Subgroups — C₂×C₁₉×#1352 #18017673

Order 4864.

712 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#399	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#323	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1352	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
7	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
8	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
11	C₁₉×#399	—	2	1	no	—
12	C₁₉×#399	—	2	1	no	—
13	C₁₉×#399	C₄	1	2	yes	complemented
14	C₁₉×#399	C₂²	1	2	yes	—
15	C₂×C₁₉×#95	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#342	—	2	1	no	—
17	C₁₉×#342	C₂²	1	2	yes	—
18	C₁₉×#323	—	2	1	no	—
19	C₁₉×#323	C₂²	1	2	yes	—
20	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	—	2	1	no	—
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂³×C₄×C₁₉	—	4	1	no	—
24	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	—	4	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
31	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
34	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
35	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
43	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₁₉×C₂²⋊C₈	—	2	2	no	—
48	C₁₉×C₂²⋊C₈	—	4	1	no	—
49	C₁₉×#95	—	2	1	no	—
50	C₁₉×#95	C₂×C₄	1	2	yes	complemented
51	C₂⁴×C₁₉	—	2	1	no	—
52	C₂⁴×C₁₉	—	2	1	no	—
53	C₂⁴×C₁₉	—	2	2	no	—
54	C₂⁴×C₁₉	—	4	2	no	—
55	C₂⁴×C₁₉	—	4	2	no	—
56	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂⁴×C₁₉	SD₁₆	1	2	yes	—
59	C₂⁴×C₁₉	Q₁₆	1	2	yes	—
60	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	—	2	4	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	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	4	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	—	4	2	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	8	2	no	—
79	C₂²×C₄×C₁₉	—	8	2	no	—
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₁₉	—	4	2	no	—
85	C₂×C₈×C₁₉	—	8	2	no	—
86	C₄⋊C₄×C₁₉	—	4	2	no	—
87	C₄⋊C₄×C₁₉	—	4	4	no	—
88	C₄⋊C₄×C₁₉	—	4	4	no	—
89	C₄⋊C₄×C₁₉	—	4	2	no	—
90	C₂²⋊C₄×C₁₉	—	2	4	no	—
91	C₂²⋊C₄×C₁₉	—	4	1	no	—
92	C₂²⋊C₄×C₁₉	—	4	1	no	—
93	C₂²⋊C₄×C₁₉	—	4	1	no	—
94	C₂²⋊C₄×C₁₉	—	4	1	no	—
95	C₂²⋊C₄×C₁₉	—	4	4	no	—
96	C₂²⋊C₄×C₁₉	—	4	4	no	—
97	C₂²⋊C₄×C₁₉	—	4	4	no	—
98	C₂²⋊C₄×C₁₉	—	4	2	no	—
99	C₂×#1352	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₁₉	—	2	2	no	—
101	C₂³×C₁₉	—	2	2	no	—
102	C₂³×C₁₉	—	2	2	no	—
103	C₂³×C₁₉	—	2	2	no	—
104	C₂³×C₁₉	—	2	1	no	—
105	C₂³×C₁₉	—	2	1	no	—
106	C₂³×C₁₉	—	2	2	no	—
107	C₂³×C₁₉	—	2	2	no	—
108	C₂³×C₁₉	—	2	1	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	4	1	no	—
111	C₂³×C₁₉	—	4	1	no	—
112	C₂³×C₁₉	—	4	1	no	—
113	C₂³×C₁₉	—	4	4	no	—
114	C₂³×C₁₉	—	4	4	no	—
115	C₂³×C₁₉	—	4	1	no	—
116	C₂³×C₁₉	—	4	2	no	—
117	C₂³×C₁₉	—	4	2	no	—
118	C₂³×C₁₉	—	8	1	no	—
119	C₂³×C₁₉	—	8	4	no	—
120	C₂³×C₁₉	—	8	1	no	—
121	C₂³×C₁₉	#99	1	1	yes	characteristic
122	C₂³×C₁₉	#99	1	1	yes	characteristic
123	C₂³×C₁₉	#103	1	2	yes	—
124	C₂³×C₁₉	#103	1	2	yes	—
