Subgroups — #18073093

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926616	C₂	1	1	yes	maximal, characteristic
2	#14563413	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561953	C₂	1	1	yes	maximal, characteristic
5	#14561483	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₄	1	1	yes	characteristic, complemented
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926616	—	2	1	no	—
11	#11926616	—	2	1	no	—
12	#11926616	—	2	1	no	—
13	#11926616	—	2	1	no	—
14	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic, complemented
15	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic, complemented
16	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#10597260	—	2	1	no	—
20	C₂×#10597260	C₄	1	1	yes	characteristic, complemented
21	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
22	#11926299	—	2	1	no	—
23	#11926299	—	2	1	no	—
24	#11926270	C₄	1	2	yes	complemented
25	#11926268	C₄	1	2	yes	complemented
26	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#99	C₄	1	2	yes	—
28	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#342	C₄	1	2	yes	—
31	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₄×D₄×C₁₉	—	2	1	no	—
35	C₄×D₄×C₁₉	—	2	1	no	—
36	C₄×D₄×C₁₉	—	2	1	no	—
37	C₄×D₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×#64520	—	2	1	no	—
47	C₂×#64520	—	2	1	no	—
48	C₂×#64520	—	4	2	no	—
49	C₂²×C₁₉⋊C₈	—	2	1	no	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	4	2	no	—
52	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
58	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
59	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
60	C₁₉×#99	—	2	4	no	—
61	C₁₉×#95	—	2	1	no	—
62	C₁₉×#95	—	2	1	no	—
63	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
70	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	#10597260	—	2	1	no	—
74	#10597260	—	2	1	no	—
75	#10597260	—	4	2	no	—
76	C₄×C₁₉⋊C₈	—	4	2	no	—
77	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
78	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	4	1	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂²⋊C₄×C₁₉	—	2	2	no	—
108	C₂²⋊C₄×C₁₉	—	2	2	no	—
109	C₂²⋊C₄×C₁₉	M₁₆	1	4	yes	complemented
110	C₄²×C₁₉	—	2	1	no	—
111	C₄²×C₁₉	—	2	1	no	—
112	C₄²×C₁₉	—	4	1	no	—
113	C₄²×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	—	4	1	no	—
116	#64520	—	4	2	no	—
117	#64520	—	4	2	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	—	2	2	no	—
120	C₂×C₁₉⋊C₈	—	2	2	no	—
121	C₂×C₁₉⋊C₈	—	2	1	no	—
122	C₂×C₁₉⋊C₈	—	2	1	no	—
123	C₂×C₁₉⋊C₈	—	2	2	no	—
124	C₂×C₁₉⋊C₈	—	2	2	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
138	#8161	—	19	1	no	maximal, Sylow
139	C₂³×C₁₉	—	2	1	no	—
140	C₂³×C₁₉	—	2	1	no	—
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
147	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
150	C₂³×C₁₉	#131	1	2	yes	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	1	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
182	C₁₉⋊C₈	—	2	1	no	—
183	C₁₉⋊C₈	—	2	1	no	—
184	C₁₉⋊C₈	—	2	1	no	—
185	C₁₉⋊C₈	—	4	2	no	—
186	C₁₉⋊C₈	—	4	2	no	—
187	C₁₉⋊C₈	—	4	1	no	—
188	C₁₉⋊C₈	—	4	1	no	—
189	C₁₉⋊C₈	#99	1	2	yes	complemented
190	C₂×#435	—	19	1	no	—
191	C₄×#99	D₁₉	1	1	yes	characteristic
192	#1752	—	19	1	no	—
193	C₈×C₂²⋊C₄	—	19	1	no	—
194	#1459	—	19	1	no	—
195	#1282	—	19	1	no	—
196	#1282	—	19	1	no	—
197	C₂²×C₁₉	—	2	1	no	—
198	C₂²×C₁₉	—	2	1	no	—
199	C₂²×C₁₉	—	2	1	no	—
200	C₂²×C₁₉	—	2	1	no	—
201	C₂²×C₁₉	—	2	1	no	—
202	C₂²×C₁₉	—	2	1	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	4	1	no	—
207	C₂²×C₁₉	—	4	1	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₁₉	C₄×M₁₆	1	1	yes	characteristic
212	C₂²×C₁₉	#405	1	1	yes	characteristic
213	C₂²×C₁₉	#435	1	2	yes	—
214	C₂²×C₁₉	#436	1	2	yes	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	—	4	1	no	—
220	C₄×C₁₉	—	4	1	no	—
221	C₄×C₁₉	—	4	1	no	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
224	C₄×C₁₉	#410	1	1	yes	characteristic
225	C₂²×M₁₆	—	19	1	no	—
226	C₂³×C₈	—	19	1	no	—
227	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
228	#435	—	38	1	no	—
229	#435	—	38	1	no	—
230	#435	—	38	1	no	—
231	#435	—	38	1	no	—
232	C₂×C₄⋊C₈	—	19	1	no	—
233	C₂×#99	Dic₁₉	1	2	yes	—
234	C₂×C₂²⋊C₈	—	19	1	no	—
235	C₂×C₂²⋊C₈	—	19	1	no	—
236	C₂×C₂²⋊C₈	—	19	1	no	—
237	C₂×C₂²⋊C₈	—	19	1	no	—
238	C₂×#97	—	19	1	no	—
