Subgroups — C₁₉×#32973 #18038932

Order 4864.

1286 conjugacy classes of subgroups.

The subgroup lattice has 564 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×#3080	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2566	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1860	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1859	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1856	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1856	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1806	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1792	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1792	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
14	C₁₉×#520	—	2	2	no	—
15	C₁₉×#520	C₂²	1	2	yes	—
16	C₁₉×#518	—	2	2	no	—
17	C₁₉×#518	—	2	2	no	—
18	C₁₉×#518	C₂²	1	1	yes	characteristic
19	C₄×#41×C₁₉	—	2	2	no	—
20	C₄×#41×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₉	—	2	2	no	—
22	C₂×C₄×D₄×C₁₉	—	2	2	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#479	—	2	2	no	—
25	C₁₉×#479	—	2	2	no	—
26	C₁₉×#478	—	2	2	no	—
27	C₁₉×#478	—	2	2	no	—
28	C₁₉×#428	C₂²	1	2	yes	complemented
29	C₁₉×#428	C₂²	1	2	yes	complemented
30	C₁₉×#423	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#104	C₂²	1	2	yes	—
32	C₂×C₁₉×#104	C₂²	1	2	yes	—
33	C₁₉×#417	C₂²	1	2	yes	—
34	C₁₉×#417	C₂²	1	2	yes	—
35	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#100	C₂²	1	1	yes	characteristic
37	C₁₉×#396	—	2	2	no	—
38	C₁₉×#390	C₂²	1	1	yes	characteristic
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#385	—	2	2	no	—
41	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#382	C₂²	1	1	yes	characteristic, complemented
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#343	C₂²	1	2	yes	complemented
45	C₁₉×#339	C₂²	1	2	yes	complemented
46	C₁₉×#339	C₂²	1	2	yes	complemented
47	C₁₉×H(5,𝔽₂)	—	2	4	no	—
48	C₁₉×H(5,𝔽₂)	—	2	2	no	—
49	C₁₉×H(5,𝔽₂)	Q₈	1	4	yes	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₉	—	2	2	no	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	—	2	2	no	—
56	C₂³×C₄×C₁₉	D₄	1	2	yes	—
57	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
58	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	D₄	1	2	yes	—
63	C₄×Q₈×C₁₉	D₄	1	2	yes	—
64	C₄×D₄×C₁₉	—	2	4	no	—
65	C₄×D₄×C₁₉	—	2	4	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₄×D₄×C₁₉	—	2	4	no	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	4	no	—
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₄×D₄×C₁₉	D₄	1	2	yes	—
77	C₄×D₄×C₁₉	D₄	1	2	yes	—
78	C₁₉×#117	—	2	4	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
97	C₂×C₄²×C₁₉	—	2	2	no	—
98	C₂×C₄²×C₁₉	—	2	2	no	—
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	2	2	no	—
103	C₁₉×#107	—	2	2	no	—
104	C₁₉×#106	—	2	2	no	—
105	C₁₉×#106	—	2	2	no	—
106	C₁₉×C₄⋊C₈	—	2	2	no	—
107	C₁₉×C₄⋊C₈	—	2	2	no	—
108	C₁₉×#104	—	2	4	no	—
109	C₁₉×#104	—	2	4	no	—
110	C₁₉×#103	—	2	2	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#102	—	2	2	no	—
114	C₁₉×#100	—	2	2	no	—
115	C₁₉×#100	—	2	2	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₁₉×#95	—	2	2	no	—
118	C₂⁴×C₁₉	—	2	2	no	—
119	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
120	#41×C₁₉	—	2	8	no	—
121	#41×C₁₉	—	2	8	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	C₂×Q₈	1	4	yes	—
125	#41×C₁₉	#41	1	4	yes	—
126	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	4	no	—
128	C₂×D₄×C₁₉	—	2	8	no	—
129	C₂×D₄×C₁₉	—	2	8	no	—
130	C₂×D₄×C₁₉	—	2	8	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	8	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
137	C₂×D₄×C₁₉	#41	1	2	yes	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	4	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	8	2	no	—
152	C₂²×C₄×C₁₉	—	8	4	no	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×C₁₉	—	2	2	no	—
159	M₁₆×C₁₉	—	2	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	4	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	—	4	1	no	—
171	C₄⋊C₄×C₁₉	—	4	2	no	—
172	C₄⋊C₄×C₁₉	—	4	1	no	—
173	C₄⋊C₄×C₁₉	—	8	2	no	—
174	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₂²⋊C₄×C₁₉	—	2	4	no	—
177	C₂²⋊C₄×C₁₉	—	2	4	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	4	no	—
