Subgroups — C₁₉×#62859 #18068818

Order 4864.

10986 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3500	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3499	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3489	C₂	1	16	yes	maximal, complemented
6	C₁₉×#3486	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3485	C₂	1	12	yes	maximal, complemented
8	C₁₉×#3449	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₉×#536	C₂	1	6	yes	maximal, complemented
10	C₁₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#585	—	2	16	no	—
12	C₂×C₁₉×2₋¹⁺⁴	—	2	16	no	—
13	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	8	yes	complemented
15	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	complemented
16	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	8	yes	complemented
17	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	6	yes	—
18	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	complemented
19	C₂²×#41×C₁₉	C₂²	1	6	yes	—
20	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₁₉	C₂²	1	3	yes	complemented
22	C₂²×#41×C₁₉	C₂²	1	6	yes	complemented
23	C₂²×#41×C₁₉	C₂²	1	8	yes	complemented
24	C₂³×Q₈×C₁₉	C₂²	1	3	yes	complemented
25	C₂³×Q₈×C₁₉	C₂²	1	2	yes	complemented
26	D₄×Q₈×C₁₉	C₂²	1	32	yes	complemented
27	C₁₉×#548	C₂²	1	32	yes	complemented
28	C₁₉×#547	C₂²	1	96	yes	complemented
29	C₁₉×#546	C₂²	1	96	yes	complemented
30	C₁₉×#537	C₂²	1	24	yes	complemented
31	C₁₉×#536	C₂²	1	12	yes	complemented
32	C₁₉×#536	C₂²	1	24	yes	complemented
33	C₁₉×#536	C₂²	1	24	yes	complemented
34	C₁₉×#536	C₂²	1	24	yes	complemented
35	C₁₉×#536	C₂²	1	12	yes	complemented
36	C₁₉×#535	C₂²	1	4	yes	complemented
37	C₁₉×#535	C₂²	1	12	yes	complemented
38	C₁₉×#534	C₂²	1	24	yes	complemented
39	C₁₉×#532	C₂²	1	24	yes	complemented
40	C₂×C₁₉×C₄⋊Q₈	C₂²	1	12	yes	complemented
41	C₂×C₁₉×#124	C₂²	1	12	yes	complemented
42	C₁₉×#525	C₂²	1	24	yes	complemented
43	C₁₉×#525	C₂²	1	24	yes	complemented
44	C₂×C₁₉×#123	C₂²	1	24	yes	complemented
45	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	24	yes	complemented
46	C₁₉×#520	C₂²	1	8	yes	complemented
47	C₁₉×#519	C₂²	1	2	yes	complemented
48	C₁₉×#518	C₂²	1	6	yes	complemented
49	C₄×#41×C₁₉	C₂²	1	8	yes	complemented
50	C₂×C₁₉×#117	C₂²	1	6	yes	complemented
51	C₁₉×2₋¹⁺⁴	—	2	64	no	—
52	C₁₉×2₋¹⁺⁴	—	2	64	no	—
53	C₁₉×2₋¹⁺⁴	—	2	32	no	—
54	C₁₉×2₋¹⁺⁴	—	2	16	no	—
55	C₁₉×H(5,𝔽₂)	—	2	32	no	—
56	C₁₉×H(5,𝔽₂)	—	2	48	no	—
57	C₂×#41×C₁₉	—	2	64	no	—
58	C₂×#41×C₁₉	—	2	48	no	—
59	C₂×#41×C₁₉	—	2	48	no	—
60	C₂×#41×C₁₉	—	2	24	no	—
61	C₂×#41×C₁₉	D₄	1	16	yes	complemented
62	C₂×#41×C₁₉	C₂³	1	12	yes	—
63	C₂×#41×C₁₉	C₂³	1	12	yes	—
64	C₂×#41×C₁₉	C₂³	1	12	yes	—
65	C₂×#41×C₁₉	C₂³	1	12	yes	—
66	C₂×#41×C₁₉	C₂³	1	4	yes	—
67	C₂×#41×C₁₉	C₂³	1	12	yes	—
68	C₂×#41×C₁₉	C₂³	1	48	yes	—
69	C₂×#41×C₁₉	C₂³	1	24	yes	—
70	C₂×#41×C₁₉	C₂³	1	8	yes	—
71	C₂×#41×C₁₉	C₂³	1	4	yes	—
72	C₂×#41×C₁₉	C₂³	1	4	yes	—
73	C₂²×Q₈×C₁₉	—	2	16	no	—
74	C₂²×Q₈×C₁₉	—	2	24	no	—
75	C₂²×Q₈×C₁₉	C₂³	1	12	yes	—
76	C₂²×Q₈×C₁₉	C₂³	1	12	yes	—
77	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
78	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
79	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
