Subgroups — #18075277

Order 4864.

614 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563615	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926281	C₂	1	2	yes	maximal
3	#14561862	C₂	1	1	yes	maximal, characteristic
4	#14561513	C₂	1	2	yes	maximal
5	C₄×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₁₉⋊#95	—	2	1	no	—
9	C₂×C₁₉⋊#95	—	2	1	no	—
10	C₂×C₁₉⋊#95	C₂²	1	2	yes	—
11	#11926299	—	2	1	no	—
12	#11926281	—	2	4	no	—
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#391	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#389	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#387	—	2	1	no	—
19	C₁₉×#385	—	2	1	no	—
20	C₁₉×#380	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
22	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
23	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂³×Dic₁₉	—	2	2	no	—
29	C₁₉×C₂²⋊Q₈	—	2	1	no	—
30	C₁₉×C₂²⋊Q₈	—	2	1	no	—
31	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
32	C₁₉×C₂²⋊Q₈	Q₈	1	2	yes	—
33	C₄×Q₈×C₁₉	—	4	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	4	2	no	—
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₁₉×#95	—	2	1	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉⋊#95	—	2	4	no	—
56	C₁₉⋊#95	—	2	2	no	—
57	C₁₉⋊#95	—	2	2	no	—
58	C₁₉⋊#95	—	4	2	no	—
59	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
62	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	4	1	no	—
65	C₂×Q₈×C₁₉	—	4	1	no	—
66	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×Dic₁₉	—	2	4	no	—
90	C₂²×Dic₁₉	—	4	2	no	—
91	C₂²×Dic₁₉	—	4	2	no	—
92	C₂²×Dic₁₉	—	4	2	no	—
93	C₂²×Dic₁₉	—	4	2	no	—
94	C₂²×Dic₁₉	—	4	2	no	—
95	C₂²×Dic₁₉	—	4	2	no	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	4	2	no	—
103	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
104	C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂²⋊C₄×C₁₉	—	4	2	no	—
107	C₄²×C₁₉	—	2	2	no	—
108	C₄²×C₁₉	—	2	2	no	—
109	C₄²×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	—	4	2	no	—
112	C₄²×C₁₉	—	4	2	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	C₂×C₁₉⋊C₈	—	4	2	no	—
116	#8574	—	19	1	no	maximal, Sylow
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₉	#121	1	1	yes	characteristic
123	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
124	C₂³×C₁₉	#135	1	2	yes	—
125	C₂³×C₁₉	#137	1	2	yes	—
126	Q₈×C₁₉	—	4	2	no	—
127	Q₈×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	2	1	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	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	4	no	—
149	C₂×C₄×C₁₉	—	4	4	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	#99	1	2	yes	—
161	C₂×C₄×C₁₉	#104	1	2	yes	—
162	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×Dic₁₉	—	4	4	no	—
167	C₂×Dic₁₉	—	4	4	no	—
168	C₂×Dic₁₉	—	4	4	no	—
169	C₂×Dic₁₉	—	8	2	no	—
170	C₂×Dic₁₉	—	8	2	no	—
171	C₂×Dic₁₉	—	8	2	no	—
172	C₂×Dic₁₉	—	8	2	no	—
173	C₁₉⋊C₈	—	8	2	no	—
174	C₄×C₂²⋊Q₈	D₁₉	1	1	yes	characteristic
175	#1797	—	19	1	no	—
176	C₂×#328	—	19	2	no	—
177	#1434	—	19	1	no	—
178	#1294	—	19	2	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	#380	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
189	C₂²×C₁₉	#410	1	1	yes	characteristic
190	C₂²×C₁₉	#416	1	1	yes	characteristic
191	C₂²×C₁₉	#419	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
193	C₂²×C₁₉	#421	1	1	yes	characteristic
194	C₂²×C₁₉	#464	1	2	yes	—
195	C₂²×C₁₉	#479	1	2	yes	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	2	no	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	8	1	no	—
207	C₄×C₁₉	—	8	1	no	—
208	Dic₁₉	—	8	4	no	—
209	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
210	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
211	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
212	C₂×C₄⋊C₈	—	38	1	no	—
213	C₂×C₂²⋊C₈	—	19	2	no	—
214	#391	Dic₁₉	1	1	yes	characteristic, complemented
215	#389	Dic₁₉	1	1	yes	characteristic, complemented
216	#387	—	2	1	no	—
217	#385	—	2	1	no	—
218	#380	C₂×D₁₉	1	1	yes	characteristic
219	C₄×C₄⋊C₄	—	2	1	no	—
