Subgroups — C₁₉×#62812 #18068771

Order 4864.

11346 conjugacy classes of subgroups.

The subgroup lattice has 446 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	2	yes	maximal, complemented
2	C₁₉×#3500	C₂	1	8	yes	maximal, complemented
3	C₁₉×#3499	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3498	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3497	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3496	C₂	1	12	yes	maximal, complemented
7	D₄×#41×C₁₉	C₂	1	16	yes	maximal, complemented
8	C₁₉×#3449	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₉×#532	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#585	—	2	32	no	—
12	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	complemented
13	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	8	yes	complemented
14	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	12	yes	complemented
15	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	8	yes	complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₉	C₂²	1	12	yes	complemented
18	C₂²×#41×C₁₉	C₂²	1	16	yes	complemented
19	C₁₉×#550	C₂²	1	16	yes	complemented
20	D₄×Q₈×C₁₉	C₂²	1	16	yes	complemented
21	C₁₉×#548	C₂²	1	32	yes	complemented
22	C₁₉×#547	C₂²	1	48	yes	complemented
23	C₁₉×#546	C₂²	1	96	yes	complemented
24	D₄²×C₁₉	C₂²	1	48	yes	complemented
25	C₁₉×#537	C₂²	1	24	yes	complemented
26	C₁₉×#536	C₂²	1	24	yes	complemented
27	C₁₉×#535	C₂²	1	24	yes	complemented
28	C₁₉×#534	C₂²	1	24	yes	complemented
29	C₁₉×#532	C₂²	1	4	yes	complemented
30	C₁₉×#532	C₂²	1	12	yes	complemented
31	C₁₉×#532	C₂²	1	24	yes	complemented
32	C₁₉×#532	C₂²	1	24	yes	complemented
33	C₁₉×#532	C₂²	1	12	yes	complemented
34	C₁₉×#532	C₂²	1	12	yes	complemented
35	C₂×C₁₉×C₄⋊Q₈	C₂²	1	6	yes	complemented
36	C₂×C₁₉×#127	C₂²	1	6	yes	complemented
37	C₂×C₁₉×#124	C₂²	1	12	yes	complemented
38	C₁₉×#525	C₂²	1	48	yes	complemented
39	C₂×C₁₉×#121	C₂²	1	24	yes	complemented
40	C₄×#41×C₁₉	C₂²	1	8	yes	complemented
41	C₄×#41×C₁₉	C₂²	1	4	yes	complemented
42	C₄×#41×C₁₉	C₂²	1	4	yes	complemented
43	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	complemented
45	C₂×C₄×D₄×C₁₉	C₂²	1	24	yes	complemented
46	C₂×C₁₉×#117	C₂²	1	3	yes	complemented
47	C₂²×C₄²×C₁₉	C₂²	1	3	yes	complemented
48	C₁₉×2₋¹⁺⁴	—	2	64	no	—
49	C₁₉×2₋¹⁺⁴	—	2	32	no	—
50	C₁₉×H(5,𝔽₂)	—	2	64	no	—
51	C₁₉×H(5,𝔽₂)	—	2	96	no	—
52	C₂×#41×C₁₉	—	2	128	no	—
53	C₂×#41×C₁₉	—	2	96	no	—
54	C₂×#41×C₁₉	D₄	1	16	yes	complemented
55	C₂×#41×C₁₉	C₂³	1	24	yes	—
56	C₂×#41×C₁₉	C₂³	1	8	yes	—
57	C₂×#41×C₁₉	C₂³	1	24	yes	—
58	C₂×#41×C₁₉	C₂³	1	24	yes	—
59	C₂×#41×C₁₉	C₂³	1	48	yes	—
60	C₂×#41×C₁₉	C₂³	1	16	yes	—
61	C₂×#41×C₁₉	C₂³	1	4	yes	—
62	C₂×#41×C₁₉	C₂³	1	4	yes	—
63	C₂²×Q₈×C₁₉	C₂³	1	12	yes	—
64	C₂²×Q₈×C₁₉	C₂³	1	16	yes	—
65	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₉	C₂³	1	24	yes	—
67	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
68	C₂²×D₄×C₁₉	C₂³	1	48	yes	—
69	C₂²×D₄×C₁₉	C₂³	1	24	yes	—
70	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
71	C₂³×C₄×C₁₉	C₂³	1	24	yes	—
72	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
73	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
74	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
75	C₁₉×C₄⋊Q₈	C₂³	1	12	yes	—
76	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
77	C₁₉×#127	C₂³	1	4	yes	—
78	C₁₉×#127	C₂³	1	12	yes	—
79	C₁₉×#127	C₂³	1	24	yes	—
80	C₁₉×#124	C₂³	1	8	yes	—
81	C₁₉×#124	C₂³	1	24	yes	—
82	C₁₉×#124	C₂³	1	48	yes	—
83	C₁₉×#123	C₂³	1	96	yes	—
