Subgroups — #18088266

Order 4864.

894 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926306	C₂	1	2	yes	maximal
3	C₂×#11926306	C₂	1	2	yes	maximal
4	#14561865	C₂	1	1	yes	maximal, characteristic
5	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	—	2	4	no	—
10	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	complemented
11	C₂×C₁₉⋊#95	—	2	1	no	—
12	C₂×C₁₉⋊#95	—	2	1	no	—
13	#11926306	—	2	4	no	—
14	#11926306	C₄	1	8	yes	complemented
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#95	—	2	1	no	—
18	C₂×C₁₉×#95	—	2	1	no	—
19	C₂³×C₄×C₁₉	—	2	2	no	—
20	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂³×Dic₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
34	C₂×C₄⋊Dic₁₉	—	2	2	no	—
35	C₂×C₄⋊Dic₁₉	—	2	2	no	—
36	C₂×C₄⋊Dic₁₉	—	2	2	no	—
37	C₂×C₄⋊Dic₁₉	—	2	2	no	—
38	C₂×C₄⋊Dic₁₉	—	2	2	no	—
39	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
40	C₂²×C₁₉⋊C₈	—	2	2	no	—
41	C₂²×C₁₉⋊C₈	—	2	1	no	—
42	C₂²×C₁₉⋊C₈	—	2	1	no	—
43	C₂²×C₁₉⋊C₈	—	2	2	no	—
44	C₂²×C₁₉⋊C₈	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
47	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
48	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
49	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
50	C₁₉×#95	—	4	2	no	—
51	C₁₉×#95	—	4	2	no	—
52	C₁₉⋊#95	—	4	2	no	—
53	C₁₉⋊#95	—	4	2	no	—
54	C₄×C₁₉⋊C₈	—	2	8	no	—
55	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	4	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	—	4	2	no	—
63	C₂²×C₄×C₁₉	—	4	2	no	—
64	C₂²×C₄×C₁₉	—	4	2	no	—
65	C₂²×C₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	—	4	2	no	—
67	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₉	D₈	1	2	yes	—
70	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
73	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	#41	1	2	yes	—
78	C₂²×C₄×C₁₉	#41	1	2	yes	—
79	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
83	C₂²×Dic₁₉	—	2	4	no	—
84	C₂²×Dic₁₉	—	4	2	no	—
85	C₂²×Dic₁₉	—	4	2	no	—
86	C₂²×Dic₁₉	—	4	2	no	—
87	C₂²×Dic₁₉	—	4	2	no	—
88	C₂²×Dic₁₉	—	4	2	no	—
89	C₂²×Dic₁₉	—	4	2	no	—
90	C₄⋊C₄×C₁₉	—	2	4	no	—
91	C₄⋊C₄×C₁₉	—	2	4	no	—
92	C₄⋊C₄×C₁₉	—	4	2	no	—
93	C₄⋊C₄×C₁₉	—	4	2	no	—
94	C₄²×C₁₉	—	2	2	no	—
95	C₄²×C₁₉	—	2	2	no	—
96	C₄²×C₁₉	—	2	4	no	—
97	C₄⋊Dic₁₉	—	2	4	no	—
98	C₄⋊Dic₁₉	—	2	4	no	—
99	C₄⋊Dic₁₉	—	4	2	no	—
100	C₄⋊Dic₁₉	—	4	2	no	—
101	C₂×C₁₉⋊C₈	—	2	2	no	—
102	C₂×C₁₉⋊C₈	—	2	2	no	—
103	C₂×C₁₉⋊C₈	—	2	2	no	—
104	C₂×C₁₉⋊C₈	—	2	2	no	—
105	C₂×C₁₉⋊C₈	—	2	4	no	—
106	C₂×C₁₉⋊C₈	—	2	4	no	—
107	C₂×C₁₉⋊C₈	—	2	4	no	—
108	C₂×C₁₉⋊C₈	—	2	4	no	—
109	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
110	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
111	#10820	—	19	1	no	maximal, Sylow
112	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂³×C₁₉	C₄×D₄	1	2	yes	—
114	C₂³×C₁₉	#121	1	2	yes	—
115	C₂³×C₁₉	#124	1	1	yes	characteristic
116	C₂³×C₁₉	#124	1	1	yes	characteristic
