Subgroups — C₂×C₁₉×#3510 #18068767

Order 4864.

7302 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3510	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₉×#559	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#556	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#551	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₉×#542	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#535	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#529	C₂	1	4	yes	maximal, complemented
10	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#559	C₂²	1	64	yes	complemented
18	C₁₉×#556	C₂²	1	64	yes	complemented
19	C₁₉×#551	C₂²	1	128	yes	complemented
20	C₁₉×#542	C₂²	1	64	yes	complemented
21	C₁₉×#536	C₂²	1	16	yes	complemented
22	C₁₉×#535	C₂²	1	16	yes	—
23	C₁₉×#533	C₂²	1	16	yes	complemented
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#127	C₂²	1	2	yes	—
27	C₁₉×#529	C₂²	1	64	yes	complemented
28	C₂×C₁₉×#126	C₂²	1	8	yes	complemented
29	C₂×C₁₉×#126	C₂²	1	8	yes	complemented
30	C₂×C₁₉×#125	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#124	C₂²	1	2	yes	—
32	C₂×C₁₉×#124	C₂²	1	2	yes	—
33	C₂×C₁₉×#124	C₂²	1	4	yes	—
34	C₂×C₁₉×#124	C₂²	1	2	yes	—
35	C₂×C₁₉×#124	C₂²	1	16	yes	complemented
36	C₂×C₁₉×#124	C₂²	1	2	yes	complemented
37	C₂×C₁₉×#124	C₂²	1	8	yes	complemented
38	C₂×C₁₉×#123	C₂²	1	4	yes	—
39	C₂×C₁₉×#123	C₂²	1	8	yes	complemented
40	C₂×C₁₉×#123	C₂²	1	8	yes	complemented
41	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
42	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
44	C₂×C₁₉×#121	C₂²	1	4	yes	—
45	C₂×C₁₉×#120	C₂²	1	4	yes	—
46	C₁₉×#519	C₂²	1	16	yes	complemented
47	C₁₉×#518	C₂²	1	16	yes	complemented
48	C₄×#41×C₁₉	C₂²	1	16	yes	complemented
49	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
50	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
51	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
52	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
53	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
54	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
55	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
56	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
58	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
59	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
60	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
61	C₂×C₁₉×#117	C₂²	1	4	yes	—
62	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
63	C₂×C₁₉×#117	C₂²	1	8	yes	complemented
64	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
65	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
66	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
67	C₂²×C₄²×C₁₉	C₂²	1	2	yes	complemented
68	C₂⁵×C₁₉	C₂³	1	2	yes	—
69	C₂×#41×C₁₉	—	2	8	no	—
70	C₂×#41×C₁₉	C₂³	1	8	yes	—
71	C₂²×Q₈×C₁₉	—	2	8	no	—
72	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
73	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
76	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₉	—	2	8	no	—
78	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
83	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
84	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
89	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	complemented
91	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	complemented
92	C₁₉×#127	C₂³	1	16	yes	—
93	C₁₉×#126	C₂³	1	64	yes	complemented
94	C₁₉×#126	C₂³	1	64	yes	complemented
95	C₁₉×#125	C₂³	1	16	yes	complemented
96	C₁₉×#124	C₂³	1	16	yes	—
97	C₁₉×#124	C₂³	1	16	yes	—
98	C₁₉×#124	C₂³	1	32	yes	—
99	C₁₉×#124	C₂³	1	16	yes	—
100	C₁₉×#124	C₂³	1	16	yes	complemented
101	C₁₉×#124	C₂³	1	64	yes	complemented
102	C₁₉×#123	C₂³	1	32	yes	—
103	C₁₉×#123	C₂³	1	64	yes	complemented
104	C₁₉×#123	C₂³	1	64	yes	complemented
