Subgroups — #36613335

Order 22784.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030792	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030116	C₂	1	2	yes	maximal
3	#26028849	C₂	1	1	yes	maximal, characteristic
4	#26021762	C₂	1	2	yes	maximal, complemented
5	#26021601	C₂	1	2	yes	maximal, complemented
6	#26021038	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020486	C₂	1	2	yes	maximal
8	#26020416	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020313	C₂	1	1	yes	maximal, characteristic
10	#26020089	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₂²	1	1	yes	characteristic
13	#19152226	C₂²	1	2	yes	—
14	#19152078	C₂²	1	2	yes	—
15	#19152005	—	2	2	no	—
16	#19152002	—	2	1	no	—
17	#19151999	—	2	1	no	—
18	#19151906	—	2	2	no	—
19	#19151899	—	2	2	no	—
20	#19151889	—	2	2	no	—
21	#19151884	—	2	2	no	—
22	#19151641	C₂²	1	2	yes	—
23	#19151641	C₂²	1	2	yes	—
24	#19151640	C₂²	1	2	yes	—
25	#19151637	—	2	2	no	—
26	#19151635	—	2	1	no	—
27	C₂×#15667946	C₂²	1	1	yes	characteristic
28	C₂×#15667946	C₂²	1	1	yes	characteristic
29	#107×D₈₉	—	2	1	no	—
30	C₂×#15667944	C₂²	1	2	yes	—
31	C₂×#15667940	C₂²	1	1	yes	characteristic
32	#19151600	C₂²	1	2	yes	—
33	#19151595	C₂²	1	1	yes	characteristic
34	#19151553	C₂²	1	1	yes	characteristic
35	#19151464	C₂²	1	2	yes	—
36	#19151366	C₂²	1	2	yes	—
37	#19151366	C₂²	1	2	yes	—
38	#19151363	C₂²	1	1	yes	characteristic
39	#19151358	C₂²	1	1	yes	characteristic
40	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
41	#427×C₈₉	C₂²	1	1	yes	characteristic
42	#424×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
44	#339×C₈₉	C₂²	1	2	yes	—
45	C₂×#13083574	C₂³	1	1	yes	characteristic
46	#15668018	—	2	2	no	—
47	#15668018	Q₈	1	4	yes	complemented
48	C₂×#13083558	C₂³	1	1	yes	characteristic
49	C₂×#13083558	C₂³	1	1	yes	characteristic
50	C₂×#13083557	—	2	1	no	—
51	C₂×C₈×D₈₉	—	2	1	no	—
52	#15668012	—	2	2	no	—
53	#15668011	—	2	2	no	—
54	#15668004	—	2	2	no	—
55	#15668003	—	2	2	no	—
56	#15667989	—	4	2	no	—
57	C₄×Dic₁₇₈	—	2	2	no	—
58	C₄×D₃₅₆	—	2	2	no	—
59	#15667972	—	4	2	no	—
60	#15667971	C₂³	1	1	yes	characteristic
61	#15667970	—	2	2	no	—
62	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
63	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
64	C₄⋊C₄×D₈₉	—	2	2	no	—
65	#15667946	—	2	2	no	—
66	#15667946	—	2	1	no	—
67	#15667946	—	2	1	no	—
68	#15667946	—	2	1	no	—
69	#15667946	—	2	1	no	—
70	#15667945	—	2	2	no	—
71	#15667945	—	2	2	no	—
72	#15667944	—	2	2	no	—
73	#15667944	—	2	2	no	—
74	#15667944	—	2	2	no	—
75	#15667943	—	2	2	no	—
76	#15667943	—	2	2	no	—
77	#15667940	Q₈	1	4	yes	complemented
78	#15667937	—	2	2	no	—
79	#15667937	D₄	1	1	yes	characteristic
80	#15667937	D₄	1	1	yes	characteristic
81	#15667934	—	2	2	no	—
82	#15667934	D₄	1	1	yes	characteristic
83	#15667934	D₄	1	1	yes	characteristic
84	#15667922	—	2	1	no	—
85	C₈×Dic₈₉	—	2	1	no	—
86	#15667919	—	4	2	no	—
87	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	#117×C₈₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	#108×C₈₉	—	2	2	no	—
93	#107×C₈₉	D₄	1	1	yes	characteristic
94	#107×C₈₉	D₄	1	1	yes	characteristic
95	#106×C₈₉	D₄	1	2	yes	—
