Subgroups — C₂²×C₁₉×H(3,ℤ/4) #18026296

Order 4864.

2270 conjugacy classes of subgroups.

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

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₄²
commutator	C₄	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	#95
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×H(3,ℤ/4)	C₂	direct (N × H)
7. C₂²×M₁₆×C₁₉	C₄	semidirect
9. C₂³×C₈×C₁₉	C₄	semidirect
12. C₂×C₁₉×#117	C₄	semidirect
16. C₂²×C₄²×C₁₉	C₄	semidirect
17. C₁₉×H(3,ℤ/4)	C₂²	direct (N × H)
34. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
38. C₂²×C₈×C₁₉	C₂×C₄	semidirect
42. C₁₉×#117	C₂×C₄	semidirect
49. C₂×C₄²×C₁₉	C₂×C₄	semidirect
91. C₂×C₈×C₁₉	C₂²×C₄	semidirect
97. C₄²×C₁₉	C₂²×C₄	semidirect
98. C₂²×H(3,ℤ/4)	C₁₉	direct (N × H)
143. C₂×H(3,ℤ/4)	C₂×C₁₉	direct (N × H)
152. C₂²×C₁₉	H(3,ℤ/4)	direct (N × H)
168. C₂²×M₁₆	C₄×C₁₉	semidirect
170. C₂³×C₈	C₄×C₁₉	semidirect
173. C₂×#117	C₄×C₁₉	semidirect
177. C₂²×C₄²	C₄×C₁₉	semidirect
178. H(3,ℤ/4)	C₂²×C₁₉	direct (N × H)
183. C₂×C₁₉	C₂×H(3,ℤ/4)	direct (N × H)
201. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
205. C₂²×C₈	C₂×C₄×C₁₉	semidirect
209. #117	C₂×C₄×C₁₉	semidirect
216. C₂×C₄²	C₂×C₄×C₁₉	semidirect
217. C₁₉	C₂²×H(3,ℤ/4)	direct (N × H)
259. C₂×C₈	C₂²×C₄×C₁₉	semidirect
265. C₄²	C₂²×C₄×C₁₉	semidirect
316. C₂²	C₁₉×H(3,ℤ/4)	direct (N × H)
333. C₂	C₂×C₁₉×H(3,ℤ/4)	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
C₂×C₁₉×H(3,ℤ/4)	2
C₂²×H(3,ℤ/4)	19

Subgroups — C22×C19×H(3,ℤ/4) #18026296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×H(3,ℤ/4) #18026296