105	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
106	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
107	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	complemented
108	C₁₉×#121	C₂³	1	32	yes	—
109	C₁₉×#120	C₂³	1	32	yes	—
110	C₄×Q₈×C₁₉	C₂³	1	16	yes	complemented
111	C₄×Q₈×C₁₉	C₂³	1	32	yes	complemented
112	C₄×Q₈×C₁₉	C₂³	1	32	yes	complemented
113	C₄×Q₈×C₁₉	C₂³	1	32	yes	complemented
114	C₄×D₄×C₁₉	C₂³	1	32	yes	—
115	C₄×D₄×C₁₉	C₂³	1	32	yes	—
116	C₄×D₄×C₁₉	C₂³	1	32	yes	—
117	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
118	C₄×D₄×C₁₉	C₂³	1	64	yes	complemented
119	C₁₉×#117	C₂³	1	8	yes	—
120	C₁₉×#117	C₂³	1	8	yes	—
121	C₁₉×#117	C₂³	1	8	yes	—
122	C₁₉×#117	C₂³	1	32	yes	—
123	C₁₉×#117	C₂³	1	16	yes	complemented
124	C₁₉×#117	C₂³	1	64	yes	complemented
125	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
129	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
132	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
137	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
138	C₂×C₂²⋊C₄×C₁₉	C₂³	1	32	yes	—
139	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
140	C₂×C₂²⋊C₄×C₁₉	C₂³	1	32	yes	—
141	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
144	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
145	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
149	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
152	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₉	C₂³	1	16	yes	complemented
155	C₂⁴×C₁₉	—	2	8	no	—
156	C₂⁴×C₁₉	—	4	8	no	—
157	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
158	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
159	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
161	#41×C₁₉	—	2	32	no	—
162	C₂×Q₈×C₁₉	—	2	8	no	—
163	C₂×Q₈×C₁₉	—	2	8	no	—
164	C₂×Q₈×C₁₉	—	2	32	no	—
165	C₂×Q₈×C₁₉	—	2	4	no	—
166	C₂×Q₈×C₁₉	—	4	8	no	—
167	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
168	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
169	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
170	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
171	C₂×D₄×C₁₉	—	2	8	no	—
172	C₂×D₄×C₁₉	—	2	8	no	—
173	C₂×D₄×C₁₉	—	2	8	no	—
174	C₂×D₄×C₁₉	—	2	32	no	—
175	C₂×D₄×C₁₉	—	2	4	no	—
176	C₂×D₄×C₁₉	—	4	16	no	—
177	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
178	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
179	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
180	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
181	C₂×D₄×C₁₉	C₂⁴	1	32	yes	—
182	C₂²×C₄×C₁₉	—	2	8	no	—
183	C₂²×C₄×C₁₉	—	2	8	no	—
184	C₂²×C₄×C₁₉	—	4	8	no	—
185	C₂²×C₄×C₁₉	—	4	16	no	—
186	C₂²×C₄×C₁₉	—	4	4	no	—
187	C₂²×C₄×C₁₉	#41	1	8	yes	—
188	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
189	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
190	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
198	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
199	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
200	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
204	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
205	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
206	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
207	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
208	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
209	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
210	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
211	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
212	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
213	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
214	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
215	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