84	C₁₉×C₂²⋊Q₈	C₂³	1	96	yes	—
85	C₁₉×#121	C₂³	1	16	yes	—
86	C₁₉×#121	C₂³	1	48	yes	—
87	C₁₉×#121	C₂³	1	48	yes	—
88	C₁₉×#121	C₂³	1	48	yes	—
89	C₁₉×#121	C₂³	1	96	yes	—
90	C₁₉×#120	C₂³	1	96	yes	—
91	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
92	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
93	C₄×D₄×C₁₉	C₂³	1	16	yes	—
94	C₄×D₄×C₁₉	C₂³	1	24	yes	—
95	C₄×D₄×C₁₉	C₂³	1	24	yes	—
96	C₄×D₄×C₁₉	C₂³	1	48	yes	—
97	C₄×D₄×C₁₉	C₂³	1	48	yes	—
98	C₄×D₄×C₁₉	C₂³	1	48	yes	—
99	C₁₉×#117	C₂³	1	12	yes	—
100	C₁₉×#117	C₂³	1	12	yes	—
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
104	C₂×C₂²⋊C₄×C₁₉	C₂³	1	48	yes	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
107	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
108	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
109	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
110	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
111	C₂⁴×C₁₉	C₂⁴	1	24	yes	—
112	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
113	#41×C₁₉	—	2	64	no	—
114	#41×C₁₉	—	2	192	no	—
115	#41×C₁₉	—	2	96	no	—
116	#41×C₁₉	—	2	32	no	—
117	#41×C₁₉	—	2	96	no	—
118	#41×C₁₉	—	2	96	no	—
119	#41×C₁₉	C₂×D₄	1	32	yes	complemented
120	#41×C₁₉	C₂×D₄	1	32	yes	complemented
121	C₂×Q₈×C₁₉	—	2	64	no	—
122	C₂×Q₈×C₁₉	—	2	48	no	—
123	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	complemented
124	C₂×Q₈×C₁₉	C₂⁴	1	24	yes	—
125	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
126	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
127	C₂×D₄×C₁₉	—	2	96	no	—
128	C₂×D₄×C₁₉	—	2	192	no	—
129	C₂×D₄×C₁₉	—	2	48	no	—
130	C₂×D₄×C₁₉	—	4	48	no	—
131	C₂×D₄×C₁₉	C₂×D₄	1	24	yes	complemented
132	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
133	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
134	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
135	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
136	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
137	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
138	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
139	C₂²×C₄×C₁₉	—	2	96	no	—
140	C₂²×C₄×C₁₉	—	4	12	no	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	24	yes	complemented
142	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
144	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
145	C₂²×C₄×C₁₉	C₂⁴	1	48	yes	—
146	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
153	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
154	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
155	C₄⋊C₄×C₁₉	C₂⁴	1	48	yes	—
156	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
157	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
158	C₂²⋊C₄×C₁₉	C₂⁴	1	96	yes	—
159	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
160	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₄²×C₁₉	C₂⁴	1	6	yes	—
162	C₄²×C₁₉	C₂⁴	1	12	yes	—
163	C₄²×C₁₉	C₂⁴	1	12	yes	—
164	C₄²×C₁₉	C₂⁴	1	2	yes	—
165	C₄²×C₁₉	C₂⁴	1	6	yes	—
166	#62812	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₉	—	2	48	no	—
168	C₂³×C₁₉	—	4	6	no	—
169	C₂³×C₁₉	—	4	48	no	—
170	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
171	C₂³×C₁₉	C₂⁵	1	16	yes	—
172	C₂³×C₁₉	C₂⁵	1	6	yes	—
173	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	48	no	—
175	Q₈×C₁₉	—	2	16	no	—
176	Q₈×C₁₉	C₂²×D₄	1	16	yes	—
177	D₄×C₁₉	—	2	96	no	—
178	D₄×C₁₉	—	2	32	no	—
179	D₄×C₁₉	—	2	48	no	—
180	D₄×C₁₉	—	2	16	no	—
181	D₄×C₁₉	—	2	32	no	—
182	D₄×C₁₉	—	4	48	no	—