125	C₂³×C₁₉	#104	1	2	yes	—
126	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
128	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
129	C₂×C₄×C₁₉	—	2	4	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	8	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	—	4	2	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	8	1	no	—
149	C₂×C₄×C₁₉	—	8	2	no	—
150	C₂×C₄×C₁₉	—	8	2	no	—
151	C₂×C₄×C₁₉	—	8	8	no	—
152	C₂×C₄×C₁₉	—	8	2	no	—
153	C₂×C₄×C₁₉	—	8	2	no	—
154	C₈×C₁₉	—	8	2	no	—
155	C₂×#399	C₂×C₁₉	1	1	yes	characteristic
156	C₂×#342	C₂×C₁₉	1	1	yes	characteristic
157	C₂×#323	C₂×C₁₉	1	1	yes	characteristic
158	#1352	C₂×C₁₉	1	4	yes	direct product factor
159	C₂²×C₁₉	—	2	1	no	—
160	C₂²×C₁₉	—	2	1	no	—
161	C₂²×C₁₉	—	2	4	no	—
162	C₂²×C₁₉	—	2	4	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	4	2	no	—
169	C₂²×C₁₉	—	4	1	no	—
170	C₂²×C₁₉	—	4	1	no	—
171	C₂²×C₁₉	—	4	1	no	—
172	C₂²×C₁₉	—	4	1	no	—
173	C₂²×C₁₉	—	4	4	no	—
174	C₂²×C₁₉	—	4	4	no	—
175	C₂²×C₁₉	—	4	1	no	—
176	C₂²×C₁₉	—	4	1	no	—
177	C₂²×C₁₉	—	8	1	no	—
178	C₂²×C₁₉	—	8	1	no	—
179	C₂²×C₁₉	—	8	2	no	—
180	C₂²×C₁₉	—	8	2	no	—
181	C₂²×C₁₉	#328	1	2	yes	—
182	C₂²×C₁₉	#328	1	2	yes	—
183	C₂²×C₁₉	#352	1	2	yes	—
184	C₂²×C₁₉	#353	1	2	yes	—
185	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
188	C₄×C₁₉	—	4	4	no	—
189	C₄×C₁₉	—	4	1	no	—
190	C₄×C₁₉	—	4	1	no	—
191	C₄×C₁₉	—	4	1	no	—
192	C₄×C₁₉	—	4	1	no	—
193	C₄×C₁₉	—	8	4	no	—
194	C₄×C₁₉	—	8	2	no	—
195	C₂²×C₄⋊C₄	—	2	1	no	—
196	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
197	C₂²×C₂²⋊C₄	—	2	1	no	—
198	C₂²×C₂²⋊C₄	—	2	1	no	—
199	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
200	C₂×C₂²⋊C₈	—	2	1	no	—
201	#399	—	2	1	no	—
202	#399	—	2	1	no	—
203	#399	C₄×C₁₉	1	2	yes	complemented
204	#399	C₂²×C₁₉	1	2	yes	—
205	C₂×#95	C₄×C₁₉	1	1	yes	characteristic, complemented
206	#342	—	2	1	no	—
207	#342	C₂²×C₁₉	1	2	yes	—
208	#323	—	2	1	no	—
209	#323	C₂²×C₁₉	1	2	yes	—
210	C₂×C₁₉	—	2	1	no	—
211	C₂×C₁₉	—	2	1	no	—
212	C₂×C₁₉	—	2	2	no	—
213	C₂×C₁₉	—	4	1	no	—
214	C₂×C₁₉	—	4	2	no	—
215	C₂×C₁₉	—	4	1	no	—
216	C₂×C₁₉	#1352	1	4	yes	direct product factor
217	C₂×C₁₉	C₂×#328	1	1	yes	characteristic
218	C₂×C₁₉	C₂×#352	1	1	yes	characteristic
219	C₂×C₁₉	C₂×#353	1	1	yes	characteristic
220	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
221	C₂³×C₄	—	2	1	no	—
222	C₂³×C₄	—	2	1	no	—
223	C₂³×C₄	—	4	1	no	—
224	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
225	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
226	C₂²×C₈	—	4	1	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	4	1	no	—
231	C₂×C₄⋊C₄	—	4	1	no	—
232	C₂×C₄⋊C₄	—	4	4	no	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
234	C₂×C₂²⋊C₄	—	2	4	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	4	1	no	—
239	C₂×C₂²⋊C₄	—	4	1	no	—
240	C₂×C₂²⋊C₄	—	4	4	no	—
241	C₂×C₂²⋊C₄	—	4	1	no	—
242	C₂×C₂²⋊C₄	—	4	2	no	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	4	1	no	—
249	#95	—	2	1	no	—
250	#95	C₂×C₄×C₁₉	1	2	yes	complemented
