Subgroups — C₁₉×#32712 #18038671

Order 4864.

964 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2615	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2077	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2075	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2034	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2034	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1999	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1780	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#121	C₂²	1	2	yes	—
13	C₂×C₁₉×#121	C₂²	1	2	yes	—
14	C₂×C₁₉×#121	C₂²	1	2	yes	—
15	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#106	C₂²	1	2	yes	—
17	C₂×C₁₉×#102	C₂²	1	2	yes	—
18	C₂×C₁₉×#102	C₂²	1	2	yes	—
19	C₂×C₁₉×#102	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₉×#393	—	2	2	no	—
25	C₁₉×#392	—	2	2	no	—
26	C₁₉×#392	—	2	2	no	—
27	C₁₉×#392	—	2	2	no	—
28	C₁₉×#380	C₂²	1	2	yes	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₁₉×#380	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	1	yes	characteristic
33	C₁₉×#340	C₂²	1	2	yes	—
34	C₁₉×#340	C₂²	1	1	yes	characteristic
35	C₂×#41×C₁₉	—	4	2	no	—
36	C₂×#41×C₁₉	—	4	1	no	—
37	C₂×#41×C₁₉	—	4	2	no	—
38	C₂×#41×C₁₉	—	4	1	no	—
39	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	D₄	1	2	yes	—
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₁₉	—	4	2	no	—
49	C₂×D₈×C₁₉	—	4	1	no	—
50	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×#121	—	4	2	no	—
54	C₁₉×#121	—	4	2	no	—
55	C₁₉×#121	—	4	2	no	—
56	C₁₉×#121	—	4	2	no	—
57	C₁₉×#121	—	4	2	no	—
58	C₁₉×#121	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₁₉×#107	—	4	1	no	—
69	C₁₉×#106	—	4	2	no	—
70	C₁₉×#102	—	4	2	no	—
71	C₁₉×#102	—	4	2	no	—
72	C₁₉×#102	—	4	2	no	—
73	C₁₉×C₂²⋊C₈	—	4	2	no	—
74	C₁₉×C₂²⋊C₈	—	4	1	no	—
75	C₁₉×C₂²⋊C₈	—	4	2	no	—
76	C₁₉×C₂²⋊C₈	—	4	1	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
83	#41×C₁₉	—	4	4	no	—
84	#41×C₁₉	—	4	8	no	—
85	#41×C₁₉	—	4	4	no	—
86	C₂×Q₈×C₁₉	—	4	2	no	—
87	C₂×Q₈×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	2	no	—
98	C₂×D₄×C₁₉	—	4	1	no	—
99	C₂×D₄×C₁₉	—	4	4	no	—
100	C₂×D₄×C₁₉	—	4	4	no	—
101	C₂×D₄×C₁₉	—	4	4	no	—
102	C₂×D₄×C₁₉	—	8	2	no	—
103	C₂×D₄×C₁₉	—	8	2	no	—
104	C₂×D₄×C₁₉	—	8	2	no	—
105	C₂×D₄×C₁₉	—	8	2	no	—
106	C₂×D₄×C₁₉	—	8	2	no	—
107	C₂×D₄×C₁₉	—	8	2	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
124	D₈×C₁₉	—	4	4	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	1	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	2	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	4	4	no	—
139	C₂²⋊C₄×C₁₉	—	4	4	no	—
140	C₂²⋊C₄×C₁₉	—	4	4	no	—
141	C₂²⋊C₄×C₁₉	—	8	2	no	—
142	C₂²⋊C₄×C₁₉	—	8	2	no	—
143	C₂²⋊C₄×C₁₉	—	8	2	no	—
144	#32712	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	1	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	1	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₉	—	4	4	no	—
166	D₄×C₁₉	—	4	4	no	—
167	D₄×C₁₉	—	4	8	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	4	2	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	8	8	no	—
173	D₄×C₁₉	—	8	8	no	—
174	D₄×C₁₉	—	8	8	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	1	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
197	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
200	C₈×C₁₉	—	4	2	no	—
201	C₈×C₁₉	—	4	1	no	—
202	C₈×C₁₉	—	4	1	no	—
203	#2615	C₂×C₁₉	1	2	yes	complemented
204	#2077	C₂×C₁₉	1	2	yes	complemented
205	#2075	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2034	C₂×C₁₉	1	2	yes	complemented
207	#2034	C₂×C₁₉	1	2	yes	complemented
208	#2033	C₂×C₁₉	1	2	yes	complemented
209	#1999	C₂×C₁₉	1	2	yes	complemented
210	#1999	C₂×C₁₉	1	1	yes	characteristic, complemented
211	#1780	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	2	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	1	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	8	2	no	—
225	C₂²×C₁₉	—	8	2	no	—
226	C₂²×C₁₉	—	8	2	no	—
227	C₂²×C₁₉	—	8	2	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	#534	1	2	yes	—
232	C₂²×C₁₉	#534	1	1	yes	characteristic
233	C₂²×C₁₉	#576	1	1	yes	characteristic
234	C₂²×C₁₉	#576	1	1	yes	characteristic
235	C₂²×C₁₉	#577	1	2	yes	—
236	C₄×C₁₉	—	4	1	no	—
237	C₄×C₁₉	—	4	2	no	—
238	C₄×C₁₉	—	8	2	no	—
239	C₄×C₁₉	—	8	2	no	—