80	C₂²×Q₈×C₁₉	C₂³	1	16	yes	—
81	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
82	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
84	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
85	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
86	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₉	C₂³	1	24	yes	—
88	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
89	C₂³×C₄×C₁₉	C₂³	1	12	yes	—
90	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
91	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
92	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
93	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
94	C₁₉×C₄⋊Q₈	C₂³	1	48	yes	—
95	C₁₉×#127	C₂³	1	8	yes	—
96	C₁₉×#124	C₂³	1	24	yes	—
97	C₁₉×#124	C₂³	1	48	yes	—
98	C₁₉×#124	C₂³	1	8	yes	—
99	C₁₉×#123	C₂³	1	48	yes	—
100	C₁₉×#123	C₂³	1	96	yes	—
101	C₁₉×#123	C₂³	1	48	yes	—
102	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
103	C₁₉×C₂²⋊Q₈	C₂³	1	96	yes	—
104	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
105	C₁₉×#121	C₂³	1	16	yes	—
106	C₁₉×#121	C₂³	1	48	yes	—
107	C₁₉×#121	C₂³	1	96	yes	—
108	C₁₉×#120	C₂³	1	16	yes	—
109	C₁₉×#120	C₂³	1	48	yes	—
110	C₄×Q₈×C₁₉	C₂³	1	16	yes	—
111	C₄×D₄×C₁₉	C₂³	1	48	yes	—
112	C₄×D₄×C₁₉	C₂³	1	96	yes	—
113	C₁₉×#117	C₂³	1	4	yes	—
114	C₁₉×#117	C₂³	1	12	yes	—
115	C₁₉×#117	C₂³	1	12	yes	—
116	C₁₉×#117	C₂³	1	12	yes	—
117	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
118	C₂×C₄⋊C₄×C₁₉	C₂³	1	48	yes	—
119	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
120	C₂×C₂²⋊C₄×C₁₉	C₂³	1	48	yes	—
121	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
122	C₂⁴×C₁₉	C₂⁴	1	12	yes	—
123	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
124	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
125	#41×C₁₉	—	2	32	no	—
126	#41×C₁₉	—	2	96	no	—
127	#41×C₁₉	—	2	192	no	—
128	#41×C₁₉	—	2	48	no	—
129	#41×C₁₉	—	2	16	no	—
130	#41×C₁₉	—	2	48	no	—
131	#41×C₁₉	—	2	48	no	—
132	#41×C₁₉	—	2	48	no	—
133	#41×C₁₉	—	2	48	no	—
134	#41×C₁₉	C₂×D₄	1	32	yes	—
135	#41×C₁₉	C₂×D₄	1	32	yes	—
136	C₂×Q₈×C₁₉	—	2	64	no	—
137	C₂×Q₈×C₁₉	—	2	32	no	—
138	C₂×Q₈×C₁₉	—	2	24	no	—
139	C₂×Q₈×C₁₉	—	2	12	no	—
140	C₂×Q₈×C₁₉	—	2	48	no	—
141	C₂×Q₈×C₁₉	—	2	48	no	—
142	C₂×Q₈×C₁₉	—	2	24	no	—
143	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
144	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
145	C₂×Q₈×C₁₉	C₂⁴	1	24	yes	—
146	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
147	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
148	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
149	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
150	C₂×D₄×C₁₉	—	2	24	no	—
151	C₂×D₄×C₁₉	—	2	48	no	—
152	C₂×D₄×C₁₉	—	2	96	no	—
153	C₂×D₄×C₁₉	—	2	4	no	—
154	C₂×D₄×C₁₉	—	2	24	no	—
155	C₂×D₄×C₁₉	C₂×D₄	1	24	yes	—
156	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
157	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
158	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
159	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
160	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
161	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
162	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
