Subgroups — C₂×C₁₉×#3501 #18068724

Order 4864.

7738 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3501	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₉×#554	C₂	1	8	yes	maximal, complemented
3	C₂×C₁₉×#554	C₂	1	4	yes	maximal, complemented
4	C₂×D₄×Q₈×C₁₉	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₉×#544	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#543	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#533	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₉×#518	C₂	1	2	yes	maximal
10	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₁₉	C₂²	1	4	yes	complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#554	C₂²	1	64	yes	complemented
15	C₁₉×#554	C₂²	1	128	yes	complemented
16	D₄×Q₈×C₁₉	C₂²	1	64	yes	complemented
17	C₁₉×#544	C₂²	1	32	yes	complemented
18	C₁₉×#543	C₂²	1	64	yes	complemented
19	C₁₉×#533	C₂²	1	32	yes	complemented
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
21	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	8	yes	complemented
23	C₂×C₁₉×#125	C₂²	1	4	yes	complemented
24	C₂×C₁₉×#125	C₂²	1	8	yes	complemented
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	—
27	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
29	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
30	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
31	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
32	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	64	yes	complemented
33	C₁₉×#518	C₂²	1	32	yes	—
34	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
35	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
36	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
37	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
38	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
40	C₂×C₄×D₄×C₁₉	C₂²	1	16	yes	—
41	C₂×C₁₉×#117	C₂²	1	4	yes	—
42	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₁₉	C₂²	1	8	yes	complemented
44	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
45	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
46	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
47	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
48	C₂⁵×C₁₉	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	4	16	no	—
50	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
51	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
52	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
53	C₂²×Q₈×C₁₉	C₂³	1	32	yes	complemented
54	C₂²×D₄×C₁₉	Q₈	1	16	yes	complemented
55	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
56	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
57	C₂³×C₄×C₁₉	—	4	8	no	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₉	C₂³	1	16	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	complemented
68	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	complemented
69	C₁₉×C₄⋊Q₈	C₂³	1	64	yes	complemented
70	C₁₉×#125	C₂³	1	32	yes	complemented
71	C₁₉×#125	C₂³	1	64	yes	complemented
72	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
73	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	—
74	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
75	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	complemented
76	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	complemented
77	C₁₉×C₂²⋊Q₈	C₂³	1	128	yes	complemented
78	C₁₉×C₂²⋊Q₈	C₂³	1	128	yes	complemented
79	C₄×Q₈×C₁₉	C₂³	1	32	yes	complemented
80	C₄×Q₈×C₁₉	C₂³	1	32	yes	complemented
81	C₄×D₄×C₁₉	C₂³	1	32	yes	—
82	C₄×D₄×C₁₉	C₂³	1	32	yes	—
83	C₄×D₄×C₁₉	C₂³	1	64	yes	—
84	C₄×D₄×C₁₉	C₂³	1	64	yes	—
85	C₁₉×#117	C₂³	1	32	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	64	yes	complemented
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	32	yes	complemented
98	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
101	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	64	yes	—
103	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
106	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
107	C₂⁴×C₁₉	—	4	4	no	—
108	C₂⁴×C₁₉	—	4	4	no	—
109	C₂⁴×C₁₉	C₂×Q₈	1	16	yes	complemented
