Subgroups — #15686781

Order 2944.

1040 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093034	C₂	1	2	yes	maximal, complemented
2	#13093032	C₂	1	2	yes	maximal, complemented
3	#13093030	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093029	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093021	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093010	C₂	1	4	yes	maximal, complemented
7	#13092999	C₂	1	4	yes	maximal, complemented
8	#13092973	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092965	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092948	C₂	1	4	yes	maximal, complemented
11	#13092944	C₂	1	4	yes	maximal, complemented
12	#13092927	C₂	1	2	yes	maximal, complemented
13	C₄×#67290	C₂	1	2	yes	maximal, complemented
14	#117×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#67290	C₂²	1	2	yes	—
17	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#123	C₂²	1	4	yes	complemented
21	C₂₃×#121	C₂²	1	2	yes	—
22	C₂₃×#121	C₂²	1	4	yes	—
23	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#117	C₂²	1	1	yes	characteristic
25	#10625110	C₂²	1	4	yes	—
26	#10625109	C₂²	1	2	yes	—
27	#10625109	C₂²	1	4	yes	—
28	#10625108	C₂²	1	4	yes	—
29	#10625107	C₂²	1	4	yes	—
30	#10625107	C₂²	1	2	yes	complemented
31	#10625106	C₂²	1	4	yes	—
32	#10625106	C₂²	1	4	yes	complemented
33	D₄×Dic₂₃	C₂²	1	4	yes	—
34	D₄×Dic₂₃	C₂²	1	2	yes	complemented
35	D₄×Dic₂₃	C₂²	1	4	yes	complemented
36	#10625100	C₂²	1	4	yes	—
37	C₄×C₂²⋊D₂₃	C₂²	1	4	yes	—
38	#10625097	C₂²	1	1	yes	characteristic
39	#10625095	C₂²	1	2	yes	—
40	#10625095	C₂²	1	4	yes	complemented
41	C₂×C₄×Dic₂₃	C₂²	1	4	yes	complemented
42	#10625069	C₂²	1	4	yes	—
43	#10625068	C₂²	1	2	yes	—
44	#10625067	C₂²	1	4	yes	—
45	#10625063	C₂²	1	2	yes	—
46	#10625063	C₂²	1	2	yes	—
47	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
48	#10625061	C₂²	1	4	yes	complemented
49	#10625060	C₂²	1	4	yes	complemented
50	#10625059	C₂²	1	2	yes	complemented
51	#10625058	C₂²	1	2	yes	complemented
52	#10625058	C₂²	1	4	yes	complemented
53	#10625056	C₂²	1	4	yes	—
54	#10625054	C₂²	1	4	yes	—
55	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	—
56	(C₂²⋊D₂₃)⋊C₄	C₂²	1	4	yes	—
57	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
58	#10625050	C₂²	1	4	yes	—
59	#10625050	C₂²	1	4	yes	complemented
60	#10625050	C₂²	1	4	yes	complemented
61	#10625049	C₂²	1	4	yes	complemented
62	#10625048	C₂²	1	2	yes	—
63	#10625048	C₂²	1	4	yes	complemented
64	#10625043	C₂²	1	1	yes	characteristic
65	#10625043	C₂²	1	1	yes	characteristic
66	C₄²×D₂₃	C₂²	1	1	yes	characteristic
67	C₄²×D₂₃	C₂²	1	1	yes	characteristic
68	#10625041	C₂²	1	1	yes	characteristic, complemented
