Subgroups — #14574423

Order 2432.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927055	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926885	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926882	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926868	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926865	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926783	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926778	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926775	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926771	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926706	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926704	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926689	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926687	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×#64541	C₂²	1	1	yes	characteristic
19	C₁₉×#123	—	2	1	no	—
20	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₁₉×#120	—	2	1	no	—
25	C₄×D₄×C₁₉	—	2	1	no	—
26	C₄×D₄×C₁₉	—	2	1	no	—
27	C₁₉×#117	C₂²	1	1	yes	characteristic
28	#10597399	—	2	1	no	—
29	C₂×#64528	C₂²	1	1	yes	characteristic, complemented
30	C₂×#64527	C₂²	1	1	yes	characteristic, complemented
31	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
32	C₂×#64525	C₂²	1	1	yes	characteristic, complemented
33	#10597376	C₂²	1	1	yes	characteristic
34	#10597376	C₂²	1	1	yes	characteristic
35	#10597375	—	2	1	no	—
36	C₄×C₂²⋊D₁₉	—	2	1	no	—
37	C₄×C₂²⋊D₁₉	—	2	1	no	—
38	#10597372	C₂²	1	1	yes	characteristic
39	#10597370	C₂²	1	1	yes	characteristic
40	#10597370	C₂²	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
42	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
43	#10597292	C₂²	1	1	yes	characteristic, complemented
44	#10597292	C₂²	1	1	yes	characteristic, complemented
45	#10597289	C₂²	1	1	yes	characteristic, complemented
46	#10597289	C₂²	1	1	yes	characteristic, complemented
47	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
48	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
49	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
50	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
51	#10597267	C₂²	1	1	yes	characteristic, complemented
52	#10597267	C₂²	1	1	yes	characteristic, complemented
53	#10597266	C₂²	1	1	yes	characteristic, complemented
54	#10597266	C₂²	1	1	yes	characteristic, complemented
55	#10597265	C₂²	1	1	yes	characteristic, complemented
56	#10597265	C₂²	1	1	yes	characteristic, complemented
57	#10597264	C₂²	1	1	yes	characteristic, complemented
58	#10597264	C₂²	1	1	yes	characteristic, complemented
59	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
60	#41×C₁₉	—	4	1	no	—
61	#41×C₁₉	—	4	1	no	—
62	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₉	—	2	1	no	—
64	C₂×D₄×C₁₉	—	2	1	no	—
65	C₂×D₄×C₁₉	—	2	1	no	—
66	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	4	1	no	—
69	C₂²×C₄×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊D₁₉	—	2	1	no	—
77	C₂×C₂²⋊D₁₉	—	2	1	no	—
78	C₂×C₂²⋊D₁₉	—	2	1	no	—
79	#64541	—	4	1	no	—
80	#64541	—	4	1	no	—
81	C₂×D₇₆	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₁₉	—	2	1	no	—
83	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₄²×C₁₉	—	2	1	no	—
94	C₂²⋊Dic₁₉	—	2	1	no	—
95	C₂²⋊Dic₁₉	—	2	1	no	—
96	C₂²⋊Dic₁₉	—	2	1	no	—
97	#64528	—	4	1	no	—
98	#64527	—	4	1	no	—
99	#64526	—	4	1	no	—
100	#64525	—	4	1	no	—
101	(C₂×D₁₉)⋊C₄	—	2	1	no	—
102	(C₂×D₁₉)⋊C₄	—	2	1	no	—
103	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
105	Dic₁₉⋊C₄	—	2	1	no	—
106	Dic₁₉⋊C₄	—	2	1	no	—
107	C₄×Dic₁₉	—	2	1	no	—
108	C₂×C₁₉⋊C₈	—	4	1	no	—
109	C₂×C₁₉⋊C₈	—	4	1	no	—
