Subgroups — #18086388

Order 4864.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926835	C₂	1	1	yes	maximal, characteristic
2	#14564595	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564428	C₂	1	1	yes	maximal, characteristic
4	#14563632	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926294	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926292	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	#11926835	—	2	2	no	—
11	#11926835	—	2	2	no	—
12	C₂×#10597274	—	2	1	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597278	—	2	1	no	—
15	C₂×#10597266	—	2	1	no	—
16	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
17	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926306	—	2	1	no	—
20	#11926306	—	2	1	no	—
21	#11926306	—	2	1	no	—
22	#11926294	—	2	2	no	—
23	#11926292	—	2	2	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₉×#384	C₂²	1	1	yes	characteristic
27	C₂²×D₇₆	D₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	—	2	1	no	—
29	C₂²×Dic₃₈	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	1	no	—
39	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
40	C₂²×C₁₉⋊C₈	—	2	1	no	—
41	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
42	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
43	C₄×D₇₆	—	2	1	no	—
44	C₄×D₇₆	—	2	1	no	—
45	C₄×D₇₆	—	2	1	no	—
46	C₄×D₇₆	—	2	1	no	—
47	#10597315	—	2	1	no	—
48	#10597315	—	2	1	no	—
49	#10597315	—	2	1	no	—
50	#10597315	D₄	1	2	yes	—
51	C₁₉×C₄⋊C₈	—	2	1	no	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
55	#10597278	—	2	4	no	—
56	(C₂×D₁₉)⋊C₈	—	4	2	no	—
57	(C₂×D₁₉)⋊C₈	—	4	2	no	—
58	#10597274	—	2	4	no	—
59	#10597266	—	4	2	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₄×C₁₉⋊C₈	—	2	1	no	—
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₂³×D₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
69	C₂²×Dic₁₉	—	2	1	no	—
70	C₂²×Dic₁₉	—	4	1	no	—
71	C₂×D₇₆	—	2	1	no	—
72	C₂×D₇₆	—	2	1	no	—
73	C₂×D₇₆	—	2	1	no	—
74	C₂×D₇₆	—	2	1	no	—
75	C₂×D₇₆	—	2	1	no	—
76	C₂×D₇₆	SD₁₆	1	2	yes	—
77	C₂×C₄×D₁₉	—	4	1	no	—
78	C₂×C₄×D₁₉	—	4	1	no	—
79	C₂×C₄×D₁₉	—	4	1	no	—
80	C₂×C₄×D₁₉	—	4	1	no	—
81	C₂×C₄×D₁₉	—	4	1	no	—
82	C₂×C₄×D₁₉	—	4	1	no	—
83	C₂×Dic₃₈	—	2	2	no	—
84	C₂×Dic₃₈	—	4	1	no	—
85	C₂×Dic₃₈	—	8	1	no	—
86	C₂×Dic₃₈	—	8	1	no	—
87	C₂×C₈×C₁₉	—	2	2	no	—
88	C₂×C₈×C₁₉	—	4	1	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₂×C₈×C₁₉	—	4	1	no	—
91	C₂×C₈×C₁₉	—	4	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₄⋊C₄×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	—	4	1	no	—
95	C₄⋊C₄×C₁₉	—	4	1	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	8	1	no	—
98	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₉	#41	1	1	yes	characteristic
101	C₄²×C₁₉	#41	1	1	yes	characteristic
102	(C₂×D₁₉)⋊C₄	—	4	1	no	—