163	C₂×D₄×C₁₉	C₂⁴	1	32	yes	—
164	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
165	C₂²×C₄×C₁₉	—	2	24	no	—
166	C₂²×C₄×C₁₉	—	2	24	no	—
167	C₂²×C₄×C₁₉	—	2	48	no	—
168	C₂²×C₄×C₁₉	C₂×D₄	1	24	yes	—
169	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
170	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
173	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
175	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
176	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
177	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
178	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
181	C₄⋊C₄×C₁₉	C₂⁴	1	96	yes	—
182	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
183	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
184	C₂²⋊C₄×C₁₉	C₂⁴	1	96	yes	—
185	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
186	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
187	C₄²×C₁₉	C₂⁴	1	8	yes	—
188	C₄²×C₁₉	C₂⁴	1	24	yes	—
189	#62859	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂³×C₁₉	—	2	4	no	—
191	C₂³×C₁₉	—	2	24	no	—
192	C₂³×C₁₉	—	4	6	no	—
193	C₂³×C₁₉	—	4	4	no	—
194	C₂³×C₁₉	—	4	24	no	—
195	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
196	C₂³×C₁₉	C₂⁵	1	8	yes	—
197	C₂³×C₁₉	C₂⁵	1	4	yes	—
198	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
199	C₂³×C₁₉	C₂⁵	1	6	yes	—
200	Q₈×C₁₉	—	2	12	no	—
201	Q₈×C₁₉	—	2	48	no	—
202	Q₈×C₁₉	—	2	12	no	—
203	Q₈×C₁₉	—	2	24	no	—
204	Q₈×C₁₉	—	2	8	no	—
205	Q₈×C₁₉	C₂²×D₄	1	16	yes	—
206	D₄×C₁₉	—	2	16	no	—
207	D₄×C₁₉	—	2	48	no	—
208	D₄×C₁₉	—	2	48	no	—
209	D₄×C₁₉	—	2	24	no	—
210	D₄×C₁₉	—	2	8	no	—
211	D₄×C₁₉	—	2	4	no	—
212	D₄×C₁₉	—	2	4	no	—
213	D₄×C₁₉	—	4	32	no	—
214	D₄×C₁₉	C₂²×D₄	1	48	yes	—
215	C₂×C₄×C₁₉	—	2	12	no	—
216	C₂×C₄×C₁₉	—	2	24	no	—
217	C₂×C₄×C₁₉	—	2	48	no	—
218	C₂×C₄×C₁₉	—	2	16	no	—
219	C₂×C₄×C₁₉	—	2	48	no	—
220	C₂×C₄×C₁₉	—	2	48	no	—
221	C₂×C₄×C₁₉	—	4	24	no	—
222	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
223	C₂×C₄×C₁₉	C₂²×D₄	1	24	yes	—
224	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₁₉	C₂²×D₄	1	24	yes	—
226	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
227	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
228	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
229	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
231	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
232	C₂×#585	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₂²×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#3500	C₂×C₁₉	1	8	yes	complemented
235	#3499	C₂×C₁₉	1	8	yes	complemented
236	#3489	C₂×C₁₉	1	16	yes	complemented
237	#3486	C₂×C₁₉	1	4	yes	complemented
238	#3485	C₂×C₁₉	1	12	yes	complemented
239	#3449	C₂×C₁₉	1	6	yes	complemented
240	C₂×#536	C₂×C₁₉	1	6	yes	complemented
241	#3428	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₂²×C₁₉	—	2	12	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	4	no	—
245	C₂²×C₁₉	—	2	8	no	—
246	C₂²×C₁₉	—	2	8	no	—
247	C₂²×C₁₉	—	2	16	no	—
248	C₂²×C₁₉	—	4	12	no	—
249	C₂²×C₁₉	—	4	8	no	—
250	C₂²×C₁₉	—	8	24	no	—
251	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
252	C₂²×C₁₉	C₂³×D₄	1	12	yes	—
