Subgroups — #18088192

Order 4864.

914 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×C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926306	C₂	1	2	yes	maximal
3	C₂×#11926306	C₂	1	2	yes	maximal
4	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
5	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄×Dic₁₉	—	2	1	no	—
10	C₄×C₄⋊Dic₁₉	—	2	2	no	—
11	C₄×C₄⋊Dic₁₉	C₄	1	4	yes	complemented
12	C₂×C₁₉⋊#95	—	2	1	no	—
13	#11926306	—	2	4	no	—
14	#11926306	C₄	1	8	yes	complemented
15	#11926299	—	2	2	no	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#95	—	2	1	no	—
19	C₂×C₁₉×#95	—	2	1	no	—
20	C₂³×C₄×C₁₉	—	2	2	no	—
21	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₉	—	2	1	no	—
25	C₂³×Dic₁₉	—	2	1	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	—	2	2	no	—
34	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₉	D₄	1	2	yes	—
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	2	no	—
39	C₂×C₄⋊Dic₁₉	—	2	1	no	—
40	C₂×C₄⋊Dic₁₉	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
46	C₂×C₄×Dic₁₉	—	2	4	no	—
47	C₂×C₄×Dic₁₉	—	4	2	no	—
48	C₂×C₄×Dic₁₉	—	4	2	no	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₂²×C₁₉⋊C₈	—	2	2	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	2	no	—
54	C₂²×C₁₉⋊C₈	—	2	2	no	—
55	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
56	C₁₉×#95	—	4	2	no	—
57	C₁₉×#95	—	4	2	no	—
58	C₁₉⋊#95	—	2	4	no	—
59	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	—	4	2	no	—
71	C₂²×C₄×C₁₉	—	4	2	no	—
72	C₂²×C₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₁₉	D₈	1	2	yes	—
76	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	#41	1	2	yes	—
83	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	#41	1	2	yes	—
85	C₂²×C₄×C₁₉	#41	1	2	yes	—
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂²×Dic₁₉	—	2	2	no	—
88	C₂²×Dic₁₉	—	2	2	no	—
89	C₂²×Dic₁₉	—	2	4	no	—
90	C₂²×Dic₁₉	—	2	2	no	—
91	C₂²×Dic₁₉	—	2	2	no	—
92	C₂²×Dic₁₉	—	4	1	no	—
93	C₂²×Dic₁₉	—	4	1	no	—
94	C₂²×Dic₁₉	—	4	1	no	—
95	C₂²×Dic₁₉	—	4	1	no	—
96	C₂²×Dic₁₉	—	4	2	no	—
97	C₂²×Dic₁₉	—	4	1	no	—
98	C₂²×Dic₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	2	4	no	—
100	C₄⋊C₄×C₁₉	—	2	4	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	4	2	no	—
103	C₄²×C₁₉	—	2	2	no	—
104	C₄²×C₁₉	—	2	2	no	—
105	C₄²×C₁₉	—	2	4	no	—
106	C₄⋊Dic₁₉	—	2	2	no	—
107	C₄⋊Dic₁₉	—	2	2	no	—
108	C₄⋊Dic₁₉	—	2	4	no	—
109	C₄⋊Dic₁₉	—	2	2	no	—
110	C₄⋊Dic₁₉	—	2	2	no	—
111	C₄⋊Dic₁₉	C₄²	1	4	yes	—
112	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
113	C₄×Dic₁₉	—	4	8	no	—
114	C₂×C₁₉⋊C₈	—	2	4	no	—
115	C₂×C₁₉⋊C₈	—	2	4	no	—
116	C₂×C₁₉⋊C₈	—	2	4	no	—
117	C₂×C₁₉⋊C₈	—	4	2	no	—
118	C₂×C₁₉⋊C₈	—	4	2	no	—
119	C₂×C₁₉⋊C₈	—	4	2	no	—
120	C₂×C₁₉⋊C₈	—	4	2	no	—
121	#10806	—	19	1	no	maximal, Sylow
122	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂³×C₁₉	C₄×D₄	1	2	yes	—
124	C₂³×C₁₉	#121	1	1	yes	characteristic
125	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂³×C₁₉	#123	1	2	yes	—
127	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