220	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic, complemented
221	C₄×C₂²⋊C₄	—	2	1	no	—
222	C₂×#95	—	19	2	no	—
223	C₂×#95	—	38	1	no	—
224	C₂×#95	—	38	1	no	—
225	#336	—	38	1	no	—
226	#328	—	38	4	no	—
227	C₂×C₁₉	—	2	2	no	—
228	C₂×C₁₉	—	2	2	no	—
229	C₂×C₁₉	#1500	1	1	yes	characteristic
230	C₂×C₁₉	#1508	1	1	yes	characteristic
231	C₂×C₁₉	#1515	1	1	yes	characteristic
232	C₂×C₁₉	#1516	1	1	yes	characteristic
233	C₂×C₁₉	#1799	1	1	yes	characteristic
234	C₂×C₁₉	#1805	1	1	yes	characteristic
235	C₂×C₁₉	#1806	1	1	yes	characteristic
236	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
237	C₂³×C₄	—	38	2	no	—
238	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
240	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
241	C₂²×C₈	—	38	2	no	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	C₂²⋊Q₈	Dic₃₈	1	2	yes	—
245	C₂²⋊Q₈	D₇₆	1	2	yes	—
246	C₄×Q₈	—	4	2	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	4	2	no	—
258	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
259	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
262	C₄⋊C₈	—	76	2	no	—
263	C₂²⋊C₈	—	38	2	no	—
264	C₂²⋊C₈	—	38	2	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	2	1	no	—
268	#95	—	2	1	no	—
269	#95	—	2	1	no	—
270	#95	—	38	4	no	—
271	#95	—	38	2	no	—
272	#95	—	38	2	no	—
273	#95	—	76	2	no	—
274	C₁₉	#8574	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	38	4	no	—
293	C₂²×C₄	—	76	2	no	—
294	C₂²×C₄	—	76	2	no	—
295	C₂²×C₄	—	76	2	no	—
296	C₂²×C₄	—	76	2	no	—
297	C₂²×C₄	—	76	2	no	—
298	C₂²×C₄	—	76	2	no	—
299	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
302	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
305	C₂²×C₄	#64541	1	1	yes	characteristic
306	C₂²×C₄	#64541	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
309	C₂×C₈	—	76	2	no	—
310	C₂×C₈	—	76	2	no	—
311	C₂×C₈	—	76	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	4	1	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	4	2	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	#10597370	1	1	yes	characteristic
334	C₂³	#10597376	1	1	yes	characteristic
335	C₂³	#10597388	1	2	yes	—
336	C₂³	#10597396	1	2	yes	—
337	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	76	4	no	—
373	C₂×C₄	—	76	4	no	—
374	C₂×C₄	—	76	4	no	—
375	C₂×C₄	—	152	2	no	—
376	C₂×C₄	—	152	2	no	—
377	C₂×C₄	—	152	2	no	—
378	C₂×C₄	—	152	2	no	—
379	C₂×C₄	#10597291	1	2	yes	—
380	C₂×C₄	#10597294	1	2	yes	—
381	C₂×C₄	#10597370	1	1	yes	characteristic
382	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
383	C₂×C₄	#10597372	1	1	yes	characteristic
384	C₂×C₄	#10597376	1	1	yes	characteristic
385	C₈	—	152	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	#11926404	1	1	yes	characteristic
395	C₂²	C₂×#10597291	1	1	yes	characteristic
396	C₂²	#11926518	1	1	yes	characteristic
397	C₂²	#11926540	1	1	yes	characteristic
398	C₂²	#11926553	1	1	yes	characteristic
399	C₂²	C₂×#10597294	1	1	yes	characteristic
400	C₂²	#11926561	1	1	yes	characteristic
401	C₂²	#11926766	1	2	yes	—
402	C₂²	#11926851	1	2	yes	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	1	no	—
415	C₄	—	152	4	no	—
416	C₂	—	2	2	no	—
417	C₂	—	2	2	no	—
418	C₂	#14562121	1	1	yes	characteristic
419	C₂	#14562155	1	1	yes	characteristic
420	C₂	#14562186	1	1	yes	characteristic
421	C₂	#14562191	1	1	yes	characteristic
422	C₂	#14563623	1	1	yes	characteristic
423	C₂	#14563650	1	1	yes	characteristic
424	C₂	#14563655	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₄×C₁₉×C₂²⋊Q₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₁₉
hypocenter	C₁₉	#8574
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
14. C₂×C₄×Q₈×C₁₉	C₄	semidirect
16. C₁₉×#391	C₄	semidirect
17. C₁₉×#389	C₄	semidirect
22. C₄×C₄⋊C₄×C₁₉	C₄	semidirect
210. C₂×C₄×Q₈	Dic₁₉	semidirect
214. #391	Dic₁₉	semidirect
215. #389	Dic₁₉	semidirect
220. C₄×C₄⋊C₄	Dic₁₉	semidirect
274. C₁₉	#8574	semidirect

Maximal subgroups

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

subgroup	index
#14563615	2
C₂×#11926281	2
#14561862	2
#14561513	2
C₄×C₁₉×C₂²⋊Q₈	2
#8574	19