Subgroups — C₂×C₁₉×#3174 #18066637

Order 4864.

1970 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#540	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3174	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#491	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#468	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#465	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#440	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×SD₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#541	—	2	4	no	—
18	C₁₉×#541	C₂²	1	8	yes	complemented
19	C₁₉×#540	—	2	4	no	—
20	C₁₉×#540	C₂²	1	8	yes	—
21	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#126	—	2	2	no	—
24	C₂×C₁₉×#125	—	2	2	no	—
25	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#123	—	2	2	no	—
28	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₉×#121	—	2	2	no	—
30	C₂×C₁₉×#121	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
33	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
34	C₁₉×#499	C₂²	1	8	yes	complemented
35	C₁₉×#492	C₂²	1	8	yes	complemented
36	C₁₉×#491	C₂²	1	8	yes	complemented
37	C₁₉×#490	C₂²	1	8	yes	complemented
38	C₁₉×#468	C₂²	1	16	yes	complemented
39	C₁₉×#465	C₂²	1	16	yes	complemented
40	C₁₉×#440	C₂²	1	16	yes	complemented
41	C₄×SD₁₆×C₁₉	C₂²	1	16	yes	complemented
42	C₂×C₁₉×#107	C₂²	1	2	yes	—
43	C₂×C₁₉×#106	C₂²	1	2	yes	—
44	C₂×C₁₉×#103	C₂²	1	2	yes	—
45	C₂×C₁₉×#103	C₂²	1	2	yes	—
46	C₂×C₁₉×#102	C₂²	1	2	yes	—
47	C₂×C₁₉×#102	C₂²	1	2	yes	—
48	C₁₉×#405	C₂²	1	8	yes	complemented
49	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
50	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
53	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₉	—	2	2	no	—
55	C₂²×D₄×C₁₉	—	2	2	no	—
56	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	—	2	2	no	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×SD₁₆×C₁₉	—	2	8	no	—
60	C₂×SD₁₆×C₁₉	—	2	8	no	—
61	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
62	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
63	C₂×M₁₆×C₁₉	—	2	4	no	—
64	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
65	C₂²×C₈×C₁₉	—	2	4	no	—
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	—	2	2	no	—
72	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
73	C₁₉×#127	—	2	2	no	—
74	C₁₉×#127	C₂³	1	4	yes	—
75	C₁₉×#126	—	2	16	no	—
76	C₁₉×#125	—	2	16	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	C₂³	1	4	yes	—
80	C₁₉×#125	C₂³	1	4	yes	—
81	C₁₉×#123	—	2	16	no	—
82	C₁₉×C₂²⋊Q₈	—	2	4	no	—
83	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
84	C₁₉×#121	—	2	4	no	—
85	C₁₉×#121	—	2	16	no	—
86	C₁₉×#121	C₂³	1	8	yes	—
87	C₄×Q₈×C₁₉	—	2	4	no	—
88	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
89	C₄×D₄×C₁₉	—	2	4	no	—
90	C₄×D₄×C₁₉	C₂³	1	8	yes	—
91	C₁₉×#117	D₄	1	4	yes	—
92	C₁₉×#117	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
105	C₂×C₄²×C₁₉	—	2	2	no	—
106	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×#107	C₂³	1	8	yes	—
109	C₁₉×#106	C₂³	1	8	yes	—
110	C₁₉×#103	C₂³	1	8	yes	—
111	C₁₉×#103	C₂³	1	8	yes	—
112	C₁₉×#102	C₂³	1	8	yes	—
113	C₁₉×#102	C₂³	1	8	yes	—
114	C₁₉×#97	C₂³	1	4	yes	—
115	C₁₉×#97	C₂³	1	4	yes	—
116	C₄×C₈×C₁₉	C₂³	1	4	yes	—
117	C₄×C₈×C₁₉	C₂³	1	4	yes	—
118	C₂⁴×C₁₉	—	2	2	no	—
119	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	4	no	—
122	C₂×Q₈×C₁₉	—	2	4	no	—
123	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
