Subgroups — C₁₉×#23905 #18029864

Order 4864.

1744 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3485	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#458	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2614	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2022	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1899	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1890	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1782	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#547	—	2	4	no	—
13	C₁₉×#546	—	2	4	no	—
14	C₁₉×#536	—	2	1	no	—
15	C₁₉×#536	—	2	8	no	—
16	C₁₉×#534	—	2	1	no	—
17	C₁₉×#534	C₂²	1	2	yes	—
18	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₉×#124	—	2	1	no	—
20	C₁₉×#525	—	2	1	no	—
21	C₂×C₁₉×#123	—	2	1	no	—
22	C₂×C₁₉×#123	C₂²	1	4	yes	—
23	C₂×C₁₉×#123	C₂²	1	2	yes	—
24	C₂×C₁₉×#123	C₂²	1	2	yes	—
25	C₂×C₁₉×#123	C₂²	1	2	yes	complemented
26	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
28	C₁₉×#518	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#458	—	2	8	no	—
31	C₂×C₁₉×#99	C₂²	1	2	yes	—
32	C₂×C₁₉×#99	C₂²	1	4	yes	—
33	C₂×C₁₉×#99	C₂²	1	2	yes	complemented
34	C₁₉×#395	—	2	4	no	—
35	C₁₉×#393	—	2	4	no	—
36	C₁₉×#381	C₂²	1	4	yes	complemented
37	C₁₉×#381	C₂²	1	2	yes	complemented
38	C₁₉×#342	C₂²	1	4	yes	complemented
39	C₁₉×H(5,𝔽₂)	—	2	4	no	—
40	C₁₉×H(5,𝔽₂)	—	4	2	no	—
41	C₂×#41×C₁₉	—	2	4	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	4	no	—
44	C₂×#41×C₁₉	—	2	2	no	—
45	C₂×#41×C₁₉	—	4	2	no	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	4	no	—
49	C₂²×Q₈×C₁₉	—	2	4	no	—
50	C₂²×Q₈×C₁₉	—	4	2	no	—
51	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×C₄⋊Q₈	—	2	8	no	—
63	C₁₉×C₄⋊Q₈	—	2	2	no	—
64	C₁₉×#124	—	2	8	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#123	—	2	4	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	4	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	2	no	—
72	C₁₉×#123	—	2	4	no	—
73	C₁₉×#123	—	2	4	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	4	no	—
76	C₁₉×#123	—	2	8	no	—
77	C₁₉×#123	—	4	4	no	—
78	C₁₉×#123	D₄	1	8	yes	complemented
79	C₁₉×C₂²⋊Q₈	—	2	8	no	—
80	C₁₉×C₂²⋊Q₈	—	2	8	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	4	no	—
83	C₁₉×#121	—	2	2	no	—
84	C₁₉×#121	—	2	4	no	—
85	C₁₉×#121	—	2	4	no	—
86	C₁₉×#120	—	2	2	no	—
87	C₁₉×#120	—	2	2	no	—
88	C₁₉×#120	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	4	no	—
90	C₄×D₄×C₁₉	—	2	4	no	—
91	C₁₉×#117	—	2	1	no	—
92	C₁₉×#117	—	2	4	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
98	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
104	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₁₉×#99	—	2	4	no	—
110	C₁₉×#99	—	2	8	no	—
111	C₁₉×#99	—	4	2	no	—
112	C₁₉×#95	—	2	8	no	—
113	C₁₉×#95	—	2	4	no	—
114	C₂⁴×C₁₉	—	2	1	no	—
115	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
116	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
119	#41×C₁₉	—	4	16	no	—
120	#41×C₁₉	—	4	8	no	—
121	#41×C₁₉	—	4	2	no	—
122	#41×C₁₉	—	4	2	no	—
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	4	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	4	1	no	—
129	C₂×Q₈×C₁₉	—	4	16	no	—
130	C₂×Q₈×C₁₉	—	4	2	no	—
131	C₂×Q₈×C₁₉	—	4	2	no	—
132	C₂×Q₈×C₁₉	—	4	2	no	—