239	C₂×#97	—	38	1	no	—
240	C₂×C₄×C₈	—	38	1	no	—
241	C₄×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
243	#342	Dic₁₉	1	2	yes	—
244	#336	—	38	1	no	—
245	#336	—	38	1	no	—
246	#324	—	19	2	no	—
247	#323	—	19	2	no	—
248	C₂×C₁₉	—	2	2	no	—
249	C₂×C₁₉	—	2	2	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	8	1	no	—
253	C₂×C₁₉	#1753	1	1	yes	characteristic
254	C₂×C₁₉	C₄×#99	1	1	yes	characteristic
255	C₂×C₁₉	#1757	1	1	yes	characteristic
256	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
257	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
259	C₂×M₁₆	—	38	1	no	—
260	C₂×M₁₆	—	38	1	no	—
261	C₂×M₁₆	—	76	2	no	—
262	C₂²×C₈	—	19	1	no	—
263	C₂²×C₈	—	19	1	no	—
264	C₂²×C₈	—	19	1	no	—
265	C₂²×C₈	—	19	1	no	—
266	C₂²×C₈	—	19	1	no	—
267	C₂²×C₈	—	19	1	no	—
268	C₂²×C₈	—	19	1	no	—
269	C₂²×C₈	—	19	1	no	—
270	C₂²×C₈	—	38	1	no	—
271	C₂²×C₈	—	38	1	no	—
272	C₂²×C₈	—	76	2	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₄×D₁₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
285	C₄⋊C₈	—	38	1	no	—
286	C₄⋊C₈	—	38	1	no	—
287	#99	—	2	4	no	—
288	C₂²⋊C₈	—	19	2	no	—
289	C₂²⋊C₈	—	19	2	no	—
290	C₂²⋊C₈	—	38	1	no	—
291	C₂²⋊C₈	—	38	1	no	—
292	C₂²⋊C₈	—	38	1	no	—
293	C₂²⋊C₈	—	38	1	no	—
294	C₂²⋊C₈	—	38	1	no	—
295	C₂²⋊C₈	—	38	1	no	—
296	#97	—	38	1	no	—
297	#97	—	38	1	no	—
298	#97	—	76	2	no	—
299	C₄×C₈	—	76	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	C₁₉	#8161	1	1	yes	characteristic, complemented, Sylow
303	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
304	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
324	C₂²×C₄	#64543	1	1	yes	characteristic
325	C₂²×C₄	#64543	1	1	yes	characteristic
326	M₁₆	—	76	2	no	—
327	M₁₆	—	76	2	no	—
328	C₂×C₈	—	19	1	no	—
329	C₂×C₈	—	19	1	no	—
330	C₂×C₈	—	19	1	no	—
331	C₂×C₈	—	19	1	no	—
332	C₂×C₈	—	38	2	no	—
333	C₂×C₈	—	38	2	no	—
334	C₂×C₈	—	38	2	no	—
335	C₂×C₈	—	38	1	no	—
336	C₂×C₈	—	38	1	no	—
337	C₂×C₈	—	38	2	no	—
338	C₂×C₈	—	38	2	no	—
339	C₂×C₈	—	76	1	no	—
340	C₂×C₈	—	76	1	no	—
341	C₂×C₈	—	76	1	no	—
342	C₂×C₈	—	76	1	no	—
343	C₂×C₈	—	76	1	no	—
344	C₂×C₈	—	76	1	no	—
345	C₂×C₈	—	76	1	no	—
346	C₂×C₈	—	76	1	no	—
347	C₂×C₈	—	76	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	#64520	1	4	yes	complemented
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	4	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	C₂×#64520	1	2	yes	—
372	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
373	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
374	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
375	C₂³	#10597394	1	2	yes	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	#10597323	1	1	yes	characteristic
404	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
405	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
406	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
407	C₈	—	19	2	no	—
408	C₈	—	38	1	no	—
409	C₈	—	38	1	no	—
410	C₈	—	38	1	no	—
411	C₈	—	76	2	no	—
412	C₈	—	76	2	no	—
413	C₈	—	76	1	no	—
414	C₈	—	76	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
429	C₂²	C₄×#64520	1	1	yes	characteristic
430	C₂²	#11926500	1	1	yes	characteristic
431	C₂²	#11926616	1	2	yes	—
432	C₂²	#11926622	1	2	yes	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	#99×D₁₉	1	1	yes	characteristic
442	C₄	#11926516	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	8	1	no	—
448	C₂	#14563419	1	1	yes	characteristic
449	C₂	#99×Dic₁₉	1	1	yes	characteristic
450	C₂	#14563437	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₄×C₁₉×#99	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄×#99	D₁₉
hypocenter	C₁₉	#8161
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₄×#99

Complements

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

N	H ≅ G/N	type
2. #14563413	C₂	semidirect
3. C₂²⋊C₄×C₁₉⋊C₈	C₂	semidirect
5. #14561483	C₂	semidirect
6. #14561483	C₂	semidirect
8. C₂²×#64520	C₄	semidirect
14. C₂×C₄⋊(C₁₉⋊C₈)	C₄	semidirect
15. C₂×C₂²⋊(C₁₉⋊C₈)	C₄	semidirect
20. C₂×#10597260	C₄	semidirect
24. #11926270	C₄	semidirect
25. #11926268	C₄	semidirect
109. C₂²⋊C₄×C₁₉	M₁₆	semidirect
189. C₁₉⋊C₈	#99	semidirect
302. C₁₉	#8161	semidirect
357. C₂²⋊C₄	#64520	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926616	2
#14563413	2
C₂²⋊C₄×C₁₉⋊C₈	2
#14561953	2
#14561483	2
C₄×C₁₉×#99	2
#8161	19