216	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
217	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
218	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
219	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
220	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
221	C₄²×C₁₉	C₂⁴	1	4	yes	—
222	C₄²×C₁₉	C₂⁴	1	4	yes	—
223	C₄²×C₁₉	C₂⁴	1	8	yes	—
224	C₄²×C₁₉	C₂⁴	1	8	yes	—
225	C₄²×C₁₉	C₂⁴	1	16	yes	—
226	C₄²×C₁₉	C₂⁴	1	32	yes	—
227	C₄²×C₁₉	C₂⁴	1	8	yes	—
228	C₄²×C₁₉	C₂⁴	1	8	yes	—
229	C₂×#3510	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂³×C₁₉	—	2	4	no	—
231	C₂³×C₁₉	—	2	4	no	—
232	C₂³×C₁₉	—	2	8	no	—
233	C₂³×C₁₉	—	2	8	no	—
234	C₂³×C₁₉	—	2	16	no	—
235	C₂³×C₁₉	—	2	16	no	—
236	C₂³×C₁₉	—	4	16	no	—
237	C₂³×C₁₉	—	8	16	no	—
238	C₂³×C₁₉	C₂×#41	1	4	yes	—
239	C₂³×C₁₉	C₂⁵	1	8	yes	—
240	C₂³×C₁₉	C₂⁵	1	4	yes	—
241	C₂³×C₁₉	C₂⁵	1	2	yes	—
242	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
243	Q₈×C₁₉	—	2	16	no	—
244	Q₈×C₁₉	—	2	16	no	—
245	Q₈×C₁₉	—	2	8	no	—
246	Q₈×C₁₉	—	4	16	no	—
247	D₄×C₁₉	—	2	16	no	—
248	D₄×C₁₉	—	2	16	no	—
249	D₄×C₁₉	—	2	16	no	—
250	D₄×C₁₉	—	2	8	no	—
251	D₄×C₁₉	—	4	32	no	—
252	C₂×C₄×C₁₉	—	2	4	no	—
253	C₂×C₄×C₁₉	—	2	16	no	—
254	C₂×C₄×C₁₉	—	2	8	no	—
255	C₂×C₄×C₁₉	—	2	4	no	—
256	C₂×C₄×C₁₉	—	2	8	no	—
257	C₂×C₄×C₁₉	—	2	8	no	—
258	C₂×C₄×C₁₉	—	2	4	no	—
259	C₂×C₄×C₁₉	—	2	8	no	—
260	C₂×C₄×C₁₉	—	2	16	no	—
261	C₂×C₄×C₁₉	—	4	16	no	—
262	C₂×C₄×C₁₉	—	4	32	no	—
263	C₂×C₄×C₁₉	—	4	8	no	—
264	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
265	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
266	C₂×C₄×C₁₉	C₂×#41	1	16	yes	—
267	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
268	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
269	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
270	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
271	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
272	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
273	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
274	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
275	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
276	#3510	C₂×C₁₉	1	32	yes	direct product factor
277	C₂×#559	C₂×C₁₉	1	4	yes	complemented
278	C₂×#556	C₂×C₁₉	1	4	yes	complemented
279	C₂×#551	C₂×C₁₉	1	8	yes	complemented
280	C₂×#542	C₂×C₁₉	1	4	yes	complemented
281	C₂×#536	C₂×C₁₉	1	1	yes	characteristic, complemented
282	C₂×#535	C₂×C₁₉	1	1	yes	characteristic
283	C₂×#533	C₂×C₁₉	1	1	yes	characteristic, complemented
284	C₂×#529	C₂×C₁₉	1	4	yes	complemented
285	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic, complemented
286	C₂×#519	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂×#518	C₂×C₁₉	1	1	yes	characteristic, complemented
288	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂²×C₁₉	—	2	4	no	—
290	C₂²×C₁₉	—	2	8	no	—
291	C₂²×C₁₉	—	2	4	no	—
292	C₂²×C₁₉	—	2	8	no	—
293	C₂²×C₁₉	—	2	8	no	—
294	C₂²×C₁₉	—	2	16	no	—
295	C₂²×C₁₉	—	4	8	no	—
296	C₂²×C₁₉	—	4	16	no	—
297	C₂²×C₁₉	—	8	16	no	—
298	C₂²×C₁₉	C₂²×#41	1	4	yes	—
299	C₂²×C₁₉	C₂²×#41	1	2	yes	—
300	C₂²×C₁₉	#585	1	4	yes	—
301	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
302	C₄×C₁₉	—	2	4	no	—
303	C₄×C₁₉	—	2	8	no	—
304	C₄×C₁₉	—	2	4	no	—
305	C₄×C₁₉	—	2	8	no	—
306	C₄×C₁₉	—	2	8	no	—
307	C₄×C₁₉	—	2	4	no	—
308	C₄×C₁₉	—	2	8	no	—
309	C₄×C₁₉	C₂²×#41	1	4	yes	—
310	C₄×C₁₉	C₂²×#41	1	4	yes	—
311	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
312	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
314	#559	C₂²×C₁₉	1	64	yes	complemented
315	#556	C₂²×C₁₉	1	64	yes	complemented
316	#551	C₂²×C₁₉	1	128	yes	complemented
317	#542	C₂²×C₁₉	1	64	yes	complemented
318	#536	C₂²×C₁₉	1	16	yes	complemented
319	#535	C₂²×C₁₉	1	16	yes	—
320	#533	C₂²×C₁₉	1	16	yes	complemented
