Subgroups — #18087813

Order 4864.

1334 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926508	C₂	1	1	yes	maximal, characteristic
2	#14566018	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926315	C₂	1	4	yes	maximal, complemented
4	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64520	C₂²	1	2	yes	—
6	C₂×#10597372	C₂²	1	2	yes	—
7	#11926508	—	2	2	no	—
8	#11926508	C₄	1	2	yes	complemented
9	#11926508	C₄	1	2	yes	complemented
10	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
11	#11926407	C₄	1	2	yes	—
12	#11926404	—	2	2	no	—
13	#11926400	C₄	1	2	yes	—
14	C₄×C₂²⋊Dic₁₉	—	2	2	no	—
15	#11926315	—	2	8	no	—
16	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₉	—	2	2	no	—
18	C₂²×M₁₆×C₁₉	—	2	2	no	—
19	C₂²×M₁₆×C₁₉	—	2	8	no	—
20	C₂²×M₁₆×C₁₉	C₄	1	2	yes	complemented
21	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
22	C₂³×C₈×C₁₉	C₄	1	2	yes	complemented
23	C₂⁵×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	—	2	4	no	—
25	C₂³×C₄×C₁₉	—	2	4	no	—
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	D₄	1	2	yes	—
32	C₂³×C₄×C₁₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₉	D₄	1	2	yes	—
34	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₉	—	2	16	no	—
37	C₂×M₁₆×C₁₉	—	2	16	no	—
38	C₂×M₁₆×C₁₉	—	2	4	no	—
39	C₂×M₁₆×C₁₉	—	2	2	no	—
40	C₂×M₁₆×C₁₉	—	2	2	no	—
41	C₂×M₁₆×C₁₉	—	2	4	no	—
42	C₂×M₁₆×C₁₉	—	2	8	no	—
43	C₂×M₁₆×C₁₉	D₄	1	8	yes	—
44	C₂²×C₈×C₁₉	—	2	4	no	—
45	C₂²×C₈×C₁₉	—	2	8	no	—
46	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
47	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
48	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
49	#10597372	—	2	4	no	—
50	#10597372	—	2	4	no	—
51	C₂×C₄⋊Dic₁₉	—	2	2	no	—
52	C₂×C₄×Dic₁₉	—	2	2	no	—
53	C₂×#64520	—	2	2	no	—
54	C₂×#64520	—	2	4	no	—
55	C₂×#64520	—	2	4	no	—
56	C₂×#64520	C₂×C₄	1	4	yes	—
57	C₂²×C₁₉⋊C₈	—	2	2	no	—
58	C₁₉⋊#95	—	2	4	no	—
59	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
61	C₂⁴×C₁₉	—	2	4	no	—
62	C₂⁴×C₁₉	—	4	4	no	—
63	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
64	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
65	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
67	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	—	2	4	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	4	no	—
74	C₂²×C₄×C₁₉	—	2	4	no	—
75	C₂²×C₄×C₁₉	—	2	4	no	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	2	8	no	—
78	C₂²×C₄×C₁₉	—	2	8	no	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
89	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	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	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	4	yes	—
101	C₂²×Dic₁₉	—	2	4	no	—
102	M₁₆×C₁₉	—	2	16	no	—
103	M₁₆×C₁₉	—	2	8	no	—
104	M₁₆×C₁₉	—	2	8	no	—
105	C₂×C₈×C₁₉	—	2	16	no	—
106	C₂×C₈×C₁₉	—	2	4	no	—
107	C₂×C₈×C₁₉	—	2	4	no	—
108	C₂×C₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
109	C₂²⋊Dic₁₉	—	2	8	no	—
110	C₂²⋊Dic₁₉	—	4	8	no	—
111	C₄⋊Dic₁₉	—	4	4	no	—
112	C₄×Dic₁₉	—	4	2	no	—
113	C₄×Dic₁₉	—	4	2	no	—
114	#64520	—	2	8	no	—
115	#64520	—	4	4	no	—
116	C₂×C₁₉⋊C₈	—	2	4	no	—
117	C₂×C₁₉⋊C₈	—	4	2	no	—
118	C₂×C₁₉⋊C₈	—	4	2	no	—
119	#10729	—	19	1	no	maximal, Sylow
120	C₂³×C₁₉	—	2	4	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	4	no	—
123	C₂³×C₁₉	—	2	4	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	4	no	—
126	C₂³×C₁₉	—	2	4	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	16	no	—
132	C₂³×C₁₉	#95	1	2	yes	—
133	C₂³×C₁₉	#95	1	2	yes	—
134	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
135	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂³×C₁₉	C₄×D₄	1	4	yes	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	4	no	—