253	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
254	C₄×C₁₉	—	2	8	no	—
255	C₄×C₁₉	—	2	12	no	—
256	C₄×C₁₉	—	2	16	no	—
257	C₄×C₁₉	C₂³×D₄	1	2	yes	—
258	C₄×C₁₉	C₂³×D₄	1	12	yes	—
259	C₄×C₁₉	C₂³×D₄	1	2	yes	—
260	#585	—	2	16	no	—
261	C₂×2₋¹⁺⁴	—	2	16	no	—
262	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	—
263	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	8	yes	complemented
264	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	8	yes	complemented
265	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	complemented
266	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	6	yes	—
267	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	complemented
268	C₂²×#41	C₂²×C₁₉	1	6	yes	—
269	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
270	C₂²×#41	C₂²×C₁₉	1	3	yes	complemented
271	C₂²×#41	C₂²×C₁₉	1	6	yes	complemented
272	C₂²×#41	C₂²×C₁₉	1	8	yes	complemented
273	C₂³×Q₈	C₂²×C₁₉	1	3	yes	complemented
274	C₂³×Q₈	C₂²×C₁₉	1	2	yes	complemented
275	D₄×Q₈	C₂²×C₁₉	1	32	yes	complemented
276	#548	C₂²×C₁₉	1	32	yes	complemented
277	#547	C₂²×C₁₉	1	96	yes	complemented
278	#546	C₂²×C₁₉	1	96	yes	complemented
279	#537	C₂²×C₁₉	1	24	yes	complemented
280	#536	C₂²×C₁₉	1	12	yes	complemented
281	#536	C₂²×C₁₉	1	24	yes	complemented
282	#536	C₂²×C₁₉	1	24	yes	complemented
283	#536	C₂²×C₁₉	1	24	yes	complemented
284	#536	C₂²×C₁₉	1	12	yes	complemented
285	#535	C₂²×C₁₉	1	4	yes	complemented
286	#535	C₂²×C₁₉	1	12	yes	complemented
287	#534	C₂²×C₁₉	1	24	yes	complemented
288	#532	C₂²×C₁₉	1	24	yes	complemented
289	C₂×C₄⋊Q₈	C₂²×C₁₉	1	12	yes	complemented
290	C₂×#124	C₂²×C₁₉	1	12	yes	complemented
291	#525	C₂²×C₁₉	1	24	yes	complemented
292	#525	C₂²×C₁₉	1	24	yes	complemented
293	C₂×#123	C₂²×C₁₉	1	24	yes	complemented
294	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	24	yes	complemented
295	#520	C₂²×C₁₉	1	8	yes	complemented
296	#519	C₂²×C₁₉	1	2	yes	complemented
297	#518	C₂²×C₁₉	1	6	yes	complemented
298	C₄×#41	C₂²×C₁₉	1	8	yes	complemented
299	C₂×#117	C₂²×C₁₉	1	6	yes	complemented
300	C₂×C₁₉	—	2	2	no	—
301	C₂×C₁₉	—	2	12	no	—
302	C₂×C₁₉	—	4	4	no	—
303	C₂×C₁₉	—	4	8	no	—
304	C₂×C₁₉	C₂⁴×D₄	1	1	yes	characteristic
305	C₂×C₁₉	2₋¹⁺⁶	1	2	yes	—
306	2₋¹⁺⁴	—	2	64	no	—
307	2₋¹⁺⁴	—	2	64	no	—
308	2₋¹⁺⁴	—	2	32	no	—
309	2₋¹⁺⁴	—	2	16	no	—
310	H(5,𝔽₂)	—	2	32	no	—
311	H(5,𝔽₂)	—	2	48	no	—
312	C₂×#41	—	2	64	no	—
313	C₂×#41	—	2	48	no	—
314	C₂×#41	—	2	48	no	—
315	C₂×#41	—	2	24	no	—
316	C₂×#41	D₄×C₁₉	1	16	yes	complemented
317	C₂×#41	C₂³×C₁₉	1	12	yes	—
318	C₂×#41	C₂³×C₁₉	1	12	yes	—
319	C₂×#41	C₂³×C₁₉	1	12	yes	—
320	C₂×#41	C₂³×C₁₉	1	12	yes	—
321	C₂×#41	C₂³×C₁₉	1	4	yes	—
322	C₂×#41	C₂³×C₁₉	1	12	yes	—
323	C₂×#41	C₂³×C₁₉	1	48	yes	—
324	C₂×#41	C₂³×C₁₉	1	24	yes	—
325	C₂×#41	C₂³×C₁₉	1	8	yes	—
326	C₂×#41	C₂³×C₁₉	1	4	yes	—
327	C₂×#41	C₂³×C₁₉	1	4	yes	—
328	C₂²×Q₈	—	2	16	no	—
329	C₂²×Q₈	—	2	24	no	—
330	C₂²×Q₈	C₂³×C₁₉	1	12	yes	—
331	C₂²×Q₈	C₂³×C₁₉	1	12	yes	—
332	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
333	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
334	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
335	C₂²×Q₈	C₂³×C₁₉	1	16	yes	—
336	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