128	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
129	C₂³×C₁₉	#135	1	2	yes	—
130	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
131	C₂³×C₁₉	#137	1	1	yes	characteristic
132	C₂³×C₁₉	#137	1	2	yes	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	4	no	—
143	C₂×C₄×C₁₉	—	4	4	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	8	2	no	—
146	C₂×C₄×C₁₉	—	8	2	no	—
147	C₂×C₄×C₁₉	—	8	2	no	—
148	C₂×C₄×C₁₉	—	8	2	no	—
149	C₂×C₄×C₁₉	#102	1	4	yes	—
150	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#117	1	2	yes	—
155	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#117	1	2	yes	—
158	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
161	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#123	1	2	yes	—
164	C₂×C₄×C₁₉	#124	1	2	yes	—
165	C₂×C₄×C₁₉	#125	1	2	yes	—
166	C₂×C₄×C₁₉	#126	1	2	yes	—
167	C₂×C₄×C₁₉	#126	1	2	yes	—
168	C₂×Dic₁₉	—	2	4	no	—
169	C₂×Dic₁₉	—	2	4	no	—
170	C₂×Dic₁₉	—	4	2	no	—
171	C₂×Dic₁₉	—	4	2	no	—
172	C₂×Dic₁₉	—	4	2	no	—
173	C₂×Dic₁₉	—	4	2	no	—
174	C₂×Dic₁₉	—	4	4	no	—
175	C₂×Dic₁₉	—	4	4	no	—
176	C₂×Dic₁₉	—	4	2	no	—
177	C₂×Dic₁₉	—	4	2	no	—
178	C₂×Dic₁₉	—	4	2	no	—
179	C₂×Dic₁₉	—	4	2	no	—
180	C₁₉⋊C₈	—	4	4	no	—
181	C₂×C₄×C₄⋊C₄	—	19	1	no	—
182	C₂×#340	—	19	2	no	—
183	C₂×#340	—	19	2	no	—
184	C₂×#336	—	19	1	no	—
185	C₄⋊#95	D₁₉	1	1	yes	characteristic
186	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₁₉	#380	1	1	yes	characteristic
188	C₂²×C₁₉	#381	1	1	yes	characteristic
189	C₂²×C₁₉	#387	1	2	yes	—
190	C₂²×C₁₉	#388	1	2	yes	—
191	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
192	C₂²×C₁₉	#416	1	1	yes	characteristic
193	C₂²×C₁₉	#417	1	1	yes	characteristic
194	C₂²×C₁₉	#419	1	1	yes	characteristic
195	C₂²×C₁₉	C₄×D₈	1	2	yes	—
196	C₂²×C₁₉	C₄×SD₁₆	1	2	yes	—
197	C₂²×C₁₉	#440	1	2	yes	—
198	C₂²×C₁₉	#441	1	2	yes	—
199	C₂²×C₁₉	#459	1	1	yes	characteristic
200	C₂²×C₁₉	#461	1	1	yes	characteristic
201	C₂²×C₁₉	#464	1	2	yes	—
202	C₂²×C₁₉	#474	1	1	yes	characteristic
203	C₂²×C₁₉	#476	1	1	yes	characteristic
204	C₂²×C₁₉	#479	1	2	yes	—
205	C₂²×C₁₉	#480	1	2	yes	—
206	C₂²×C₁₉	#482	1	2	yes	—
207	C₂²×C₁₉	#483	1	2	yes	—
208	C₂²×C₁₉	#485	1	2	yes	—
209	C₄×C₁₉	—	2	4	no	—
210	C₄×C₁₉	—	4	2	no	—
211	C₄×C₁₉	—	8	4	no	—
212	C₄×C₁₉	#376	1	1	yes	characteristic
213	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₄×C₁₉	#382	1	1	yes	characteristic
215	C₄×C₁₉	#383	1	1	yes	characteristic
216	C₄×C₁₉	#387	1	2	yes	—
217	C₄×C₁₉	#388	1	2	yes	—
218	Dic₁₉	—	4	4	no	—
219	Dic₁₉	—	4	4	no	—
220	C₂³×C₈	—	19	2	no	—
221	C₂²×C₄⋊C₄	—	19	1	no	—
222	C₂²×C₄⋊C₄	—	19	1	no	—
223	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
224	C₂²×C₄²	—	38	1	no	—
225	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
226	C₄×C₄⋊C₄	—	19	4	no	—
227	C₄×C₄⋊C₄	—	38	2	no	—
228	C₂×#95	—	2	1	no	—
229	C₂×#95	—	2	1	no	—
230	C₂×#95	—	38	1	no	—
231	#340	—	19	8	no	—
232	#340	—	38	4	no	—
233	#336	—	38	2	no	—
234	C₂×C₁₉	#1434	1	1	yes	characteristic
235	C₂×C₁₉	C₄×#102	1	1	yes	characteristic
