Subgroups — #18078749

Order 4864.

578 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926750	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926621	C₂	1	1	yes	maximal, characteristic
3	#14564595	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563632	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926289	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64516	—	2	1	no	—
9	C₂²×#64515	—	2	1	no	—
10	C₂×#10597315	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
12	#11926750	—	2	2	no	—
13	#11926750	C₄	1	4	yes	complemented
14	#11926621	—	2	2	no	—
15	#11926621	—	2	2	no	—
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#10597273	—	2	1	no	—
18	C₂×#10597266	—	2	1	no	—
19	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
20	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	#11926306	—	2	1	no	—
22	#11926306	—	2	1	no	—
23	#11926306	—	2	1	no	—
24	#11926289	—	2	2	no	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₂²×D₇₆	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	—	2	1	no	—
30	C₂²×Dic₃₈	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	1	no	—
39	C₂×C₄⋊Dic₁₉	—	2	1	no	—
40	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	—	2	1	no	—
42	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
43	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
44	C₂×#64516	—	2	4	no	—
45	C₂×#64516	—	4	2	no	—
46	C₂×#64516	—	4	2	no	—
47	C₂×#64515	—	2	4	no	—
48	C₂×#64515	—	4	2	no	—
49	C₂×#64515	—	4	2	no	—
50	C₄×D₇₆	—	2	1	no	—
51	C₄×D₇₆	—	2	1	no	—
52	C₄×D₇₆	C₂×C₄	1	2	yes	—
53	C₄×D₇₆	D₄	1	2	yes	—
54	#10597315	—	2	1	no	—
55	#10597315	—	2	1	no	—
56	#10597315	—	2	1	no	—
57	#10597315	C₂×C₄	1	2	yes	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
62	(C₂×D₁₉)⋊C₈	—	2	4	no	—
63	#10597273	—	2	4	no	—
64	#10597266	—	4	2	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₂³×D₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	4	1	no	—
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
74	C₂²×Dic₁₉	—	2	1	no	—
75	C₂²×Dic₁₉	—	4	1	no	—
76	C₂×D₇₆	—	2	1	no	—
77	C₂×D₇₆	—	2	1	no	—
78	C₂×D₇₆	—	2	1	no	—
79	C₂×D₇₆	—	2	1	no	—
80	C₂×D₇₆	—	2	1	no	—
81	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
82	C₂×C₄×D₁₉	—	2	2	no	—
83	C₂×C₄×D₁₉	—	2	2	no	—
84	C₂×C₄×D₁₉	—	4	1	no	—
85	C₂×C₄×D₁₉	—	4	1	no	—
86	C₂×C₄×D₁₉	—	4	1	no	—
87	C₂×C₄×D₁₉	—	4	1	no	—
88	C₂×Dic₃₈	—	2	2	no	—
89	C₂×Dic₃₈	—	4	1	no	—
90	C₂×Dic₃₈	—	4	1	no	—
91	C₂×Dic₃₈	—	4	1	no	—
92	C₂×Dic₃₈	—	4	1	no	—
93	C₂×Dic₃₈	—	4	1	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	8	1	no	—
105	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₉	#41	1	1	yes	characteristic
109	(C₂×D₁₉)⋊C₄	—	2	2	no	—
110	(C₂×D₁₉)⋊C₄	—	2	2	no	—
111	C₄⋊Dic₁₉	—	2	1	no	—
112	C₄⋊Dic₁₉	—	2	2	no	—
113	C₄⋊Dic₁₉	—	2	2	no	—
114	C₄⋊Dic₁₉	—	4	1	no	—
115	C₄⋊Dic₁₉	—	4	1	no	—
