Subgroups — C₁₉×#32971 #18038930

Order 4864.

1294 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3079	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1860	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1856	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1806	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1792	C₂	1	2	yes	maximal
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₁₉×#520	—	2	2	no	—
12	C₁₉×#520	C₂²	1	2	yes	—
13	C₁₉×#518	—	2	2	no	—
14	C₁₉×#518	—	2	2	no	—
15	C₁₉×#518	C₂²	1	1	yes	characteristic
16	C₄×#41×C₁₉	—	2	2	no	—
17	C₄×#41×C₁₉	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₉	—	2	2	no	—
19	C₂×C₄×D₄×C₁₉	—	2	2	no	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#477	—	2	2	no	—
22	C₁₉×#476	—	2	2	no	—
23	C₁₉×#475	—	2	2	no	—
24	C₁₉×#474	—	2	2	no	—
25	C₁₉×#428	C₂²	1	4	yes	complemented
26	C₁₉×#423	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#104	C₂²	1	4	yes	—
28	C₁₉×#417	C₂²	1	4	yes	—
29	C₂×C₁₉×#100	C₂²	1	2	yes	—
30	C₁₉×#393	—	2	2	no	—
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#382	C₂²	1	2	yes	complemented
33	C₁₉×#380	—	2	2	no	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#343	C₂²	1	2	yes	complemented
36	C₁₉×#339	C₂²	1	4	yes	complemented
37	C₁₉×H(5,𝔽₂)	—	2	4	no	—
38	C₁₉×H(5,𝔽₂)	—	2	2	no	—
39	C₁₉×H(5,𝔽₂)	Q₈	1	4	yes	complemented
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	—	2	2	no	—
47	C₂³×C₄×C₁₉	D₄	1	2	yes	—
48	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₄×Q₈×C₁₉	—	2	2	no	—
52	C₄×Q₈×C₁₉	D₄	1	2	yes	—
53	C₄×Q₈×C₁₉	D₄	1	2	yes	—
54	C₄×D₄×C₁₉	—	2	4	no	—
55	C₄×D₄×C₁₉	—	2	4	no	—
56	C₄×D₄×C₁₉	—	2	4	no	—
57	C₄×D₄×C₁₉	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₄×D₄×C₁₉	—	2	2	no	—
60	C₄×D₄×C₁₉	—	2	4	no	—
61	C₄×D₄×C₁₉	—	2	2	no	—
62	C₄×D₄×C₁₉	—	2	2	no	—
63	C₄×D₄×C₁₉	—	2	2	no	—
64	C₄×D₄×C₁₉	—	2	2	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	D₄	1	2	yes	—
67	C₄×D₄×C₁₉	D₄	1	2	yes	—
68	C₁₉×#117	—	2	4	no	—
69	C₁₉×#117	—	2	2	no	—
70	C₁₉×#117	—	2	2	no	—
71	C₁₉×#117	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
83	C₂×C₄²×C₁₉	—	2	2	no	—
84	C₂×C₄²×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₁₉×#107	—	2	4	no	—
88	C₁₉×#106	—	2	4	no	—
89	C₁₉×C₄⋊C₈	—	2	2	no	—
90	C₁₉×C₄⋊C₈	—	2	2	no	—
91	C₁₉×#104	—	2	8	no	—
92	C₁₉×#103	—	2	4	no	—
93	C₁₉×#102	—	2	4	no	—
94	C₁₉×#100	—	2	4	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₁₉×#95	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
99	#41×C₁₉	—	2	8	no	—
100	#41×C₁₉	—	2	8	no	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	2	2	no	—
103	#41×C₁₉	C₂×Q₈	1	4	yes	—
104	#41×C₁₉	#41	1	4	yes	—
105	C₂×Q₈×C₁₉	—	4	2	no	—
106	C₂×Q₈×C₁₉	—	8	2	no	—
107	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₁₉	—	2	4	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	8	no	—
111	C₂×D₄×C₁₉	—	2	8	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	8	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
118	C₂×D₄×C₁₉	#41	1	2	yes	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	8	4	no	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₁₉	—	2	4	no	—
137	M₁₆×C₁₉	—	2	4	no	—
138	C₂×C₈×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	2	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	4	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₄⋊C₄×C₁₉	—	4	1	no	—
146	C₄⋊C₄×C₁₉	—	4	1	no	—
147	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₁₉	—	2	4	no	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	2	2	no	—
154	C₂²⋊C₄×C₁₉	—	2	4	no	—
155	C₂²⋊C₄×C₁₉	—	8	4	no	—
156	C₄²×C₁₉	—	2	4	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	2	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	4	no	—
161	C₄²×C₁₉	C₂×D₄	1	2	yes	—
162	C₄²×C₁₉	C₂×D₄	1	2	yes	—