110	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
111	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
112	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
113	C₂×Q₈×C₁₉	—	2	16	no	—
114	C₂×Q₈×C₁₉	—	4	16	no	—
115	C₂×Q₈×C₁₉	—	4	8	no	—
116	C₂×Q₈×C₁₉	—	4	64	no	—
117	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
118	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
119	C₂×Q₈×C₁₉	C₂⁴	1	32	yes	—
120	C₂×D₄×C₁₉	C₂×Q₈	1	32	yes	complemented
121	C₂×D₄×C₁₉	C₂×Q₈	1	64	yes	complemented
122	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	16	no	—
125	C₂²×C₄×C₁₉	—	4	32	no	—
126	C₂²×C₄×C₁₉	—	4	8	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	4	16	no	—
129	C₂²×C₄×C₁₉	—	4	2	no	—
130	C₂²×C₄×C₁₉	—	4	16	no	—
131	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	complemented
132	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
141	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
144	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
148	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
149	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
150	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
151	C₄⋊C₄×C₁₉	C₂⁴	1	64	yes	—
152	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
153	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
154	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
155	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
156	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
157	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
158	C₂²⋊C₄×C₁₉	C₂⁴	1	64	yes	—
159	C₄²×C₁₉	C₂⁴	1	8	yes	—
160	C₄²×C₁₉	C₂⁴	1	8	yes	—
161	C₄²×C₁₉	C₂⁴	1	32	yes	—
162	C₂×#3501	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	8	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	8	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	4	8	no	—
168	C₂³×C₁₉	—	4	32	no	—
169	C₂³×C₁₉	—	4	8	no	—
170	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
171	C₂³×C₁₉	C₂²×Q₈	1	16	yes	—
172	C₂³×C₁₉	C₂²×Q₈	1	32	yes	complemented
173	C₂³×C₁₉	C₂⁵	1	2	yes	—
174	C₂³×C₁₉	C₂⁵	1	8	yes	—
175	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
176	Q₈×C₁₉	—	2	32	no	—
177	Q₈×C₁₉	—	4	32	no	—
178	Q₈×C₁₉	—	4	16	no	—
179	D₄×C₁₉	C₂²×Q₈	1	64	yes	complemented
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	8	no	—
182	C₂×C₄×C₁₉	—	2	16	no	—
183	C₂×C₄×C₁₉	—	2	16	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	8	no	—
186	C₂×C₄×C₁₉	—	2	32	no	—
187	C₂×C₄×C₁₉	—	4	16	no	—
188	C₂×C₄×C₁₉	—	4	8	no	—
189	C₂×C₄×C₁₉	—	4	32	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	32	no	—
192	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
193	C₂×C₄×C₁₉	C₂²×Q₈	1	16	yes	complemented
194	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
195	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
196	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
197	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
198	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
199	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
200	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
201	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
202	#3501	C₂×C₁₉	1	32	yes	direct product factor
203	C₂×#554	C₂×C₁₉	1	4	yes	complemented
204	C₂×#554	C₂×C₁₉	1	8	yes	complemented
205	C₂×D₄×Q₈	C₂×C₁₉	1	4	yes	complemented
206	C₂×#544	C₂×C₁₉	1	2	yes	complemented
207	C₂×#543	C₂×C₁₉	1	4	yes	complemented
208	C₂×#533	C₂×C₁₉	1	2	yes	complemented
209	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	4	yes	complemented
210	C₂×#518	C₂×C₁₉	1	2	yes	—
211	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic
212	C₂²×C₁₉	—	2	8	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	8	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	2	8	no	—
217	C₂²×C₁₉	—	2	32	no	—
218	C₂²×C₁₉	—	4	32	no	—
219	C₂²×C₁₉	C₂³×Q₈	1	4	yes	—
220	C₂²×C₁₉	C₂³×Q₈	1	16	yes	—
221	C₂²×C₁₉	C₂³×Q₈	1	2	yes	—
222	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
223	C₂²×C₁₉	#585	1	2	yes	—
224	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
225	C₄×C₁₉	—	2	2	no	—