183	D₄×C₁₉	C₂²×D₄	1	48	yes	—
184	C₂×C₄×C₁₉	—	2	48	no	—
185	C₂×C₄×C₁₉	—	2	32	no	—
186	C₂×C₄×C₁₉	—	2	96	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	24	no	—
189	C₂×C₄×C₁₉	—	4	12	no	—
190	C₂×C₄×C₁₉	—	4	6	no	—
191	C₂×C₄×C₁₉	C₂²×D₄	1	24	yes	—
192	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₁₉	C₂²×D₄	1	24	yes	—
194	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
195	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
196	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
197	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
198	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
200	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
201	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
202	C₂×#585	C₂×C₁₉	1	2	yes	complemented
203	#3500	C₂×C₁₉	1	8	yes	complemented
204	#3499	C₂×C₁₉	1	4	yes	complemented
205	#3498	C₂×C₁₉	1	4	yes	complemented
206	#3497	C₂×C₁₉	1	4	yes	complemented
207	#3496	C₂×C₁₉	1	12	yes	complemented
208	D₄×#41	C₂×C₁₉	1	16	yes	complemented
209	#3449	C₂×C₁₉	1	6	yes	complemented
210	C₂×#532	C₂×C₁₉	1	6	yes	complemented
211	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	12	no	—
214	C₂²×C₁₉	—	2	16	no	—
215	C₂²×C₁₉	—	2	32	no	—
216	C₂²×C₁₉	—	4	12	no	—
217	C₂²×C₁₉	—	8	48	no	—
218	C₂²×C₁₉	C₂³×D₄	1	12	yes	—
219	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
220	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
221	C₄×C₁₉	—	2	16	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	2	12	no	—
224	C₄×C₁₉	C₂³×D₄	1	2	yes	—
225	C₄×C₁₉	C₂³×D₄	1	12	yes	—
226	C₄×C₁₉	C₂³×D₄	1	2	yes	—
227	C₄×C₁₉	#585	1	4	yes	complemented
228	#585	—	2	32	no	—
229	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	complemented
230	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	8	yes	complemented
231	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	12	yes	complemented
232	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	8	yes	complemented
233	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
234	C₂²×#41	C₂²×C₁₉	1	12	yes	complemented
235	C₂²×#41	C₂²×C₁₉	1	16	yes	complemented
236	#550	C₂²×C₁₉	1	16	yes	complemented
237	D₄×Q₈	C₂²×C₁₉	1	16	yes	complemented
238	#548	C₂²×C₁₉	1	32	yes	complemented
239	#547	C₂²×C₁₉	1	48	yes	complemented
240	#546	C₂²×C₁₉	1	96	yes	complemented
241	D₄²	C₂²×C₁₉	1	48	yes	complemented
242	#537	C₂²×C₁₉	1	24	yes	complemented
243	#536	C₂²×C₁₉	1	24	yes	complemented
244	#535	C₂²×C₁₉	1	24	yes	complemented
245	#534	C₂²×C₁₉	1	24	yes	complemented
246	#532	C₂²×C₁₉	1	4	yes	complemented
247	#532	C₂²×C₁₉	1	12	yes	complemented
248	#532	C₂²×C₁₉	1	24	yes	complemented
249	#532	C₂²×C₁₉	1	24	yes	complemented
250	#532	C₂²×C₁₉	1	12	yes	complemented
251	#532	C₂²×C₁₉	1	12	yes	complemented
252	C₂×C₄⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
253	C₂×#127	C₂²×C₁₉	1	6	yes	complemented
254	C₂×#124	C₂²×C₁₉	1	12	yes	complemented
255	#525	C₂²×C₁₉	1	48	yes	complemented
256	C₂×#121	C₂²×C₁₉	1	24	yes	complemented
257	C₄×#41	C₂²×C₁₉	1	8	yes	complemented
258	C₄×#41	C₂²×C₁₉	1	4	yes	complemented
259	C₄×#41	C₂²×C₁₉	1	4	yes	complemented
260	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
261	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	complemented
262	C₂×C₄×D₄	C₂²×C₁₉	1	24	yes	complemented
263	C₂×#117	C₂²×C₁₉	1	3	yes	complemented
264	C₂²×C₄²	C₂²×C₁₉	1	3	yes	complemented
265	C₂×C₁₉	—	2	2	no	—
266	C₂×C₁₉	—	2	12	no	—
267	C₂×C₁₉	—	4	16	no	—
268	C₂×C₁₉	C₂⁴×D₄	1	1	yes	characteristic