110	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
112	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
113	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
114	C₂³×C₁₉	—	2	2	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	4	1	no	—
117	C₂³×C₁₉	—	4	1	no	—
118	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×D₁₉	—	2	1	no	—
122	Q₈×C₁₉	—	2	1	no	—
123	Q₈×C₁₉	—	2	1	no	—
124	D₄×C₁₉	—	2	1	no	—
125	D₄×C₁₉	—	2	1	no	—
126	D₄×C₁₉	—	4	2	no	—
127	D₄×C₁₉	—	4	2	no	—
128	D₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₂²⋊D₁₉	—	4	2	no	—
147	C₂²⋊D₁₉	—	4	2	no	—
148	C₂²⋊D₁₉	—	4	2	no	—
149	C₂×Dic₁₉	—	2	1	no	—
150	C₂×Dic₁₉	—	2	1	no	—
151	C₂×Dic₁₉	—	2	1	no	—
152	D₇₆	—	2	1	no	—
153	D₇₆	—	2	1	no	—
154	C₄×D₁₉	—	4	2	no	—
155	Dic₃₈	—	2	1	no	—
156	Dic₃₈	—	2	1	no	—
157	C₁₉⋊C₈	—	2	1	no	—
158	C₁₉⋊C₈	—	2	1	no	—
159	C₁₉⋊C₈	—	2	1	no	—
160	C₁₉⋊C₈	—	2	1	no	—
161	#3191	—	19	1	no	maximal, Sylow
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	4	4	no	—
171	C₂²×C₁₉	—	4	1	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	1	no	—
174	C₂²×C₁₉	#135	1	2	yes	—
175	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×D₁₉	—	4	1	no	—
177	C₂×D₁₉	—	4	1	no	—
178	C₂×D₁₉	—	4	1	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	2	1	no	—
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	4	1	no	—
183	C₄×C₁₉	—	4	1	no	—
184	C₄×C₁₉	—	4	1	no	—
185	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
186	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
187	Dic₁₉	—	4	1	no	—
188	Dic₁₉	—	4	1	no	—
189	Dic₁₉	—	4	1	no	—
190	#525	—	19	1	no	—
191	#525	D₁₉	1	1	yes	characteristic, complemented
192	#485	—	19	1	no	—
193	#485	—	19	1	no	—
194	#482	—	19	1	no	—
195	#482	—	19	1	no	—
196	#467	—	19	1	no	—
197	#466	—	19	1	no	—
198	#465	—	19	1	no	—
199	#465	—	19	1	no	—
200	#452	—	19	1	no	—
201	#452	—	19	1	no	—
202	#449	—	19	1	no	—
203	#449	—	19	1	no	—
204	C₂×C₂²⋊C₈	—	19	1	no	—
205	C₂×C₁₉	—	2	2	no	—
206	C₂×C₁₉	—	4	1	no	—
207	C₂×C₁₉	—	4	1	no	—
208	C₂×C₁₉	—	8	1	no	—
209	C₂×C₁₉	#534	1	1	yes	characteristic
210	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
211	C₂×C₁₉	#575	1	1	yes	characteristic
212	D₁₉	—	8	1	no	—
213	C₂×#41	—	19	1	no	—
214	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
215	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
216	C₂×Q₁₆	—	19	1	no	—
217	C₂×SD₁₆	—	19	1	no	—
218	C₂×SD₁₆	—	19	1	no	—
219	C₂×D₈	—	19	1	no	—
220	C₂²×C₈	—	19	1	no	—
221	C₂²×C₈	—	19	1	no	—
222	#123	—	2	1	no	—
223	#123	—	38	1	no	—
224	C₂²⋊Q₈	—	19	1	no	—
225	C₂²⋊Q₈	—	19	1	no	—
226	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
227	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
228	#121	—	19	1	no	—
229	#121	—	19	1	no	—
230	#121	C₂×D₁₉	1	1	yes	characteristic
231	#121	C₂×D₁₉	1	1	yes	characteristic
232	#120	—	2	1	no	—
233	#120	—	38	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	38	1	no	—
237	C₄×D₄	—	38	1	no	—
238	#117	—	19	1	no	—
239	#117	C₂×D₁₉	1	1	yes	characteristic
240	#107	—	19	1	no	—
241	#107	—	19	1	no	—
242	#106	—	19	1	no	—
243	#106	—	19	1	no	—
244	#103	—	19	1	no	—
245	#103	—	19	1	no	—
246	#103	—	19	1	no	—
247	#103	—	19	1	no	—
248	#102	—	19	1	no	—
249	#102	—	19	1	no	—
250	#102	—	19	1	no	—
251	#102	—	19	1	no	—
252	C₂²⋊C₈	—	19	1	no	—
253	C₂²⋊C₈	—	19	1	no	—
254	C₂²⋊C₈	—	19	1	no	—
255	C₂²⋊C₈	—	19	1	no	—
256	C₁₉	#3191	1	1	yes	characteristic, complemented, Sylow
257	C₂⁴	C₂²⋊D₁₉	1	1	yes	characteristic
258	#41	—	4	1	no	—
259	#41	—	4	1	no	—
260	#41	—	76	1	no	—
261	#41	—	76	1	no	—
262	C₂×Q₈	—	19	1	no	—
263	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	19	1	no	—
268	C₂×D₄	—	38	1	no	—
269	C₂×D₄	—	38	1	no	—
270	C₂×D₄	—	38	1	no	—