69	#10625040	C₂²	1	1	yes	characteristic, complemented
70	C₄×Dic₄₆	C₂²	1	2	yes	complemented
71	C₂³×D₂₃	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₂₃	C₂³	1	2	yes	—
73	C₂×D₄×C₂₃	C₂³	1	4	yes	—
74	C₂×D₄×C₂₃	C₂³	1	4	yes	—
75	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
79	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Dic₂₃	C₂³	1	4	yes	—
81	C₂²×Dic₂₃	C₂³	1	4	yes	—
82	#67290	—	2	8	no	—
83	C₂×C₄×D₂₃	—	2	4	no	—
84	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
86	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
87	C₂×C₄×D₂₃	C₂³	1	2	yes	—
88	C₂×C₄×D₂₃	C₂³	1	2	yes	—
89	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
90	C₂×Dic₄₆	C₂³	1	2	yes	—
91	C₂×Dic₄₆	C₂³	1	4	yes	—
92	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
93	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
94	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
95	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
96	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
97	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
98	C₄²×C₂₃	C₂³	1	1	yes	characteristic
99	C₄²×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
101	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
102	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
103	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
104	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
105	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
106	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
107	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
108	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
110	C₄⋊Dic₂₃	C₂³	1	2	yes	—
111	C₄⋊Dic₂₃	C₂³	1	4	yes	—
112	C₄⋊Dic₂₃	C₂³	1	2	yes	—
113	C₄⋊Dic₂₃	C₂³	1	4	yes	—
114	Dic₂₃⋊C₄	C₂³	1	4	yes	—
115	Dic₂₃⋊C₄	C₂³	1	4	yes	—
116	Dic₂₃⋊C₄	C₂³	1	2	yes	—
117	Dic₂₃⋊C₄	C₂³	1	2	yes	—
118	Dic₂₃⋊C₄	C₂³	1	4	yes	—
119	Dic₂₃⋊C₄	C₂³	1	4	yes	—
120	Dic₂₃⋊C₄	C₂³	1	4	yes	—
121	C₄×Dic₂₃	C₂³	1	4	yes	—
122	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
123	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
124	C₄×Dic₂₃	C₂³	1	2	yes	—
125	C₄×Dic₂₃	C₂³	1	2	yes	—
126	C₄×Dic₂₃	C₂³	1	4	yes	—
127	C₄×Dic₂₃	C₂³	1	4	yes	—
128	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
129	C₂³×C₂₃	C₂⁴	1	4	yes	—
130	C₂²×D₂₃	—	2	2	no	—
131	C₂²×D₂₃	—	4	2	no	—
132	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
133	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
134	D₄×C₂₃	—	2	4	no	—
135	D₄×C₂₃	—	4	4	no	—
136	D₄×C₂₃	—	4	4	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	4	4	no	—
139	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
