Subgroups — #18074637

Order 4864.

756 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564597	C₂	1	1	yes	maximal, characteristic
2	#14563640	C₂	1	1	yes	maximal, characteristic
3	#14563640	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926290	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×#10597292	—	2	1	no	—
11	C₂×#10597292	—	2	1	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926414	C₂²	1	1	yes	characteristic
14	#11926306	—	2	1	no	—
15	#11926306	—	2	1	no	—
16	#11926306	—	2	2	no	—
17	#11926290	—	2	2	no	—
18	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
19	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
20	C₁₉×#557	—	2	2	no	—
21	C₁₉×#557	—	2	2	no	—
22	C₁₉×#557	—	2	2	no	—
23	C₁₉×#557	C₄	1	4	yes	complemented
24	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#125	—	2	2	no	—
27	C₂×C₁₉×#125	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×Q₈×C₁₉	—	2	1	no	—
33	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
34	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
35	C₁₉×C₄⋊Q₈	—	2	4	no	—
36	C₁₉×C₄⋊Q₈	—	2	4	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
40	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
41	C₁₉×#125	—	2	8	no	—
42	C₁₉×#125	—	2	4	no	—
43	C₁₉×#125	—	2	8	no	—
44	C₁₉×#125	—	2	4	no	—
45	C₄×Q₈×C₁₉	—	2	4	no	—
46	C₄×Q₈×C₁₉	—	2	4	no	—
47	C₄×Q₈×C₁₉	—	2	4	no	—
48	C₄×Q₈×C₁₉	—	2	4	no	—
49	C₄×Q₈×C₁₉	—	2	1	no	—
50	C₄×Q₈×C₁₉	—	2	1	no	—
51	C₄×Q₈×C₁₉	—	2	1	no	—
52	C₄×Q₈×C₁₉	—	2	1	no	—
53	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
54	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₁₉	D₄	1	2	yes	—
56	C₄×Q₈×C₁₉	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄²×C₁₉	—	2	2	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊Dic₁₉	—	2	1	no	—
71	C₂×C₄⋊Dic₁₉	—	2	1	no	—
72	C₂×C₄⋊Dic₁₉	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	—	2	1	no	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	#10597292	—	4	2	no	—
77	#10597292	—	4	2	no	—
78	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
79	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
80	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
81	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
82	C₄×C₁₉⋊C₈	—	2	1	no	—
83	C₄×C₁₉⋊C₈	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	1	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×Q₈×C₁₉	—	2	1	no	—
91	C₂×Q₈×C₁₉	—	2	1	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	4	1	no	—
95	C₂×Q₈×C₁₉	—	4	1	no	—
96	C₂×Q₈×C₁₉	—	4	1	no	—
97	C₂×Q₈×C₁₉	—	4	1	no	—
98	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
99	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
100	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
101	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×Dic₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	2	8	no	—
112	C₄⋊C₄×C₁₉	—	2	8	no	—
113	C₄⋊C₄×C₁₉	—	2	8	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	1	no	—
121	C₄⋊C₄×C₁₉	—	2	1	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
124	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
125	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
126	C₄²×C₁₉	—	2	8	no	—
127	C₄²×C₁₉	—	2	2	no	—
128	C₄²×C₁₉	—	2	2	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₄⋊Dic₁₉	—	4	2	no	—
136	C₄⋊Dic₁₉	—	4	1	no	—
137	C₄⋊Dic₁₉	—	4	1	no	—
138	C₄⋊Dic₁₉	—	4	1	no	—
139	C₄⋊Dic₁₉	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	2	2	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	#8448	—	19	1	no	maximal, Sylow
150	C₂³×C₁₉	#120	1	1	yes	characteristic