337	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
339	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
340	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
341	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₁₉	1	24	yes	—
343	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
344	C₂³×C₄	C₂³×C₁₉	1	12	yes	—
345	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
346	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
347	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
348	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
349	C₄⋊Q₈	C₂³×C₁₉	1	48	yes	—
350	#127	C₂³×C₁₉	1	8	yes	—
351	#124	C₂³×C₁₉	1	24	yes	—
352	#124	C₂³×C₁₉	1	48	yes	—
353	#124	C₂³×C₁₉	1	8	yes	—
354	#123	C₂³×C₁₉	1	48	yes	—
355	#123	C₂³×C₁₉	1	96	yes	—
356	#123	C₂³×C₁₉	1	48	yes	—
357	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
358	C₂²⋊Q₈	C₂³×C₁₉	1	96	yes	—
359	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
360	#121	C₂³×C₁₉	1	16	yes	—
361	#121	C₂³×C₁₉	1	48	yes	—
362	#121	C₂³×C₁₉	1	96	yes	—
363	#120	C₂³×C₁₉	1	16	yes	—
364	#120	C₂³×C₁₉	1	48	yes	—
365	C₄×Q₈	C₂³×C₁₉	1	16	yes	—
366	C₄×D₄	C₂³×C₁₉	1	48	yes	—
367	C₄×D₄	C₂³×C₁₉	1	96	yes	—
368	#117	C₂³×C₁₉	1	4	yes	—
369	#117	C₂³×C₁₉	1	12	yes	—
370	#117	C₂³×C₁₉	1	12	yes	—
371	#117	C₂³×C₁₉	1	12	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	48	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₉	1	48	yes	—
376	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
377	C₁₉	#62859	1	1	yes	characteristic, direct product factor, Sylow
378	C₂⁴	C₂⁴×C₁₉	1	12	yes	—
379	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
380	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
381	#41	—	2	32	no	—
382	#41	—	2	96	no	—
383	#41	—	2	192	no	—
384	#41	—	2	48	no	—
385	#41	—	2	16	no	—
386	#41	—	2	48	no	—
387	#41	—	2	48	no	—
388	#41	—	2	48	no	—
389	#41	—	2	48	no	—
390	#41	C₂×D₄×C₁₉	1	32	yes	—
391	#41	C₂×D₄×C₁₉	1	32	yes	—
392	C₂×Q₈	—	2	64	no	—
393	C₂×Q₈	—	2	32	no	—
394	C₂×Q₈	—	2	24	no	—
395	C₂×Q₈	—	2	12	no	—
396	C₂×Q₈	—	2	48	no	—
397	C₂×Q₈	—	2	48	no	—
398	C₂×Q₈	—	2	24	no	—
399	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
400	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
401	C₂×Q₈	C₂⁴×C₁₉	1	24	yes	—
402	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
403	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
404	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
405	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
406	C₂×D₄	—	2	24	no	—
407	C₂×D₄	—	2	48	no	—
408	C₂×D₄	—	2	96	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	24	no	—
411	C₂×D₄	C₂×D₄×C₁₉	1	24	yes	—
412	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
413	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
414	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
415	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
416	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
417	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
418	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
419	C₂×D₄	C₂⁴×C₁₉	1	32	yes	—
420	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
421	C₂²×C₄	—	2	24	no	—