103	(C₂×D₁₉)⋊C₄	—	4	1	no	—
104	C₄⋊Dic₁₉	—	2	1	no	—
105	C₄⋊Dic₁₉	—	2	2	no	—
106	C₄⋊Dic₁₉	—	2	2	no	—
107	C₄⋊Dic₁₉	—	2	1	no	—
108	C₄⋊Dic₁₉	—	4	1	no	—
109	C₄⋊Dic₁₉	—	4	1	no	—
110	C₂×C₁₉⋊C₈	—	2	1	no	—
111	C₂×C₁₉⋊C₈	—	2	1	no	—
112	C₂×C₁₉⋊C₈	—	2	1	no	—
113	C₂×C₁₉⋊C₈	—	2	1	no	—
114	C₂×C₁₉⋊C₈	—	2	1	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	—
119	#10480	—	19	1	no	maximal, Sylow
120	C₂³×C₁₉	#121	1	1	yes	characteristic
121	C₂²×D₁₉	—	2	2	no	—
122	C₂²×D₁₉	—	4	1	no	—
123	C₂²×D₁₉	—	4	1	no	—
124	C₂²×D₁₉	—	4	1	no	—
125	C₂²×D₁₉	—	4	1	no	—
126	C₂²×D₁₉	—	4	1	no	—
127	C₂²×D₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	8	1	no	—
131	C₂×C₄×C₁₉	—	8	1	no	—
132	C₂×C₄×C₁₉	—	8	1	no	—
133	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
138	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
143	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
147	C₂×Dic₁₉	—	4	2	no	—
148	C₂×Dic₁₉	—	4	1	no	—
149	C₂×Dic₁₉	—	4	1	no	—
150	C₂×Dic₁₉	—	4	1	no	—
151	C₂×Dic₁₉	—	8	1	no	—
152	C₂×Dic₁₉	—	8	1	no	—
153	D₇₆	—	2	2	no	—
154	D₇₆	—	2	2	no	—
155	D₇₆	—	4	1	no	—
156	D₇₆	—	4	1	no	—
157	C₄×D₁₉	—	8	1	no	—
158	C₄×D₁₉	—	8	1	no	—
159	C₄×D₁₉	—	8	1	no	—
160	C₄×D₁₉	—	8	1	no	—
161	Dic₃₈	—	8	2	no	—
162	Dic₃₈	—	8	2	no	—
163	C₈×C₁₉	—	4	2	no	—
164	C₈×C₁₉	—	8	1	no	—
165	C₁₉⋊C₈	—	2	2	no	—
166	C₁₉⋊C₈	—	4	1	no	—
167	C₁₉⋊C₈	—	8	1	no	—
168	C₂×#476	—	19	1	no	—
169	#1990	—	19	1	no	—
170	#1954	—	19	1	no	—
171	#1802	—	19	1	no	—
172	C₂×#334	—	19	1	no	—
173	C₂×#333	—	19	1	no	—
174	#1296	D₁₉	1	1	yes	characteristic, complemented
175	C₂²×C₁₉	#394	1	1	yes	characteristic
176	C₂²×C₁₉	#461	1	1	yes	characteristic
177	C₂²×C₁₉	#463	1	1	yes	characteristic
178	C₂²×C₁₉	#465	1	1	yes	characteristic
179	C₂²×C₁₉	#470	1	1	yes	characteristic
180	C₂²×C₁₉	#471	1	1	yes	characteristic
181	C₂²×C₁₉	#472	1	1	yes	characteristic
182	C₂×D₁₉	—	4	2	no	—
183	C₂×D₁₉	—	4	2	no	—
184	C₂×D₁₉	—	4	2	no	—
185	C₂×D₁₉	—	8	1	no	—
186	C₂×D₁₉	—	8	1	no	—
187	C₂×D₁₉	—	8	1	no	—
188	C₂×D₁₉	—	8	1	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	16	1	no	—
192	C₄×C₁₉	#448	1	1	yes	characteristic
193	C₄×C₁₉	#452	1	1	yes	characteristic
194	C₄×C₁₉	#460	1	1	yes	characteristic
195	C₄×C₁₉	#464	1	1	yes	characteristic
196	C₄×C₁₉	#465	1	1	yes	characteristic
197	C₄×C₁₉	#468	1	1	yes	characteristic
198	C₄×C₁₉	#483	1	1	yes	characteristic
199	C₄×C₁₉	#485	1	1	yes	characteristic
200	Dic₁₉	—	8	2	no	—
201	Dic₁₉	—	8	1	no	—
202	C₂×C₄⋊Q₈	—	19	1	no	—
203	C₂×C₄×D₄	—	19	1	no	—
204	#476	—	38	2	no	—
205	#476	—	38	2	no	—
206	C₂×#106	—	38	1	no	—
207	C₂×C₄⋊C₈	—	19	1	no	—
208	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
210	C₂×#102	—	38	1	no	—
211	C₂×#102	—	38	1	no	—
212	C₂×C₂²⋊C₈	—	38	1	no	—
213	C₂×C₂²⋊C₈	—	38	1	no	—
214	C₂×C₄×C₈	—	19	1	no	—
215	#384	C₂×D₁₉	1	1	yes	characteristic
216	#340	—	38	1	no	—
