—
289	#103	—	2	1	no	—
290	#102	—	2	1	no	—
291	#102	—	2	1	no	—
292	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
293	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
294	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
295	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
296	C₂×C₁₃	—	4	1	no	—
297	C₂×C₁₃	—	16	1	no	—
298	C₂×C₁₃	#3205	1	1	yes	characteristic
299	C₂×C₁₃	#3414	1	1	yes	characteristic
300	C₂×C₁₃	#3414	1	1	yes	characteristic
301	D₁₃	—	16	2	no	—
302	#41	—	52	4	no	—
303	#41	—	52	4	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	26	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	26	2	no	—
309	C₂×D₄	—	52	2	no	—
310	C₂×D₄	—	52	1	no	—
311	C₂×D₄	—	52	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	52	2	no	—
314	C₂²×C₄	#6104	1	1	yes	characteristic
315	C₂²×C₄	#6104	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
317	Q₁₆	—	2	2	no	—
318	Q₁₆	—	26	2	no	—
319	Q₁₆	—	26	2	no	—
320	Q₁₆	—	52	2	no	—
321	SD₁₆	—	4	2	no	—
322	SD₁₆	—	52	4	no	—
323	SD₁₆	—	52	4	no	—
324	D₈	—	2	2	no	—
325	D₈	—	26	2	no	—
326	D₈	—	26	2	no	—
327	D₈	—	52	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
331	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
332	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
333	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	52	1	no	—
341	C₄⋊C₄	—	52	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	52	2	no	—
348	C₂²⋊C₄	—	52	2	no	—
349	C₄²	—	4	1	no	—
350	C₄²	#6104	1	1	yes	characteristic
351	C₄²	#6104	1	1	yes	characteristic
352	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
353	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
354	C₁₆	—	26	2	no	—
355	C₁₆	—	26	2	no	—
356	C₁₃	#33785	1	1	yes	characteristic, complemented, Sylow
357	C₂³	—	4	1	no	—
358	C₂³	—	52	2	no	—
359	C₂³	C₂×#6104	1	1	yes	characteristic
360	Q₈	—	4	1	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	52	2	no	—
363	Q₈	—	52	2	no	—
364	D₄	—	4	1	no	—
365	D₄	—	4	1	no	—
366	D₄	—	8	2	no	—
367	D₄	—	52	2	no	—
368	D₄	—	52	2	no	—
369	D₄	—	104	2	no	—
370	D₄	—	104	2	no	—
371	D₄	—	104	4	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	52	2	no	—
381	C₂×C₄	—	104	4	no	—
382	C₂×C₄	C₂×#6104	1	1	yes	characteristic
383	C₂×C₄	C₂×#6104	1	1	yes	characteristic
384	C₂×C₄	C₂×#6104	1	1	yes	characteristic
385	C₂×C₄	C₂×#6104	1	1	yes	characteristic
386	C₂×C₄	C₂×#6104	1	1	yes	characteristic
387	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	#88203	1	2	yes	—
391	C₈	#88256	1	2	yes	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	104	2	no	—
399	C₂²	—	104	2	no	—
400	C₂²	—	104	2	no	—
401	C₂²	C₂²×#6104	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	104	2	no	—
411	C₄	C₂×#88203	1	1	yes	characteristic
412	C₄	#11719535	1	1	yes	characteristic
413	C₂	—	4	1	no	—
414	C₂	—	16	1	no	—
415	C₂	—	208	2	no	—
416	C₂	#13125751	1	1	yes	characteristic
417	C₂	#13127970	1	1	yes	characteristic
418	C₂	#13127970	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#3168	C₂
socle	C₂²×C₁₃	C₂²×D₈
hypercenter	#3168	D₁₃
hypocenter	C₁₃	#33785
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #13125264	C₂	semidirect
2. #13117108	C₂	semidirect
3. #13117103	C₂	semidirect
4. #13117083	C₂	semidirect
5. #13117079	C₂	semidirect
6. #13116898	C₂	semidirect
7. #13116891	C₂	semidirect
8. #13116774	C₂	semidirect
9. #13116757	C₂	semidirect
10. #13116639	C₂	semidirect
11. C₁₃×#3168	C₂	semidirect
148. #3168	D₁₃	semidirect
356. C₁₃	#33785	semidirect

Maximal subgroups

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

subgroup	index
#13125264	2
#13117108	2
#13117103	2
#13117083	2
#13117079	2
#13116898	2
#13116891	2
#13116774	2
#13116757	2
#13116639	2
C₁₃×#3168	2
#33785	13