163	#32971	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	8	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	8	2	no	—
171	C₂³×C₁₉	—	8	2	no	—
172	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
173	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	2	no	—
175	Q₈×C₁₉	—	8	4	no	—
176	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	—
177	D₄×C₁₉	—	2	16	no	—
178	D₄×C₁₉	—	2	4	no	—
179	D₄×C₁₉	—	2	4	no	—
180	D₄×C₁₉	—	2	4	no	—
181	D₄×C₁₉	—	2	2	no	—
182	D₄×C₁₉	—	2	4	no	—
183	D₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	4	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	—	8	2	no	—
203	C₂×C₄×C₁₉	—	8	2	no	—
204	C₂×C₄×C₁₉	—	8	4	no	—
205	C₂×C₄×C₁₉	—	8	2	no	—
206	C₂×C₄×C₁₉	#120	1	2	yes	—
207	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
212	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
213	C₈×C₁₉	—	4	4	no	—
214	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
215	#3079	C₂×C₁₉	1	2	yes	complemented
216	#2563	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#1860	C₂×C₁₉	1	4	yes	complemented
218	#1856	C₂×C₁₉	1	2	yes	complemented
219	#1806	C₂×C₁₉	1	2	yes	complemented
220	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1792	C₂×C₁₉	1	2	yes	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	4	no	—
225	C₂²×C₁₉	—	2	4	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	4	2	no	—
228	C₂²×C₁₉	—	4	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	8	2	no	—
232	C₂²×C₁₉	—	8	8	no	—
233	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
234	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	C₂²×C₁₉	#525	1	1	yes	characteristic
236	C₄×C₁₉	—	2	4	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	2	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	8	2	no	—
243	C₄×C₁₉	—	8	2	no	—
244	C₄×C₁₉	#455	1	2	yes	—
245	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
246	C₄×C₁₉	#525	1	2	yes	—
247	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
249	#520	—	2	2	no	—
250	#520	C₂²×C₁₉	1	2	yes	—
251	#518	—	2	2	no	—
252	#518	—	2	2	no	—
253	#518	C₂²×C₁₉	1	1	yes	characteristic
254	C₄×#41	—	2	2	no	—
255	C₄×#41	C₂²×C₁₉	1	2	yes	—
256	C₂×C₄×D₄	—	2	2	no	—
257	C₂×C₄×D₄	—	2	2	no	—
258	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
259	#477	—	2	2	no	—
260	#476	—	2	2	no	—
261	#475	—	2	2	no	—
262	#474	—	2	2	no	—
263	#428	C₂²×C₁₉	1	4	yes	complemented
264	#423	C₂²×C₁₉	1	2	yes	complemented
265	C₂×#104	C₂²×C₁₉	1	4	yes	—
266	#417	C₂²×C₁₉	1	4	yes	—
267	C₂×#100	C₂²×C₁₉	1	2	yes	—
268	#393	—	2	2	no	—
269	#390	C₂²×C₁₉	1	2	yes	—
270	#382	C₂²×C₁₉	1	2	yes	complemented
271	#380	—	2	2	no	—
272	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
273	#343	C₂²×C₁₉	1	2	yes	complemented
274	#339	C₂²×C₁₉	1	4	yes	complemented
275	C₂×C₁₉	—	2	1	no	—
276	C₂×C₁₉	—	2	1	no	—
277	C₂×C₁₉	—	4	4	no	—
278	C₂×C₁₉	—	4	4	no	—
279	C₂×C₁₉	#2848	1	1	yes	characteristic
280	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
281	C₂×C₁₉	#3021	1	1	yes	characteristic
282	H(5,𝔽₂)	—	2	4	no	—
283	H(5,𝔽₂)	—	2	2	no	—
284	H(5,𝔽₂)	Q₈×C₁₉	1	4	yes	complemented
285	C₂×#41	—	2	2	no	—
286	C₂×#41	C₂³×C₁₉	1	2	yes	—
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂³×C₄	—	2	2	no	—
292	C₂³×C₄	D₄×C₁₉	1	2	yes	—
293	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	D₄×C₁₉	1	2	yes	—
298	C₄×Q₈	D₄×C₁₉	1	2	yes	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	D₄×C₁₉	1	2	yes	—
312	C₄×D₄	D₄×C₁₉	1	2	yes	—
313	#117	—	2	4	no	—
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	#117	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
331	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
332	#107	—	2	4	no	—
333	#106	—	2	4	no	—
334	C₄⋊C₈	—	2	2	no	—
335	C₄⋊C₈	—	2	2	no	—
336	#104	—	2	8	no	—