117	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
118	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
119	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
120	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
121	C₂³×C₁₉	#135	1	2	yes	—
122	C₂³×C₁₉	#135	1	2	yes	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	4	no	—
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	2	4	no	—
131	C₂×C₄×C₁₉	—	4	4	no	—
132	C₂×C₄×C₁₉	—	4	4	no	—
133	C₂×C₄×C₁₉	—	4	4	no	—
134	C₂×C₄×C₁₉	—	8	2	no	—
135	C₂×C₄×C₁₉	—	8	2	no	—
136	C₂×C₄×C₁₉	—	8	2	no	—
137	C₂×C₄×C₁₉	—	8	2	no	—
138	C₂×C₄×C₁₉	#106	1	4	yes	—
139	C₂×C₄×C₁₉	#107	1	4	yes	—
140	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#117	1	2	yes	—
145	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#117	1	2	yes	—
147	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
152	C₂×C₄×C₁₉	#123	1	2	yes	—
153	C₂×C₄×C₁₉	#123	1	2	yes	—
154	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#126	1	2	yes	—
157	C₂×C₄×C₁₉	#126	1	2	yes	—
158	C₂×Dic₁₉	—	4	4	no	—
159	C₂×Dic₁₉	—	4	4	no	—
160	C₂×Dic₁₉	—	4	4	no	—
161	C₂×Dic₁₉	—	8	2	no	—
162	C₂×Dic₁₉	—	8	2	no	—
163	C₂×Dic₁₉	—	8	2	no	—
164	C₂×Dic₁₉	—	8	2	no	—
165	C₁₉⋊C₈	—	2	4	no	—
166	C₁₉⋊C₈	—	2	4	no	—
167	C₂²×C₄×C₈	—	19	1	no	—
168	C₂×#340	—	19	2	no	—
169	C₂×#340	—	19	2	no	—
170	C₄⋊#95	—	19	1	no	—
171	C₄⋊#95	D₁₉	1	1	yes	characteristic
172	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₁₉	#380	1	1	yes	characteristic
174	C₂²×C₁₉	#382	1	1	yes	characteristic
175	C₂²×C₁₉	#388	1	2	yes	—
176	C₂²×C₁₉	#388	1	2	yes	—
177	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
179	C₂²×C₁₉	#427	1	1	yes	characteristic
180	C₂²×C₁₉	#427	1	1	yes	characteristic
181	C₂²×C₁₉	C₄×D₈	1	2	yes	—
182	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
183	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
184	C₂²×C₁₉	C₄×Q₁₆	1	2	yes	—
185	C₂²×C₁₉	#465	1	2	yes	—
186	C₂²×C₁₉	#465	1	2	yes	—
187	C₂²×C₁₉	#466	1	2	yes	—
188	C₂²×C₁₉	#467	1	2	yes	—
189	C₂²×C₁₉	#486	1	1	yes	characteristic
190	C₂²×C₁₉	#486	1	1	yes	characteristic
191	C₂²×C₁₉	#487	1	1	yes	characteristic
192	C₂²×C₁₉	#487	1	1	yes	characteristic
193	C₂²×C₁₉	#488	1	2	yes	—
194	C₂²×C₁₉	#488	1	2	yes	—
195	C₄×C₁₉	—	2	4	no	—
196	C₄×C₁₉	—	2	4	no	—
197	C₄×C₁₉	—	8	4	no	—
198	C₄×C₁₉	#376	1	1	yes	characteristic
199	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
200	C₄×C₁₉	#381	1	1	yes	characteristic
201	C₄×C₁₉	#383	1	1	yes	characteristic
202	C₄×C₁₉	#387	1	2	yes	—
203	C₄×C₁₉	#387	1	2	yes	—
204	Dic₁₉	—	8	4	no	—
205	C₂³×C₈	—	19	1	no	—
206	C₂³×C₈	—	19	1	no	—
207	C₂²×C₄⋊C₄	—	19	2	no	—
208	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
209	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
210	C₂×C₄×C₈	—	19	4	no	—
211	C₂×C₄×C₈	—	38	4	no	—
212	C₂×#95	—	2	1	no	—
213	C₂×#95	—	2	1	no	—
214	C₂×#95	—	38	1	no	—
215	C₂×#95	—	38	1	no	—
216	#340	—	19	8	no	—
217	#340	—	38	4	no	—