251	C₁₉	C₂×#1352	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁴	—	2	1	no	—
253	C₂⁴	—	2	1	no	—
254	C₂⁴	—	2	2	no	—
255	C₂⁴	—	4	2	no	—
256	C₂⁴	—	4	2	no	—
257	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
258	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
259	C₂⁴	SD₁₆×C₁₉	1	2	yes	—
260	C₂⁴	Q₁₆×C₁₉	1	2	yes	—
261	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	8	2	no	—
280	C₂²×C₄	—	8	2	no	—
281	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	—	8	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	4	1	no	—
293	C₂²⋊C₄	—	4	1	no	—
294	C₂²⋊C₄	—	4	1	no	—
295	C₂²⋊C₄	—	4	1	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	—	4	1	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	8	1	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	8	1	no	—
321	C₂³	C₁₉×#99	1	1	yes	characteristic
322	C₂³	C₁₉×#99	1	1	yes	characteristic
323	C₂³	C₁₉×#103	1	2	yes	—
324	C₂³	C₁₉×#103	1	2	yes	—
325	C₂³	C₁₉×#104	1	2	yes	—
326	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
327	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
328	C₂³	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	8	1	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	8	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	8	2	no	—
354	C₈	—	8	2	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	8	1	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	C₁₉×#328	1	2	yes	—
378	C₂²	C₁₉×#328	1	2	yes	—
379	C₂²	C₁₉×#352	1	2	yes	—
380	C₂²	C₁₉×#353	1	2	yes	—
381	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
382	C₂²	C₂×C₁₉×#103	1	1	yes	characteristic
383	C₂²	C₂×C₁₉×#104	1	1	yes	characteristic
384	C₄	—	4	4	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	4	no	—
390	C₄	—	8	2	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	2	2	no	—
394	C₂	—	4	1	no	—
395	C₂	—	4	1	no	—
396	C₂	—	4	2	no	—
397	C₂	C₁₉×#1352	1	4	yes	direct product factor
398	C₂	C₂×C₁₉×#328	1	1	yes	characteristic
399	C₂	C₂×C₁₉×#352	1	1	yes	characteristic
400	C₂	C₂×C₁₉×#353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#99
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂²×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#1352	C₂	direct (N × H)
6. C₂²×C₄⋊C₄×C₁₉	C₄	semidirect
13. C₁₉×#399	C₄	semidirect
15. C₂×C₁₉×#95	C₄	semidirect
33. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
50. C₁₉×#95	C₂×C₄	semidirect
99. C₂×#1352	C₁₉	direct (N × H)
158. #1352	C₂×C₁₉	direct (N × H)
196. C₂²×C₄⋊C₄	C₄×C₁₉	semidirect
203. #399	C₄×C₁₉	semidirect
205. C₂×#95	C₄×C₁₉	semidirect
216. C₂×C₁₉	#1352	direct (N × H)
233. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
250. #95	C₂×C₄×C₁₉	semidirect
251. C₁₉	C₂×#1352	direct (N × H)
397. C₂	C₁₉×#1352	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#399	2
C₂×C₁₉×#342	2
C₂×C₁₉×#323	2
C₁₉×#1352	2
C₂×#1352	19

Subgroups — C2×C19×#1352 #18017673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1352 #18017673