269	C₂×C₁₉	C₂×#585	1	2	yes	—
270	2₋¹⁺⁴	—	2	64	no	—
271	2₋¹⁺⁴	—	2	32	no	—
272	H(5,𝔽₂)	—	2	64	no	—
273	H(5,𝔽₂)	—	2	96	no	—
274	C₂×#41	—	2	128	no	—
275	C₂×#41	—	2	96	no	—
276	C₂×#41	D₄×C₁₉	1	16	yes	complemented
277	C₂×#41	C₂³×C₁₉	1	24	yes	—
278	C₂×#41	C₂³×C₁₉	1	8	yes	—
279	C₂×#41	C₂³×C₁₉	1	24	yes	—
280	C₂×#41	C₂³×C₁₉	1	24	yes	—
281	C₂×#41	C₂³×C₁₉	1	48	yes	—
282	C₂×#41	C₂³×C₁₉	1	16	yes	—
283	C₂×#41	C₂³×C₁₉	1	4	yes	—
284	C₂×#41	C₂³×C₁₉	1	4	yes	—
285	C₂²×Q₈	C₂³×C₁₉	1	12	yes	—
286	C₂²×Q₈	C₂³×C₁₉	1	16	yes	—
287	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₂²×D₄	C₂³×C₁₉	1	24	yes	—
289	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
290	C₂²×D₄	C₂³×C₁₉	1	48	yes	—
291	C₂²×D₄	C₂³×C₁₉	1	24	yes	—
292	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
293	C₂³×C₄	C₂³×C₁₉	1	24	yes	—
294	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
295	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
296	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
297	C₄⋊Q₈	C₂³×C₁₉	1	12	yes	—
298	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
299	#127	C₂³×C₁₉	1	4	yes	—
300	#127	C₂³×C₁₉	1	12	yes	—
301	#127	C₂³×C₁₉	1	24	yes	—
302	#124	C₂³×C₁₉	1	8	yes	—
303	#124	C₂³×C₁₉	1	24	yes	—
304	#124	C₂³×C₁₉	1	48	yes	—
305	#123	C₂³×C₁₉	1	96	yes	—
306	C₂²⋊Q₈	C₂³×C₁₉	1	96	yes	—
307	#121	C₂³×C₁₉	1	16	yes	—
308	#121	C₂³×C₁₉	1	48	yes	—
309	#121	C₂³×C₁₉	1	48	yes	—
310	#121	C₂³×C₁₉	1	48	yes	—
311	#121	C₂³×C₁₉	1	96	yes	—
312	#120	C₂³×C₁₉	1	96	yes	—
313	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
314	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
315	C₄×D₄	C₂³×C₁₉	1	16	yes	—
316	C₄×D₄	C₂³×C₁₉	1	24	yes	—
317	C₄×D₄	C₂³×C₁₉	1	24	yes	—
318	C₄×D₄	C₂³×C₁₉	1	48	yes	—
319	C₄×D₄	C₂³×C₁₉	1	48	yes	—
320	C₄×D₄	C₂³×C₁₉	1	48	yes	—
321	#117	C₂³×C₁₉	1	12	yes	—
322	#117	C₂³×C₁₉	1	12	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₉	1	48	yes	—
327	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
328	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
329	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
330	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
331	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
332	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
333	C₁₉	#62812	1	1	yes	characteristic, direct product factor, Sylow
334	C₂⁴	C₂⁴×C₁₉	1	24	yes	—
335	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
336	#41	—	2	64	no	—
337	#41	—	2	192	no	—
338	#41	—	2	96	no	—
339	#41	—	2	32	no	—
340	#41	—	2	96	no	—
341	#41	—	2	96	no	—
342	#41	C₂×D₄×C₁₉	1	32	yes	complemented
343	#41	C₂×D₄×C₁₉	1	32	yes	complemented
344	C₂×Q₈	—	2	64	no	—
345	C₂×Q₈	—	2	48	no	—
346	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	complemented
347	C₂×Q₈	C₂⁴×C₁₉	1	24	yes	—
348	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
349	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
350	C₂×D₄	—	2	96	no	—
351	C₂×D₄	—	2	192	no	—
352	C₂×D₄	—	2	48	no	—
353	C₂×D₄	—	4	48	no	—
354	C₂×D₄	C₂×D₄×C₁₉	1	24	yes	complemented
355	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
356	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
357	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
358	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
359	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
360	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
361	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
362	C₂²×C₄	—	2	96	no	—