217	#340	—	38	1	no	—
218	#340	—	38	1	no	—
219	#334	—	38	2	no	—
220	#333	—	38	2	no	—
221	C₂×C₁₉	#1671	1	1	yes	characteristic
222	C₂×C₁₉	#1677	1	1	yes	characteristic
223	C₂×C₁₉	#1695	1	1	yes	characteristic
224	C₂×C₁₉	#1703	1	1	yes	characteristic
225	C₂×C₁₉	#2035	1	1	yes	characteristic
226	C₂×C₁₉	#2051	1	1	yes	characteristic
227	C₂×C₁₉	#2055	1	1	yes	characteristic
228	D₁₉	—	8	2	no	—
229	C₂²×Q₈	—	38	1	no	—
230	C₂²×D₄	—	19	1	no	—
231	C₂³×C₄	—	38	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	19	1	no	—
235	C₂²×C₈	—	19	1	no	—
236	C₂²×C₈	—	38	1	no	—
237	C₄⋊Q₈	—	19	2	no	—
238	C₄⋊Q₈	—	38	1	no	—
239	C₄⋊Q₈	—	38	1	no	—
240	C₄⋊Q₈	—	38	1	no	—
241	C₄×D₄	—	38	1	no	—
242	C₄×D₄	—	38	1	no	—
243	C₄×D₄	—	38	1	no	—
244	C₄×D₄	—	38	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	19	1	no	—
249	C₂×C₄⋊C₄	—	38	1	no	—
250	C₂×C₄⋊C₄	—	38	1	no	—
251	C₂×C₂²⋊C₄	—	38	1	no	—
252	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
253	#106	—	38	4	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	38	1	no	—
258	C₄⋊C₈	—	38	1	no	—
259	C₄⋊C₈	D₇₆	1	2	yes	—
260	#102	—	38	4	no	—
261	#102	—	76	2	no	—
262	C₂²⋊C₈	—	76	2	no	—
263	C₂²⋊C₈	—	76	2	no	—
264	C₄×C₈	—	38	1	no	—
265	C₄×C₈	—	38	1	no	—
266	C₁₉	#10480	1	1	yes	characteristic, complemented, Sylow
267	C₂⁴	—	38	1	no	—
268	C₂×Q₈	—	38	2	no	—
269	C₂×Q₈	—	76	1	no	—
270	C₂×Q₈	—	152	1	no	—
271	C₂×Q₈	—	152	1	no	—
272	C₂×D₄	—	19	2	no	—
273	C₂×D₄	—	38	1	no	—
274	C₂×D₄	—	38	1	no	—
275	C₂×D₄	—	38	1	no	—
276	C₂×D₄	—	38	1	no	—
277	C₂×D₄	—	38	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	38	1	no	—
280	C₂²×C₄	—	76	1	no	—
281	C₂²×C₄	—	76	1	no	—
282	C₂²×C₄	—	76	1	no	—
283	C₂²×C₄	—	76	1	no	—
284	C₂²×C₄	—	76	1	no	—
285	C₂²×C₄	—	76	1	no	—
286	C₂²×C₄	—	76	1	no	—
287	C₂²×C₄	#64541	1	1	yes	characteristic
288	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
289	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	19	2	no	—
297	C₂×C₈	—	38	1	no	—
298	C₂×C₈	—	38	1	no	—
299	C₂×C₈	—	38	1	no	—
300	C₂×C₈	—	38	1	no	—
301	C₂×C₈	—	38	1	no	—
302	C₂×C₈	—	76	1	no	—
303	C₂×C₈	—	76	1	no	—
304	C₂×C₈	—	76	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	8	1	no	—
310	C₄⋊C₄	—	38	2	no	—
311	C₄⋊C₄	—	38	1	no	—
312	C₄⋊C₄	—	38	2	no	—
313	C₄⋊C₄	—	38	1	no	—
314	C₄⋊C₄	—	76	1	no	—
315	C₄⋊C₄	—	76	1	no	—
316	C₂²⋊C₄	—	76	1	no	—
317	C₂²⋊C₄	—	76	1	no	—
318	C₄²	C₂×D₇₆	1	1	yes	characteristic
319	C₄²	#64541	1	1	yes	characteristic
320	C₄²	D₄×D₁₉	1	1	yes	characteristic
321	C₄²	#64545	1	1	yes	characteristic
322	C₂³	—	38	2	no	—
323	C₂³	—	76	1	no	—
324	C₂³	—	76	1	no	—
325	C₂³	—	76	1	no	—
326	C₂³	—	76	1	no	—
327	C₂³	—	76	1	no	—
328	C₂³	—	76	1	no	—
329	C₂³	#10597330	1	1	yes	characteristic
330	Q₈	—	152	2	no	—
331	Q₈	—	152	2	no	—
332	D₄	—	38	2	no	—
333	D₄	—	38	2	no	—
334	D₄	—	76	1	no	—
