Subgroups — #18075267

Order 4864.

658 conjugacy classes of subgroups.

The subgroup lattice has 462 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	#14561865	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	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
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	C₂×C₄⋊Dic₁₉	—	2	4	no	—
50	C₂×C₄⋊Dic₁₉	—	4	2	no	—
51	C₂×C₄⋊Dic₁₉	—	4	2	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉⋊#95	—	2	2	no	—
59	C₁₉⋊#95	—	2	2	no	—
60	C₁₉⋊#95	—	4	2	no	—
61	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
63	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
64	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×Q₈×C₁₉	—	2	1	no	—
66	C₂×Q₈×C₁₉	—	4	1	no	—
67	C₂×Q₈×C₁₉	—	4	1	no	—
68	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	complemented
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×Dic₁₉	—	2	4	no	—
94	C₂²×Dic₁₉	—	4	2	no	—
95	C₂²×Dic₁₉	—	4	2	no	—
96	C₂²×Dic₁₉	—	4	2	no	—
97	C₂²×Dic₁₉	—	4	2	no	—
98	C₂²×Dic₁₉	—	4	2	no	—
99	C₂²×Dic₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	4	2	no	—
106	C₄⋊C₄×C₁₉	—	4	2	no	—
107	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
108	C₂²⋊C₄×C₁₉	—	2	2	no	—
109	C₂²⋊C₄×C₁₉	—	2	2	no	—
110	C₂²⋊C₄×C₁₉	—	4	1	no	—
111	C₂²⋊C₄×C₁₉	—	4	1	no	—
112	C₄²×C₁₉	—	2	2	no	—
113	C₄²×C₁₉	—	2	2	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	—	4	1	no	—
116	C₄²×C₁₉	—	4	2	no	—
117	C₄²×C₁₉	—	4	2	no	—
118	C₄⋊Dic₁₉	—	4	8	no	—
119	C₂×C₁₉⋊C₈	—	4	2	no	—
120	C₂×C₁₉⋊C₈	—	4	2	no	—
121	C₂×C₁₉⋊C₈	—	4	2	no	—
122	#8572	—	19	1	no	maximal, Sylow
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂³×C₁₉	#121	1	1	yes	characteristic
129	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
130	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
131	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
132	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
133	C₂³×C₁₉	#137	1	1	yes	characteristic
134	Q₈×C₁₉	—	4	2	no	—
135	Q₈×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	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	4	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	2	2	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	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	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	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	#99	1	2	yes	—
169	C₂×C₄×C₁₉	#103	1	2	yes	—
170	C₂×C₄×C₁₉	#103	1	2	yes	—
171	C₂×C₄×C₁₉	#104	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×Dic₁₉	—	4	4	no	—
177	C₂×Dic₁₉	—	4	4	no	—
178	C₂×Dic₁₉	—	4	4	no	—
179	C₂×Dic₁₉	—	8	2	no	—
180	C₂×Dic₁₉	—	8	2	no	—
181	C₂×Dic₁₉	—	8	2	no	—
182	C₂×Dic₁₉	—	8	2	no	—
183	C₁₉⋊C₈	—	8	2	no	—
184	C₄×C₂²⋊Q₈	D₁₉	1	1	yes	characteristic
185	#1797	—	19	1	no	—
186	C₂×#328	—	19	2	no	—
187	C₄⋊#95	—	19	1	no	—
188	#1294	—	19	2	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	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	#380	1	1	yes	characteristic
202	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
203	C₂²×C₁₉	#410	1	1	yes	characteristic
204	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
205	C₂²×C₁₉	#417	1	1	yes	characteristic
206	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
207	C₂²×C₁₉	#421	1	1	yes	characteristic
208	C₂²×C₁₉	#460	1	1	yes	characteristic
209	C₂²×C₁₉	#462	1	1	yes	characteristic
210	C₂²×C₁₉	#475	1	1	yes	characteristic
211	C₂²×C₁₉	#477	1	1	yes	characteristic
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	1	no	—
220	C₄×C₁₉	—	4	1	no	—
221	C₄×C₁₉	—	8	1	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	#328	1	4	yes	complemented
224	Dic₁₉	—	8	4	no	—
225	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
226	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
227	C₂²×C₄⋊C₄	—	38	1	no	—
228	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
229	C₂×C₄⋊C₈	—	38	1	no	—
230	C₂×C₂²⋊C₈	—	19	2	no	—
231	#391	Dic₁₉	1	1	yes	characteristic, complemented
232	#389	Dic₁₉	1	1	yes	characteristic, complemented
233	#387	—	2	1	no	—
234	#385	—	2	1	no	—
235	#380	C₂×D₁₉	1	1	yes	characteristic
236	C₄×C₄⋊C₄	—	2	1	no	—
237	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic, complemented
238	C₄×C₂²⋊C₄	—	2	1	no	—
239	C₂×#95	—	19	2	no	—
240	C₂×#95	—	38	1	no	—
241	#336	—	38	1	no	—
242	#328	—	38	4	no	—
243	C₂×C₁₉	—	2	1	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	2	1	no	—
247	C₂×C₁₉	C₂×#328	1	1	yes	characteristic
248	C₂×C₁₉	#1509	1	1	yes	characteristic