124	C₂×D₄×C₁₉	—	2	8	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	8	no	—
127	C₂×D₄×C₁₉	—	2	4	no	—
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	8	4	no	—
130	C₂×D₄×C₁₉	—	8	4	no	—
131	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	8	no	—
138	C₂²×C₄×C₁₉	—	8	4	no	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
145	SD₁₆×C₁₉	—	2	16	no	—
146	SD₁₆×C₁₉	—	2	16	no	—
147	M₁₆×C₁₉	—	2	8	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	2	2	no	—
150	C₂×C₈×C₁₉	—	2	8	no	—
151	C₂×C₈×C₁₉	#41	1	4	yes	—
152	C₂×C₈×C₁₉	#41	1	4	yes	—
153	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
154	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
155	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
156	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
157	C₄⋊C₄×C₁₉	—	2	8	no	—
158	C₄⋊C₄×C₁₉	—	2	8	no	—
159	C₄⋊C₄×C₁₉	—	2	8	no	—
160	C₄⋊C₄×C₁₉	—	2	8	no	—
161	C₄⋊C₄×C₁₉	—	2	8	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
165	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
166	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
167	C₂²⋊C₄×C₁₉	—	2	8	no	—
168	C₂²⋊C₄×C₁₉	—	2	8	no	—
169	C₂²⋊C₄×C₁₉	—	2	8	no	—
170	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
171	C₄²×C₁₉	—	2	8	no	—
172	C₄²×C₁₉	C₂×D₄	1	2	yes	—
173	C₄²×C₁₉	C₂×D₄	1	2	yes	—
174	C₄²×C₁₉	C₂⁴	1	2	yes	—
175	C₄²×C₁₉	C₂⁴	1	2	yes	—
176	C₂×#3174	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	4	no	—
179	C₂³×C₁₉	—	2	4	no	—
180	C₂³×C₁₉	—	4	4	no	—
181	C₂³×C₁₉	—	4	4	no	—
182	C₂³×C₁₉	—	4	4	no	—
183	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
184	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₉	—	2	4	no	—
186	Q₈×C₁₉	—	2	4	no	—
187	Q₈×C₁₉	—	4	4	no	—
188	D₄×C₁₉	—	2	4	no	—
189	D₄×C₁₉	—	2	4	no	—
190	D₄×C₁₉	—	4	4	no	—
191	D₄×C₁₉	—	8	8	no	—
192	D₄×C₁₉	—	8	8	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	4	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	8	8	no	—
206	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
211	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
212	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
213	C₈×C₁₉	—	2	2	no	—
214	C₈×C₁₉	—	2	2	no	—
215	C₈×C₁₉	C₂×#41	1	4	yes	—
216	C₈×C₁₉	C₂×#41	1	4	yes	—
217	C₂×#541	C₂×C₁₉	1	1	yes	characteristic, complemented
218	C₂×#540	C₂×C₁₉	1	1	yes	characteristic
219	#3174	C₂×C₁₉	1	16	yes	direct product factor
220	C₂×#499	C₂×C₁₉	1	1	yes	characteristic, complemented
221	C₂×#492	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂×#491	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂×#490	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂×#468	C₂×C₁₉	1	2	yes	complemented
225	C₂×#465	C₂×C₁₉	1	2	yes	complemented
226	C₂×#440	C₂×C₁₉	1	2	yes	complemented
227	C₂×C₄×SD₁₆	C₂×C₁₉	1	2	yes	complemented
228	C₂×#405	C₂×C₁₉	1	1	yes	characteristic, complemented
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	4	no	—
231	C₂²×C₁₉	—	4	4	no	—
232	C₂²×C₁₉	—	4	4	no	—
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	4	no	—
235	C₂²×C₁₉	—	8	8	no	—
236	C₂²×C₁₉	#532	1	2	yes	—
237	C₂²×C₁₉	#577	1	4	yes	—
238	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
239	C₄×C₁₉	—	2	2	no	—
240	C₄×C₁₉	—	2	4	no	—
241	C₄×C₁₉	—	2	4	no	—
242	C₄×C₁₉	—	4	4	no	—
243	C₄×C₁₉	—	4	4	no	—
244	C₄×C₁₉	—	4	4	no	—
245	C₄×C₁₉	#532	1	2	yes	—
246	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