182	C₂²⋊C₄×C₁₉	—	4	4	no	—
183	C₂²⋊C₄×C₁₉	—	8	2	no	—
184	C₄²×C₁₉	—	2	4	no	—
185	C₄²×C₁₉	—	2	2	no	—
186	C₄²×C₁₉	—	2	2	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	C₂×D₄	1	2	yes	—
191	C₄²×C₁₉	C₂×D₄	1	2	yes	—
192	#32973	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂³×C₁₉	—	2	8	no	—
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	8	2	no	—
200	C₂³×C₁₉	—	8	2	no	—
201	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
202	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₉	—	2	2	no	—
204	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	—
205	D₄×C₁₉	—	2	16	no	—
206	D₄×C₁₉	—	2	4	no	—
207	D₄×C₁₉	—	2	4	no	—
208	D₄×C₁₉	—	2	4	no	—
209	D₄×C₁₉	—	2	2	no	—
210	D₄×C₁₉	—	2	4	no	—
211	D₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
212	C₂×C₄×C₁₉	—	2	8	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	4	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	8	2	no	—
235	C₂×C₄×C₁₉	—	8	2	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	4	no	—
238	C₂×C₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#120	1	2	yes	—
241	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
246	C₈×C₁₉	—	4	2	no	—
247	C₈×C₁₉	—	4	2	no	—
248	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
249	#3080	C₂×C₁₉	1	2	yes	complemented
250	#2566	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#1860	C₂×C₁₉	1	2	yes	complemented
252	#1859	C₂×C₁₉	1	2	yes	complemented
253	#1856	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#1856	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#1806	C₂×C₁₉	1	2	yes	complemented
256	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1792	C₂×C₁₉	1	1	yes	characteristic
258	#1792	C₂×C₁₉	1	1	yes	characteristic
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	4	no	—
262	C₂²×C₁₉	—	2	4	no	—
263	C₂²×C₁₉	—	4	4	no	—
264	C₂²×C₁₉	—	4	2	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	2	no	—
268	C₂²×C₁₉	—	8	2	no	—
269	C₂²×C₁₉	—	8	8	no	—
270	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
271	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
272	C₂²×C₁₉	#525	1	1	yes	characteristic
273	C₄×C₁₉	—	2	4	no	—
274	C₄×C₁₉	—	2	2	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	4	2	no	—
278	C₄×C₁₉	—	4	2	no	—
279	C₄×C₁₉	—	4	2	no	—
280	C₄×C₁₉	—	4	2	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	—	8	1	no	—
284	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
285	C₄×C₁₉	#525	1	2	yes	—
286	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic, complemented
288	#520	—	2	2	no	—
289	#520	C₂²×C₁₉	1	2	yes	—
290	#518	—	2	2	no	—
291	#518	—	2	2	no	—
292	#518	C₂²×C₁₉	1	1	yes	characteristic
293	C₄×#41	—	2	2	no	—
294	C₄×#41	C₂²×C₁₉	1	2	yes	—
295	C₂×C₄×D₄	—	2	2	no	—
296	C₂×C₄×D₄	—	2	2	no	—
297	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
298	#479	—	2	2	no	—
299	#479	—	2	2	no	—
300	#478	—	2	2	no	—
301	#478	—	2	2	no	—
302	#428	C₂²×C₁₉	1	2	yes	complemented
303	#428	C₂²×C₁₉	1	2	yes	complemented
304	#423	C₂²×C₁₉	1	2	yes	complemented
305	C₂×#104	C₂²×C₁₉	1	2	yes	—
306	C₂×#104	C₂²×C₁₉	1	2	yes	—
307	#417	C₂²×C₁₉	1	2	yes	—
308	#417	C₂²×C₁₉	1	2	yes	—
309	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#100	C₂²×C₁₉	1	1	yes	characteristic
311	#396	—	2	2	no	—
312	#390	C₂²×C₁₉	1	1	yes	characteristic
313	#390	C₂²×C₁₉	1	1	yes	characteristic
314	#385	—	2	2	no	—
315	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	#382	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
318	#343	C₂²×C₁₉	1	2	yes	complemented
319	#339	C₂²×C₁₉	1	2	yes	complemented
320	#339	C₂²×C₁₉	1	2	yes	complemented
321	C₂×C₁₉	—	2	1	no	—
322	C₂×C₁₉	—	2	1	no	—
323	C₂×C₁₉	—	4	4	no	—
324	C₂×C₁₉	—	4	4	no	—
325	C₂×C₁₉	#2848	1	1	yes	characteristic
326	C₂×C₁₉	#3018	1	1	yes	characteristic
327	C₂×C₁₉	#3019	1	1	yes	characteristic
328	H(5,𝔽₂)	—	2	4	no	—
329	H(5,𝔽₂)	—	2	2	no	—
330	H(5,𝔽₂)	Q₈×C₁₉	1	4	yes	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	C₂³×C₁₉	1	2	yes	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
336	C₂³×C₄	—	2	2	no	—
337	C₂³×C₄	D₄×C₁₉	1	2	yes	—
338	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
339	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
340	#125	—	2	2	no	—
