Subgroups — #18071980

Order 4864.

922 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572268	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#14561467	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×Dic₁₉	—	2	1	no	—
6	C₂²×C₄×Dic₁₉	—	2	1	no	—
7	C₂²×C₄×Dic₁₉	C₄	1	2	yes	—
8	#11926601	—	2	1	no	—
9	#11926601	C₄	1	2	yes	complemented
10	#11926597	—	2	1	no	—
11	#11926597	C₂²	1	2	yes	—
12	#11926568	C₄	1	2	yes	complemented
13	#11926508	—	2	1	no	—
14	C₄×#64520	—	2	1	no	—
15	C₄²×Dic₁₉	—	2	1	no	—
16	C₄²×Dic₁₉	—	2	1	no	—
17	C₄²×Dic₁₉	C₄	1	2	yes	—
18	C₄²×Dic₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#432	—	2	1	no	—
21	C₁₉×#432	C₄	1	2	yes	complemented
22	C₁₉×#431	—	2	1	no	—
23	C₁₉×#431	C₂²	1	2	yes	—
24	C₁₉×#423	C₄	1	2	yes	complemented
25	C₁₉×#407	—	2	1	no	—
26	C₄×M₁₆×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×Dic₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₄×Dic₁₉	—	2	8	no	—
45	C₂×C₄×Dic₁₉	—	2	8	no	—
46	C₂×C₄×Dic₁₉	—	2	2	no	—
47	C₂×C₄×Dic₁₉	—	2	2	no	—
48	C₂×C₄×Dic₁₉	—	2	2	no	—
49	C₂×C₄×Dic₁₉	—	2	2	no	—
50	C₂×C₄×Dic₁₉	—	2	2	no	—
51	C₂×C₄×Dic₁₉	—	2	8	no	—
52	C₂×C₄×Dic₁₉	C₂×C₄	1	4	yes	—
53	C₂×#64520	—	2	2	no	—
54	C₁₉×C₄⋊C₈	—	2	2	no	—
55	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
56	C₁₉×C₂²⋊C₈	—	2	2	no	—
57	C₁₉×C₂²⋊C₈	—	2	2	no	—
58	C₁₉×#97	—	2	2	no	—
59	C₄×C₈×C₁₉	—	2	2	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
63	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	complemented
64	#10597260	—	2	2	no	—
65	C₄×C₁₉⋊C₈	—	2	2	no	—
66	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	—	2	4	no	—
68	C₂²×C₄×C₁₉	—	2	4	no	—
69	C₂²×C₄×C₁₉	—	2	4	no	—
70	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₁₉	—	2	8	no	—
89	C₂²×Dic₁₉	—	2	8	no	—
90	C₂²×Dic₁₉	—	2	8	no	—
91	C₂²×Dic₁₉	—	2	4	no	—
92	M₁₆×C₁₉	—	4	4	no	—
93	C₂×C₈×C₁₉	—	2	4	no	—
94	C₄²×C₁₉	C₄²	1	1	yes	characteristic
95	C₄²×C₁₉	C₄²	1	1	yes	characteristic
96	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₄×Dic₁₉	—	2	8	no	—
111	C₄×Dic₁₉	—	2	8	no	—
112	C₄×Dic₁₉	—	2	8	no	—
113	C₄×Dic₁₉	—	2	8	no	—
114	C₄×Dic₁₉	—	2	8	no	—
115	C₄×Dic₁₉	—	2	4	no	—
116	C₄×Dic₁₉	M₁₆	1	8	yes	complemented
117	#64520	—	4	4	no	—
118	C₂×C₁₉⋊C₈	—	2	4	no	—
119	#7867	—	19	1	no	maximal, Sylow
120	C₂³×C₁₉	—	2	2	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	#95	1	1	yes	characteristic
124	C₂³×C₁₉	#95	1	1	yes	characteristic
125	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	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	—	2	2	no	—
141	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#104	1	4	yes	—
148	C₂×C₄×C₁₉	#104	1	4	yes	—
149	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
156	C₂×Dic₁₉	—	2	8	no	—
157	C₂×Dic₁₉	—	2	8	no	—
158	C₂×Dic₁₉	—	2	32	no	—
159	C₂×Dic₁₉	—	2	8	no	—
160	C₈×C₁₉	—	4	4	no	—
161	C₁₉⋊C₈	—	4	4	no	—
162	#2920	—	19	1	no	—
163	#2920	D₁₉	1	1	yes	characteristic
164	C₂×C₄³	—	19	1	no	—
165	#1276	—	19	4	no	—
166	C₂²×C₁₉	—	2	8	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	#339	1	2	yes	—
174	C₂²×C₁₉	#339	1	2	yes	—
175	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
176	C₂²×C₁₉	#407	1	2	yes	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	2	1	no	—
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	#339	1	2	yes	—
184	C₄×C₁₉	#339	1	2	yes	—
185	C₄×C₁₉	C₄×M₁₆	1	2	yes	—
186	C₄×C₁₉	C₂×#104	1	2	yes	—
187	C₄×C₁₉	C₂×#104	1	2	yes	—
188	C₄×C₁₉	#423	1	2	yes	—
189	Dic₁₉	—	2	16	no	—
190	C₂²×C₄²	—	19	2	no	—
191	C₂²×C₄²	—	38	1	no	—
192	C₂²×C₄²	—	38	1	no	—
193	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
194	#432	—	2	1	no	—
195	#432	—	19	2	no	—
196	#432	—	38	1	no	—
197	#432	Dic₁₉	1	2	yes	complemented
198	#431	—	2	1	no	—
199	#431	—	19	2	no	—
200	#431	—	38	1	no	—
201	#431	C₂×D₁₉	1	2	yes	—
202	#423	—	19	2	no	—
203	#423	Dic₁₉	1	2	yes	complemented
204	#407	—	2	1	no	—
205	#407	—	38	1	no	—
206	C₄×M₁₆	—	2	1	no	—
207	C₄×M₁₆	—	38	1	no	—
208	C₄³	—	19	2	no	—
209	C₄³	—	19	2	no	—
210	C₄³	—	38	1	no	—
211	C₄³	—	38	1	no	—
212	C₂×C₁₉	—	2	2	no	—
213	C₂×C₁₉	—	2	2	no	—
214	C₂×C₁₉	—	2	2	no	—
215	C₂×C₁₉	#1728	1	1	yes	characteristic
216	C₂×C₁₉	C₂×#339	1	1	yes	characteristic
217	C₂×C₁₉	C₂×#339	1	1	yes	characteristic
218	C₂³×C₄	—	38	2	no	—
219	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
220	C₂³×C₄	D₇₆	1	1	yes	characteristic
221	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	38	2	no	—
224	C₂×C₄²	—	19	4	no	—
225	C₂×C₄²	—	38	8	no	—
226	C₂×C₄²	—	38	8	no	—
227	C₂×C₄²	—	38	8	no	—
228	C₂×C₄²	—	38	2	no	—
229	C₂×C₄²	—	38	2	no	—