226	C₄×C₁₉	—	2	8	no	—
227	C₄×C₁₉	—	2	16	no	—
228	C₄×C₁₉	—	2	16	no	—
229	C₄×C₁₉	—	2	4	no	—
230	C₄×C₁₉	C₂³×Q₈	1	8	yes	—
231	C₄×C₁₉	C₂×H(5,𝔽₂)	1	4	yes	—
232	C₂³×Q₈	C₂²×C₁₉	1	4	yes	complemented
233	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
234	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
235	#554	C₂²×C₁₉	1	64	yes	complemented
236	#554	C₂²×C₁₉	1	128	yes	complemented
237	D₄×Q₈	C₂²×C₁₉	1	64	yes	complemented
238	#544	C₂²×C₁₉	1	32	yes	complemented
239	#543	C₂²×C₁₉	1	64	yes	complemented
240	#533	C₂²×C₁₉	1	32	yes	complemented
241	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
242	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
243	C₂×C₄⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
244	C₂×#125	C₂²×C₁₉	1	4	yes	complemented
245	C₂×#125	C₂²×C₁₉	1	8	yes	complemented
246	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
247	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	—
248	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
249	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
250	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
251	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	16	yes	complemented
252	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	16	yes	complemented
253	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	64	yes	complemented
254	#518	C₂²×C₁₉	1	32	yes	—
255	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
256	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
257	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
258	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
259	C₂×C₄×D₄	C₂²×C₁₉	1	16	yes	—
260	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
261	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
262	C₂×#117	C₂²×C₁₉	1	4	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₁₉	1	8	yes	complemented
265	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
266	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
268	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
269	C₂×C₁₉	—	2	4	no	—
270	C₂×C₁₉	—	2	16	no	—
271	C₂×C₁₉	#3501	1	4	yes	direct product factor
272	C₂×C₁₉	C₂⁴×Q₈	1	1	yes	characteristic
273	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×C₁₉	C₂×#585	1	1	yes	characteristic
275	C₂⁵	C₂³×C₁₉	1	2	yes	—
276	C₂²×Q₈	—	4	16	no	—
277	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
278	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
279	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
280	C₂²×Q₈	C₂³×C₁₉	1	32	yes	complemented
281	C₂²×D₄	Q₈×C₁₉	1	16	yes	complemented
282	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
283	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
284	C₂³×C₄	—	4	8	no	—
285	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
290	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
291	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
292	C₂³×C₄	C₂³×C₁₉	1	16	yes	—
293	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
294	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
295	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
296	C₄⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
297	#125	C₂³×C₁₉	1	32	yes	complemented
298	#125	C₂³×C₁₉	1	64	yes	complemented
299	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
300	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	—
301	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
302	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
303	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
304	C₂²⋊Q₈	C₂³×C₁₉	1	128	yes	complemented
305	C₂²⋊Q₈	C₂³×C₁₉	1	128	yes	complemented
306	C₄×Q₈	C₂³×C₁₉	1	32	yes	complemented
307	C₄×Q₈	C₂³×C₁₉	1	32	yes	complemented
308	C₄×D₄	C₂³×C₁₉	1	32	yes	—
309	C₄×D₄	C₂³×C₁₉	1	32	yes	—
310	C₄×D₄	C₂³×C₁₉	1	64	yes	—
311	C₄×D₄	C₂³×C₁₉	1	64	yes	—
312	#117	C₂³×C₁₉	1	32	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₉	1	64	yes	complemented
324	C₂×C₄⋊C₄	C₂³×C₁₉	1	32	yes	complemented
325	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₉	1	64	yes	—