321	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
322	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
323	C₂×#127	C₂²×C₁₉	1	2	yes	—
324	#529	C₂²×C₁₉	1	64	yes	complemented
325	C₂×#126	C₂²×C₁₉	1	8	yes	complemented
326	C₂×#126	C₂²×C₁₉	1	8	yes	complemented
327	C₂×#125	C₂²×C₁₉	1	2	yes	complemented
328	C₂×#124	C₂²×C₁₉	1	2	yes	—
329	C₂×#124	C₂²×C₁₉	1	2	yes	—
330	C₂×#124	C₂²×C₁₉	1	4	yes	—
331	C₂×#124	C₂²×C₁₉	1	2	yes	—
332	C₂×#124	C₂²×C₁₉	1	16	yes	complemented
333	C₂×#124	C₂²×C₁₉	1	2	yes	complemented
334	C₂×#124	C₂²×C₁₉	1	8	yes	complemented
335	C₂×#123	C₂²×C₁₉	1	4	yes	—
336	C₂×#123	C₂²×C₁₉	1	8	yes	complemented
337	C₂×#123	C₂²×C₁₉	1	8	yes	complemented
338	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
339	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
340	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
341	C₂×#121	C₂²×C₁₉	1	4	yes	—
342	C₂×#120	C₂²×C₁₉	1	4	yes	—
343	#519	C₂²×C₁₉	1	16	yes	complemented
344	#518	C₂²×C₁₉	1	16	yes	complemented
345	C₄×#41	C₂²×C₁₉	1	16	yes	complemented
346	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
347	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
348	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
349	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
350	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
351	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
352	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
353	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	complemented
354	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
355	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
356	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#117	C₂²×C₁₉	1	4	yes	—
359	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
360	C₂×#117	C₂²×C₁₉	1	8	yes	complemented
361	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
362	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
363	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
364	C₂²×C₄²	C₂²×C₁₉	1	2	yes	complemented
365	C₂×C₁₉	—	2	4	no	—
366	C₂×C₁₉	—	4	4	no	—
367	C₂×C₁₉	—	4	8	no	—
368	C₂×C₁₉	#3510	1	4	yes	direct product factor
369	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
370	C₂×C₁₉	C₂×#585	1	2	yes	—
371	C₂⁵	C₂³×C₁₉	1	2	yes	—
372	C₂×#41	—	2	8	no	—
373	C₂×#41	C₂³×C₁₉	1	8	yes	—
374	C₂²×Q₈	—	2	8	no	—
375	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
376	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
377	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
379	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
380	C₂²×D₄	—	2	8	no	—
381	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
382	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
383	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
384	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
386	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
387	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
388	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
389	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
390	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
391	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
392	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
393	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
394	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
395	#127	C₂³×C₁₉	1	16	yes	—
396	#126	C₂³×C₁₉	1	64	yes	complemented
397	#126	C₂³×C₁₉	1	64	yes	complemented
398	#125	C₂³×C₁₉	1	16	yes	complemented
399	#124	C₂³×C₁₉	1	16	yes	—
400	#124	C₂³×C₁₉	1	16	yes	—
401	#124	C₂³×C₁₉	1	32	yes	—
402	#124	C₂³×C₁₉	1	16	yes	—
403	#124	C₂³×C₁₉	1	16	yes	complemented
404	#124	C₂³×C₁₉	1	64	yes	complemented
405	#123	C₂³×C₁₉	1	32	yes	—
