Subgroups — C₂²×C₁₉×#339 #18026300

Order 4864.

2830 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#339	C₂	1	12	yes	maximal, direct product factor
5	C₂⁴×C₄×C₁₉	—	2	1	no	—
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₉	—	2	4	no	—
8	C₂²×M₁₆×C₁₉	—	2	3	no	—
9	C₂²×M₁₆×C₁₉	C₄	1	8	yes	complemented
10	C₂²×M₁₆×C₁₉	C₂²	1	6	yes	—
11	C₂³×C₈×C₁₉	—	2	1	no	—
12	C₂×C₁₉×#117	—	2	3	no	—
13	C₂×C₁₉×#117	—	2	3	no	—
14	C₂×C₁₉×#117	C₄	1	6	yes	complemented
15	C₂×C₁₉×#117	C₂²	1	6	yes	—
16	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	complemented
17	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄²×C₁₉	—	2	3	no	—
19	C₂²×C₄²×C₁₉	—	2	4	no	—
20	C₂²×C₄²×C₁₉	—	2	1	no	—
21	C₂²×C₄²×C₁₉	C₄	1	8	yes	complemented
22	C₂²×C₄²×C₁₉	C₂²	1	6	yes	—
23	C₁₉×#339	C₂²	1	16	yes	direct product factor
24	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	—	2	16	no	—
26	C₂³×C₄×C₁₉	—	2	8	no	—
27	C₂³×C₄×C₁₉	—	2	6	no	—
28	C₂³×C₄×C₁₉	—	2	2	no	—
29	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
30	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂×C₄	1	3	yes	—
33	C₂³×C₄×C₁₉	D₄	1	3	yes	—
34	C₂³×C₄×C₁₉	D₄	1	4	yes	—
35	C₂³×C₄×C₁₉	D₄	1	3	yes	—
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
39	C₂×M₁₆×C₁₉	—	2	24	no	—
40	C₂×M₁₆×C₁₉	—	2	12	no	—
41	C₂×M₁₆×C₁₉	—	2	6	no	—
42	C₂×M₁₆×C₁₉	C₂×C₄	1	24	yes	complemented
43	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
44	C₂²×C₈×C₁₉	—	2	8	no	—
45	C₂²×C₈×C₁₉	—	2	6	no	—
46	C₁₉×#117	—	2	12	no	—
47	C₁₉×#117	—	2	6	no	—
48	C₁₉×#117	—	2	6	no	—
49	C₁₉×#117	C₂×C₄	1	12	yes	complemented
50	C₁₉×#117	C₂³	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	12	yes	complemented
53	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
55	C₂×C₄²×C₁₉	—	2	24	no	—
56	C₂×C₄²×C₁₉	—	2	6	no	—
57	C₂×C₄²×C₁₉	—	2	6	no	—
58	C₂×C₄²×C₁₉	—	2	12	no	—
59	C₂×C₄²×C₁₉	—	2	6	no	—
60	C₂×C₄²×C₁₉	C₂×C₄	1	24	yes	complemented
61	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
62	C₂⁴×C₁₉	—	2	8	no	—
63	C₂⁴×C₁₉	C₂²⋊C₄	1	3	yes	—
64	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
65	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂⁴×C₁₉	C₄⋊C₄	1	4	yes	—
67	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
68	C₂²×C₄×C₁₉	—	2	64	no	—
69	C₂²×C₄×C₁₉	—	2	48	no	—
70	C₂²×C₄×C₁₉	—	2	24	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	2	12	no	—
73	C₂²×C₄×C₁₉	—	4	8	no	—
74	C₂²×C₄×C₁₉	C₄²	1	12	yes	—
75	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	12	yes	—
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	3	yes	—
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	3	yes	—
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	6	yes	—
80	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	12	yes	—
82	C₂²×C₄×C₁₉	C₄⋊C₄	1	12	yes	—
83	C₂²×C₄×C₁₉	C₄⋊C₄	1	12	yes	—
84	C₂²×C₄×C₁₉	C₄⋊C₄	1	12	yes	—
85	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
95	C₂²×C₄×C₁₉	C₂×Q₈	1	6	yes	—
96	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
97	M₁₆×C₁₉	—	2	24	no	—
98	M₁₆×C₁₉	—	2	4	no	—
99	M₁₆×C₁₉	C₂²×C₄	1	8	yes	complemented
100	C₂×C₈×C₁₉	—	2	24	no	—
101	C₂×C₈×C₁₉	—	2	4	no	—
102	C₄⋊C₄×C₁₉	—	2	12	no	—
103	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	complemented
104	C₂²⋊C₄×C₁₉	—	2	12	no	—
105	C₂²⋊C₄×C₁₉	—	2	4	no	—
106	C₄²×C₁₉	—	2	24	no	—
107	C₄²×C₁₉	—	2	12	no	—
108	C₄²×C₁₉	—	2	4	no	—
109	C₄²×C₁₉	—	2	4	no	—
110	C₄²×C₁₉	C₂²×C₄	1	8	yes	complemented