141	C₂×C₄×C₁₉	—	2	4	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	#95	1	2	yes	—
153	C₂×C₄×C₁₉	#95	1	2	yes	—
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#117	1	2	yes	—
160	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
161	C₂×C₄×C₁₉	#120	1	2	yes	—
162	C₂×C₄×C₁₉	#120	1	2	yes	—
163	C₂×C₄×C₁₉	#121	1	4	yes	—
164	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
165	C₂×C₄×C₁₉	#123	1	2	yes	—
166	C₂×C₄×C₁₉	#123	1	2	yes	—
167	C₂×Dic₁₉	—	4	8	no	—
168	C₂×Dic₁₉	—	4	4	no	—
169	C₈×C₁₉	—	2	8	no	—
170	C₁₉⋊C₈	—	4	4	no	—
171	C₂³×M₁₆	D₁₉	1	1	yes	characteristic
172	C₂×#407	—	19	1	no	—
173	#2280	—	19	1	no	—
174	C₂×#344	—	19	4	no	—
175	C₂²×C₁₉	—	2	8	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	4	4	no	—
185	C₂²×C₁₉	—	4	8	no	—
186	C₂²×C₁₉	—	4	8	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	#344	1	4	yes	complemented
189	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
190	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
191	C₂²×C₁₉	#385	1	2	yes	—
192	C₂²×C₁₉	#386	1	2	yes	—
193	C₄×C₁₉	—	2	2	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	#379	1	1	yes	characteristic
196	C₄×C₁₉	#380	1	2	yes	—
197	C₄×C₁₉	#381	1	1	yes	characteristic
198	C₄×C₁₉	#385	1	2	yes	—
199	C₄×C₁₉	#386	1	2	yes	—
200	Dic₁₉	—	8	4	no	—
201	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
202	C₂²×M₁₆	—	2	2	no	—
203	C₂²×M₁₆	—	2	2	no	—
204	C₂²×M₁₆	—	2	8	no	—
205	C₂²×M₁₆	—	19	2	no	—
206	C₂²×M₁₆	Dic₁₉	1	2	yes	complemented
207	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
208	C₂³×C₈	Dic₁₉	1	2	yes	complemented
209	C₂×#117	—	19	2	no	—
210	#407	—	19	2	no	—
211	#407	—	19	2	no	—
212	#407	—	38	2	no	—
213	C₂×C₂²⋊C₈	—	38	2	no	—
214	#381	—	19	2	no	—
215	#380	—	38	2	no	—
216	#379	—	19	2	no	—
217	C₄×C₂²⋊C₄	—	38	2	no	—
218	#344	—	38	8	no	—
219	C₂×C₁₉	—	2	2	no	—
220	C₂×C₁₉	—	2	4	no	—
221	C₂×C₁₉	—	2	2	no	—
222	C₂×C₁₉	—	2	2	no	—
223	C₂×C₁₉	—	4	2	no	—
224	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
225	C₂×C₁₉	C₂×#344	1	2	yes	—
226	C₂⁵	C₄×D₁₉	1	1	yes	characteristic
227	C₂³×C₄	—	2	4	no	—
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	Dic₃₈	1	2	yes	—
230	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
231	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
232	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
233	C₂³×C₄	D₇₆	1	2	yes	—
234	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
236	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
237	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
238	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
239	C₂×M₁₆	—	2	16	no	—
240	C₂×M₁₆	—	2	16	no	—
241	C₂×M₁₆	—	2	4	no	—
242	C₂×M₁₆	—	2	4	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	8	no	—
246	C₂×M₁₆	—	19	4	no	—
247	C₂×M₁₆	—	38	2	no	—
248	C₂×M₁₆	—	38	4	no	—
249	C₂×M₁₆	—	38	4	no	—
250	C₂×M₁₆	C₂²⋊D₁₉	1	8	yes	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	—	2	8	no	—
253	C₂²×C₈	—	38	2	no	—
254	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
255	#117	—	38	4	no	—
256	#117	—	38	4	no	—
257	C₂×C₄⋊C₄	—	38	2	no	—
258	C₂×C₂²⋊C₄	—	19	4	no	—
259	C₂×C₂²⋊C₄	—	38	4	no	—
260	C₂×C₄²	—	38	2	no	—
261	C₂²⋊C₈	—	38	4	no	—
262	C₂²⋊C₈	—	38	4	no	—
263	#95	—	38	4	no	—
264	C₁₉	#10729	1	1	yes	characteristic, complemented, Sylow
265	C₂⁴	—	2	4	no	—
266	C₂⁴	—	4	4	no	—
267	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
268	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
269	C₂⁴	Dic₁₉⋊C₄	1	2	yes	—
270	C₂⁴	(C₂×D₁₉)⋊C₄	1	2	yes	—
271	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	38	4	no	—