218	C₂×C₁₉	#1434	1	1	yes	characteristic
219	C₂×C₁₉	C₄×#106	1	1	yes	characteristic
220	C₂×C₁₉	C₄×#107	1	1	yes	characteristic
221	C₂×C₁₉	#1807	1	1	yes	characteristic
222	C₂×C₁₉	#1808	1	1	yes	characteristic
223	C₂×C₁₉	#1834	1	1	yes	characteristic
224	C₂×C₁₉	#1835	1	1	yes	characteristic
225	C₂×C₁₉	#1933	1	2	yes	—
226	C₂×C₁₉	#1933	1	2	yes	—
227	C₂×C₁₉	#1934	1	2	yes	—
228	C₂×C₁₉	#1934	1	2	yes	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	38	2	no	—
231	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
234	C₂²×C₈	—	19	4	no	—
235	C₂²×C₈	—	19	2	no	—
236	C₂²×C₈	—	19	2	no	—
237	C₂²×C₈	—	19	4	no	—
238	C₂²×C₈	—	38	2	no	—
239	C₂²×C₈	—	38	2	no	—
240	C₂²×C₈	—	38	1	no	—
241	C₂²×C₈	—	38	1	no	—
242	C₂²×C₈	—	38	1	no	—
243	C₂²×C₈	—	38	1	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	19	4	no	—
250	C₂×C₄⋊C₄	—	38	2	no	—
251	C₂×C₄⋊C₄	—	38	2	no	—
252	C₂×C₄⋊C₄	—	38	2	no	—
253	C₂×C₄⋊C₄	—	38	2	no	—
254	C₂×C₄⋊C₄	—	38	2	no	—
255	C₂×C₄⋊C₄	C₄×D₁₉	1	4	yes	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	Dic₃₈	1	2	yes	—
259	C₂×C₄²	C₄×D₁₉	1	2	yes	—
260	C₄×C₈	—	38	8	no	—
261	#95	—	4	2	no	—
262	#95	—	4	2	no	—
263	#95	—	76	2	no	—
264	#95	—	76	2	no	—
265	C₁₉	#10820	1	1	yes	characteristic, complemented, Sylow
266	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	38	4	no	—
279	C₂²×C₄	—	76	2	no	—
280	C₂²×C₄	—	76	2	no	—
281	C₂²×C₄	—	76	2	no	—
282	C₂²×C₄	—	76	2	no	—
283	C₂²×C₄	—	76	2	no	—
284	C₂²×C₄	—	76	2	no	—
285	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
286	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
287	C₂²×C₄	#64525	1	2	yes	—
288	C₂²×C₄	#64526	1	2	yes	—
289	C₂²×C₄	#64527	1	2	yes	—
290	C₂²×C₄	#64528	1	2	yes	—
291	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
293	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
294	C₂²×C₄	#64541	1	2	yes	—
295	C₂²×C₄	D₄×D₁₉	1	2	yes	—
296	C₂²×C₄	#64543	1	2	yes	—
297	C₂²×C₄	#64543	1	1	yes	characteristic
298	C₂²×C₄	#64543	1	1	yes	characteristic
299	C₂²×C₄	#64545	1	1	yes	characteristic
300	C₂²×C₄	#64545	1	1	yes	characteristic
301	C₂×C₈	—	19	4	no	—
302	C₂×C₈	—	19	4	no	—
303	C₂×C₈	—	38	2	no	—
304	C₂×C₈	—	38	2	no	—
305	C₂×C₈	—	38	4	no	—
306	C₂×C₈	—	38	4	no	—
307	C₂×C₈	—	38	2	no	—
308	C₂×C₈	—	38	2	no	—
309	C₂×C₈	—	38	4	no	—
310	C₂×C₈	—	38	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	38	4	no	—
316	C₄⋊C₄	—	38	4	no	—
317	C₄⋊C₄	—	76	2	no	—
318	C₄⋊C₄	—	76	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	4	no	—
321	C₄²	—	2	2	no	—
322	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
323	C₂³	C₄×C₂²⋊D₁₉	1	2	yes	—
324	C₂³	C₂×#64525	1	1	yes	characteristic
325	C₂³	C₂×#64526	1	1	yes	characteristic
326	C₂³	#10597382	1	1	yes	characteristic
327	C₂³	#10597385	1	2	yes	—
328	C₂³	C₂×#64527	1	1	yes	characteristic
329	C₂³	C₂×#64528	1	1	yes	characteristic
330	C₂³	#10597393	1	1	yes	characteristic
331	C₂³	#10597396	1	2	yes	—