422	C₂²×C₄	—	2	24	no	—
423	C₂²×C₄	—	2	48	no	—
424	C₂²×C₄	C₂×D₄×C₁₉	1	24	yes	—
425	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
426	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
427	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
428	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
429	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
430	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
431	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
432	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
433	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
434	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
435	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
436	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
437	C₄⋊C₄	C₂⁴×C₁₉	1	96	yes	—
438	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
439	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
440	C₂²⋊C₄	C₂⁴×C₁₉	1	96	yes	—
441	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
442	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
443	C₄²	C₂⁴×C₁₉	1	8	yes	—
444	C₄²	C₂⁴×C₁₉	1	24	yes	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	24	no	—
447	C₂³	—	4	6	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	24	no	—
450	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
451	C₂³	C₂⁵×C₁₉	1	8	yes	—
452	C₂³	C₂⁵×C₁₉	1	4	yes	—
453	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
454	C₂³	C₂⁵×C₁₉	1	6	yes	—
455	Q₈	—	2	12	no	—
456	Q₈	—	2	48	no	—
457	Q₈	—	2	12	no	—
458	Q₈	—	2	24	no	—
459	Q₈	—	2	8	no	—
460	Q₈	C₂²×D₄×C₁₉	1	16	yes	—
461	D₄	—	2	16	no	—
462	D₄	—	2	48	no	—
463	D₄	—	2	48	no	—
464	D₄	—	2	24	no	—
465	D₄	—	2	8	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	4	32	no	—
469	D₄	C₂²×D₄×C₁₉	1	48	yes	—
470	C₂×C₄	—	2	12	no	—
471	C₂×C₄	—	2	24	no	—
472	C₂×C₄	—	2	48	no	—
473	C₂×C₄	—	2	16	no	—
474	C₂×C₄	—	2	48	no	—
475	C₂×C₄	—	2	48	no	—
476	C₂×C₄	—	4	24	no	—
477	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
478	C₂×C₄	C₂²×D₄×C₁₉	1	24	yes	—
479	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₉	1	24	yes	—
481	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
482	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
483	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
484	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
486	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
487	C₂²	—	2	12	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	16	no	—
493	C₂²	—	4	12	no	—
494	C₂²	—	4	8	no	—
495	C₂²	—	8	24	no	—
496	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
497	C₂²	C₂³×D₄×C₁₉	1	12	yes	—
498	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
499	C₄	—	2	8	no	—
500	C₄	—	2	12	no	—
501	C₄	—	2	16	no	—
502	C₄	C₂³×D₄×C₁₉	1	2	yes	—
503	C₄	C₂³×D₄×C₁₉	1	12	yes	—
504	C₄	C₂³×D₄×C₁₉	1	2	yes	—
505	C₂	—	2	2	no	—
506	C₂	—	2	12	no	—
507	C₂	—	4	4	no	—
508	C₂	—	4	8	no	—
509	C₂	C₂⁴×D₄×C₁₉	1	1	yes	characteristic
510	C₂	C₁₉×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#585	C₂	semidirect
2. C₂²×C₁₉×2₋¹⁺⁴	C₂	semidirect
3. C₁₉×#3500	C₂	semidirect
4. C₁₉×#3499	C₂	semidirect
5. C₁₉×#3489	C₂	semidirect