337	#103	—	2	4	no	—
338	#102	—	2	4	no	—
339	#100	—	2	4	no	—
340	#95	—	2	1	no	—
341	#95	—	2	4	no	—
342	C₁₉	#32971	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁴	—	2	2	no	—
344	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
345	#41	—	2	8	no	—
346	#41	—	2	8	no	—
347	#41	—	2	2	no	—
348	#41	—	2	2	no	—
349	#41	C₂×Q₈×C₁₉	1	4	yes	—
350	#41	#41×C₁₉	1	4	yes	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	—	8	2	no	—
353	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
363	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
364	C₂×D₄	#41×C₁₉	1	2	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	8	4	no	—
378	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	C₂×C₈	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	1	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
394	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	8	4	no	—
402	C₄²	—	2	4	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	4	no	—
407	C₄²	C₂×D₄×C₁₉	1	2	yes	—
408	C₄²	C₂×D₄×C₁₉	1	2	yes	—
409	C₂³	—	2	8	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
418	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	—	8	4	no	—
421	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	—
422	D₄	—	2	16	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	4	no	—
425	D₄	—	2	4	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	4	no	—
428	D₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	—	8	4	no	—
449	C₂×C₄	—	8	2	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	C₁₉×#120	1	2	yes	—
452	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
453	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
455	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
457	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
458	C₈	—	4	4	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	8	no	—
470	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
471	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
472	C₂²	C₁₉×#525	1	1	yes	characteristic
473	C₄	—	2	1	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	4	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	2	no	—
481	C₄	C₁₉×#455	1	2	yes	—
482	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
483	C₄	C₁₉×#525	1	2	yes	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	4	4	no	—
487	C₂	—	4	4	no	—
488	C₂	C₁₉×#2848	1	1	yes	characteristic
489	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
490	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3079	C₂	semidirect
3. C₁₉×#2563	C₂	semidirect
4. C₁₉×#1860	C₂	semidirect
5. C₁₉×#1856	C₂	semidirect
6. C₁₉×#1806	C₂	semidirect
7. C₁₉×#1800	C₂	semidirect
10. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
25. C₁₉×#428	C₂²	semidirect
26. C₁₉×#423	C₂²	semidirect
32. C₁₉×#382	C₂²	semidirect
34. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
35. C₁₉×#343	C₂²	semidirect
36. C₁₉×#339	C₂²	semidirect
39. C₁₉×H(5,𝔽₂)	Q₈	semidirect
163. #32971	C₁₉	direct (N × H)
215. #3079	C₂×C₁₉	semidirect
216. #2563	C₂×C₁₉	semidirect
217. #1860	C₂×C₁₉	semidirect
218. #1856	C₂×C₁₉	semidirect
219. #1806	C₂×C₁₉	semidirect
220. #1800	C₂×C₁₉	semidirect
248. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
263. #428	C₂²×C₁₉	semidirect
264. #423	C₂²×C₁₉	semidirect
270. #382	C₂²×C₁₉	semidirect
272. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
273. #343	C₂²×C₁₉	semidirect
274. #339	C₂²×C₁₉	semidirect
284. H(5,𝔽₂)	Q₈×C₁₉	semidirect
342. C₁₉	#32971	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₉×H(5,𝔽₂)	2
C₁₉×#3079	2
C₁₉×#2563	2
C₁₉×#1860	2
C₁₉×#1856	2
C₁₉×#1806	2
C₁₉×#1800	2
C₁₉×#1792	2
#32971	19

Subgroups — C19×#32971 #18038930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32971 #18038930