140	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
141	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
142	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
143	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₂₃	—	2	8	no	—
145	C₂²⋊D₂₃	—	4	4	no	—
146	C₂×Dic₂₃	—	2	2	no	—
147	C₂×Dic₂₃	—	2	8	no	—
148	C₂×Dic₂₃	—	4	4	no	—
149	C₂×Dic₂₃	C₂⁴	1	2	yes	—
150	C₂×Dic₂₃	C₂⁴	1	4	yes	—
151	C₂×Dic₂₃	C₂⁴	1	4	yes	—
152	C₂×Dic₂₃	C₂⁴	1	2	yes	—
153	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
154	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
155	C₄×D₂₃	—	2	2	no	—
156	C₄×D₂₃	—	2	2	no	—
157	C₄×D₂₃	—	2	2	no	—
158	C₄×D₂₃	—	4	2	no	—
159	C₄×D₂₃	—	4	2	no	—
160	C₄×D₂₃	#41	1	4	yes	—
161	Dic₄₆	—	2	4	no	—
162	Dic₄₆	—	4	4	no	—
163	#3455	—	23	1	no	maximal, Sylow
164	C₂²×C₂₃	—	2	4	no	—
165	C₂²×C₂₃	—	2	1	no	—
166	C₂²×C₂₃	—	2	4	no	—
167	C₂²×C₂₃	—	2	4	no	—
168	C₂²×C₂₃	—	2	2	no	—
169	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
170	C₂×D₂₃	—	2	2	no	—
171	C₂×D₂₃	—	2	1	no	—
172	C₂×D₂₃	—	2	2	no	—
173	C₂×D₂₃	—	4	4	no	—
174	C₂×D₂₃	C₂×#41	1	2	yes	—
175	C₄×C₂₃	—	2	1	no	—
176	C₄×C₂₃	—	2	4	no	—
177	C₄×C₂₃	—	2	2	no	—
178	C₄×C₂₃	—	2	2	no	—
179	C₄×C₂₃	C₂×#41	1	2	yes	—
180	Dic₂₃	—	2	4	no	—
181	Dic₂₃	—	2	1	no	—
182	Dic₂₃	—	2	2	no	—
183	Dic₂₃	—	2	4	no	—
184	Dic₂₃	—	2	2	no	—
185	Dic₂₃	C₂×#41	1	2	yes	—
186	#542	—	23	2	no	—
187	#542	—	23	2	no	—
188	#541	—	23	1	no	—
189	#541	—	23	1	no	—
190	#540	—	23	1	no	—
191	#540	D₂₃	1	1	yes	characteristic, complemented
192	#539	—	23	4	no	—
193	#538	—	23	4	no	—
194	#533	—	23	1	no	—
195	#532	—	23	1	no	—
196	#529	—	23	4	no	—
197	#529	—	23	4	no	—
198	#525	—	23	2	no	—
199	C₄×#41	—	23	2	no	—
200	C₂×#117	—	23	1	no	—
201	C₂×C₂₃	—	4	1	no	—
202	C₂×C₂₃	—	4	4	no	—
203	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
204	C₂×C₂₃	#585	1	2	yes	—
205	D₂₃	—	2	2	no	—
206	D₂₃	—	4	1	no	—
207	C₂×#41	—	23	2	no	—
208	C₂³×C₄	—	23	1	no	—
209	C₄⋊Q₈	—	23	2	no	—
210	C₄⋊Q₈	—	23	1	no	—
211	#127	C₂×D₂₃	1	1	yes	characteristic, complemented
212	#126	—	23	4	no	—
213	#126	—	23	4	no	—
214	#126	—	23	4	no	—
215	#126	—	23	4	no	—
216	#125	—	23	4	no	—
217	#125	—	23	4	no	—
218	#125	—	23	1	no	—
219	#125	C₂×D₂₃	1	1	yes	characteristic, complemented
220	#124	—	23	4	no	—
221	#124	—	23	2	no	—
222	#124	—	23	4	no	—
223	#123	—	23	4	no	—
224	#123	—	23	4	no	—
225	#123	—	23	4	no	—
226	#123	—	23	4	no	—
227	#123	C₂×D₂₃	1	4	yes	complemented
228	C₂²⋊Q₈	—	23	2	no	—
229	C₂²⋊Q₈	—	23	4	no	—
230	C₂²⋊Q₈	—	23	2	no	—
231	C₂²⋊Q₈	—	23	4	no	—
232	C₂²⋊Q₈	—	23	4	no	—
233	#121	—	23	2	no	—
234	#121	—	23	4	no	—
235	#121	—	23	4	no	—
236	#121	C₂×D₂₃	1	2	yes	—
237	#121	C₂×D₂₃	1	4	yes	—