247	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
248	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
249	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
250	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
251	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
252	#541	—	2	4	no	—
253	#541	C₂²×C₁₉	1	8	yes	complemented
254	#540	—	2	4	no	—
255	#540	C₂²×C₁₉	1	8	yes	—
256	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#126	—	2	2	no	—
259	C₂×#125	—	2	2	no	—
260	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
261	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#123	—	2	2	no	—
263	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
264	C₂×#121	—	2	2	no	—
265	C₂×#121	C₂²×C₁₉	1	2	yes	—
266	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
267	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
268	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
269	#499	C₂²×C₁₉	1	8	yes	complemented
270	#492	C₂²×C₁₉	1	8	yes	complemented
271	#491	C₂²×C₁₉	1	8	yes	complemented
272	#490	C₂²×C₁₉	1	8	yes	complemented
273	#468	C₂²×C₁₉	1	16	yes	complemented
274	#465	C₂²×C₁₉	1	16	yes	complemented
275	#440	C₂²×C₁₉	1	16	yes	complemented
276	C₄×SD₁₆	C₂²×C₁₉	1	16	yes	complemented
277	C₂×#107	C₂²×C₁₉	1	2	yes	—
278	C₂×#106	C₂²×C₁₉	1	2	yes	—
279	C₂×#103	C₂²×C₁₉	1	2	yes	—
280	C₂×#103	C₂²×C₁₉	1	2	yes	—
281	C₂×#102	C₂²×C₁₉	1	2	yes	—
282	C₂×#102	C₂²×C₁₉	1	2	yes	—
283	#405	C₂²×C₁₉	1	8	yes	complemented
284	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₁₉	—	4	2	no	—
289	C₂×C₁₉	—	8	4	no	—
290	C₂×C₁₉	#3174	1	4	yes	direct product factor
291	C₂×C₁₉	C₂×#532	1	1	yes	characteristic
292	C₂×C₁₉	C₂×#577	1	2	yes	—
293	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
299	C₂×SD₁₆	—	2	8	no	—
300	C₂×SD₁₆	—	2	8	no	—
301	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
302	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
303	C₂×M₁₆	—	2	4	no	—
304	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
305	C₂²×C₈	—	2	4	no	—
306	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
308	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
313	#127	—	2	2	no	—
314	#127	C₂³×C₁₉	1	4	yes	—
315	#126	—	2	16	no	—
316	#125	—	2	16	no	—
317	#125	—	2	2	no	—
318	#125	—	2	2	no	—
319	#125	C₂³×C₁₉	1	4	yes	—
320	#125	C₂³×C₁₉	1	4	yes	—
321	#123	—	2	16	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
324	#121	—	2	4	no	—
325	#121	—	2	16	no	—
326	#121	C₂³×C₁₉	1	8	yes	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	C₂³×C₁₉	1	8	yes	—
331	#117	D₄×C₁₉	1	4	yes	—
332	#117	C₂³×C₁₉	1	4	yes	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
348	#107	C₂³×C₁₉	1	8	yes	—
349	#106	C₂³×C₁₉	1	8	yes	—
350	#103	C₂³×C₁₉	1	8	yes	—
351	#103	C₂³×C₁₉	1	8	yes	—
352	#102	C₂³×C₁₉	1	8	yes	—
353	#102	C₂³×C₁₉	1	8	yes	—
354	#97	C₂³×C₁₉	1	4	yes	—
355	#97	C₂³×C₁₉	1	4	yes	—
356	C₄×C₈	C₂³×C₁₉	1	4	yes	—
357	C₄×C₈	C₂³×C₁₉	1	4	yes	—
358	C₁₉	C₂×#3174	1	1	yes	characteristic, direct product factor, Sylow
359	C₂⁴	—	2	2	no	—
360	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	8	4	no	—
371	C₂×D₄	—	8	4	no	—
372	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	8	4	no	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
386	SD₁₆	—	2	16	no	—
387	SD₁₆	—	2	16	no	—
388	M₁₆	—	2	8	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	8	no	—
392	C₂×C₈	#41×C₁₉	1	4	yes	—
393	C₂×C₈	#41×C₁₉	1	4	yes	—