335	D₄	—	76	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	8	1	no	—
339	C₂×C₄	—	8	1	no	—
340	C₂×C₄	—	8	1	no	—
341	C₂×C₄	—	76	1	no	—
342	C₂×C₄	—	76	2	no	—
343	C₂×C₄	—	76	1	no	—
344	C₂×C₄	—	76	1	no	—
345	C₂×C₄	—	152	1	no	—
346	C₂×C₄	—	152	1	no	—
347	C₂×C₄	—	152	1	no	—
348	C₂×C₄	—	152	1	no	—
349	C₂×C₄	—	152	1	no	—
350	C₂×C₄	—	152	1	no	—
351	C₂×C₄	#10597321	1	1	yes	characteristic
352	C₂×C₄	#10597328	1	1	yes	characteristic
353	C₂×C₄	#10597330	1	1	yes	characteristic
354	C₂×C₄	#10597340	1	1	yes	characteristic
355	C₂×C₄	#10597340	1	1	yes	characteristic
356	C₂×C₄	#10597341	1	1	yes	characteristic
357	C₂×C₄	#10597357	1	1	yes	characteristic
358	C₂×C₄	#10597358	1	1	yes	characteristic
359	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
360	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
361	C₂×C₄	#10597361	1	1	yes	characteristic
362	C₂×C₄	#10597362	1	1	yes	characteristic
363	C₂×C₄	#10597364	1	1	yes	characteristic
364	C₂×C₄	#10597364	1	1	yes	characteristic
365	C₈	—	4	2	no	—
366	C₈	—	8	1	no	—
367	C₈	—	38	2	no	—
368	C₈	—	76	1	no	—
369	C₈	—	152	1	no	—
370	C₂²	—	76	2	no	—
371	C₂²	—	76	2	no	—
372	C₂²	—	76	2	no	—
373	C₂²	—	152	1	no	—
374	C₂²	—	152	1	no	—
375	C₂²	—	152	1	no	—
376	C₂²	—	152	1	no	—
377	C₂²	#11926462	1	1	yes	characteristic
378	C₂²	#11926748	1	1	yes	characteristic
379	C₂²	#11926758	1	1	yes	characteristic
380	C₂²	#11926772	1	1	yes	characteristic
381	C₂²	#11926801	1	1	yes	characteristic
382	C₂²	#11926810	1	1	yes	characteristic
383	C₂²	#11926813	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	16	1	no	—
387	C₄	—	152	2	no	—
388	C₄	—	152	1	no	—
389	C₄	#11926684	1	1	yes	characteristic
390	C₄	#11926707	1	1	yes	characteristic
391	C₄	#11926743	1	1	yes	characteristic
392	C₄	#11926769	1	1	yes	characteristic
393	C₄	#11926774	1	1	yes	characteristic
394	C₄	#11926791	1	1	yes	characteristic
395	C₄	#11926876	1	1	yes	characteristic
396	C₄	#11926887	1	1	yes	characteristic
397	C₂	—	152	2	no	—
398	C₂	#14563009	1	1	yes	characteristic
399	C₂	#14563043	1	1	yes	characteristic
400	C₂	#14563157	1	1	yes	characteristic
401	C₂	#14563209	1	1	yes	characteristic
402	C₂	#14564834	1	1	yes	characteristic
403	C₂	#14564930	1	1	yes	characteristic
404	C₂	#14564954	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597330
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₇₆	D₄
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#10480
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #14564595	C₂	semidirect
5. C₂×#11926294	C₂	semidirect
6. C₂×#11926292	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
174. #1296	D₁₉	semidirect
266. C₁₉	#10480	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926835	2
#14564595	2
#14564428	2
#14563632	2
C₂×#11926294	2
C₂×#11926292	2
C₁₉×#1296	2
#10480	19