332	C₂³	#10597396	1	2	yes	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	76	4	no	—
349	C₂×C₄	—	76	4	no	—
350	C₂×C₄	—	76	4	no	—
351	C₂×C₄	—	152	2	no	—
352	C₂×C₄	—	152	2	no	—
353	C₂×C₄	—	152	2	no	—
354	C₂×C₄	—	152	2	no	—
355	C₂×C₄	#10597264	1	4	yes	—
356	C₂×C₄	#10597265	1	4	yes	—
357	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
358	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
359	C₂×C₄	#10597318	1	1	yes	characteristic
360	C₂×C₄	#10597323	1	1	yes	characteristic
361	C₂×C₄	#10597323	1	2	yes	—
362	C₂×C₄	#10597324	1	2	yes	—
363	C₂×C₄	#10597325	1	2	yes	—
364	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
365	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
366	C₂×C₄	#10597329	1	2	yes	—
367	C₂×C₄	#10597336	1	1	yes	characteristic
368	C₂×C₄	#10597336	1	1	yes	characteristic
369	C₂×C₄	#10597338	1	1	yes	characteristic
370	C₂×C₄	#10597338	1	2	yes	—
371	C₂×C₄	#10597338	1	1	yes	characteristic
372	C₂×C₄	#10597339	1	2	yes	—
373	C₂×C₄	#10597340	1	2	yes	—
374	C₂×C₄	#10597344	1	2	yes	—
375	C₈	—	38	4	no	—
376	C₈	—	38	4	no	—
377	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
378	C₂²	#11926402	1	1	yes	characteristic
379	C₂²	#11926409	1	1	yes	characteristic
380	C₂²	#11926434	1	2	yes	—
381	C₂²	#11926438	1	2	yes	—
382	C₂²	C₂×#10597265	1	1	yes	characteristic
383	C₂²	C₂×#10597264	1	1	yes	characteristic
384	C₂²	#11926580	1	1	yes	characteristic
385	C₂²	#11926580	1	1	yes	characteristic
386	C₂²	C₄×#64525	1	2	yes	—
387	C₂²	C₄×#64526	1	2	yes	—
388	C₂²	C₄×#64527	1	2	yes	—
389	C₂²	C₄×#64528	1	2	yes	—
390	C₂²	#11926771	1	2	yes	—
391	C₂²	#11926775	1	2	yes	—
392	C₂²	#11926778	1	2	yes	—
393	C₂²	#11926783	1	2	yes	—
394	C₂²	#11926890	1	1	yes	characteristic
395	C₂²	#11926892	1	1	yes	characteristic
396	C₂²	#11926894	1	1	yes	characteristic
397	C₂²	#11926896	1	1	yes	characteristic
398	C₂²	#11926898	1	2	yes	—
399	C₂²	#11926901	1	2	yes	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	8	4	no	—
403	C₄	—	152	4	no	—
404	C₄	#11926389	1	1	yes	characteristic
405	C₄	#11926391	1	1	yes	characteristic
406	C₄	#11926406	1	1	yes	characteristic
407	C₄	#11926411	1	1	yes	characteristic
408	C₄	#11926427	1	2	yes	—
409	C₄	#11926431	1	2	yes	—
410	C₂	#14561861	1	1	yes	characteristic
411	C₂	C₄×#10597265	1	1	yes	characteristic
412	C₂	C₄×#10597264	1	1	yes	characteristic
413	C₂	#14563658	1	1	yes	characteristic
414	C₂	#14563662	1	1	yes	characteristic
415	C₂	#14563762	1	1	yes	characteristic
416	C₂	#14563765	1	1	yes	characteristic
417	C₂	#14564310	1	2	yes	—
418	C₂	#14564314	1	2	yes	—
419	C₂	#14564317	1	2	yes	—
420	C₂	#14564321	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄⋊#95	D₁₉
hypocenter	C₁₉	#10820
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
10. C₂×C₄×C₁₉⋊C₈	C₄	semidirect
14. #11926306	C₄	semidirect
265. C₁₉	#10820	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₁₉⋊C₈	2
C₂×#11926306	2
#14561865	2
C₁₉×C₄⋊#95	2
#10820	19