249	C₂×C₁₉	#1513	1	1	yes	characteristic
250	C₂×C₁₉	#1518	1	1	yes	characteristic
251	C₂×C₁₉	#1799	1	1	yes	characteristic
252	C₂×C₁₉	#1803	1	1	yes	characteristic
253	C₂×C₁₉	#1806	1	1	yes	characteristic
254	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
255	C₂³×C₄	—	38	2	no	—
256	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
257	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
258	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
259	C₂²×C₈	—	38	2	no	—
260	C₂²⋊Q₈	—	2	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	Dic₃₈	1	2	yes	—
263	C₂²⋊Q₈	D₇₆	1	2	yes	—
264	C₄×Q₈	—	4	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	38	4	no	—
269	C₂×C₄⋊C₄	—	76	2	no	—
270	C₂×C₄⋊C₄	—	76	2	no	—
271	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	4	2	no	—
279	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
280	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
281	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
282	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
283	C₄⋊C₈	—	76	2	no	—
284	C₂²⋊C₈	—	38	2	no	—
285	C₂²⋊C₈	—	38	2	no	—
286	#95	—	2	1	no	—
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	#95	—	38	2	no	—
292	#95	—	38	2	no	—
293	#95	—	76	2	no	—
294	C₁₉	#8572	1	1	yes	characteristic, complemented, Sylow
295	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	complemented
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	38	4	no	—
313	C₂²×C₄	—	76	2	no	—
314	C₂²×C₄	—	76	2	no	—
315	C₂²×C₄	—	76	2	no	—
316	C₂²×C₄	—	76	2	no	—
317	C₂²×C₄	—	76	2	no	—
318	C₂²×C₄	—	76	2	no	—
319	C₂²×C₄	#64527	1	2	yes	—
320	C₂²×C₄	#64528	1	2	yes	—
321	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
323	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
327	C₂²×C₄	#64541	1	1	yes	characteristic
328	C₂²×C₄	#64541	1	1	yes	characteristic
329	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
331	C₂×C₈	—	76	2	no	—
332	C₂×C₈	—	76	2	no	—
333	C₂×C₈	—	76	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	76	8	no	—
342	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	complemented
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	2	no	—
352	C₄²	—	4	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	#10597370	1	1	yes	characteristic
358	C₂³	#10597376	1	1	yes	characteristic
359	C₂³	C₂×#64527	1	1	yes	characteristic
360	C₂³	C₂×#64528	1	1	yes	characteristic
361	C₂³	#10597395	1	1	yes	characteristic
362	C₂³	#10597397	1	1	yes	characteristic
363	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	76	4	no	—
399	C₂×C₄	—	76	4	no	—
400	C₂×C₄	—	76	4	no	—
401	C₂×C₄	—	152	2	no	—
402	C₂×C₄	—	152	2	no	—
403	C₂×C₄	—	152	2	no	—
404	C₂×C₄	—	152	2	no	—
405	C₂×C₄	#10597291	1	2	yes	—
406	C₂×C₄	#10597292	1	2	yes	—
407	C₂×C₄	#10597292	1	2	yes	—
408	C₂×C₄	#10597294	1	2	yes	—
409	C₂×C₄	#10597370	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
411	C₂×C₄	#10597372	1	1	yes	characteristic
412	C₂×C₄	#10597376	1	1	yes	characteristic
413	C₈	—	152	2	no	—
414	C₂²	—	2	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	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	#11926404	1	1	yes	characteristic
427	C₂²	C₂×#10597291	1	1	yes	characteristic
428	C₂²	#11926518	1	1	yes	characteristic
429	C₂²	C₂×#10597292	1	1	yes	characteristic
430	C₂²	#11926545	1	1	yes	characteristic
431	C₂²	C₂×#10597294	1	1	yes	characteristic
432	C₂²	#11926561	1	1	yes	characteristic
433	C₂²	#11926744	1	1	yes	characteristic
434	C₂²	#11926754	1	1	yes	characteristic
435	C₂²	#11926829	1	1	yes	characteristic
436	C₂²	#11926839	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	152	4	no	—
449	C₄	#11926281	1	4	yes	complemented
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	C₂×#11926281	1	1	yes	characteristic
455	C₂	#14562160	1	1	yes	characteristic
456	C₂	#14562178	1	1	yes	characteristic
457	C₂	#14562199	1	1	yes	characteristic
458	C₂	#14563623	1	1	yes	characteristic
459	C₂	#14563640	1	1	yes	characteristic
460	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	#8572
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
68. C₂×Q₈×C₁₉	C₄⋊C₄	semidirect
107. C₄⋊C₄×C₁₉	C₄⋊C₄	semidirect
223. C₄×C₁₉	#328	semidirect
226. C₂×C₄×Q₈	Dic₁₉	semidirect
231. #391	Dic₁₉	semidirect
232. #389	Dic₁₉	semidirect
237. C₄×C₄⋊C₄	Dic₁₉	semidirect
294. C₁₉	#8572	semidirect
299. C₂×Q₈	C₄⋊Dic₁₉	semidirect
342. C₄⋊C₄	C₄⋊Dic₁₉	semidirect
449. C₄	#11926281	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
#14561865	2
#14561513	2
C₄×C₁₉×C₂²⋊Q₈	2
#8572	19