363	C₂²×C₄	—	4	12	no	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	24	yes	complemented
365	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
367	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
368	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
369	C₂²×C₄	C₂⁴×C₁₉	1	48	yes	—
370	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
371	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
372	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
374	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
375	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
376	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
377	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
378	C₄⋊C₄	C₂⁴×C₁₉	1	48	yes	—
379	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
380	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
381	C₂²⋊C₄	C₂⁴×C₁₉	1	96	yes	—
382	C₄²	C₂⁴×C₁₉	1	2	yes	—
383	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
384	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
385	C₄²	C₂⁴×C₁₉	1	6	yes	—
386	C₄²	C₂⁴×C₁₉	1	6	yes	—
387	C₄²	C₂⁴×C₁₉	1	12	yes	—
388	C₄²	C₂⁴×C₁₉	1	12	yes	—
389	C₂³	—	2	48	no	—
390	C₂³	—	4	6	no	—
391	C₂³	—	4	48	no	—
392	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
393	C₂³	C₂⁵×C₁₉	1	16	yes	—
394	C₂³	C₂⁵×C₁₉	1	6	yes	—
395	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
396	Q₈	—	2	48	no	—
397	Q₈	—	2	16	no	—
398	Q₈	C₂²×D₄×C₁₉	1	16	yes	—
399	D₄	—	2	96	no	—
400	D₄	—	2	32	no	—
401	D₄	—	2	48	no	—
402	D₄	—	2	16	no	—
403	D₄	—	2	32	no	—
404	D₄	—	4	48	no	—
405	D₄	C₂²×D₄×C₁₉	1	48	yes	—
406	C₂×C₄	—	2	48	no	—
407	C₂×C₄	—	2	32	no	—
408	C₂×C₄	—	2	96	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	24	no	—
411	C₂×C₄	—	4	12	no	—
412	C₂×C₄	—	4	6	no	—
413	C₂×C₄	C₂²×D₄×C₁₉	1	24	yes	—
414	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
415	C₂×C₄	C₂²×D₄×C₁₉	1	24	yes	—
416	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
417	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
418	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
419	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
420	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
421	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
422	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
423	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	12	no	—
426	C₂²	—	2	16	no	—
427	C₂²	—	2	32	no	—
428	C₂²	—	4	12	no	—
429	C₂²	—	8	48	no	—
430	C₂²	C₂³×D₄×C₁₉	1	12	yes	—
431	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
432	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
433	C₄	—	2	16	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	12	no	—
436	C₄	C₂³×D₄×C₁₉	1	2	yes	—
437	C₄	C₂³×D₄×C₁₉	1	12	yes	—
438	C₄	C₂³×D₄×C₁₉	1	2	yes	—
439	C₄	C₁₉×#585	1	4	yes	complemented
440	C₂	—	2	2	no	—
441	C₂	—	2	12	no	—
442	C₂	—	4	16	no	—
443	C₂	C₂⁴×D₄×C₁₉	1	1	yes	characteristic
444	C₂	C₂×C₁₉×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
socle	C₂²×C₁₉	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×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. C₁₉×#3500	C₂	semidirect
3. C₁₉×#3499	C₂	semidirect
4. C₁₉×#3498	C₂	semidirect
5. C₁₉×#3497	C₂	semidirect
6. C₁₉×#3496	C₂	semidirect
7. D₄×#41×C₁₉	C₂	semidirect
8. C₁₉×#3449	C₂	semidirect
9. C₂×C₁₉×#532	C₂	semidirect
10. C₂×C₄×#41×C₁₉	C₂	semidirect
12. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
13. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
14. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
15. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×#41×C₁₉	C₂²	semidirect
18. C₂²×#41×C₁₉	C₂²	semidirect
19. C₁₉×#550	C₂²	semidirect
20. D₄×Q₈×C₁₉	C₂²	semidirect
21. C₁₉×#548	C₂²	semidirect
22. C₁₉×#547	C₂²	semidirect
23. C₁₉×#546	C₂²	semidirect
24. D₄²×C₁₉	C₂²	semidirect
25. C₁₉×#537	C₂²	semidirect
26. C₁₉×#536	C₂²	semidirect
27. C₁₉×#535	C₂²	semidirect
28. C₁₉×#534	C₂²	semidirect
29. C₁₉×#532	C₂²	semidirect
30. C₁₉×#532	C₂²	semidirect
31. C₁₉×#532	C₂²	semidirect
32. C₁₉×#532	C₂²	semidirect
33. C₁₉×#532	C₂²	semidirect
34. C₁₉×#532	C₂²	semidirect
35. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₁₉×#127	C₂²	semidirect
37. C₂×C₁₉×#124	C₂²	semidirect
38. C₁₉×#525	C₂²	semidirect
39. C₂×C₁₉×#121	C₂²	semidirect
40. C₄×#41×C₁₉	C₂²	semidirect
41. C₄×#41×C₁₉	C₂²	semidirect
42. C₄×#41×C₁₉	C₂²	semidirect
43. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
44. C₂×C₄×D₄×C₁₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₉	C₂²	semidirect
46. C₂×C₁₉×#117	C₂²	semidirect
47. C₂²×C₄²×C₁₉	C₂²	semidirect
54. C₂×#41×C₁₉	D₄	semidirect
119. #41×C₁₉	C₂×D₄	semidirect
120. #41×C₁₉	C₂×D₄	semidirect
123. C₂×Q₈×C₁₉	C₂×D₄	semidirect
131. C₂×D₄×C₁₉	C₂×D₄	semidirect
141. C₂²×C₄×C₁₉	C₂×D₄	semidirect
166. #62812	C₁₉	direct (N × H)
202. C₂×#585	C₂×C₁₉	semidirect
203. #3500	C₂×C₁₉	semidirect
204. #3499	C₂×C₁₉	semidirect
205. #3498	C₂×C₁₉	semidirect
206. #3497	C₂×C₁₉	semidirect
207. #3496	C₂×C₁₉	semidirect
208. D₄×#41	C₂×C₁₉	semidirect
209. #3449	C₂×C₁₉	semidirect
210. C₂×#532	C₂×C₁₉	semidirect
211. C₂×C₄×#41	C₂×C₁₉	semidirect
227. C₄×C₁₉	#585	semidirect
229. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
230. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
231. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
232. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
234. C₂²×#41	C₂²×C₁₉	semidirect
235. C₂²×#41	C₂²×C₁₉	semidirect
236. #550	C₂²×C₁₉	semidirect
237. D₄×Q₈	C₂²×C₁₉	semidirect
238. #548	C₂²×C₁₉	semidirect
239. #547	C₂²×C₁₉	semidirect
240. #546	C₂²×C₁₉	semidirect
241. D₄²	C₂²×C₁₉	semidirect
242. #537	C₂²×C₁₉	semidirect
243. #536	C₂²×C₁₉	semidirect
244. #535	C₂²×C₁₉	semidirect
245. #534	C₂²×C₁₉	semidirect
246. #532	C₂²×C₁₉	semidirect
247. #532	C₂²×C₁₉	semidirect
248. #532	C₂²×C₁₉	semidirect
249. #532	C₂²×C₁₉	semidirect
250. #532	C₂²×C₁₉	semidirect
251. #532	C₂²×C₁₉	semidirect
252. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
253. C₂×#127	C₂²×C₁₉	semidirect
254. C₂×#124	C₂²×C₁₉	semidirect
255. #525	C₂²×C₁₉	semidirect
256. C₂×#121	C₂²×C₁₉	semidirect
257. C₄×#41	C₂²×C₁₉	semidirect
258. C₄×#41	C₂²×C₁₉	semidirect
259. C₄×#41	C₂²×C₁₉	semidirect
260. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
261. C₂×C₄×D₄	C₂²×C₁₉	semidirect
262. C₂×C₄×D₄	C₂²×C₁₉	semidirect
263. C₂×#117	C₂²×C₁₉	semidirect
264. C₂²×C₄²	C₂²×C₁₉	semidirect
276. C₂×#41	D₄×C₁₉	semidirect
333. C₁₉	#62812	direct (N × H)
342. #41	C₂×D₄×C₁₉	semidirect
343. #41	C₂×D₄×C₁₉	semidirect
346. C₂×Q₈	C₂×D₄×C₁₉	semidirect
354. C₂×D₄	C₂×D₄×C₁₉	semidirect
364. C₂²×C₄	C₂×D₄×C₁₉	semidirect
439. C₄	C₁₉×#585	semidirect

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
C₁₉×#3500	2
C₁₉×#3499	2
C₁₉×#3498	2
C₁₉×#3497	2
C₁₉×#3496	2
D₄×#41×C₁₉	2
C₁₉×#3449	2
C₂×C₁₉×#532	2
C₂×C₄×#41×C₁₉	2
#62812	19

Subgroups — C19×#62812 #18068771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62812 #18068771