111	C₂²×#339	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₉	—	2	16	no	—
113	C₂³×C₁₉	—	2	16	no	—
114	C₂³×C₁₉	—	2	12	no	—
115	C₂³×C₁₉	—	2	12	no	—
116	C₂³×C₁₉	#95	1	12	yes	—
117	C₂³×C₁₉	#95	1	4	yes	—
118	C₂³×C₁₉	#104	1	8	yes	—
119	C₂³×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
121	C₂³×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
122	C₂³×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
123	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	—	2	16	no	—
125	C₂×C₄×C₁₉	—	2	96	no	—
126	C₂×C₄×C₁₉	—	2	8	no	—
127	C₂×C₄×C₁₉	—	2	8	no	—
128	C₂×C₄×C₁₉	—	4	24	no	—
129	C₂×C₄×C₁₉	#95	1	24	yes	—
130	C₂×C₄×C₁₉	#95	1	12	yes	—
131	C₂×C₄×C₁₉	#95	1	12	yes	—
132	C₂×C₄×C₁₉	C₂×C₄²	1	6	yes	—
133	C₂×C₄×C₁₉	C₂×C₄²	1	6	yes	—
134	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
135	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
136	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
137	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
138	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
139	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
140	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
141	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
142	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
143	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	6	yes	—
144	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
150	C₈×C₁₉	—	2	8	no	—
151	C₂³×M₁₆	C₂×C₁₉	1	1	yes	characteristic
152	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic
153	C₂³×C₄²	C₂×C₁₉	1	1	yes	characteristic
154	C₂×#339	C₂×C₁₉	1	12	yes	direct product factor
155	C₂²×C₁₉	—	2	2	no	—
156	C₂²×C₁₉	—	2	6	no	—
157	C₂²×C₁₉	—	2	12	no	—
158	C₂²×C₁₉	—	2	24	no	—
159	C₂²×C₁₉	—	2	12	no	—
160	C₂²×C₁₉	#339	1	16	yes	direct product factor
161	C₂²×C₁₉	C₂×#95	1	6	yes	—
162	C₂²×C₁₉	C₂×#95	1	6	yes	—
163	C₂²×C₁₉	C₂×#104	1	12	yes	—
164	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₄×C₁₉	—	2	16	no	—
168	C₄×C₁₉	—	4	8	no	—
169	C₄×C₁₉	C₂×#95	1	6	yes	—
170	C₄×C₁₉	C₂×#95	1	6	yes	—
171	C₄×C₁₉	C₂²×C₄²	1	1	yes	characteristic
172	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
173	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₄×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₂⁴×C₄	—	2	1	no	—
176	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
177	C₂²×M₁₆	—	2	4	no	—
178	C₂²×M₁₆	—	2	3	no	—
179	C₂²×M₁₆	C₄×C₁₉	1	8	yes	complemented
180	C₂²×M₁₆	C₂²×C₁₉	1	6	yes	—
181	C₂³×C₈	—	2	1	no	—
182	C₂×#117	—	2	3	no	—
183	C₂×#117	—	2	3	no	—
184	C₂×#117	C₄×C₁₉	1	6	yes	complemented
185	C₂×#117	C₂²×C₁₉	1	6	yes	—
186	C₂²×C₄⋊C₄	C₄×C₁₉	1	2	yes	complemented
187	C₂²×C₂²⋊C₄	—	2	1	no	—
188	C₂²×C₄²	—	2	3	no	—
189	C₂²×C₄²	—	2	4	no	—
190	C₂²×C₄²	—	2	1	no	—
191	C₂²×C₄²	C₄×C₁₉	1	8	yes	complemented
192	C₂²×C₄²	C₂²×C₁₉	1	6	yes	—
193	#339	C₂²×C₁₉	1	16	yes	direct product factor
194	C₂×C₁₉	—	2	1	no	—
195	C₂×C₁₉	—	2	1	no	—
196	C₂×C₁₉	—	2	6	no	—
197	C₂×C₁₉	C₂×#339	1	12	yes	direct product factor
198	C₂×C₁₉	C₂²×#95	1	1	yes	characteristic
199	C₂×C₁₉	C₂²×#104	1	2	yes	—
200	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
201	C₂³×C₄	—	2	16	no	—
202	C₂³×C₄	—	2	8	no	—
203	C₂³×C₄	—	2	6	no	—
204	C₂³×C₄	—	2	2	no	—
205	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
206	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
207	C₂³×C₄	C₂×C₄×C₁₉	1	3	yes	—
208	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