240	C₄×C₁₉	—	8	2	no	—
241	C₄×C₁₉	#560	1	2	yes	—
242	C₄×C₁₉	#560	1	1	yes	characteristic
243	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
244	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
245	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×#121	C₂²×C₁₉	1	2	yes	—
247	C₂×#121	C₂²×C₁₉	1	2	yes	—
248	C₂×#121	C₂²×C₁₉	1	2	yes	—
249	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×#106	C₂²×C₁₉	1	2	yes	—
251	C₂×#102	C₂²×C₁₉	1	2	yes	—
252	C₂×#102	C₂²×C₁₉	1	2	yes	—
253	C₂×#102	C₂²×C₁₉	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
258	#393	—	2	2	no	—
259	#392	—	2	2	no	—
260	#392	—	2	2	no	—
261	#392	—	2	2	no	—
262	#380	C₂²×C₁₉	1	2	yes	—
263	#380	C₂²×C₁₉	1	2	yes	—
264	#380	C₂²×C₁₉	1	2	yes	—
265	#340	C₂²×C₁₉	1	2	yes	—
266	#340	C₂²×C₁₉	1	1	yes	characteristic
267	#340	C₂²×C₁₉	1	1	yes	characteristic
268	#340	C₂²×C₁₉	1	2	yes	—
269	C₂×C₁₉	—	8	1	no	—
270	C₂×C₁₉	—	8	2	no	—
271	C₂×C₁₉	—	16	2	no	—
272	C₂×C₁₉	#2812	1	1	yes	characteristic
273	C₂×C₁₉	#3198	1	2	yes	—
274	C₂×C₁₉	#3198	1	2	yes	—
275	C₂×C₁₉	#3199	1	1	yes	characteristic
276	C₂×C₁₉	#3204	1	1	yes	characteristic
277	C₂×#41	—	4	2	no	—
278	C₂×#41	—	4	1	no	—
279	C₂×#41	—	4	2	no	—
280	C₂×#41	—	4	1	no	—
281	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	D₄×C₁₉	1	2	yes	—
286	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
287	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
290	C₂×D₈	—	4	2	no	—
291	C₂×D₈	—	4	1	no	—
292	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
295	#121	—	4	2	no	—
296	#121	—	4	2	no	—
297	#121	—	4	2	no	—
298	#121	—	4	2	no	—
299	#121	—	4	2	no	—
300	#121	—	4	2	no	—
301	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	#107	—	4	1	no	—
311	#106	—	4	2	no	—
312	#102	—	4	2	no	—
313	#102	—	4	2	no	—
314	#102	—	4	2	no	—
315	C₂²⋊C₈	—	4	2	no	—
316	C₂²⋊C₈	—	4	1	no	—
317	C₂²⋊C₈	—	4	2	no	—
318	C₂²⋊C₈	—	4	1	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	C₁₉	#32712	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	—	2	2	no	—
324	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
325	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
326	#41	—	4	8	no	—
327	#41	—	4	4	no	—
328	#41	—	4	4	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	8	2	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	—	8	2	no	—
348	C₂×D₄	—	8	2	no	—
349	C₂×D₄	—	8	2	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
367	D₈	—	4	4	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	8	2	no	—
385	C₂²⋊C₄	—	8	2	no	—
386	C₂²⋊C₄	—	8	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
407	Q₈	—	4	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	8	8	no	—
415	D₄	—	8	8	no	—
416	D₄	—	8	8	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
439	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	C₁₉×#534	1	2	yes	—
465	C₂²	C₁₉×#534	1	1	yes	characteristic
466	C₂²	C₁₉×#576	1	1	yes	characteristic
467	C₂²	C₁₉×#576	1	1	yes	characteristic
468	C₂²	C₁₉×#577	1	2	yes	—
469	C₄	—	4	1	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	2	no	—
474	C₄	C₁₉×#560	1	2	yes	—
475	C₄	C₁₉×#560	1	1	yes	characteristic
476	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
477	C₂	—	8	1	no	—
478	C₂	—	8	2	no	—
479	C₂	—	16	2	no	—
480	C₂	C₁₉×#2812	1	1	yes	characteristic
481	C₂	C₁₉×#3198	1	2	yes	—
482	C₂	C₁₉×#3198	1	2	yes	—
483	C₂	C₁₉×#3199	1	1	yes	characteristic
484	C₂	C₁₉×#3204	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2615	C₂	semidirect
2. C₁₉×#2077	C₂	semidirect
3. C₁₉×#2075	C₂	semidirect
4. C₁₉×#2034	C₂	semidirect
5. C₁₉×#2034	C₂	semidirect
6. C₁₉×#2033	C₂	semidirect
7. C₁₉×#1999	C₂	semidirect
8. C₁₉×#1999	C₂	semidirect
9. C₁₉×#1780	C₂	semidirect
144. #32712	C₁₉	direct (N × H)
203. #2615	C₂×C₁₉	semidirect
204. #2077	C₂×C₁₉	semidirect
205. #2075	C₂×C₁₉	semidirect
206. #2034	C₂×C₁₉	semidirect
207. #2034	C₂×C₁₉	semidirect
208. #2033	C₂×C₁₉	semidirect
209. #1999	C₂×C₁₉	semidirect
210. #1999	C₂×C₁₉	semidirect
211. #1780	C₂×C₁₉	semidirect
322. C₁₉	#32712	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×#2615	2
C₁₉×#2077	2
C₁₉×#2075	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#1999	2
C₁₉×#1780	2
#32712	19

Subgroups — C19×#32712 #18038671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32712 #18038671