96	C₄⋊C₈×C₈₉	—	2	2	no	—
97	C₄⋊C₈×C₈₉	—	2	2	no	—
98	C₄×C₈×C₈₉	—	2	2	no	—
99	#13083574	—	2	1	no	—
100	#13083574	—	2	1	no	—
101	#13083574	C₂×Q₈	1	2	yes	—
102	#13083574	C₂×Q₈	1	2	yes	—
103	C₂×Dic₁₇₈	—	4	2	no	—
104	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
105	C₂×D₃₅₆	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₈₉	—	2	1	no	—
107	C₂²×Dic₈₉	—	2	2	no	—
108	C₂²×Dic₈₉	—	2	2	no	—
109	C₂×C₄×D₈₉	—	2	1	no	—
110	C₂×C₄×D₈₉	—	4	2	no	—
111	#13083558	—	2	1	no	—
112	#13083558	—	2	1	no	—
113	#13083558	C₂×Q₈	1	2	yes	—
114	#13083558	C₂×Q₈	1	2	yes	—
115	#13083557	—	2	4	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₈×D₈₉	—	2	4	no	—
119	C₄⋊Dic₈₉	—	2	2	no	—
120	C₄⋊Dic₈₉	—	2	2	no	—
121	C₄⋊Dic₈₉	—	2	2	no	—
122	C₄⋊Dic₈₉	—	2	2	no	—
123	C₄⋊Dic₈₉	—	4	2	no	—
124	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
125	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
126	#13083553	—	4	2	no	—
127	#13083553	—	4	2	no	—
128	#13083553	—	4	2	no	—
129	C₂²⋊Dic₈₉	—	2	1	no	—
130	#13083551	—	4	2	no	—
131	C₄×Dic₈₉	—	2	1	no	—
132	C₄×Dic₈₉	—	4	2	no	—
133	C₂²×C₄×C₈₉	—	2	1	no	—
134	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₈₉	—	2	2	no	—
136	M₁₆×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	—	2	1	no	—
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
145	C₂×C₈×C₈₉	#41	1	2	yes	—
146	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
152	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂²×D₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	—	4	1	no	—
159	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂²⋊D₈₉	—	2	2	no	—
166	C₂²⋊D₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	2	1	no	—
168	C₂×Dic₈₉	—	2	1	no	—
169	C₂×Dic₈₉	—	2	1	no	—
170	C₂×Dic₈₉	—	4	2	no	—
171	C₂×Dic₈₉	—	4	2	no	—
172	C₂×Dic₈₉	—	8	2	no	—
173	C₂×Dic₈₉	—	8	2	no	—
174	D₃₅₆	—	2	1	no	—
175	D₃₅₆	C₄⋊Q₈	1	2	yes	—
176	C₄×D₈₉	—	2	2	no	—
177	C₄×D₈₉	—	2	2	no	—
178	C₄×D₈₉	—	16	2	no	—
179	Dic₁₇₈	—	2	1	no	—
180	Dic₁₇₈	—	16	2	no	—
181	Dic₁₇₈	C₄⋊Q₈	1	2	yes	—
182	C₈×C₈₉	—	2	1	no	—
183	C₈×C₈₉	—	2	1	no	—
184	C₈×C₈₉	—	4	2	no	—
185	C₈×C₈₉	C₂²⋊Q₈	1	2	yes	—
186	C₈×C₈₉	C₂²⋊Q₈	1	2	yes	—
187	#10623494	—	2	2	no	—
188	#10623494	—	2	2	no	—
189	C₂²×C₈₉	—	2	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	#544	1	1	yes	characteristic
192	C₂²×C₈₉	D₄²	1	1	yes	characteristic
193	C₂²×C₈₉	#554	1	1	yes	characteristic
194	C₂×D₈₉	—	2	2	no	—
195	C₂×D₈₉	—	4	1	no	—
196	C₂×D₈₉	—	4	1	no	—
197	C₄×C₈₉	—	4	2	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	4	2	no	—
200	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
201	C₄×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
202	C₄×C₈₉	#547	1	1	yes	characteristic
203	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
204	Dic₈₉	—	2	2	no	—
205	Dic₈₉	—	4	1	no	—
206	Dic₈₉	—	4	1	no	—
207	Dic₈₉	—	8	2	no	—
208	Dic₈₉	—	8	2	no	—
209	#26082	—	89	1	no	maximal, Sylow
210	C₂×C₈₉	—	2	1	no	—
211	C₂×C₈₉	—	2	1	no	—
212	C₂×C₈₉	#2440	1	1	yes	characteristic
213	C₂×C₈₉	#3290	1	1	yes	characteristic
214	C₂×C₈₉	#3290	1	1	yes	characteristic
215	D₈₉	—	4	2	no	—
216	#3164	—	89	1	no	—
217	#3084	—	89	2	no	—
218	#2913	—	89	1	no	—