330	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
331	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
334	C₁₉	C₂×#3501	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	—	4	4	no	—
336	C₂⁴	—	4	4	no	—
337	C₂⁴	C₂×Q₈×C₁₉	1	16	yes	complemented
338	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
339	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
340	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
341	C₂×Q₈	—	2	16	no	—
342	C₂×Q₈	—	4	16	no	—
343	C₂×Q₈	—	4	8	no	—
344	C₂×Q₈	—	4	64	no	—
345	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
346	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
347	C₂×Q₈	C₂⁴×C₁₉	1	32	yes	—
348	C₂×D₄	C₂×Q₈×C₁₉	1	32	yes	complemented
349	C₂×D₄	C₂×Q₈×C₁₉	1	64	yes	complemented
350	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	16	no	—
353	C₂²×C₄	—	4	32	no	—
354	C₂²×C₄	—	4	8	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	16	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	16	no	—
359	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	complemented
360	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
363	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
364	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
365	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
367	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
369	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
370	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
371	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
372	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
375	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
376	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
377	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
378	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
379	C₄⋊C₄	C₂⁴×C₁₉	1	64	yes	—
380	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
381	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
382	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
383	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
384	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
385	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
386	C₂²⋊C₄	C₂⁴×C₁₉	1	64	yes	—
387	C₄²	C₂⁴×C₁₉	1	8	yes	—
388	C₄²	C₂⁴×C₁₉	1	8	yes	—
389	C₄²	C₂⁴×C₁₉	1	32	yes	—
390	C₂³	—	2	8	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	8	no	—
395	C₂³	—	4	32	no	—
396	C₂³	—	4	8	no	—
397	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
398	C₂³	C₂²×Q₈×C₁₉	1	16	yes	—
399	C₂³	C₂²×Q₈×C₁₉	1	32	yes	complemented
400	C₂³	C₂⁵×C₁₉	1	2	yes	—
401	C₂³	C₂⁵×C₁₉	1	8	yes	—
402	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
403	Q₈	—	2	32	no	—
404	Q₈	—	4	32	no	—
405	Q₈	—	4	16	no	—
406	D₄	C₂²×Q₈×C₁₉	1	64	yes	complemented
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	16	no	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	32	no	—
414	C₂×C₄	—	4	16	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	32	no	—
417	C₂×C₄	—	4	32	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
420	C₂×C₄	C₂²×Q₈×C₁₉	1	16	yes	complemented
421	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
422	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
423	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
424	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
425	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
426	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
427	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
428	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
429	C₂²	—	2	8	no	—
430	C₂²	—	2	32	no	—
431	C₂²	—	2	8	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	32	no	—
436	C₂²	C₂³×Q₈×C₁₉	1	4	yes	—
437	C₂²	C₂³×Q₈×C₁₉	1	16	yes	—
438	C₂²	C₂³×Q₈×C₁₉	1	2	yes	—
439	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
440	C₂²	C₁₉×#585	1	2	yes	—
441	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	8	no	—
444	C₄	—	2	16	no	—
445	C₄	—	2	16	no	—
446	C₄	—	2	4	no	—
447	C₄	C₂³×Q₈×C₁₉	1	8	yes	—
448	C₄	C₂×C₁₉×H(5,𝔽₂)	1	4	yes	—
449	C₂	—	2	4	no	—
450	C₂	—	2	16	no	—