236	C₂×C₁₉	#1763	1	1	yes	characteristic
237	C₂×C₁₉	#1802	1	1	yes	characteristic
238	C₂×C₁₉	#1805	1	1	yes	characteristic
239	C₂×C₁₉	#1823	1	1	yes	characteristic
240	C₂×C₁₉	#1825	1	1	yes	characteristic
241	C₂×C₁₉	#1918	1	2	yes	—
242	C₂×C₁₉	#1920	1	2	yes	—
243	C₂×C₁₉	#1925	1	2	yes	—
244	C₂×C₁₉	#1927	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	—	38	1	no	—
247	C₂³×C₄	—	38	1	no	—
248	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
249	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
250	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
251	C₂²×C₈	—	19	4	no	—
252	C₂²×C₈	—	38	2	no	—
253	C₂²×C₈	—	38	2	no	—
254	C₂²×C₈	—	38	2	no	—
255	C₂²×C₈	—	38	2	no	—
256	C₂²×C₈	—	38	2	no	—
257	C₂²×C₈	—	38	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	19	4	no	—
264	C₂×C₄⋊C₄	—	19	2	no	—
265	C₂×C₄⋊C₄	—	19	2	no	—
266	C₂×C₄⋊C₄	—	19	2	no	—
267	C₂×C₄⋊C₄	—	19	2	no	—
268	C₂×C₄⋊C₄	—	38	1	no	—
269	C₂×C₄⋊C₄	—	38	1	no	—
270	C₂×C₄⋊C₄	—	38	2	no	—
271	C₂×C₄⋊C₄	—	38	1	no	—
272	C₂×C₄⋊C₄	—	38	1	no	—
273	C₂×C₄⋊C₄	C₄×D₁₉	1	4	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	38	4	no	—
277	C₂×C₄²	—	76	2	no	—
278	C₂×C₄²	—	76	2	no	—
279	C₂×C₄²	C₄×D₁₉	1	2	yes	—
280	C₂×C₄²	D₇₆	1	2	yes	—
281	#95	—	4	2	no	—
282	#95	—	4	2	no	—
283	#95	—	38	4	no	—
284	C₁₉	#10806	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	38	2	no	—
300	C₂²×C₄	—	38	2	no	—
301	C₂²×C₄	—	38	2	no	—
302	C₂²×C₄	—	38	2	no	—
303	C₂²×C₄	—	38	4	no	—
304	C₂²×C₄	—	76	1	no	—
305	C₂²×C₄	—	76	1	no	—
306	C₂²×C₄	—	76	1	no	—
307	C₂²×C₄	—	76	1	no	—
308	C₂²×C₄	—	76	1	no	—
309	C₂²×C₄	—	76	1	no	—
310	C₂²×C₄	—	76	2	no	—
311	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
312	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
313	C₂²×C₄	#64525	1	2	yes	—
314	C₂²×C₄	#64527	1	2	yes	—
315	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
317	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
318	C₂²×C₄	#64541	1	2	yes	—
319	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
320	C₂²×C₄	#64543	1	1	yes	characteristic
321	C₂²×C₄	#64543	1	2	yes	—
322	C₂²×C₄	#64543	1	2	yes	—
323	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
324	C₂²×C₄	#64545	1	1	yes	characteristic
325	C₂×C₈	—	38	4	no	—
326	C₂×C₈	—	38	4	no	—
327	C₂×C₈	—	38	4	no	—
328	C₂×C₈	—	76	2	no	—
329	C₂×C₈	—	76	2	no	—
330	C₂×C₈	—	76	2	no	—
331	C₂×C₈	—	76	2	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	19	4	no	—
337	C₄⋊C₄	—	19	4	no	—
338	C₄⋊C₄	—	38	2	no	—
339	C₄⋊C₄	—	38	4	no	—
340	C₄⋊C₄	—	38	2	no	—
341	C₄⋊C₄	—	38	2	no	—
342	C₄⋊C₄	—	38	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	76	8	no	—
347	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
348	C₂³	C₄×C₂²⋊D₁₉	1	2	yes	—
349	C₂³	C₂×#64525	1	1	yes	characteristic
350	C₂³	#10597378	1	1	yes	characteristic
351	C₂³	#10597381	1	2	yes	—
352	C₂³	#10597384	1	1	yes	characteristic
353	C₂³	C₂×#64527	1	1	yes	characteristic
354	C₂³	#10597388	1	1	yes	characteristic
355	C₂³	#10597392	1	1	yes	characteristic
356	C₂³	#10597396	1	2	yes	—
