Subgroups — #18074222

Order 4864.

1034 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563623	C₂	1	1	yes	maximal, characteristic
2	#14563570	C₂	1	2	yes	maximal, complemented
3	#14562207	C₂	1	2	yes	maximal, complemented
4	#14561953	C₂	1	1	yes	maximal, characteristic
5	C₂×D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597292	—	2	4	no	—
7	C₂×#10597291	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	#11926404	C₂²	1	2	yes	—
10	#11926311	—	2	1	no	—
11	#11926281	—	2	4	no	—
12	#11926270	—	2	1	no	—
13	#11926268	—	2	1	no	—
14	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
15	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	D₄×Q₈×C₁₉	—	2	4	no	—
17	D₄×Q₈×C₁₉	—	2	4	no	—
18	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
20	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
23	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₁₉	—	2	1	no	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×C₁₉	—	2	2	no	—
28	C₂²×Q₈×C₁₉	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	—	2	1	no	—
31	C₂²×Q₈×C₁₉	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	4	4	no	—
33	C₂²×Q₈×C₁₉	—	4	4	no	—
34	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
38	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂³×C₄×C₁₉	—	2	1	no	—
41	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₁₉×C₄⋊Q₈	—	2	8	no	—
44	C₁₉×C₄⋊Q₈	—	2	2	no	—
45	C₁₉×C₄⋊Q₈	—	2	2	no	—
46	C₁₉×C₂²⋊Q₈	—	2	8	no	—
47	C₁₉×C₂²⋊Q₈	—	2	8	no	—
48	C₁₉×C₂²⋊Q₈	—	2	2	no	—
49	C₁₉×C₂²⋊Q₈	—	2	2	no	—
50	C₁₉×C₂²⋊Q₈	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
52	C₄×Q₈×C₁₉	—	2	2	no	—
53	C₄×Q₈×C₁₉	—	2	2	no	—
54	C₄×D₄×C₁₉	—	2	8	no	—
55	C₄×D₄×C₁₉	—	2	2	no	—
56	C₄×D₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
71	C₂×C₄⋊Dic₁₉	—	2	2	no	—
72	C₂²×C₁₉⋊C₈	—	2	2	no	—
73	#10597292	—	4	8	no	—
74	#10597291	—	4	2	no	—
75	C₁₉⋊#95	—	2	2	no	—
76	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
78	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	2	4	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	4	no	—
86	C₂×Q₈×C₁₉	—	2	8	no	—
87	C₂×Q₈×C₁₉	—	4	2	no	—
88	C₂×Q₈×C₁₉	—	4	4	no	—
89	C₂×Q₈×C₁₉	—	4	2	no	—
90	C₂×Q₈×C₁₉	—	4	4	no	—
91	C₂×Q₈×C₁₉	—	4	4	no	—
92	C₂×Q₈×C₁₉	—	4	8	no	—
93	C₂×Q₈×C₁₉	—	4	8	no	—
94	C₂×Q₈×C₁₉	—	4	4	no	—
95	C₂×Q₈×C₁₉	—	4	4	no	—
96	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
97	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
98	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
102	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×Dic₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
131	C₂²⋊C₄×C₁₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₉	—	2	4	no	—
133	C₂²⋊C₄×C₁₉	—	2	2	no	—
134	C₂²⋊C₄×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	1	no	—
137	C₄²×C₁₉	—	2	1	no	—
138	C₂²⋊Dic₁₉	—	4	2	no	—
139	C₂²⋊Dic₁₉	—	4	2	no	—
140	C₄⋊Dic₁₉	—	4	4	no	—
141	C₂×C₁₉⋊C₈	—	4	4	no	—
142	C₂×C₁₉⋊C₈	—	4	2	no	—
143	#8379	—	19	1	no	maximal, Sylow
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	2	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	1	no	—
149	C₂³×C₁₉	—	4	1	no	—
150	C₂³×C₁₉	#103	1	2	yes	complemented
151	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₉	#120	1	2	yes	—
153	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
154	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
155	C₂³×C₁₉	#137	1	2	yes	—
156	Q₈×C₁₉	—	2	4	no	—
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	4	no	—
159	Q₈×C₁₉	—	4	8	no	—
160	Q₈×C₁₉	—	4	2	no	—
161	Q₈×C₁₉	—	4	8	no	—
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	4	2	no	—
164	Q₈×C₁₉	#99	1	4	yes	complemented
165	D₄×C₁₉	—	2	4	no	—
166	D₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	8	no	—
181	C₂×C₄×C₁₉	—	4	8	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	#103	1	2	yes	complemented
190	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#120	1	2	yes	—
193	C₂×Dic₁₉	—	8	2	no	—
194	C₂×Dic₁₉	—	8	2	no	—
195	C₂×Dic₁₉	—	8	2	no	—
196	C₁₉⋊C₈	—	8	2	no	—
197	C₂×D₄×Q₈	D₁₉	1	1	yes	characteristic
198	#1799	—	19	1	no	—
199	#1787	—	19	2	no	—
200	#1520	—	19	2	no	—
201	#1459	—	19	1	no	—
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	2	1	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	4	1	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	1	no	—
213	C₂²×C₁₉	—	4	1	no	—
214	C₂²×C₁₉	#379	1	1	yes	characteristic
215	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
216	C₂²×C₁₉	#419	1	1	yes	characteristic
217	C₂²×C₁₉	#448	1	2	yes	—
218	C₂²×C₁₉	#451	1	2	yes	—
219	C₄×C₁₉	—	2	2	no	—
220	C₄×C₁₉	—	2	4	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	4	1	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	2	no	—
227	C₄×C₁₉	—	4	1	no	—
228	C₄×C₁₉	C₂×#99	1	2	yes	—
229	Dic₁₉	—	16	2	no	—
230	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
231	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
232	D₄×Q₈	—	2	4	no	—
233	D₄×Q₈	—	2	4	no	—
234	C₂×C₄⋊Q₈	—	2	1	no	—
235	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic, complemented
236	C₂×C₂²⋊Q₈	—	2	1	no	—