406	#123	C₂³×C₁₉	1	64	yes	complemented
407	#123	C₂³×C₁₉	1	64	yes	complemented
408	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
409	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	complemented
410	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
411	#121	C₂³×C₁₉	1	32	yes	—
412	#120	C₂³×C₁₉	1	32	yes	—
413	C₄×Q₈	C₂³×C₁₉	1	16	yes	complemented
414	C₄×Q₈	C₂³×C₁₉	1	32	yes	complemented
415	C₄×Q₈	C₂³×C₁₉	1	32	yes	complemented
416	C₄×Q₈	C₂³×C₁₉	1	32	yes	complemented
417	C₄×D₄	C₂³×C₁₉	1	32	yes	—
418	C₄×D₄	C₂³×C₁₉	1	32	yes	—
419	C₄×D₄	C₂³×C₁₉	1	32	yes	—
420	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
421	C₄×D₄	C₂³×C₁₉	1	64	yes	complemented
422	#117	C₂³×C₁₉	1	8	yes	—
423	#117	C₂³×C₁₉	1	8	yes	—
424	#117	C₂³×C₁₉	1	8	yes	—
425	#117	C₂³×C₁₉	1	32	yes	—
426	#117	C₂³×C₁₉	1	16	yes	complemented
427	#117	C₂³×C₁₉	1	64	yes	complemented
428	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
432	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₉	1	32	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₁₉	1	32	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
448	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
449	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
450	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
451	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
452	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
453	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
455	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
456	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
457	C₂×C₄²	C₂³×C₁₉	1	16	yes	complemented
458	C₁₉	C₂×#3510	1	1	yes	characteristic, direct product factor, Sylow
459	C₂⁴	—	2	8	no	—
460	C₂⁴	—	4	8	no	—
461	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
462	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
463	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
464	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
465	#41	—	2	32	no	—
466	C₂×Q₈	—	2	8	no	—
467	C₂×Q₈	—	2	8	no	—
468	C₂×Q₈	—	2	32	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	4	8	no	—
471	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
472	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
473	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
474	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	8	no	—
477	C₂×D₄	—	2	8	no	—
478	C₂×D₄	—	2	32	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	4	16	no	—
481	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
482	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
483	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
484	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
485	C₂×D₄	C₂⁴×C₁₉	1	32	yes	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	4	8	no	—
489	C₂²×C₄	—	4	16	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	#41×C₁₉	1	8	yes	—
492	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
500	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
501	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
502	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
503	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
504	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
507	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
508	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
509	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
510	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
511	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
512	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
513	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
514	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
515	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
