Subgroups — #18072308

Order 4864.

606 conjugacy classes of subgroups.

The subgroup lattice has 382 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	#14566042	C₂	1	1	yes	maximal, characteristic
3	#14561492	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597372	C₄	1	2	yes	—
6	#11926601	C₄	1	2	yes	complemented
7	#11926601	C₂²	1	2	yes	—
8	#11926597	—	2	1	no	—
9	#11926597	—	2	1	no	—
10	#11926568	—	2	1	no	—
11	#11926508	—	2	1	no	—
12	C₄×#64520	C₄	1	2	yes	complemented
13	#11926414	—	2	1	no	—
14	#11926410	—	2	1	no	—
15	#11926404	—	2	1	no	—
16	#11926404	—	2	1	no	—
17	C₄×C₄⋊Dic₁₉	C₄	1	2	yes	—
18	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#432	—	2	1	no	—
21	C₁₉×#432	C₂²	1	2	yes	—
22	C₁₉×#431	—	2	1	no	—
23	C₁₉×#431	C₄	1	2	yes	complemented
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	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
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	D₄	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	Q₈	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
44	#10597372	—	4	4	no	—
45	C₂×C₄⋊Dic₁₉	—	2	2	no	—
46	C₂×C₄⋊Dic₁₉	—	2	2	no	—
47	C₂×C₄⋊Dic₁₉	—	2	2	no	—
48	C₂×C₄×Dic₁₉	C₂×C₄	1	4	yes	—
49	C₂×#64520	—	2	2	no	—
50	C₁₉×C₄⋊C₈	—	2	2	no	—
51	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
52	C₁₉×C₂²⋊C₈	—	2	2	no	—
53	C₁₉×C₂²⋊C₈	—	2	2	no	—
54	C₁₉×#97	—	2	2	no	—
55	C₄×C₈×C₁₉	—	2	2	no	—
56	C₁₉⋊#95	—	2	2	no	—
57	C₁₉⋊#95	—	2	2	no	—
58	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
62	#10597260	C₂×C₄	1	4	yes	—
63	C₄×C₁₉⋊C₈	—	2	2	no	—
64	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²⋊C₄	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	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×Dic₁₉	—	2	4	no	—
88	M₁₆×C₁₉	—	4	4	no	—
89	C₂×C₈×C₁₉	—	2	4	no	—
90	C₄²×C₁₉	C₄²	1	1	yes	characteristic
91	C₄²×C₁₉	C₄²	1	1	yes	characteristic
92	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²⋊Dic₁₉	—	4	4	no	—
107	C₄⋊Dic₁₉	—	4	4	no	—
108	C₄⋊Dic₁₉	—	4	4	no	—
109	C₄⋊Dic₁₉	—	4	4	no	—
110	C₄×Dic₁₉	—	4	4	no	—
111	#64520	—	4	4	no	—
112	C₂×C₁₉⋊C₈	—	2	4	no	—
113	#7953	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	4	1	no	—
117	C₂³×C₁₉	—	4	1	no	—
118	C₂³×C₁₉	#95	1	1	yes	characteristic
119	C₂³×C₁₉	#95	1	1	yes	characteristic
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
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	—	4	1	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
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	#100	1	2	yes	—
146	C₂×C₄×C₁₉	#101	1	2	yes	—
147	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×Dic₁₉	—	4	4	no	—
154	C₂×Dic₁₉	—	4	4	no	—
155	C₂×Dic₁₉	—	4	4	no	—
156	C₈×C₁₉	—	4	4	no	—
157	C₁₉⋊C₈	—	4	4	no	—
158	#2920	—	19	1	no	—
159	#2920	D₁₉	1	1	yes	characteristic
160	#2285	—	19	1	no	—
161	#1285	—	19	4	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	4	2	no	—
171	C₂²×C₁₉	—	4	2	no	—
172	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
173	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
174	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
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	H(3,ℤ/4)	1	2	yes	—
184	C₄×C₁₉	#343	1	2	yes	—
185	C₄×C₁₉	#343	1	2	yes	—
186	C₄×C₁₉	#421	1	2	yes	—
187	Dic₁₉	—	8	4	no	—
188	C₂×#117	—	19	2	no	—
189	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
190	#432	—	2	1	no	—
191	#432	—	19	2	no	—
192	#432	—	19	2	no	—
193	#432	C₂×D₁₉	1	2	yes	—
194	#431	—	2	1	no	—
195	#431	—	38	1	no	—
196	#431	—	38	1	no	—
197	#431	Dic₁₉	1	2	yes	complemented
198	#423	—	38	1	no	—
199	#423	Dic₁₉	1	2	yes	complemented
200	#407	—	2	1	no	—
201	#407	—	38	1	no	—
202	C₄×M₁₆	—	2	1	no	—
203	C₄×M₁₆	—	19	2	no	—
204	#384	—	38	1	no	—
205	#382	—	38	1	no	—
206	#380	—	38	1	no	—
207	#380	—	38	1	no	—
208	C₄×C₄⋊C₄	—	19	2	no	—
209	C₄×C₄⋊C₄	—	19	2	no	—
210	C₂×C₁₉	—	2	1	no	—
211	C₂×C₁₉	—	2	1	no	—
212	C₂×C₁₉	—	4	1	no	—
213	C₂×C₁₉	—	4	1	no	—
214	C₂×C₁₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
215	C₂×C₁₉	#1733	1	1	yes	characteristic
216	C₂×C₁₉	C₂×#343	1	1	yes	characteristic