237	C₂×C₂²⋊Q₈	—	2	1	no	—
238	C₂×C₂²⋊Q₈	Dic₁₉	1	1	yes	characteristic, complemented
239	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
240	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
241	C₂×C₄×D₄	—	2	1	no	—
242	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
243	C₂×#103	—	38	4	no	—
244	C₂×#99	—	38	1	no	—
245	C₂×C₂²⋊C₈	—	19	2	no	—
246	#380	—	19	2	no	—
247	#342	—	38	1	no	—
248	#328	—	38	4	no	—
249	#324	—	38	1	no	—
250	#323	—	38	1	no	—
251	C₂×C₁₉	—	2	2	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	2	2	no	—
255	C₂×C₁₉	—	4	2	no	—
256	C₂×C₁₉	#1781	1	1	yes	characteristic
257	C₂×C₁₉	#1787	1	1	yes	characteristic
258	C₂×C₁₉	#1796	1	1	yes	characteristic
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	—	2	2	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×Q₈	—	2	2	no	—
264	C₂²×Q₈	—	4	4	no	—
265	C₂²×Q₈	—	4	4	no	—
266	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
267	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
268	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
269	C₂²×Q₈	C₂²⋊D₁₉	1	4	yes	—
270	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
274	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
275	C₂²×C₈	—	38	2	no	—
276	C₄⋊Q₈	—	2	8	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₂²⋊Q₈	—	2	8	no	—
280	C₂²⋊Q₈	—	2	8	no	—
281	C₂²⋊Q₈	—	2	2	no	—
282	C₂²⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	C₂²⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×D₄	—	2	8	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	38	2	no	—
296	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	38	2	no	—
301	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
305	#103	—	76	8	no	—
306	#99	—	76	2	no	—
307	C₂²⋊C₈	—	38	2	no	—
308	C₂²⋊C₈	—	38	2	no	—
309	#95	—	38	2	no	—
310	C₁₉	#8379	1	1	yes	characteristic, complemented, Sylow
311	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
312	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	8	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	—	4	4	no	—
325	C₂×Q₈	—	4	8	no	—
326	C₂×Q₈	—	4	8	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	—	4	4	no	—
329	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
330	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
331	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	#64527	1	2	yes	—
335	C₂×D₄	#64528	1	2	yes	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	76	2	no	—
349	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
354	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
355	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
356	C₂×C₈	—	76	4	no	—
357	C₂×C₈	—	76	2	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	76	4	no	—
366	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	76	2	no	—
372	C₂²⋊C₄	—	76	2	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	#10597292	1	2	yes	complemented
383	C₂³	C₂×#64527	1	1	yes	characteristic
384	C₂³	#10597388	1	2	yes	—
385	C₂³	C₂×#64528	1	1	yes	characteristic
386	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
387	C₂³	#10597399	1	2	yes	—
388	Q₈	—	2	4	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	4	8	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	8	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	#10597291	1	4	yes	complemented
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	152	2	no	—
422	C₂×C₄	—	152	2	no	—
423	C₂×C₄	—	152	2	no	—
424	C₂×C₄	#10597292	1	2	yes	complemented
425	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
426	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
427	C₂×C₄	#10597399	1	2	yes	—
428	C₈	—	152	2	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	#11926400	1	1	yes	characteristic
442	C₂²	C₂×#10597292	1	1	yes	characteristic
443	C₂²	#11926553	1	1	yes	characteristic
444	C₂²	#11926683	1	2	yes	—
445	C₂²	#11926700	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	1	no	—
455	C₄	—	304	2	no	—
456	C₄	C₂×#10597291	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	2	no	—
461	C₂	—	4	2	no	—
462	C₂	#14563550	1	1	yes	characteristic
463	C₂	#14563570	1	1	yes	characteristic
464	C₂	#14563610	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×D₄×Q₈×C₁₉	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×D₄×Q₈	D₁₉
hypocenter	C₁₉	#8379
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #14563570	C₂	semidirect
3. #14562207	C₂	semidirect
14. C₂³×Q₈×C₁₉	C₄	semidirect
19. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
22. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
24. C₂×C₄×Q₈×C₁₉	C₄	semidirect
150. C₂³×C₁₉	#103	semidirect
164. Q₈×C₁₉	#99	semidirect
189. C₂×C₄×C₁₉	#103	semidirect
230. C₂³×Q₈	Dic₁₉	semidirect
235. C₂×C₄⋊Q₈	Dic₁₉	semidirect
238. C₂×C₂²⋊Q₈	Dic₁₉	semidirect
240. C₂×C₄×Q₈	Dic₁₉	semidirect
310. C₁₉	#8379	semidirect
382. C₂³	#10597292	semidirect
396. Q₈	#10597291	semidirect
424. C₂×C₄	#10597292	semidirect

Maximal subgroups

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

subgroup	index
#14563623	2
#14563570	2
#14562207	2
#14561953	2
C₂×D₄×Q₈×C₁₉	2
#8379	19