516	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
517	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
518	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
519	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
520	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
521	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
522	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
523	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
524	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
525	C₄²	C₂⁴×C₁₉	1	4	yes	—
526	C₄²	C₂⁴×C₁₉	1	4	yes	—
527	C₄²	C₂⁴×C₁₉	1	8	yes	—
528	C₄²	C₂⁴×C₁₉	1	8	yes	—
529	C₄²	C₂⁴×C₁₉	1	16	yes	—
530	C₄²	C₂⁴×C₁₉	1	32	yes	—
531	C₄²	C₂⁴×C₁₉	1	8	yes	—
532	C₄²	C₂⁴×C₁₉	1	8	yes	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	8	no	—
536	C₂³	—	2	8	no	—
537	C₂³	—	2	16	no	—
538	C₂³	—	2	16	no	—
539	C₂³	—	4	16	no	—
540	C₂³	—	8	16	no	—
541	C₂³	C₂×#41×C₁₉	1	4	yes	—
542	C₂³	C₂⁵×C₁₉	1	8	yes	—
543	C₂³	C₂⁵×C₁₉	1	4	yes	—
544	C₂³	C₂⁵×C₁₉	1	2	yes	—
545	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
546	Q₈	—	2	16	no	—
547	Q₈	—	2	16	no	—
548	Q₈	—	2	8	no	—
549	Q₈	—	4	16	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	16	no	—
552	D₄	—	2	16	no	—
553	D₄	—	2	8	no	—
554	D₄	—	4	32	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	16	no	—
564	C₂×C₄	—	4	16	no	—
565	C₂×C₄	—	4	32	no	—
566	C₂×C₄	—	4	8	no	—
567	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
568	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
569	C₂×C₄	C₂×#41×C₁₉	1	16	yes	—
570	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
571	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
572	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
573	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
574	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
575	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
576	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
577	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
578	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	2	16	no	—
585	C₂²	—	4	16	no	—
586	C₂²	—	4	8	no	—
587	C₂²	—	8	16	no	—
588	C₂²	C₂²×#41×C₁₉	1	4	yes	—
589	C₂²	C₂²×#41×C₁₉	1	2	yes	—
590	C₂²	C₁₉×#585	1	4	yes	—
591	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	4	no	—
595	C₄	—	2	8	no	—
596	C₄	—	2	8	no	—
597	C₄	—	2	4	no	—
598	C₄	—	2	8	no	—
599	C₄	C₂²×#41×C₁₉	1	4	yes	—
600	C₄	C₂²×#41×C₁₉	1	4	yes	—
601	C₂	—	2	4	no	—
602	C₂	—	4	8	no	—
603	C₂	—	4	4	no	—
604	C₂	C₁₉×#3510	1	4	yes	direct product factor
605	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
606	C₂	C₂×C₁₉×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
prime radical	C₂×C₁₉×#535	C₂
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×#3510	C₂	direct (N × H)
2. C₂×C₁₉×#559	C₂	semidirect
3. C₂×C₁₉×#556	C₂	semidirect
4. C₂×C₁₉×#551	C₂	semidirect
5. C₂×C₁₉×#542	C₂	semidirect
6. C₂×C₁₉×#536	C₂	semidirect
8. C₂×C₁₉×#533	C₂	semidirect
9. C₂×C₁₉×#529	C₂	semidirect
10. C₂²×C₁₉×#124	C₂	semidirect
11. C₂×C₁₉×#519	C₂	semidirect
12. C₂×C₁₉×#518	C₂	semidirect
13. C₂×C₄×#41×C₁₉	C₂	semidirect
17. C₁₉×#559	C₂²	semidirect
18. C₁₉×#556	C₂²	semidirect
19. C₁₉×#551	C₂²	semidirect
20. C₁₉×#542	C₂²	semidirect
21. C₁₉×#536	C₂²	semidirect
23. C₁₉×#533	C₂²	semidirect
24. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
27. C₁₉×#529	C₂²	semidirect
28. C₂×C₁₉×#126	C₂²	semidirect
29. C₂×C₁₉×#126	C₂²	semidirect
30. C₂×C₁₉×#125	C₂²	semidirect
35. C₂×C₁₉×#124	C₂²	semidirect
36. C₂×C₁₉×#124	C₂²	semidirect
37. C₂×C₁₉×#124	C₂²	semidirect
39. C₂×C₁₉×#123	C₂²	semidirect
40. C₂×C₁₉×#123	C₂²	semidirect
42. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
43. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