451	C₂	C₁₉×#3501	1	4	yes	direct product factor
452	C₂	C₂⁴×Q₈×C₁₉	1	1	yes	characteristic
453	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂	C₂×C₁₉×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3501	C₂	direct (N × H)
2. C₂×C₁₉×#554	C₂	semidirect
3. C₂×C₁₉×#554	C₂	semidirect
4. C₂×D₄×Q₈×C₁₉	C₂	semidirect
5. C₂×C₁₉×#544	C₂	semidirect
6. C₂×C₁₉×#543	C₂	semidirect
7. C₂×C₁₉×#533	C₂	semidirect
8. C₂²×C₁₉×C₂²⋊Q₈	C₂	semidirect
11. C₂³×Q₈×C₁₉	C₂²	semidirect
14. C₁₉×#554	C₂²	semidirect
15. C₁₉×#554	C₂²	semidirect
16. D₄×Q₈×C₁₉	C₂²	semidirect
17. C₁₉×#544	C₂²	semidirect
18. C₁₉×#543	C₂²	semidirect
19. C₁₉×#533	C₂²	semidirect
20. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₁₉×#125	C₂²	semidirect
24. C₂×C₁₉×#125	C₂²	semidirect
28. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
35. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
43. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
53. C₂²×Q₈×C₁₉	C₂³	semidirect
54. C₂²×D₄×C₁₉	Q₈	semidirect
67. C₁₉×C₄⋊Q₈	C₂³	semidirect
68. C₁₉×C₄⋊Q₈	C₂³	semidirect
69. C₁₉×C₄⋊Q₈	C₂³	semidirect
70. C₁₉×#125	C₂³	semidirect
71. C₁₉×#125	C₂³	semidirect
75. C₁₉×C₂²⋊Q₈	C₂³	semidirect
76. C₁₉×C₂²⋊Q₈	C₂³	semidirect
77. C₁₉×C₂²⋊Q₈	C₂³	semidirect
78. C₁₉×C₂²⋊Q₈	C₂³	semidirect
79. C₄×Q₈×C₁₉	C₂³	semidirect
80. C₄×Q₈×C₁₉	C₂³	semidirect
96. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
97. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
109. C₂⁴×C₁₉	C₂×Q₈	semidirect
120. C₂×D₄×C₁₉	C₂×Q₈	semidirect
121. C₂×D₄×C₁₉	C₂×Q₈	semidirect
131. C₂²×C₄×C₁₉	C₂×Q₈	semidirect
162. C₂×#3501	C₁₉	direct (N × H)
172. C₂³×C₁₉	C₂²×Q₈	semidirect
179. D₄×C₁₉	C₂²×Q₈	semidirect
193. C₂×C₄×C₁₉	C₂²×Q₈	semidirect
202. #3501	C₂×C₁₉	direct (N × H)
203. C₂×#554	C₂×C₁₉	semidirect
204. C₂×#554	C₂×C₁₉	semidirect
205. C₂×D₄×Q₈	C₂×C₁₉	semidirect
206. C₂×#544	C₂×C₁₉	semidirect
207. C₂×#543	C₂×C₁₉	semidirect
208. C₂×#533	C₂×C₁₉	semidirect
209. C₂²×C₂²⋊Q₈	C₂×C₁₉	semidirect
232. C₂³×Q₈	C₂²×C₁₉	semidirect
235. #554	C₂²×C₁₉	semidirect
236. #554	C₂²×C₁₉	semidirect
237. D₄×Q₈	C₂²×C₁₉	semidirect
238. #544	C₂²×C₁₉	semidirect
239. #543	C₂²×C₁₉	semidirect
240. #533	C₂²×C₁₉	semidirect
241. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
242. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
243. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
244. C₂×#125	C₂²×C₁₉	semidirect
245. C₂×#125	C₂²×C₁₉	semidirect
249. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
250. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
251. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
252. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
253. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
255. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
256. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
264. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
265. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
271. C₂×C₁₉	#3501	direct (N × H)
280. C₂²×Q₈	C₂³×C₁₉	semidirect
281. C₂²×D₄	Q₈×C₁₉	semidirect
294. C₄⋊Q₈	C₂³×C₁₉	semidirect
295. C₄⋊Q₈	C₂³×C₁₉	semidirect
296. C₄⋊Q₈	C₂³×C₁₉	semidirect
297. #125	C₂³×C₁₉	semidirect
298. #125	C₂³×C₁₉	semidirect
302. C₂²⋊Q₈	C₂³×C₁₉	semidirect
303. C₂²⋊Q₈	C₂³×C₁₉	semidirect
304. C₂²⋊Q₈	C₂³×C₁₉	semidirect
305. C₂²⋊Q₈	C₂³×C₁₉	semidirect
306. C₄×Q₈	C₂³×C₁₉	semidirect
307. C₄×Q₈	C₂³×C₁₉	semidirect
323. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
324. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
334. C₁₉	C₂×#3501	direct (N × H)
337. C₂⁴	C₂×Q₈×C₁₉	semidirect
348. C₂×D₄	C₂×Q₈×C₁₉	semidirect
349. C₂×D₄	C₂×Q₈×C₁₉	semidirect
359. C₂²×C₄	C₂×Q₈×C₁₉	semidirect
399. C₂³	C₂²×Q₈×C₁₉	semidirect
406. D₄	C₂²×Q₈×C₁₉	semidirect
420. C₂×C₄	C₂²×Q₈×C₁₉	semidirect
451. C₂	C₁₉×#3501	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3501	2
C₂×C₁₉×#554	2
C₂×D₄×Q₈×C₁₉	2
C₂×C₁₉×#544	2
C₂×C₁₉×#543	2
C₂×C₁₉×#533	2
C₂²×C₁₉×C₂²⋊Q₈	2
C₂×C₁₉×#518	2
C₂²×C₄×D₄×C₁₉	2
C₂×#3501	19

Subgroups — C2×C19×#3501 #18068724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3501 #18068724