238	#120	—	23	4	no	—
239	C₄×Q₈	—	23	2	no	—
240	C₄×Q₈	—	23	4	no	—
241	C₄×Q₈	—	23	2	no	—
242	C₄×D₄	—	23	2	no	—
243	C₄×D₄	—	23	4	no	—
244	C₄×D₄	—	23	4	no	—
245	C₄×D₄	—	23	4	no	—
246	C₄×D₄	—	23	4	no	—
247	C₄×D₄	—	23	4	no	—
248	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
249	#117	—	23	1	no	—
250	#117	—	23	2	no	—
251	#117	—	23	2	no	—
252	#117	—	23	2	no	—
253	#117	—	23	4	no	—
254	#117	—	23	1	no	—
255	#117	—	23	1	no	—
256	#117	C₂×D₂₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	—	23	2	no	—
258	C₂×C₂²⋊C₄	—	23	2	no	—
259	C₂×C₄²	—	23	4	no	—
260	C₂×C₄²	—	23	1	no	—
261	C₂×C₄²	—	23	1	no	—
262	C₂₃	#3455	1	1	yes	characteristic, complemented, Sylow
263	C₂⁴	—	23	1	no	—
264	#41	—	46	8	no	—
265	C₂×Q₈	—	23	2	no	—
266	C₂×Q₈	—	23	4	no	—
267	C₂×D₄	—	23	4	no	—
268	C₂×D₄	—	23	4	no	—
269	C₂×D₄	C₂²×D₂₃	1	2	yes	—
270	C₂×D₄	C₂²×D₂₃	1	4	yes	—
271	C₂×D₄	C₂²×D₂₃	1	4	yes	—
272	C₂²×C₄	—	23	1	no	—
273	C₂²×C₄	—	23	4	no	—
274	C₂²×C₄	—	23	1	no	—
275	C₂²×C₄	—	23	4	no	—
276	C₂²×C₄	—	23	1	no	—
277	C₂²×C₄	—	23	1	no	—
278	C₂²×C₄	—	23	1	no	—
279	C₂²×C₄	—	23	2	no	—
280	C₂²×C₄	—	23	2	no	—
281	C₂²×C₄	—	46	4	no	—
282	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
284	C₄⋊C₄	—	23	2	no	—
285	C₄⋊C₄	—	23	2	no	—
286	C₄⋊C₄	—	23	2	no	—
287	C₄⋊C₄	—	23	2	no	—
288	C₄⋊C₄	—	23	4	no	—
289	C₄⋊C₄	—	23	4	no	—
290	C₄⋊C₄	—	23	4	no	—
291	C₄⋊C₄	—	23	4	no	—
292	C₄⋊C₄	—	23	4	no	—
293	C₄⋊C₄	—	23	4	no	—
294	C₄⋊C₄	—	23	4	no	—
295	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
296	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
297	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
298	C₂²⋊C₄	—	23	2	no	—
299	C₂²⋊C₄	—	23	4	no	—
300	C₂²⋊C₄	—	23	4	no	—
301	C₂²⋊C₄	—	23	4	no	—
302	C₂²⋊C₄	—	23	4	no	—
303	C₂²⋊C₄	—	23	4	no	—
304	C₂²⋊C₄	—	23	2	no	—
305	C₂²⋊C₄	—	23	2	no	—
306	C₂²⋊C₄	—	23	4	no	—
307	C₂²⋊C₄	—	23	4	no	—
308	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
309	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
310	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
311	C₄²	—	23	2	no	—
312	C₄²	—	23	2	no	—
313	C₄²	—	23	4	no	—
314	C₄²	—	23	1	no	—
315	C₄²	—	23	1	no	—
316	C₄²	—	23	4	no	—
317	C₄²	—	23	4	no	—
318	C₄²	C₂²×D₂₃	1	1	yes	characteristic
319	C₄²	C₂²×D₂₃	1	1	yes	characteristic
320	C₂³	—	23	1	no	—
321	C₂³	—	23	1	no	—
322	C₂³	—	46	2	no	—
323	C₂³	—	92	2	no	—
324	C₂³	C₂³×D₂₃	1	1	yes	characteristic
325	C₂³	C₂³×D₂₃	1	4	yes	—
326	Q₈	—	46	4	no	—
327	Q₈	—	92	4	no	—
328	D₄	—	2	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	46	8	no	—
332	D₄	—	92	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	23	1	no	—
336	C₂×C₄	—	23	4	no	—
337	C₂×C₄	—	23	2	no	—
338	C₂×C₄	—	23	2	no	—