394	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
395	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
396	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
397	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
406	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
407	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
412	C₄²	—	2	8	no	—
413	C₄²	C₂×D₄×C₁₉	1	2	yes	—
414	C₄²	C₂×D₄×C₁₉	1	2	yes	—
415	C₄²	C₂⁴×C₁₉	1	2	yes	—
416	C₄²	C₂⁴×C₁₉	1	2	yes	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	4	no	—
423	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
424	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
425	Q₈	—	2	4	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	4	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	4	no	—
431	D₄	—	8	8	no	—
432	D₄	—	8	8	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	8	8	no	—
446	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
448	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
451	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
452	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	C₂×#41×C₁₉	1	4	yes	—
456	C₈	C₂×#41×C₁₉	1	4	yes	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	8	no	—
464	C₂²	C₁₉×#532	1	2	yes	—
465	C₂²	C₁₉×#577	1	4	yes	—
466	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	C₁₉×#532	1	2	yes	—
474	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
475	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
476	C₂	—	4	2	no	—
477	C₂	—	8	4	no	—
478	C₂	C₁₉×#3174	1	4	yes	direct product factor
479	C₂	C₂×C₁₉×#532	1	1	yes	characteristic
480	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#541	C₂	semidirect
3. C₁₉×#3174	C₂	direct (N × H)
4. C₂×C₁₉×#499	C₂	semidirect
5. C₂×C₁₉×#492	C₂	semidirect
6. C₂×C₁₉×#491	C₂	semidirect
7. C₂×C₁₉×#490	C₂	semidirect
8. C₂×C₁₉×#468	C₂	semidirect
9. C₂×C₁₉×#465	C₂	semidirect
10. C₂×C₁₉×#440	C₂	semidirect
11. C₂×C₄×SD₁₆×C₁₉	C₂	semidirect
12. C₂×C₁₉×#405	C₂	semidirect
18. C₁₉×#541	C₂²	semidirect
34. C₁₉×#499	C₂²	semidirect
35. C₁₉×#492	C₂²	semidirect
36. C₁₉×#491	C₂²	semidirect
37. C₁₉×#490	C₂²	semidirect
38. C₁₉×#468	C₂²	semidirect
39. C₁₉×#465	C₂²	semidirect
40. C₁₉×#440	C₂²	semidirect
41. C₄×SD₁₆×C₁₉	C₂²	semidirect
48. C₁₉×#405	C₂²	semidirect
176. C₂×#3174	C₁₉	direct (N × H)
217. C₂×#541	C₂×C₁₉	semidirect
219. #3174	C₂×C₁₉	direct (N × H)
220. C₂×#499	C₂×C₁₉	semidirect
221. C₂×#492	C₂×C₁₉	semidirect
222. C₂×#491	C₂×C₁₉	semidirect
223. C₂×#490	C₂×C₁₉	semidirect
224. C₂×#468	C₂×C₁₉	semidirect
225. C₂×#465	C₂×C₁₉	semidirect
226. C₂×#440	C₂×C₁₉	semidirect
227. C₂×C₄×SD₁₆	C₂×C₁₉	semidirect
228. C₂×#405	C₂×C₁₉	semidirect
253. #541	C₂²×C₁₉	semidirect
269. #499	C₂²×C₁₉	semidirect
270. #492	C₂²×C₁₉	semidirect
271. #491	C₂²×C₁₉	semidirect
272. #490	C₂²×C₁₉	semidirect
273. #468	C₂²×C₁₉	semidirect
274. #465	C₂²×C₁₉	semidirect
275. #440	C₂²×C₁₉	semidirect
276. C₄×SD₁₆	C₂²×C₁₉	semidirect
283. #405	C₂²×C₁₉	semidirect
290. C₂×C₁₉	#3174	direct (N × H)
358. C₁₉	C₂×#3174	direct (N × H)
478. C₂	C₁₉×#3174	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×#541	2
C₂×C₁₉×#540	2
C₁₉×#3174	2
C₂×C₁₉×#499	2
C₂×C₁₉×#492	2
C₂×C₁₉×#491	2
C₂×C₁₉×#490	2
C₂×C₁₉×#468	2
C₂×C₁₉×#465	2
C₂×C₁₉×#440	2
C₂×C₄×SD₁₆×C₁₉	2
C₂×C₁₉×#405	2
C₂×#3174	19

Subgroups — C2×C19×#3174 #18066637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3174 #18066637