217	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
218	C₂³×C₄	D₇₆	1	1	yes	characteristic
219	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	38	2	no	—
222	#117	—	76	4	no	—
223	C₂×C₄⋊C₄	—	38	2	no	—
224	C₂×C₄⋊C₄	—	38	2	no	—
225	C₂×C₄⋊C₄	—	38	2	no	—
226	C₂×C₂²⋊C₄	—	38	2	no	—
227	C₂×C₄²	—	19	4	no	—
228	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
229	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
233	C₂×C₄²	D₇₆	1	1	yes	characteristic
234	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
236	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
237	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	38	2	no	—
242	C₄⋊C₈	—	38	2	no	—
243	C₄⋊C₈	C₂×Dic₁₉	1	4	yes	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	38	2	no	—
247	C₂²⋊C₈	—	38	2	no	—
248	#97	—	2	2	no	—
249	#97	—	19	4	no	—
250	C₄×C₈	—	2	2	no	—
251	C₄×C₈	—	38	2	no	—
252	#95	—	38	2	no	—
253	#95	—	38	2	no	—
254	C₁₉	#7953	1	1	yes	characteristic, complemented, Sylow
255	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	38	4	no	—
261	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
262	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
263	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
279	M₁₆	—	4	4	no	—
280	M₁₆	—	76	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	38	4	no	—
283	C₄⋊C₄	—	76	4	no	—
284	C₄⋊C₄	—	76	4	no	—
285	C₄⋊C₄	—	76	4	no	—
286	C₂²⋊C₄	—	76	4	no	—
287	C₄²	—	76	4	no	—
288	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
289	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
290	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
292	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
294	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
295	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
296	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
297	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
298	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
299	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
300	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
302	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
303	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	C₁₉⋊#95	1	1	yes	characteristic
309	C₂³	C₁₉⋊#95	1	1	yes	characteristic
310	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
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	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	76	4	no	—
330	C₂×C₄	—	76	4	no	—
331	C₂×C₄	—	76	4	no	—
332	C₂×C₄	#10597280	1	2	yes	—
333	C₂×C₄	#10597281	1	2	yes	—
334	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
335	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
336	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
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	C₂×C₄×Dic₁₉	1	1	yes	characteristic
341	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
344	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	76	4	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
359	C₂²	C₂×#10597280	1	1	yes	characteristic
360	C₂²	C₂×#10597281	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
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	—	152	4	no	—
370	C₄	#11926301	1	2	yes	—
371	C₄	#11926312	1	2	yes	—
372	C₄	#11926312	1	2	yes	—
373	C₄	#11926561	1	2	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	4	1	no	—
377	C₂	—	4	1	no	—
378	C₂	C₂×#11926301	1	1	yes	characteristic
379	C₂	#14563344	1	1	yes	characteristic
380	C₂	C₂×#11926312	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₁₉⋊#95
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	#7953
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #14561492	C₂	semidirect
6. #11926601	C₄	semidirect
12. C₄×#64520	C₄	semidirect
23. C₁₉×#431	C₄	semidirect
24. C₁₉×#423	C₄	semidirect
197. #431	Dic₁₉	semidirect
199. #423	Dic₁₉	semidirect
254. C₁₉	#7953	semidirect

Maximal subgroups

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

subgroup	index
#14572268	2
#14566042	2
#14561492	2
C₁₉×#2920	2
#7953	19