286	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
288	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
289	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
290	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
291	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
292	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
293	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
294	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
295	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
296	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
297	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
298	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
301	C₂²×C₄	#64541	1	4	yes	—
302	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
304	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
306	M₁₆	—	2	16	no	—
307	M₁₆	—	2	8	no	—
308	M₁₆	—	2	8	no	—
309	M₁₆	—	38	8	no	—
310	M₁₆	—	76	4	no	—
311	C₂×C₈	—	2	16	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	38	4	no	—
315	C₂×C₈	—	76	2	no	—
316	C₂×C₈	—	76	2	no	—
317	C₂×C₈	C₂²⋊Dic₁₉	1	8	yes	complemented
318	C₄⋊C₄	—	76	4	no	—
319	C₂²⋊C₄	—	38	8	no	—
320	C₂²⋊C₄	—	76	8	no	—
321	C₄²	—	76	2	no	—
322	C₄²	—	76	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	16	no	—
335	C₂³	C₁₉⋊#95	1	2	yes	—
336	C₂³	C₁₉⋊#95	1	2	yes	—
337	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
338	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
339	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
340	C₂³	C₄×C₂²⋊D₁₉	1	4	yes	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	76	8	no	—
356	C₂×C₄	—	76	4	no	—
357	C₂×C₄	C₁₉⋊#95	1	2	yes	—
358	C₂×C₄	C₁₉⋊#95	1	2	yes	—
359	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
360	C₂×C₄	#10597370	1	4	yes	—
361	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
362	C₂×C₄	#10597372	1	2	yes	—
363	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
365	C₂×C₄	#10597375	1	2	yes	—
366	C₂×C₄	#10597375	1	2	yes	—
367	C₂×C₄	#10597376	1	4	yes	—
368	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
370	C₂×C₄	#10597399	1	2	yes	—
371	C₂×C₄	#10597399	1	2	yes	—
372	C₈	—	2	8	no	—
373	C₈	—	76	4	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	4	no	—
387	C₂²	#11926315	1	4	yes	complemented
388	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
389	C₂²	C₄×C₂²⋊Dic₁₉	1	2	yes	—
390	C₂²	#11926417	1	2	yes	—
391	C₂²	#11926423	1	2	yes	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	152	4	no	—
395	C₄	#11926400	1	1	yes	characteristic
396	C₄	#11926404	1	2	yes	—
397	C₄	#11926407	1	1	yes	characteristic
398	C₄	#11926417	1	2	yes	—
399	C₄	#11926423	1	2	yes	—
400	C₂	—	2	2	no	—
401	C₂	—	2	4	no	—
402	C₂	—	2	2	no	—
403	C₂	—	2	2	no	—
404	C₂	—	4	2	no	—
405	C₂	#14561858	1	1	yes	characteristic
406	C₂	C₂×#11926315	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂³×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁵×C₁₉	C₂×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂³×M₁₆	D₁₉
hypocenter	C₁₉	#10729
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ C₂³×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×#11926315	C₂	semidirect
8. #11926508	C₄	semidirect
9. #11926508	C₄	semidirect
20. C₂²×M₁₆×C₁₉	C₄	semidirect
22. C₂³×C₈×C₁₉	C₄	semidirect
108. C₂×C₈×C₁₉	C₂²⋊C₄	semidirect
188. C₂²×C₁₉	#344	semidirect
206. C₂²×M₁₆	Dic₁₉	semidirect
208. C₂³×C₈	Dic₁₉	semidirect
264. C₁₉	#10729	semidirect
317. C₂×C₈	C₂²⋊Dic₁₉	semidirect
387. C₂²	#11926315	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926508	2
#14566018	2
C₂×#11926315	2
C₂³×M₁₆×C₁₉	2
#10729	19