133	C₂×Q₈×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	4	no	—
144	C₂×D₄×C₁₉	—	2	4	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	4	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	4	1	no	—
149	C₂×D₄×C₁₉	—	4	8	no	—
150	C₂×D₄×C₁₉	—	4	2	no	—
151	C₂×D₄×C₁₉	—	4	2	no	—
152	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	4	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	4	no	—
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	4	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
178	C₄⋊C₄×C₁₉	—	2	4	no	—
179	C₄⋊C₄×C₁₉	—	2	4	no	—
180	C₄⋊C₄×C₁₉	—	2	8	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	4	no	—
183	C₄⋊C₄×C₁₉	—	2	8	no	—
184	C₄⋊C₄×C₁₉	—	2	4	no	—
185	C₄⋊C₄×C₁₉	—	4	8	no	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	4	no	—
188	C₂²⋊C₄×C₁₉	—	2	8	no	—
189	C₂²⋊C₄×C₁₉	—	2	4	no	—
190	C₂²⋊C₄×C₁₉	—	2	8	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	4	no	—
195	C₂²⋊C₄×C₁₉	—	2	4	no	—
196	C₂²⋊C₄×C₁₉	—	2	4	no	—
197	C₂²⋊C₄×C₁₉	—	2	4	no	—
198	C₂²⋊C₄×C₁₉	—	4	8	no	—
199	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
200	C₄²×C₁₉	—	2	4	no	—
201	C₄²×C₁₉	—	2	2	no	—
202	#23905	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂³×C₁₉	—	2	1	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	—	2	1	no	—
206	C₂³×C₁₉	—	2	2	no	—
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	4	no	—
210	C₂³×C₁₉	—	4	2	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	4	2	no	—
213	C₂³×C₁₉	—	4	2	no	—
214	C₂³×C₁₉	—	4	4	no	—
215	C₂³×C₁₉	—	8	2	no	—
216	C₂³×C₁₉	#120	1	2	yes	—
217	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
219	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
220	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
221	Q₈×C₁₉	—	4	4	no	—
222	Q₈×C₁₉	—	4	8	no	—
223	Q₈×C₁₉	—	4	8	no	—
224	Q₈×C₁₉	—	4	2	no	—
225	D₄×C₁₉	—	2	8	no	—
226	D₄×C₁₉	—	4	4	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	4	4	no	—
229	D₄×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	4	4	no	—
232	D₄×C₁₉	—	4	4	no	—
233	D₄×C₁₉	—	8	4	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	8	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	2	4	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	1	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	8	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	4	4	no	—
251	C₂×C₄×C₁₉	—	4	4	no	—
252	C₂×C₄×C₁₉	—	4	4	no	—
253	C₂×C₄×C₁₉	—	4	4	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	4	no	—
258	C₂×C₄×C₁₉	—	4	4	no	—
259	C₂×C₄×C₁₉	—	4	8	no	—
260	C₂×C₄×C₁₉	—	4	4	no	—
261	C₂×C₄×C₁₉	—	8	2	no	—
262	C₂×C₄×C₁₉	#120	1	2	yes	—
263	C₂×C₄×C₁₉	#120	1	2	yes	—
264	C₂×C₄×C₁₉	#120	1	2	yes	—
265	#3485	C₂×C₁₉	1	1	yes	characteristic
266	C₂×#536	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₂×#458	C₂×C₁₉	1	2	yes	complemented
268	#2614	C₂×C₁₉	1	2	yes	complemented
269	#2022	C₂×C₁₉	1	4	yes	complemented
270	#1899	C₂×C₁₉	1	2	yes	complemented
271	#1890	C₂×C₁₉	1	2	yes	complemented
272	#1782	C₂×C₁₉	1	1	yes	characteristic, complemented
273	C₂²×C₁₉	—	2	4	no	—
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	4	2	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	2	no	—
279	C₂²×C₁₉	—	4	2	no	—
280	C₂²×C₁₉	—	4	2	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	2	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	4	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	4	no	—