46. C₁₉×#519	C₂²	semidirect
47. C₁₉×#518	C₂²	semidirect
48. C₄×#41×C₁₉	C₂²	semidirect
49. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
50. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
51. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
52. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
56. C₂×C₄×D₄×C₁₉	C₂²	semidirect
57. C₂×C₄×D₄×C₁₉	C₂²	semidirect
62. C₂×C₁₉×#117	C₂²	semidirect
63. C₂×C₁₉×#117	C₂²	semidirect
67. C₂²×C₄²×C₁₉	C₂²	semidirect
90. C₁₉×C₄⋊Q₈	C₂³	semidirect
91. C₁₉×C₄⋊Q₈	C₂³	semidirect
93. C₁₉×#126	C₂³	semidirect
94. C₁₉×#126	C₂³	semidirect
95. C₁₉×#125	C₂³	semidirect
100. C₁₉×#124	C₂³	semidirect
101. C₁₉×#124	C₂³	semidirect
103. C₁₉×#123	C₂³	semidirect
104. C₁₉×#123	C₂³	semidirect
106. C₁₉×C₂²⋊Q₈	C₂³	semidirect
107. C₁₉×C₂²⋊Q₈	C₂³	semidirect
110. C₄×Q₈×C₁₉	C₂³	semidirect
111. C₄×Q₈×C₁₉	C₂³	semidirect
112. C₄×Q₈×C₁₉	C₂³	semidirect
113. C₄×Q₈×C₁₉	C₂³	semidirect
117. C₄×D₄×C₁₉	C₂³	semidirect
118. C₄×D₄×C₁₉	C₂³	semidirect
123. C₁₉×#117	C₂³	semidirect
124. C₁₉×#117	C₂³	semidirect
154. C₂×C₄²×C₁₉	C₂³	semidirect
229. C₂×#3510	C₁₉	direct (N × H)
276. #3510	C₂×C₁₉	direct (N × H)
277. C₂×#559	C₂×C₁₉	semidirect
278. C₂×#556	C₂×C₁₉	semidirect
279. C₂×#551	C₂×C₁₉	semidirect
280. C₂×#542	C₂×C₁₉	semidirect
281. C₂×#536	C₂×C₁₉	semidirect
283. C₂×#533	C₂×C₁₉	semidirect
284. C₂×#529	C₂×C₁₉	semidirect
285. C₂²×#124	C₂×C₁₉	semidirect
286. C₂×#519	C₂×C₁₉	semidirect
287. C₂×#518	C₂×C₁₉	semidirect
288. C₂×C₄×#41	C₂×C₁₉	semidirect
314. #559	C₂²×C₁₉	semidirect
315. #556	C₂²×C₁₉	semidirect
316. #551	C₂²×C₁₉	semidirect
317. #542	C₂²×C₁₉	semidirect
318. #536	C₂²×C₁₉	semidirect
320. #533	C₂²×C₁₉	semidirect
321. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
322. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
324. #529	C₂²×C₁₉	semidirect
325. C₂×#126	C₂²×C₁₉	semidirect
326. C₂×#126	C₂²×C₁₉	semidirect
327. C₂×#125	C₂²×C₁₉	semidirect
332. C₂×#124	C₂²×C₁₉	semidirect
333. C₂×#124	C₂²×C₁₉	semidirect
334. C₂×#124	C₂²×C₁₉	semidirect
336. C₂×#123	C₂²×C₁₉	semidirect
337. C₂×#123	C₂²×C₁₉	semidirect
339. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
340. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
343. #519	C₂²×C₁₉	semidirect
344. #518	C₂²×C₁₉	semidirect
345. C₄×#41	C₂²×C₁₉	semidirect
346. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
347. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
348. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
349. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
353. C₂×C₄×D₄	C₂²×C₁₉	semidirect
354. C₂×C₄×D₄	C₂²×C₁₉	semidirect
359. C₂×#117	C₂²×C₁₉	semidirect
360. C₂×#117	C₂²×C₁₉	semidirect
364. C₂²×C₄²	C₂²×C₁₉	semidirect
368. C₂×C₁₉	#3510	direct (N × H)
393. C₄⋊Q₈	C₂³×C₁₉	semidirect
394. C₄⋊Q₈	C₂³×C₁₉	semidirect
396. #126	C₂³×C₁₉	semidirect
397. #126	C₂³×C₁₉	semidirect
398. #125	C₂³×C₁₉	semidirect
403. #124	C₂³×C₁₉	semidirect
404. #124	C₂³×C₁₉	semidirect
406. #123	C₂³×C₁₉	semidirect
407. #123	C₂³×C₁₉	semidirect
409. C₂²⋊Q₈	C₂³×C₁₉	semidirect
410. C₂²⋊Q₈	C₂³×C₁₉	semidirect
413. C₄×Q₈	C₂³×C₁₉	semidirect
414. C₄×Q₈	C₂³×C₁₉	semidirect
415. C₄×Q₈	C₂³×C₁₉	semidirect
416. C₄×Q₈	C₂³×C₁₉	semidirect
420. C₄×D₄	C₂³×C₁₉	semidirect
421. C₄×D₄	C₂³×C₁₉	semidirect
426. #117	C₂³×C₁₉	semidirect
427. #117	C₂³×C₁₉	semidirect
457. C₂×C₄²	C₂³×C₁₉	semidirect
458. C₁₉	C₂×#3510	direct (N × H)
604. C₂	C₁₉×#3510	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×#3510	2
C₂×C₁₉×#559	2
C₂×C₁₉×#556	2
C₂×C₁₉×#551	2
C₂×C₁₉×#542	2
C₂×C₁₉×#536	2
C₂×C₁₉×#535	2
C₂×C₁₉×#533	2
C₂×C₁₉×#529	2
C₂²×C₁₉×#124	2
C₂×C₁₉×#519	2
C₂×C₁₉×#518	2
C₂×C₄×#41×C₁₉	2
C₂×#3510	19

Subgroups — C2×C19×#3510 #18068767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3510 #18068767