151	Q₈×C₁₉	—	2	2	no	—
152	Q₈×C₁₉	—	2	2	no	—
153	Q₈×C₁₉	—	2	2	no	—
154	Q₈×C₁₉	—	2	2	no	—
155	Q₈×C₁₉	—	2	2	no	—
156	Q₈×C₁₉	—	4	2	no	—
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	4	1	no	—
159	Q₈×C₁₉	—	4	2	no	—
160	Q₈×C₁₉	—	4	1	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	Q₈×C₁₉	#103	1	4	yes	complemented
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	4	1	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	1	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	1	no	—
178	C₂×C₄×C₁₉	—	4	1	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
190	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
194	C₂×Dic₁₉	—	8	1	no	—
195	C₂×Dic₁₉	—	8	1	no	—
196	C₂×Dic₁₉	—	8	1	no	—
197	C₁₉⋊C₈	—	4	2	no	—
198	C₁₉⋊C₈	—	8	1	no	—
199	C₁₉⋊C₈	—	8	1	no	—
200	C₂×#557	D₁₉	1	1	yes	characteristic
201	#1990	—	19	1	no	—
202	#1803	—	19	1	no	—
203	#1803	—	19	1	no	—
204	C₂×#332	—	19	1	no	—
205	C₂×Q₈⋊C₈	—	19	1	no	—
206	C₂×Q₈⋊C₈	—	19	1	no	—
207	C₂²×C₁₉	#379	1	1	yes	characteristic
208	C₂²×C₁₉	#448	1	1	yes	characteristic
209	C₂²×C₁₉	#449	1	1	yes	characteristic
210	C₂²×C₁₉	#451	1	1	yes	characteristic
211	C₂²×C₁₉	#452	1	1	yes	characteristic
212	C₂²×C₁₉	#454	1	1	yes	characteristic
213	C₂²×C₁₉	#456	1	1	yes	characteristic
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	2	4	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	4	2	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
222	C₄×C₁₉	#416	1	1	yes	characteristic
223	C₄×C₁₉	#417	1	1	yes	characteristic
224	C₄×C₁₉	#419	1	1	yes	characteristic
225	C₄×C₁₉	#448	1	1	yes	characteristic
226	C₄×C₁₉	#449	1	1	yes	characteristic
227	C₄×C₁₉	#451	1	1	yes	characteristic
228	C₄×C₁₉	#452	1	1	yes	characteristic
229	Dic₁₉	—	16	1	no	—
230	#557	—	2	2	no	—
231	#557	—	2	2	no	—
232	#557	—	2	2	no	—
233	#557	Dic₁₉	1	4	yes	complemented
234	C₂×C₄⋊Q₈	—	2	1	no	—
235	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
236	C₂×#125	—	2	2	no	—
237	C₂×#125	—	2	1	no	—
238	C₂×C₄×Q₈	—	2	1	no	—
239	C₂×C₄×Q₈	—	2	1	no	—
240	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
242	C₂×C₄⋊C₈	—	19	1	no	—
243	C₂×C₄⋊C₈	—	19	1	no	—
244	C₂×#103	—	38	1	no	—
245	C₂×#103	—	38	1	no	—
246	C₂×C₄×C₈	—	19	1	no	—
247	#384	—	19	1	no	—
248	#340	—	38	1	no	—
249	#340	—	38	1	no	—
250	#340	—	38	2	no	—
251	#332	—	38	2	no	—
252	Q₈⋊C₈	—	38	2	no	—
253	Q₈⋊C₈	—	38	2	no	—
254	C₂×C₁₉	#1626	1	1	yes	characteristic
255	C₂×C₁₉	#1636	1	1	yes	characteristic
256	C₂×C₁₉	#1648	1	1	yes	characteristic
257	C₂×C₁₉	#1653	1	1	yes	characteristic
258	C₂×C₁₉	#1787	1	1	yes	characteristic
259	C₂×C₁₉	#1788	1	1	yes	characteristic
260	C₂×C₁₉	#1793	1	1	yes	characteristic
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
263	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
264	C₂²×C₈	—	38	1	no	—
265	C₂²×C₈	—	38	1	no	—
266	C₂²×C₈	—	38	1	no	—
267	C₄⋊Q₈	—	2	4	no	—
268	C₄⋊Q₈	—	2	4	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
272	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
273	#125	—	2	8	no	—
274	#125	—	2	4	no	—
275	#125	—	2	8	no	—
276	#125	—	2	4	no	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	C₂×Dic₁₉	1	2	yes	—
286	C₄×Q₈	C₂×Dic₁₉	1	2	yes	—
287	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
288	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	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	1	no	—
296	C₂×C₄⋊C₄	—	38	1	no	—
297	C₂×C₄⋊C₄	—	38	1	no	—
298	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
305	C₄⋊C₈	—	38	1	no	—
306	C₄⋊C₈	—	38	1	no	—
307	C₄⋊C₈	—	38	1	no	—
308	C₄⋊C₈	—	38	1	no	—
309	#103	—	76	2	no	—
310	#103	—	76	2	no	—