6. C₁₉×#3486	C₂	semidirect
7. C₁₉×#3485	C₂	semidirect
8. C₁₉×#3449	C₂	semidirect
9. C₂×C₁₉×#536	C₂	semidirect
10. C₁₉×#3428	C₂	semidirect
14. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
16. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
18. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
21. C₂²×#41×C₁₉	C₂²	semidirect
22. C₂²×#41×C₁₉	C₂²	semidirect
23. C₂²×#41×C₁₉	C₂²	semidirect
24. C₂³×Q₈×C₁₉	C₂²	semidirect
25. C₂³×Q₈×C₁₉	C₂²	semidirect
26. D₄×Q₈×C₁₉	C₂²	semidirect
27. C₁₉×#548	C₂²	semidirect
28. C₁₉×#547	C₂²	semidirect
29. C₁₉×#546	C₂²	semidirect
30. C₁₉×#537	C₂²	semidirect
31. C₁₉×#536	C₂²	semidirect
32. C₁₉×#536	C₂²	semidirect
33. C₁₉×#536	C₂²	semidirect
34. C₁₉×#536	C₂²	semidirect
35. C₁₉×#536	C₂²	semidirect
36. C₁₉×#535	C₂²	semidirect
37. C₁₉×#535	C₂²	semidirect
38. C₁₉×#534	C₂²	semidirect
39. C₁₉×#532	C₂²	semidirect
40. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₁₉×#124	C₂²	semidirect
42. C₁₉×#525	C₂²	semidirect
43. C₁₉×#525	C₂²	semidirect
44. C₂×C₁₉×#123	C₂²	semidirect
45. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
46. C₁₉×#520	C₂²	semidirect
47. C₁₉×#519	C₂²	semidirect
48. C₁₉×#518	C₂²	semidirect
49. C₄×#41×C₁₉	C₂²	semidirect
50. C₂×C₁₉×#117	C₂²	semidirect
61. C₂×#41×C₁₉	D₄	semidirect
189. #62859	C₁₉	direct (N × H)
232. C₂×#585	C₂×C₁₉	semidirect
233. C₂²×2₋¹⁺⁴	C₂×C₁₉	semidirect
234. #3500	C₂×C₁₉	semidirect
235. #3499	C₂×C₁₉	semidirect
236. #3489	C₂×C₁₉	semidirect
237. #3486	C₂×C₁₉	semidirect
238. #3485	C₂×C₁₉	semidirect
239. #3449	C₂×C₁₉	semidirect
240. C₂×#536	C₂×C₁₉	semidirect
241. #3428	C₂×C₁₉	semidirect
263. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
264. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
265. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
267. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
270. C₂²×#41	C₂²×C₁₉	semidirect
271. C₂²×#41	C₂²×C₁₉	semidirect
272. C₂²×#41	C₂²×C₁₉	semidirect
273. C₂³×Q₈	C₂²×C₁₉	semidirect
274. C₂³×Q₈	C₂²×C₁₉	semidirect
275. D₄×Q₈	C₂²×C₁₉	semidirect
276. #548	C₂²×C₁₉	semidirect
277. #547	C₂²×C₁₉	semidirect
278. #546	C₂²×C₁₉	semidirect
279. #537	C₂²×C₁₉	semidirect
280. #536	C₂²×C₁₉	semidirect
281. #536	C₂²×C₁₉	semidirect
282. #536	C₂²×C₁₉	semidirect
283. #536	C₂²×C₁₉	semidirect
284. #536	C₂²×C₁₉	semidirect
285. #535	C₂²×C₁₉	semidirect
286. #535	C₂²×C₁₉	semidirect
287. #534	C₂²×C₁₉	semidirect
288. #532	C₂²×C₁₉	semidirect
289. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
290. C₂×#124	C₂²×C₁₉	semidirect
291. #525	C₂²×C₁₉	semidirect
292. #525	C₂²×C₁₉	semidirect
293. C₂×#123	C₂²×C₁₉	semidirect
294. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
295. #520	C₂²×C₁₉	semidirect
296. #519	C₂²×C₁₉	semidirect
297. #518	C₂²×C₁₉	semidirect
298. C₄×#41	C₂²×C₁₉	semidirect
299. C₂×#117	C₂²×C₁₉	semidirect
316. C₂×#41	D₄×C₁₉	semidirect
377. C₁₉	#62859	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×#585	2
C₂²×C₁₉×2₋¹⁺⁴	2
C₁₉×#3500	2
C₁₉×#3499	2
C₁₉×#3489	2
C₁₉×#3486	2
C₁₉×#3485	2
C₁₉×#3449	2
C₂×C₁₉×#536	2
C₁₉×#3428	2
#62859	19

Subgroups — C19×#62859 #18068818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62859 #18068818