287	C₂²×C₁₉	—	8	1	no	—
288	C₂²×C₁₉	—	16	2	no	—
289	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
290	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
291	C₂²×C₁₉	#534	1	1	yes	characteristic
292	C₂²×C₁₉	D₄²	1	4	yes	—
293	C₄×C₁₉	—	2	2	no	—
294	C₄×C₁₉	—	2	2	no	—
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	4	4	no	—
297	C₄×C₁₉	—	4	2	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	4	no	—
300	C₄×C₁₉	—	4	4	no	—
301	C₄×C₁₉	—	8	4	no	—
302	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
303	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
304	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
305	#547	—	2	4	no	—
306	#546	—	2	4	no	—
307	#536	—	2	1	no	—
308	#536	—	2	8	no	—
309	#534	—	2	1	no	—
310	#534	C₂²×C₁₉	1	2	yes	—
311	C₂×C₄⋊Q₈	—	2	1	no	—
312	C₂×#124	—	2	1	no	—
313	#525	—	2	1	no	—
314	C₂×#123	—	2	1	no	—
315	C₂×#123	C₂²×C₁₉	1	4	yes	—
316	C₂×#123	C₂²×C₁₉	1	2	yes	—
317	C₂×#123	C₂²×C₁₉	1	2	yes	—
318	C₂×#123	C₂²×C₁₉	1	2	yes	complemented
319	C₂×C₂²⋊Q₈	—	2	1	no	—
320	C₂×C₂²⋊Q₈	—	2	1	no	—
321	#518	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
323	#458	—	2	8	no	—
324	C₂×#99	C₂²×C₁₉	1	2	yes	—
325	C₂×#99	C₂²×C₁₉	1	4	yes	—
326	C₂×#99	C₂²×C₁₉	1	2	yes	complemented
327	#395	—	2	4	no	—
328	#393	—	2	4	no	—
329	#381	C₂²×C₁₉	1	4	yes	complemented
330	#381	C₂²×C₁₉	1	2	yes	complemented
331	#342	C₂²×C₁₉	1	4	yes	complemented
332	C₂×C₁₉	—	2	1	no	—
333	C₂×C₁₉	—	2	4	no	—
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	4	2	no	—
336	C₂×C₁₉	—	8	1	no	—
337	C₂×C₁₉	—	8	2	no	—
338	C₂×C₁₉	#2403	1	1	yes	characteristic
339	C₂×C₁₉	#3028	1	2	yes	—
340	H(5,𝔽₂)	—	2	4	no	—
341	H(5,𝔽₂)	—	4	2	no	—
342	C₂×#41	—	2	4	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	4	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	4	2	no	—
347	C₂²×Q₈	—	2	1	no	—
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×Q₈	—	2	4	no	—
350	C₂²×Q₈	—	2	4	no	—
351	C₂²×Q₈	—	4	2	no	—
352	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
357	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
360	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
363	C₄⋊Q₈	—	2	8	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	#124	—	2	8	no	—
366	#124	—	2	2	no	—
367	#123	—	2	4	no	—
368	#123	—	2	2	no	—
369	#123	—	2	4	no	—
370	#123	—	2	2	no	—
371	#123	—	2	2	no	—
372	#123	—	2	2	no	—
373	#123	—	2	4	no	—
374	#123	—	2	4	no	—
375	#123	—	2	2	no	—
376	#123	—	2	4	no	—
377	#123	—	2	8	no	—
378	#123	—	4	4	no	—
379	#123	D₄×C₁₉	1	8	yes	complemented
380	C₂²⋊Q₈	—	2	8	no	—
381	C₂²⋊Q₈	—	2	8	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	4	no	—
384	#121	—	2	2	no	—
385	#121	—	2	4	no	—
386	#121	—	2	4	no	—
387	#120	—	2	2	no	—
388	#120	—	2	2	no	—
389	#120	—	2	2	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	4	no	—
392	#117	—	2	1	no	—
393	#117	—	2	4	no	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	4	no	—
399	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	2	4	no	—
405	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
409	C₂×C₄²	—	2	1	no	—
410	#99	—	2	4	no	—
411	#99	—	2	8	no	—
412	#99	—	4	2	no	—
413	#95	—	2	8	no	—
414	#95	—	2	4	no	—