209	C₂³×C₄	D₄×C₁₉	1	3	yes	—
210	C₂³×C₄	D₄×C₁₉	1	3	yes	—
211	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₁₉	1	4	yes	—
213	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
214	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
215	C₂×M₁₆	—	2	24	no	—
216	C₂×M₁₆	—	2	12	no	—
217	C₂×M₁₆	—	2	6	no	—
218	C₂×M₁₆	C₂×C₄×C₁₉	1	24	yes	complemented
219	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
220	C₂²×C₈	—	2	8	no	—
221	C₂²×C₈	—	2	6	no	—
222	#117	—	2	12	no	—
223	#117	—	2	6	no	—
224	#117	—	2	6	no	—
225	#117	C₂×C₄×C₁₉	1	12	yes	complemented
226	#117	C₂³×C₁₉	1	4	yes	—
227	C₂×C₄⋊C₄	—	2	6	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	12	yes	complemented
229	C₂×C₂²⋊C₄	—	2	6	no	—
230	C₂×C₂²⋊C₄	—	2	6	no	—
231	C₂×C₄²	—	2	6	no	—
232	C₂×C₄²	—	2	24	no	—
233	C₂×C₄²	—	2	6	no	—
234	C₂×C₄²	—	2	6	no	—
235	C₂×C₄²	—	2	12	no	—
236	C₂×C₄²	C₂×C₄×C₁₉	1	24	yes	complemented
237	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
238	C₁₉	C₂²×#339	1	1	yes	characteristic, direct product factor, Sylow
239	C₂⁴	—	2	8	no	—
240	C₂⁴	C₂²⋊C₄×C₁₉	1	3	yes	—
241	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	—
242	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
243	C₂⁴	C₄⋊C₄×C₁₉	1	4	yes	—
244	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
245	C₂²×C₄	—	2	48	no	—
246	C₂²×C₄	—	2	64	no	—
247	C₂²×C₄	—	2	24	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	12	no	—
250	C₂²×C₄	—	4	8	no	—
251	C₂²×C₄	C₄²×C₁₉	1	12	yes	—
252	C₂²×C₄	C₄²×C₁₉	1	4	yes	—
253	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
254	C₂²×C₄	C₂²⋊C₄×C₁₉	1	12	yes	—
255	C₂²×C₄	C₂²⋊C₄×C₁₉	1	12	yes	—
256	C₂²×C₄	C₂²⋊C₄×C₁₉	1	3	yes	—
257	C₂²×C₄	C₂²⋊C₄×C₁₉	1	3	yes	—
258	C₂²×C₄	C₂²⋊C₄×C₁₉	1	6	yes	—
259	C₂²×C₄	C₄⋊C₄×C₁₉	1	12	yes	—
260	C₂²×C₄	C₄⋊C₄×C₁₉	1	12	yes	—
261	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
262	C₂²×C₄	C₄⋊C₄×C₁₉	1	4	yes	—
263	C₂²×C₄	C₄⋊C₄×C₁₉	1	12	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
268	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
269	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
270	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
271	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
272	C₂²×C₄	C₂×Q₈×C₁₉	1	6	yes	—
273	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
274	M₁₆	—	2	24	no	—
275	M₁₆	—	2	4	no	—
276	M₁₆	C₂²×C₄×C₁₉	1	8	yes	complemented
277	C₂×C₈	—	2	24	no	—
278	C₂×C₈	—	2	4	no	—
279	C₄⋊C₄	—	2	12	no	—
280	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	complemented
281	C₂²⋊C₄	—	2	12	no	—
282	C₂²⋊C₄	—	2	4	no	—
283	C₄²	—	2	24	no	—
284	C₄²	—	2	12	no	—
285	C₄²	—	2	4	no	—
286	C₄²	—	2	4	no	—
287	C₄²	C₂²×C₄×C₁₉	1	8	yes	complemented
288	C₂³	—	2	12	no	—
289	C₂³	—	2	12	no	—
290	C₂³	—	2	16	no	—
291	C₂³	—	2	16	no	—
292	C₂³	C₁₉×#95	1	12	yes	—
293	C₂³	C₁₉×#95	1	4	yes	—
294	C₂³	C₁₉×#104	1	8	yes	—
295	C₂³	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
296	C₂³	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
297	C₂³	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
298	C₂³	C₂×C₄⋊C₄×C₁₉	1	6	yes	—
299	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
300	C₂×C₄	—	2	96	no	—
301	C₂×C₄	—	2	16	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	4	24	no	—
305	C₂×C₄	C₁₉×#95	1	24	yes	—
306	C₂×C₄	C₁₉×#95	1	12	yes	—
307	C₂×C₄	C₁₉×#95	1	12	yes	—
308	C₂×C₄	C₂×C₄²×C₁₉	1	6	yes	—
309	C₂×C₄	C₂×C₄²×C₁₉	1	6	yes	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