271	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	38	1	no	—
276	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
279	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
282	Q₁₆	—	76	1	no	—
283	SD₁₆	—	76	1	no	—
284	SD₁₆	—	76	1	no	—
285	D₈	—	76	1	no	—
286	C₂×C₈	—	19	1	no	—
287	C₂×C₈	—	19	1	no	—
288	C₂×C₈	—	19	1	no	—
289	C₂×C₈	—	19	1	no	—
290	C₂×C₈	—	76	1	no	—
291	C₂×C₈	—	76	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	19	1	no	—
295	C₄⋊C₄	—	19	1	no	—
296	C₄⋊C₄	—	38	1	no	—
297	C₄⋊C₄	—	38	1	no	—
298	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
299	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	38	1	no	—
306	C₂²⋊C₄	—	38	1	no	—
307	C₂²⋊C₄	—	38	1	no	—
308	C₂²⋊C₄	—	38	1	no	—
309	C₂²⋊C₄	—	38	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	38	1	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	38	1	no	—
317	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
319	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
320	Q₈	—	2	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	38	1	no	—
323	Q₈	—	38	1	no	—
324	D₄	—	2	1	no	—
325	D₄	—	2	1	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	38	1	no	—
330	D₄	—	38	1	no	—
331	D₄	—	76	2	no	—
332	D₄	—	76	2	no	—
333	D₄	—	76	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	38	1	no	—
348	C₂×C₄	—	38	1	no	—
349	C₂×C₄	—	38	1	no	—
350	C₂×C₄	—	76	2	no	—
351	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
352	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
353	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
354	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
355	C₈	—	38	1	no	—
356	C₈	—	38	1	no	—
357	C₈	—	38	1	no	—
358	C₈	—	38	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	76	1	no	—
372	C₂²	—	76	1	no	—
373	C₂²	—	76	1	no	—
374	C₂²	#10597396	1	2	yes	—
375	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	76	1	no	—
383	C₄	—	76	1	no	—
384	C₄	—	76	1	no	—
385	C₄	#10597430	1	1	yes	characteristic
386	C₄	#10597430	1	1	yes	characteristic
387	C₂	—	2	2	no	—
388	C₂	—	4	1	no	—
389	C₂	—	4	1	no	—
390	C₂	—	8	1	no	—
391	C₂	—	152	1	no	—
392	C₂	#11927103	1	1	yes	characteristic
393	C₂	C₂×#10597396	1	1	yes	characteristic
394	C₂	#11927342	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#525	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#525	D₁₉
hypocenter	C₁₉	#3191
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #11927055	C₂	semidirect
2. #11926885	C₂	semidirect
3. #11926882	C₂	semidirect
4. #11926868	C₂	semidirect
5. #11926865	C₂	semidirect
6. #11926783	C₂	semidirect
7. #11926778	C₂	semidirect
8. #11926775	C₂	semidirect
9. #11926771	C₂	semidirect
10. #11926706	C₂	semidirect
11. #11926704	C₂	semidirect
12. #11926689	C₂	semidirect
13. #11926687	C₂	semidirect
14. C₂×C₂²⋊(C₁₉⋊C₈)	C₂	semidirect
15. C₁₉×#525	C₂	semidirect
29. C₂×#64528	C₂²	semidirect
30. C₂×#64527	C₂²	semidirect
31. C₂×#64526	C₂²	semidirect
32. C₂×#64525	C₂²	semidirect
43. #10597292	C₂²	semidirect
44. #10597292	C₂²	semidirect
45. #10597289	C₂²	semidirect
46. #10597289	C₂²	semidirect
51. #10597267	C₂²	semidirect
52. #10597267	C₂²	semidirect
53. #10597266	C₂²	semidirect
54. #10597266	C₂²	semidirect
55. #10597265	C₂²	semidirect
56. #10597265	C₂²	semidirect
57. #10597264	C₂²	semidirect
58. #10597264	C₂²	semidirect
191. #525	D₁₉	semidirect
256. C₁₉	#3191	semidirect

Maximal subgroups

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

subgroup	index
#11927055	2
#11926885	2
#11926882	2
#11926868	2
#11926865	2
#11926783	2
#11926778	2
#11926775	2
#11926771	2
#11926706	2
#11926704	2
#11926689	2
#11926687	2
C₂×C₂²⋊(C₁₉⋊C₈)	2
C₁₉×#525	2
#3191	19