357	C₂³	#10597397	1	2	yes	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	38	4	no	—
375	C₂×C₄	—	38	4	no	—
376	C₂×C₄	—	76	2	no	—
377	C₂×C₄	—	76	2	no	—
378	C₂×C₄	—	76	2	no	—
379	C₂×C₄	—	76	2	no	—
380	C₂×C₄	—	76	2	no	—
381	C₂×C₄	—	76	2	no	—
382	C₂×C₄	—	76	4	no	—
383	C₂×C₄	—	76	4	no	—
384	C₂×C₄	—	76	2	no	—
385	C₂×C₄	—	76	2	no	—
386	C₂×C₄	#10597266	1	4	yes	—
387	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
388	C₂×C₄	#10597318	1	1	yes	characteristic
389	C₂×C₄	C₄×D₇₆	1	2	yes	—
390	C₂×C₄	#10597323	1	1	yes	characteristic
391	C₂×C₄	#10597323	1	2	yes	—
392	C₂×C₄	#10597323	1	1	yes	characteristic
393	C₂×C₄	#10597325	1	2	yes	—
394	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
395	C₂×C₄	#10597331	1	2	yes	—
396	C₂×C₄	#10597332	1	2	yes	—
397	C₂×C₄	#10597333	1	2	yes	—
398	C₂×C₄	#10597335	1	2	yes	—
399	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
400	C₂×C₄	#10597338	1	1	yes	characteristic
401	C₂×C₄	#10597338	1	2	yes	—
402	C₂×C₄	#10597341	1	1	yes	characteristic
403	C₂×C₄	#10597343	1	1	yes	characteristic
404	C₂×C₄	#10597344	1	2	yes	—
405	C₈	—	76	4	no	—
406	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
407	C₂²	#11926401	1	1	yes	characteristic
408	C₂²	#11926405	1	1	yes	characteristic
409	C₂²	#11926425	1	2	yes	—
410	C₂²	#11926432	1	2	yes	—
411	C₂²	C₂×#10597266	1	1	yes	characteristic
412	C₂²	#11926538	1	1	yes	characteristic
413	C₂²	#11926543	1	1	yes	characteristic
414	C₂²	#11926552	1	1	yes	characteristic
415	C₂²	C₄×#64525	1	2	yes	—
416	C₂²	C₄×#64527	1	2	yes	—
417	C₂²	#11926644	1	2	yes	—
418	C₂²	#11926649	1	2	yes	—
419	C₂²	#11926736	1	1	yes	characteristic
420	C₂²	#11926746	1	1	yes	characteristic
421	C₂²	#11926763	1	2	yes	—
422	C₂²	#11926821	1	1	yes	characteristic
423	C₂²	#11926831	1	1	yes	characteristic
424	C₂²	#11926848	1	2	yes	—
425	C₂²	#11926855	1	2	yes	—
426	C₂²	#11926865	1	2	yes	—
427	C₂²	#11926872	1	2	yes	—
428	C₂²	#11926882	1	2	yes	—
429	C₄	—	2	4	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	4	no	—
432	C₄	—	76	4	no	—
433	C₄	—	76	4	no	—
434	C₄	#11926389	1	1	yes	characteristic
435	C₄	#11926395	1	1	yes	characteristic
436	C₄	#11926408	1	1	yes	characteristic
437	C₄	#11926411	1	1	yes	characteristic
438	C₄	#11926429	1	2	yes	—
439	C₄	#11926436	1	2	yes	—
440	C₂	#14561859	1	1	yes	characteristic
441	C₂	C₄×#10597266	1	1	yes	characteristic
442	C₂	#14563468	1	1	yes	characteristic
443	C₂	#14563632	1	1	yes	characteristic
444	C₂	#14563647	1	1	yes	characteristic
445	C₂	#14563719	1	1	yes	characteristic
446	C₂	#14563727	1	1	yes	characteristic
447	C₂	#14564203	1	2	yes	—
448	C₂	#14564217	1	2	yes	—
449	C₂	#14564252	1	2	yes	—
450	C₂	#14564266	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄⋊#95	D₁₉
hypocenter	C₁₉	#10806
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
11. C₄×C₄⋊Dic₁₉	C₄	semidirect
14. #11926306	C₄	semidirect
284. C₁₉	#10806	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄⋊Dic₁₉	2
C₂×#11926306	2
C₂×#11926299	2
C₁₉×C₄⋊#95	2
#10806	19