311	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
312	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	3	yes	—
313	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
314	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
315	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	6	yes	—
316	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	6	yes	—
317	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	6	yes	—
318	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	6	yes	—
319	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	6	yes	—
320	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
322	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
323	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
324	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
325	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
326	C₈	—	2	8	no	—
327	C₂²	—	2	12	no	—
328	C₂²	—	2	12	no	—
329	C₂²	—	2	24	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	6	no	—
332	C₂²	C₁₉×#339	1	16	yes	direct product factor
333	C₂²	C₂×C₁₉×#95	1	6	yes	—
334	C₂²	C₂×C₁₉×#95	1	6	yes	—
335	C₂²	C₂×C₁₉×#104	1	12	yes	—
336	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
337	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
338	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
339	C₄	—	2	16	no	—
340	C₄	—	4	8	no	—
341	C₄	C₂×C₁₉×#95	1	6	yes	—
342	C₄	C₂×C₁₉×#95	1	6	yes	—
343	C₄	C₂²×C₄²×C₁₉	1	1	yes	characteristic
344	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
345	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
346	C₄	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
347	C₂	—	2	1	no	—
348	C₂	—	2	6	no	—
349	C₂	—	2	1	no	—
350	C₂	C₂×C₁₉×#339	1	12	yes	direct product factor
351	C₂	C₂²×C₁₉×#95	1	1	yes	characteristic
352	C₂	C₂²×C₁₉×#104	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₉	D₄
commutator	C₄	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂⁴×C₁₉	C₂²⋊C₄
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₁₉×#339	C₂	direct (N × H)
9. C₂²×M₁₆×C₁₉	C₄	semidirect
14. C₂×C₁₉×#117	C₄	semidirect
16. C₂²×C₄⋊C₄×C₁₉	C₄	semidirect
21. C₂²×C₄²×C₁₉	C₄	semidirect
23. C₁₉×#339	C₂²	direct (N × H)
42. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
49. C₁₉×#117	C₂×C₄	semidirect
52. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
60. C₂×C₄²×C₁₉	C₂×C₄	semidirect
99. M₁₆×C₁₉	C₂²×C₄	semidirect
103. C₄⋊C₄×C₁₉	C₂²×C₄	semidirect
110. C₄²×C₁₉	C₂²×C₄	semidirect
111. C₂²×#339	C₁₉	direct (N × H)
154. C₂×#339	C₂×C₁₉	direct (N × H)
160. C₂²×C₁₉	#339	direct (N × H)
179. C₂²×M₁₆	C₄×C₁₉	semidirect
184. C₂×#117	C₄×C₁₉	semidirect
186. C₂²×C₄⋊C₄	C₄×C₁₉	semidirect
191. C₂²×C₄²	C₄×C₁₉	semidirect
193. #339	C₂²×C₁₉	direct (N × H)
197. C₂×C₁₉	C₂×#339	direct (N × H)
218. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
225. #117	C₂×C₄×C₁₉	semidirect
228. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
236. C₂×C₄²	C₂×C₄×C₁₉	semidirect
238. C₁₉	C₂²×#339	direct (N × H)
276. M₁₆	C₂²×C₄×C₁₉	semidirect
280. C₄⋊C₄	C₂²×C₄×C₁₉	semidirect
287. C₄²	C₂²×C₄×C₁₉	semidirect
332. C₂²	C₁₉×#339	direct (N × H)
350. C₂	C₂×C₁₉×#339	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₁₉	2
C₂²×C₁₉×#117	2
C₂³×C₄²×C₁₉	2
C₂×C₁₉×#339	2
C₂²×#339	19

Subgroups — C22×C19×#339 #18026300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#339 #18026300