116	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
117	C₂×C₁₉⋊C₈	—	2	1	no	—
118	C₂×C₁₉⋊C₈	—	2	1	no	—
119	C₂×C₁₉⋊C₈	—	2	1	no	—
120	C₂×C₁₉⋊C₈	—	2	1	no	—
121	C₂×C₁₉⋊C₈	—	2	1	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	complemented
126	#64516	—	4	8	no	—
127	#64515	—	4	8	no	—
128	#9225	—	19	1	no	maximal, Sylow
129	C₂³×C₁₉	#121	1	1	yes	characteristic
130	C₂²×D₁₉	—	2	2	no	—
131	C₂²×D₁₉	—	4	1	no	—
132	C₂²×D₁₉	—	4	1	no	—
133	C₂²×D₁₉	—	4	1	no	—
134	C₂²×D₁₉	—	4	1	no	—
135	C₂²×D₁₉	—	4	1	no	—
136	C₂²×D₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	8	1	no	—
140	C₂×C₄×C₁₉	—	8	1	no	—
141	C₂×C₄×C₁₉	—	8	1	no	—
142	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
150	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
156	C₂×Dic₁₉	—	2	2	no	—
157	C₂×Dic₁₉	—	4	1	no	—
158	C₂×Dic₁₉	—	4	1	no	—
159	C₂×Dic₁₉	—	4	2	no	—
160	C₂×Dic₁₉	—	8	1	no	—
161	C₂×Dic₁₉	—	8	1	no	—
162	D₇₆	—	2	2	no	—
163	D₇₆	—	2	2	no	—
164	D₇₆	—	4	1	no	—
165	D₇₆	—	4	1	no	—
166	C₄×D₁₉	—	4	2	no	—
167	C₄×D₁₉	—	4	2	no	—
168	C₄×D₁₉	—	4	2	no	—
169	C₄×D₁₉	—	4	2	no	—
170	Dic₃₈	—	4	2	no	—
171	Dic₃₈	—	4	2	no	—
172	Dic₃₈	—	8	1	no	—
173	Dic₃₈	—	8	1	no	—
174	C₈×C₁₉	—	4	2	no	—
175	C₈×C₁₉	—	4	2	no	—
176	C₁₉⋊C₈	—	2	2	no	—
177	C₁₉⋊C₈	—	4	1	no	—
178	C₁₉⋊C₈	—	8	1	no	—
179	C₂×#461	—	19	1	no	—
180	C₂×#436	—	19	1	no	—
181	#1990	—	19	1	no	—
182	#1802	—	19	1	no	—
183	C₂×#332	—	19	1	no	—
184	#1296	D₁₉	1	1	yes	characteristic, complemented
185	#1277	—	19	1	no	—
186	C₂²×C₁₉	#386	1	1	yes	characteristic
187	C₂²×C₁₉	#461	1	1	yes	characteristic
188	C₂²×C₁₉	#463	1	1	yes	characteristic
189	C₂²×C₁₉	#468	1	1	yes	characteristic
190	C₂²×C₁₉	#469	1	1	yes	characteristic
191	C₂²×C₁₉	#471	1	1	yes	characteristic
192	C₂²×C₁₉	#473	1	1	yes	characteristic
193	C₂×D₁₉	—	4	2	no	—
194	C₂×D₁₉	—	4	2	no	—
195	C₂×D₁₉	—	4	2	no	—
196	C₂×D₁₉	—	8	1	no	—
197	C₂×D₁₉	—	8	1	no	—
198	C₂×D₁₉	—	8	1	no	—
199	C₂×D₁₉	—	8	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	16	1	no	—
203	C₄×C₁₉	#417	1	1	yes	characteristic
204	C₄×C₁₉	#418	1	1	yes	characteristic
205	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
206	C₄×C₁₉	#440	1	1	yes	characteristic
207	C₄×C₁₉	#450	1	1	yes	characteristic
208	C₄×C₁₉	#452	1	1	yes	characteristic
209	C₄×C₁₉	#468	1	1	yes	characteristic
210	C₄×C₁₉	#469	1	1	yes	characteristic
211	Dic₁₉	—	4	2	no	—
212	Dic₁₉	—	8	2	no	—
213	C₂²×SD₁₆	—	38	1	no	—
214	C₂²×M₁₆	—	38	1	no	—
215	C₂×C₄⋊Q₈	—	19	1	no	—
216	C₂×C₄×D₄	—	19	1	no	—
217	#461	—	19	4	no	—
218	#461	—	38	2	no	—
219	#436	—	38	2	no	—
220	#436	—	38	2	no	—
221	C₂×C₄⋊C₈	—	19	1	no	—
222	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
224	C₂×#103	—	38	1	no	—
225	C₂×#102	—	38	1	no	—
226	C₂×C₂²⋊C₈	—	38	1	no	—
227	C₂×C₄×C₈	—	19	1	no	—
228	#384	C₂×D₁₉	1	1	yes	characteristic
229	#340	—	38	1	no	—
230	#340	—	38	1	no	—
231	#340	—	38	1	no	—