311	C₄×C₈	—	38	1	no	—
312	C₄×C₈	—	38	1	no	—
313	C₁₉	#8448	1	1	yes	characteristic, complemented, Sylow
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	1	no	—
328	C₂×Q₈	#64527	1	2	yes	—
329	C₂×Q₈	#64528	1	2	yes	—
330	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
331	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	76	1	no	—
338	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
341	C₂×C₈	—	38	2	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	C₂×C₈	—	76	1	no	—
349	C₂×C₈	—	76	1	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	76	2	no	—
363	C₄⋊C₄	—	76	1	no	—
364	C₄⋊C₄	—	76	1	no	—
365	C₄⋊C₄	—	76	1	no	—
366	C₄⋊C₄	—	76	1	no	—
367	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
368	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
369	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
370	C₄²	—	2	8	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
376	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
377	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
378	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
379	C₂³	#10597399	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	1	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	4	2	no	—
391	Q₈	#10597292	1	4	yes	complemented
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	152	1	no	—
410	C₂×C₄	—	152	1	no	—
411	C₂×C₄	—	152	1	no	—
412	C₂×C₄	C₂×#64527	1	1	yes	characteristic
413	C₂×C₄	#10597388	1	1	yes	characteristic
414	C₂×C₄	#10597388	1	1	yes	characteristic
415	C₂×C₄	C₂×#64528	1	1	yes	characteristic
416	C₂×C₄	#10597395	1	1	yes	characteristic
417	C₂×C₄	#10597396	1	1	yes	characteristic
418	C₂×C₄	#10597396	1	1	yes	characteristic
419	C₂×C₄	#10597397	1	1	yes	characteristic
420	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
423	C₂×C₄	#10597399	1	1	yes	characteristic
424	C₂×C₄	#10597399	1	1	yes	characteristic
425	C₂×C₄	#10597399	1	1	yes	characteristic
426	C₈	—	76	2	no	—
427	C₈	—	152	1	no	—
428	C₈	—	152	1	no	—
429	C₂²	#11926400	1	1	yes	characteristic
430	C₂²	#11926683	1	1	yes	characteristic
431	C₂²	#11926689	1	1	yes	characteristic
432	C₂²	#11926700	1	1	yes	characteristic
433	C₂²	#11926706	1	1	yes	characteristic
434	C₂²	#11926717	1	1	yes	characteristic
435	C₂²	#11926727	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	304	1	no	—
444	C₄	C₂×#10597292	1	1	yes	characteristic
445	C₄	#11926540	1	1	yes	characteristic
446	C₄	#11926545	1	1	yes	characteristic
447	C₄	#11926553	1	1	yes	characteristic
448	C₄	#11926683	1	1	yes	characteristic
449	C₄	#11926689	1	1	yes	characteristic
450	C₄	#11926700	1	1	yes	characteristic
451	C₄	#11926706	1	1	yes	characteristic
452	C₂	#14562731	1	1	yes	characteristic
453	C₂	#14562793	1	1	yes	characteristic
454	C₂	#14562877	1	1	yes	characteristic
455	C₂	#14562912	1	1	yes	characteristic
456	C₂	#14563570	1	1	yes	characteristic
457	C₂	#14563575	1	1	yes	characteristic
458	C₂	#14563594	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#557	C₂
socle, prime radical	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#557	D₁₉
hypocenter	C₁₉	#8448
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#557

Complements

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

N	H ≅ G/N	type
23. C₁₉×#557	C₄	semidirect
162. Q₈×C₁₉	#103	semidirect
233. #557	Dic₁₉	semidirect
313. C₁₉	#8448	semidirect
391. Q₈	#10597292	semidirect

Maximal subgroups

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

subgroup	index
#14564597	2
#14563640	2
C₂×#11926290	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×C₁₉×#557	2
#8448	19