219	#2090	—	89	2	no	—
220	#2061	—	89	2	no	—
221	#1952	—	89	1	no	—
222	#1945	D₈₉	1	1	yes	characteristic, complemented
223	#1860	—	89	2	no	—
224	#1846	—	89	1	no	—
225	#1816	—	89	1	no	—
226	#1764	—	89	1	no	—
227	C₈₉	#26082	1	1	yes	characteristic, complemented, Sylow
228	C₂×#131	—	89	1	no	—
229	#544	—	89	2	no	—
230	#520	—	89	2	no	—
231	#501	—	178	2	no	—
232	#500	—	178	1	no	—
233	#499	—	178	1	no	—
234	#479	—	178	2	no	—
235	#478	—	178	2	no	—
236	#476	—	178	2	no	—
237	#475	—	178	2	no	—
238	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
239	#428	—	89	2	no	—
240	#428	—	89	2	no	—
241	#428	—	89	2	no	—
242	#428	—	178	2	no	—
243	#427	—	178	1	no	—
244	#427	C₂×D₈₉	1	1	yes	characteristic
245	C₂×#107	—	89	1	no	—
246	C₂×#107	—	89	1	no	—
247	C₂×#107	—	178	1	no	—
248	C₂×#106	—	89	2	no	—
249	#424	C₂×D₈₉	1	2	yes	—
250	C₂×#104	—	89	1	no	—
251	#417	—	89	2	no	—
252	#416	—	89	1	no	—
253	#405	—	89	1	no	—
254	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
255	#382	—	89	2	no	—
256	#343	—	89	2	no	—
257	#343	—	89	2	no	—
258	#341	—	89	1	no	—
259	#339	—	89	1	no	—
260	#339	C₂×D₈₉	1	2	yes	—
261	C₂×#41	—	89	1	no	—
262	#131	—	89	4	no	—
263	#131	—	178	2	no	—
264	C₂×M₁₆	—	89	1	no	—
265	C₂×M₁₆	—	89	1	no	—
266	C₂×M₁₆	—	178	1	no	—
267	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
268	C₂²×C₈	—	178	1	no	—
269	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
271	C₄⋊Q₈	—	178	2	no	—
272	C₄⋊Q₈	—	178	2	no	—
273	#125	—	178	2	no	—
274	#125	—	178	2	no	—
275	C₂²⋊Q₈	—	356	2	no	—
276	C₄×Q₈	—	178	2	no	—
277	C₄×D₄	—	356	2	no	—
278	C₄×D₄	—	178	2	no	—
279	#117	—	89	1	no	—
280	#117	—	178	2	no	—
281	#117	C₂²×D₈₉	1	2	yes	—
282	C₂×C₄⋊C₄	—	89	2	no	—
283	C₂×C₄⋊C₄	—	89	2	no	—
284	C₂×C₄⋊C₄	—	178	2	no	—
285	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
286	#108	—	2	2	no	—
287	#107	—	178	2	no	—
288	#107	—	178	1	no	—
289	#107	—	178	1	no	—
290	#107	—	178	1	no	—
291	#107	—	178	1	no	—
292	#107	—	178	2	no	—
293	#107	—	178	2	no	—
294	#107	D₃₅₆	1	1	yes	characteristic
295	#107	D₃₅₆	1	1	yes	characteristic
296	#106	—	178	2	no	—
297	#106	—	178	2	no	—
298	#106	—	178	2	no	—
299	#106	—	178	2	no	—
300	#106	—	178	2	no	—
301	#106	D₃₅₆	1	2	yes	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	#104	—	89	4	no	—
305	#103	—	89	1	no	—
306	#103	—	89	1	no	—
307	#103	—	178	2	no	—
308	#102	—	89	1	no	—
309	#102	—	89	1	no	—
310	#102	—	178	2	no	—
311	#97	—	178	1	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	178	1	no	—
314	#95	—	356	2	no	—
315	#41	—	89	2	no	—
316	#41	—	89	2	no	—
317	#41	—	178	1	no	—
318	#41	—	178	1	no	—
319	C₂×Q₈	—	89	1	no	—
320	C₂×Q₈	—	356	2	no	—
321	C₂×D₄	—	89	1	no	—
322	C₂×D₄	—	178	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	356	2	no	—
325	C₂²×C₄	—	178	2	no	—
326	C₂²×C₄	—	178	2	no	—
327	C₂²×C₄	—	178	1	no	—
328	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	89	2	no	—
332	M₁₆	—	89	2	no	—
333	M₁₆	—	178	1	no	—
334	M₁₆	—	178	1	no	—
335	M₁₆	—	178	4	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	178	1	no	—
340	C₂×C₈	—	178	1	no	—
341	C₂×C₈	—	178	4	no	—
342	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