232	#332	—	38	2	no	—
233	C₂×C₁₉	#1691	1	1	yes	characteristic
234	C₂×C₁₉	#1693	1	1	yes	characteristic
235	C₂×C₁₉	#1699	1	1	yes	characteristic
236	C₂×C₁₉	#1701	1	1	yes	characteristic
237	C₂×C₁₉	#1877	1	1	yes	characteristic
238	C₂×C₁₉	#1895	1	1	yes	characteristic
239	C₂×C₁₉	#1908	1	1	yes	characteristic
240	D₁₉	—	8	2	no	—
241	C₂²×Q₈	—	38	1	no	—
242	C₂²×D₄	—	19	1	no	—
243	C₂³×C₄	—	38	1	no	—
244	C₂×SD₁₆	—	38	4	no	—
245	C₂×SD₁₆	—	76	2	no	—
246	C₂×SD₁₆	—	76	2	no	—
247	C₂×M₁₆	—	38	4	no	—
248	C₂×M₁₆	—	76	2	no	—
249	C₂×M₁₆	—	76	2	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	19	1	no	—
253	C₂²×C₈	—	19	1	no	—
254	C₂²×C₈	—	38	1	no	—
255	C₄⋊Q₈	—	19	2	no	—
256	C₄⋊Q₈	—	38	1	no	—
257	C₄⋊Q₈	—	38	1	no	—
258	C₄⋊Q₈	—	38	1	no	—
259	C₄×D₄	—	19	2	no	—
260	C₄×D₄	—	19	2	no	—
261	C₄×D₄	—	38	1	no	—
262	C₄×D₄	—	38	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	19	1	no	—
267	C₂×C₄⋊C₄	—	38	1	no	—
268	C₂×C₄⋊C₄	—	38	1	no	—
269	C₂×C₂²⋊C₄	—	38	1	no	—
270	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	38	1	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
276	C₄⋊C₈	D₇₆	1	2	yes	—
277	#103	—	38	4	no	—
278	#102	—	76	2	no	—
279	C₂²⋊C₈	—	38	4	no	—
280	C₄×C₈	—	38	1	no	—
281	C₄×C₈	—	38	1	no	—
282	C₁₉	#9225	1	1	yes	characteristic, complemented, Sylow
283	C₂⁴	—	38	1	no	—
284	C₂×Q₈	—	38	2	no	—
285	C₂×Q₈	—	76	1	no	—
286	C₂×Q₈	—	76	1	no	—
287	C₂×Q₈	—	76	1	no	—
288	C₂×Q₈	—	76	1	no	—
289	C₂×Q₈	—	76	1	no	—
290	C₂×D₄	—	19	2	no	—
291	C₂×D₄	—	38	1	no	—
292	C₂×D₄	—	38	1	no	—
293	C₂×D₄	—	38	1	no	—
294	C₂×D₄	—	38	1	no	—
295	C₂×D₄	—	38	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	38	1	no	—
298	C₂²×C₄	—	38	2	no	—
299	C₂²×C₄	—	38	2	no	—
300	C₂²×C₄	—	76	1	no	—
301	C₂²×C₄	—	76	1	no	—
302	C₂²×C₄	—	76	1	no	—
303	C₂²×C₄	—	76	1	no	—
304	C₂²×C₄	—	76	1	no	—
305	C₂²×C₄	#64541	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
308	SD₁₆	—	76	8	no	—
309	M₁₆	—	76	8	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	19	2	no	—
317	C₂×C₈	—	38	1	no	—
318	C₂×C₈	—	38	1	no	—
319	C₂×C₈	—	38	1	no	—
320	C₂×C₈	—	38	1	no	—
321	C₂×C₈	—	38	1	no	—
322	C₂×C₈	—	76	1	no	—
323	C₂×C₈	—	76	1	no	—
324	C₂×C₈	—	76	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	8	1	no	—
330	C₄⋊C₄	—	19	2	no	—
331	C₄⋊C₄	—	38	1	no	—
332	C₄⋊C₄	—	38	2	no	—
333	C₄⋊C₄	—	38	2	no	—
334	C₄⋊C₄	—	76	1	no	—
335	C₄⋊C₄	—	76	1	no	—
336	C₂²⋊C₄	—	38	2	no	—
337	C₂²⋊C₄	—	38	2	no	—
338	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
339	C₄²	C₂×D₇₆	1	1	yes	characteristic
340	C₄²	D₄×D₁₉	1	1	yes	characteristic
341	C₄²	#64545	1	1	yes	characteristic
342	C₂³	—	38	2	no	—
343	C₂³	—	76	1	no	—
344	C₂³	—	76	1	no	—
345	C₂³	—	76	1	no	—
346	C₂³	—	76	1	no	—
347	C₂³	—	76	1	no	—
348	C₂³	—	76	1	no	—
349	C₂³	#10597330	1	1	yes	characteristic
350	Q₈	—	76	2	no	—
351	Q₈	—	76	2	no	—
352	Q₈	—	152	1	no	—
353	Q₈	—	152	1	no	—