415	C₁₉	#23905	1	1	yes	characteristic, direct product factor, Sylow
416	C₂⁴	—	2	1	no	—
417	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
418	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
421	#41	—	4	16	no	—
422	#41	—	4	8	no	—
423	#41	—	4	2	no	—
424	#41	—	4	2	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	4	1	no	—
431	C₂×Q₈	—	4	16	no	—
432	C₂×Q₈	—	4	2	no	—
433	C₂×Q₈	—	4	2	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
475	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
476	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	4	8	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	4	8	no	—
501	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	2	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	8	2	no	—
517	C₂³	C₁₉×#120	1	2	yes	—
518	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
519	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
520	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
521	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
522	Q₈	—	4	4	no	—
523	Q₈	—	4	8	no	—
524	Q₈	—	4	8	no	—
525	Q₈	—	4	2	no	—
526	D₄	—	2	8	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	8	4	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	C₁₉×#120	1	2	yes	—
564	C₂×C₄	C₁₉×#120	1	2	yes	—
565	C₂×C₄	C₁₉×#120	1	2	yes	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	4	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	16	2	no	—
582	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
583	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
584	C₂²	C₁₉×#534	1	1	yes	characteristic
585	C₂²	D₄²×C₁₉	1	4	yes	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	4	4	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	4	no	—
593	C₄	—	4	4	no	—
594	C₄	—	8	4	no	—
595	C₂	—	2	1	no	—
596	C₂	—	2	4	no	—
597	C₂	—	2	1	no	—
598	C₂	—	4	2	no	—
599	C₂	—	8	1	no	—
600	C₂	—	8	2	no	—
601	C₂	C₁₉×#2403	1	1	yes	characteristic
602	C₂	C₁₉×#3028	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₁₉×#3485	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#536	C₂	semidirect
3. C₂×C₁₉×#458	C₂	semidirect
4. C₁₉×#2614	C₂	semidirect
5. C₁₉×#2022	C₂	semidirect
6. C₁₉×#1899	C₂	semidirect
7. C₁₉×#1890	C₂	semidirect
8. C₁₉×#1782	C₂	semidirect
11. C₂³×Q₈×C₁₉	C₂²	semidirect
25. C₂×C₁₉×#123	C₂²	semidirect
29. C₂×C₁₉×#117	C₂²	semidirect
33. C₂×C₁₉×#99	C₂²	semidirect
36. C₁₉×#381	C₂²	semidirect
37. C₁₉×#381	C₂²	semidirect
38. C₁₉×#342	C₂²	semidirect
78. C₁₉×#123	D₄	semidirect
202. #23905	C₁₉	direct (N × H)
266. C₂×#536	C₂×C₁₉	semidirect
267. C₂×#458	C₂×C₁₉	semidirect
268. #2614	C₂×C₁₉	semidirect
269. #2022	C₂×C₁₉	semidirect
270. #1899	C₂×C₁₉	semidirect
271. #1890	C₂×C₁₉	semidirect
272. #1782	C₂×C₁₉	semidirect
304. C₂³×Q₈	C₂²×C₁₉	semidirect
318. C₂×#123	C₂²×C₁₉	semidirect
322. C₂×#117	C₂²×C₁₉	semidirect
326. C₂×#99	C₂²×C₁₉	semidirect
329. #381	C₂²×C₁₉	semidirect
330. #381	C₂²×C₁₉	semidirect
331. #342	C₂²×C₁₉	semidirect
379. #123	D₄×C₁₉	semidirect
415. C₁₉	#23905	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×#3485	2
C₂×C₁₉×#536	2
C₂×C₁₉×#458	2
C₁₉×#2614	2
C₁₉×#2022	2
C₁₉×#1899	2
C₁₉×#1890	2
C₁₉×#1782	2
#23905	19

Subgroups — C19×#23905 #18029864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23905 #18029864