230	C₂×C₄²	—	38	2	no	—
231	C₂×C₄²	—	38	2	no	—
232	C₂×C₄²	—	38	2	no	—
233	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
234	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
235	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
236	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
237	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
238	C₂×C₄²	D₇₆	1	1	yes	characteristic
239	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
241	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	19	4	no	—
247	C₄⋊C₈	—	38	2	no	—
248	C₄⋊C₈	C₂×Dic₁₉	1	4	yes	complemented
249	C₂²⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	38	2	no	—
252	C₂²⋊C₈	—	38	2	no	—
253	#97	—	2	2	no	—
254	#97	—	38	2	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	—	38	2	no	—
257	C₁₉	#7867	1	1	yes	characteristic, complemented, Sylow
258	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	38	8	no	—
263	C₂²×C₄	—	38	8	no	—
264	C₂²×C₄	—	38	8	no	—
265	C₂²×C₄	—	38	4	no	—
266	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
267	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
268	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
274	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
284	M₁₆	—	4	4	no	—
285	M₁₆	—	76	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	38	4	no	—
288	C₄²	—	19	8	no	—
289	C₄²	—	38	8	no	—
290	C₄²	—	38	8	no	—
291	C₄²	—	38	8	no	—
292	C₄²	—	38	8	no	—
293	C₄²	—	38	8	no	—
294	C₄²	—	38	4	no	—
295	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
296	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
297	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
298	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
299	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
300	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
301	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
302	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
303	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
304	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
305	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
306	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
307	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
308	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
309	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
310	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	C₁₉⋊#95	1	1	yes	characteristic
315	C₂³	C₁₉⋊#95	1	1	yes	characteristic
316	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	38	8	no	—
333	C₂×C₄	—	38	8	no	—
334	C₂×C₄	—	38	32	no	—
335	C₂×C₄	—	38	8	no	—
336	C₂×C₄	#10597282	1	4	yes	—
337	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
340	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
341	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
342	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
343	C₂×C₄	#10597294	1	4	yes	—
344	C₂×C₄	M₁₆×D₁₉	1	4	yes	—
345	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
346	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
349	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
351	C₈	—	4	4	no	—
352	C₈	—	76	4	no	—
353	C₂²	—	2	8	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	#11926303	1	2	yes	—
361	C₂²	#11926305	1	2	yes	—
362	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
363	C₂²	#11926507	1	2	yes	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	38	16	no	—
371	C₄	#11926303	1	2	yes	—
372	C₄	#11926305	1	2	yes	—
373	C₄	M₁₆×Dic₁₉	1	2	yes	—
374	C₄	C₂×#10597282	1	2	yes	—
375	C₄	C₂×#10597294	1	2	yes	—
376	C₄	#11926567	1	2	yes	—
377	C₂	—	2	2	no	—
378	C₂	—	2	2	no	—
379	C₂	—	2	2	no	—
380	C₂	#14563328	1	1	yes	characteristic
381	C₂	C₂×#11926303	1	1	yes	characteristic
382	C₂	C₂×#11926305	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2920	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2920	D₁₉
hypocenter	C₁₉	#7867
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #14561467	C₂	semidirect
9. #11926601	C₄	semidirect
12. #11926568	C₄	semidirect
21. C₁₉×#432	C₄	semidirect
24. C₁₉×#423	C₄	semidirect
55. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
63. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
116. C₄×Dic₁₉	M₁₆	semidirect
197. #432	Dic₁₉	semidirect
203. #423	Dic₁₉	semidirect
248. C₄⋊C₈	C₂×Dic₁₉	semidirect
257. C₁₉	#7867	semidirect

Maximal subgroups

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

subgroup	index
#14572268	2
C₂×C₄²×Dic₁₉	2
#14561467	2
C₁₉×#2920	2
#7867	19