343	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
344	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
345	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
346	C₂×C₈	Q₈×D₈₉	1	2	yes	—
347	C₂×C₈	#13083573	1	2	yes	—
348	C₄⋊C₄	—	89	1	no	—
349	C₄⋊C₄	—	89	1	no	—
350	C₄⋊C₄	—	356	2	no	—
351	C₄⋊C₄	—	356	2	no	—
352	C₄⋊C₄	—	356	2	no	—
353	C₄⋊C₄	—	356	2	no	—
354	C₄⋊C₄	—	178	2	no	—
355	C₄⋊C₄	—	178	2	no	—
356	C₄⋊C₄	—	178	2	no	—
357	C₄⋊C₄	—	178	2	no	—
358	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
359	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	356	2	no	—
362	C₂²⋊C₄	—	178	1	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	356	2	no	—
366	C₄²	—	178	1	no	—
367	C₄²	Q₈×D₈₉	1	2	yes	—
368	C₂³	—	178	1	no	—
369	C₂³	#15668058	1	1	yes	characteristic
370	Q₈	—	89	2	no	—
371	Q₈	—	1424	2	no	—
372	Q₈	—	178	1	no	—
373	D₄	—	89	2	no	—
374	D₄	—	178	2	no	—
375	D₄	—	178	2	no	—
376	D₄	—	178	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	356	2	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	1424	2	no	—
385	C₂×C₄	—	178	1	no	—
386	C₂×C₄	—	178	1	no	—
387	C₂×C₄	—	178	1	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	—	178	2	no	—
390	C₂×C₄	—	712	2	no	—
391	C₂×C₄	—	712	2	no	—
392	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
394	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
395	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
397	C₂×C₄	#15668059	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	4	2	no	—
401	C₈	—	178	2	no	—
402	C₈	—	178	2	no	—
403	C₈	#15667992	1	2	yes	—
404	C₈	#15667992	1	2	yes	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	356	1	no	—
408	C₂²	—	356	1	no	—
409	C₂²	—	178	2	no	—
410	C₂²	#19152228	1	1	yes	characteristic
411	C₂²	D₄×D₃₅₆	1	1	yes	characteristic
412	C₂²	#19152306	1	1	yes	characteristic
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	356	1	no	—
417	C₄	—	356	1	no	—
418	C₄	—	178	2	no	—
419	C₄	—	712	2	no	—
420	C₄	—	712	2	no	—
421	C₄	C₂×#15667992	1	1	yes	characteristic
422	C₄	C₄⋊Q₈×D₈₉	1	1	yes	characteristic
423	C₄	#19152248	1	1	yes	characteristic
424	C₄	Q₈×D₃₅₆	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	356	2	no	—
428	C₂	#26023952	1	1	yes	characteristic
429	C₂	#26032040	1	1	yes	characteristic
430	C₂	#26032040	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₅₆
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1945	C₂
socle	C₂²×C₈₉	D₄²
prime radical	C₂×#13083574	C₂³
hypercenter	#1945	D₈₉
hypocenter	C₈₉	#26082
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1945

Complements

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

N	H ≅ G/N	type
1. #26030792	C₂	semidirect
4. #26021762	C₂	semidirect
5. #26021601	C₂	semidirect
6. #26021038	C₂	semidirect
8. #26020416	C₂	semidirect
11. C₈₉×#1945	C₂	semidirect
47. #15668018	Q₈	semidirect
77. #15667940	Q₈	semidirect
222. #1945	D₈₉	semidirect
227. C₈₉	#26082	semidirect

Maximal subgroups

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

subgroup	index
#26030792	2
#26030116	2
#26028849	2
#26021762	2
#26021601	2
#26021038	2
#26020486	2
#26020416	2
#26020313	2
#26020089	2
C₈₉×#1945	2
#26082	89