354	D₄	—	38	2	no	—
355	D₄	—	38	2	no	—
356	D₄	—	76	1	no	—
357	D₄	—	76	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	8	1	no	—
363	C₂×C₄	—	38	2	no	—
364	C₂×C₄	—	76	1	no	—
365	C₂×C₄	—	76	1	no	—
366	C₂×C₄	—	76	2	no	—
367	C₂×C₄	—	76	2	no	—
368	C₂×C₄	—	76	2	no	—
369	C₂×C₄	—	76	2	no	—
370	C₂×C₄	—	76	2	no	—
371	C₂×C₄	—	152	1	no	—
372	C₂×C₄	—	152	1	no	—
373	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
374	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
375	C₂×C₄	#10597328	1	1	yes	characteristic
376	C₂×C₄	#10597339	1	1	yes	characteristic
377	C₂×C₄	#10597340	1	1	yes	characteristic
378	C₂×C₄	#10597341	1	1	yes	characteristic
379	C₂×C₄	#10597357	1	1	yes	characteristic
380	C₂×C₄	#10597357	1	1	yes	characteristic
381	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
382	C₂×C₄	#10597360	1	1	yes	characteristic
383	C₂×C₄	#10597360	1	1	yes	characteristic
384	C₂×C₄	#10597362	1	1	yes	characteristic
385	C₂×C₄	#10597364	1	1	yes	characteristic
386	C₂×C₄	#10597364	1	1	yes	characteristic
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	38	2	no	—
390	C₈	—	76	1	no	—
391	C₈	—	152	1	no	—
392	C₂²	—	76	2	no	—
393	C₂²	—	76	2	no	—
394	C₂²	—	76	2	no	—
395	C₂²	—	152	1	no	—
396	C₂²	—	152	1	no	—
397	C₂²	—	152	1	no	—
398	C₂²	—	152	1	no	—
399	C₂²	#11926422	1	1	yes	characteristic
400	C₂²	#11926748	1	1	yes	characteristic
401	C₂²	#11926758	1	1	yes	characteristic
402	C₂²	#11926793	1	1	yes	characteristic
403	C₂²	#11926796	1	1	yes	characteristic
404	C₂²	#11926806	1	1	yes	characteristic
405	C₂²	#11926818	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	16	1	no	—
409	C₄	—	76	2	no	—
410	C₄	—	152	2	no	—
411	C₄	#11926544	1	1	yes	characteristic
412	C₄	#11926547	1	1	yes	characteristic
413	C₄	#11926631	1	1	yes	characteristic
414	C₄	#11926643	1	1	yes	characteristic
415	C₄	#11926696	1	1	yes	characteristic
416	C₄	#11926709	1	1	yes	characteristic
417	C₄	#11926791	1	1	yes	characteristic
418	C₄	#11926798	1	1	yes	characteristic
419	C₂	—	152	2	no	—
420	C₂	#14563137	1	1	yes	characteristic
421	C₂	#14563147	1	1	yes	characteristic
422	C₂	#14563181	1	1	yes	characteristic
423	C₂	#14563195	1	1	yes	characteristic
424	C₂	#14563970	1	1	yes	characteristic
425	C₂	#14564072	1	1	yes	characteristic
426	C₂	#14564151	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597330
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#9225
LCS	G ▷ 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
3. #14564595	C₂	semidirect
5. C₂×#11926289	C₂	semidirect
6. #14561469	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
13. #11926750	C₄	semidirect
125. C₂×C₁₉⋊C₈	SD₁₆	semidirect
184. #1296	D₁₉	semidirect
282. C₁₉	#9225	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926750	2
C₂×#11926621	2
#14564595	2
#14563632	2
C₂×#11926289	2
#14561469	2
C₁₉×#1296	2
#9225	19