339	C₂×C₄	—	23	4	no	—
340	C₂×C₄	—	23	4	no	—
341	C₂×C₄	—	23	1	no	—
342	C₂×C₄	—	46	2	no	—
343	C₂×C₄	—	46	2	no	—
344	C₂×C₄	—	46	2	no	—
345	C₂×C₄	—	46	8	no	—
346	C₂×C₄	—	46	2	no	—
347	C₂×C₄	—	92	2	no	—
348	C₂×C₄	—	92	2	no	—
349	C₂×C₄	—	92	4	no	—
350	C₂×C₄	C₂³×D₂₃	1	2	yes	—
351	C₂×C₄	C₂³×D₂₃	1	4	yes	—
352	C₂×C₄	C₂³×D₂₃	1	2	yes	—
353	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
354	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
355	C₂²	—	2	1	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	23	2	no	—
361	C₂²	—	46	2	no	—
362	C₂²	—	46	1	no	—
363	C₂²	—	46	2	no	—
364	C₂²	—	92	4	no	—
365	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	2	no	—
370	C₄	—	23	2	no	—
371	C₄	—	46	1	no	—
372	C₄	—	46	4	no	—
373	C₄	—	46	2	no	—
374	C₄	—	46	4	no	—
375	C₄	—	46	2	no	—
376	C₄	#41×D₂₃	1	2	yes	—
377	C₂	—	4	1	no	—
378	C₂	—	4	4	no	—
379	C₂	—	46	2	no	—
380	C₂	—	92	1	no	—
381	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
382	C₂	#13093252	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#540	C₂
hypercenter	#540	D₂₃
hypocenter	C₂₃	#3455
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #13093034	C₂	semidirect
2. #13093032	C₂	semidirect
3. #13093030	C₂	semidirect
4. #13093029	C₂	semidirect
5. #13093021	C₂	semidirect
6. #13093010	C₂	semidirect
7. #13092999	C₂	semidirect
8. #13092973	C₂	semidirect
9. #13092965	C₂	semidirect
10. #13092948	C₂	semidirect
11. #13092944	C₂	semidirect
12. #13092927	C₂	semidirect
13. C₄×#67290	C₂	semidirect
14. #117×D₂₃	C₂	semidirect
15. C₂₃×#540	C₂	semidirect
18. C₂₃×#127	C₂²	semidirect
19. C₂₃×#125	C₂²	semidirect
20. C₂₃×#123	C₂²	semidirect
23. C₄×D₄×C₂₃	C₂²	semidirect
30. #10625107	C₂²	semidirect
32. #10625106	C₂²	semidirect
34. D₄×Dic₂₃	C₂²	semidirect
35. D₄×Dic₂₃	C₂²	semidirect
40. #10625095	C₂²	semidirect
41. C₂×C₄×Dic₂₃	C₂²	semidirect
48. #10625061	C₂²	semidirect
49. #10625060	C₂²	semidirect
50. #10625059	C₂²	semidirect
51. #10625058	C₂²	semidirect
52. #10625058	C₂²	semidirect
59. #10625050	C₂²	semidirect
60. #10625050	C₂²	semidirect
61. #10625049	C₂²	semidirect
63. #10625048	C₂²	semidirect
68. #10625041	C₂²	semidirect
69. #10625040	C₂²	semidirect
70. C₄×Dic₄₆	C₂²	semidirect
191. #540	D₂₃	semidirect
211. #127	C₂×D₂₃	semidirect
219. #125	C₂×D₂₃	semidirect
227. #123	C₂×D₂₃	semidirect
248. C₄×D₄	C₂×D₂₃	semidirect
262. C₂₃	#3455	semidirect

Maximal subgroups

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

subgroup	index
#13093034	2
#13093032	2
#13093030	2
#13093029	2
#13093021	2
#13093010	2
#13092999	2
#13092973	2
#13092965	2
#13092948	2
#13092944	2
#13092927	2
C₄×#67290	2
#117×D₂₃	2
C₂₃×#540	2
#3455	23