341	#125	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	D₄×C₁₉	1	2	yes	—
344	C₄×Q₈	D₄×C₁₉	1	2	yes	—
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	—	2	4	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	4	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	D₄×C₁₉	1	2	yes	—
358	C₄×D₄	D₄×C₁₉	1	2	yes	—
359	#117	—	2	4	no	—
360	#117	—	2	2	no	—
361	#117	—	2	2	no	—
362	#117	C₂³×C₁₉	1	2	yes	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	—	2	2	no	—
380	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
383	#107	—	2	2	no	—
384	#107	—	2	2	no	—
385	#106	—	2	2	no	—
386	#106	—	2	2	no	—
387	C₄⋊C₈	—	2	2	no	—
388	C₄⋊C₈	—	2	2	no	—
389	#104	—	2	4	no	—
390	#104	—	2	4	no	—
391	#103	—	2	2	no	—
392	#103	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	—	2	2	no	—
395	#100	—	2	2	no	—
396	#100	—	2	2	no	—
397	#95	—	2	1	no	—
398	#95	—	2	2	no	—
399	C₁₉	#32973	1	1	yes	characteristic, direct product factor, Sylow
400	C₂⁴	—	2	2	no	—
401	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
402	#41	—	2	8	no	—
403	#41	—	2	8	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	C₂×Q₈×C₁₉	1	4	yes	—
407	#41	#41×C₁₉	1	4	yes	—
408	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
418	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
419	C₂×D₄	#41×C₁₉	1	2	yes	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	8	2	no	—
434	C₂²×C₄	—	8	4	no	—
435	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	8	2	no	—
456	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
457	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	4	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	8	2	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	C₂×D₄×C₁₉	1	2	yes	—
473	C₄²	C₂×D₄×C₁₉	1	2	yes	—
474	C₂³	—	2	8	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	8	2	no	—
481	C₂³	—	8	2	no	—
482	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
483	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
484	Q₈	—	2	2	no	—
485	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	—
486	D₄	—	2	16	no	—
487	D₄	—	2	4	no	—
488	D₄	—	2	4	no	—
489	D₄	—	2	4	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	4	no	—
492	D₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	4	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
521	C₂×C₄	C₁₉×#120	1	2	yes	—
522	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
524	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
525	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
526	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
527	C₈	—	4	2	no	—
528	C₈	—	4	2	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	8	2	no	—
539	C₂²	—	8	8	no	—
540	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
541	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
542	C₂²	C₁₉×#525	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	4	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	8	1	no	—
552	C₄	—	8	1	no	—
553	C₄	—	8	1	no	—
554	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
555	C₄	C₁₉×#525	1	2	yes	—
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	4	4	no	—
559	C₂	—	4	4	no	—
560	C₂	C₁₉×#2848	1	1	yes	characteristic
561	C₂	C₁₉×#3018	1	1	yes	characteristic
562	C₂	C₁₉×#3019	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×#3080	C₂	semidirect
3. C₁₉×#2566	C₂	semidirect
4. C₁₉×#1860	C₂	semidirect
5. C₁₉×#1859	C₂	semidirect
6. C₁₉×#1856	C₂	semidirect
7. C₁₉×#1856	C₂	semidirect
8. C₁₉×#1806	C₂	semidirect
9. C₁₉×#1800	C₂	semidirect
13. C₂×C₁₉×#125	C₂²	semidirect
28. C₁₉×#428	C₂²	semidirect
29. C₁₉×#428	C₂²	semidirect
30. C₁₉×#423	C₂²	semidirect
41. C₁₉×#384	C₂²	semidirect
42. C₁₉×#382	C₂²	semidirect
43. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
44. C₁₉×#343	C₂²	semidirect
45. C₁₉×#339	C₂²	semidirect
46. C₁₉×#339	C₂²	semidirect
192. #32973	C₁₉	direct (N × H)
249. #3080	C₂×C₁₉	semidirect
250. #2566	C₂×C₁₉	semidirect
251. #1860	C₂×C₁₉	semidirect
252. #1859	C₂×C₁₉	semidirect
253. #1856	C₂×C₁₉	semidirect
254. #1856	C₂×C₁₉	semidirect
255. #1806	C₂×C₁₉	semidirect
256. #1800	C₂×C₁₉	semidirect
287. C₂×#125	C₂²×C₁₉	semidirect
302. #428	C₂²×C₁₉	semidirect
303. #428	C₂²×C₁₉	semidirect
304. #423	C₂²×C₁₉	semidirect
315. #384	C₂²×C₁₉	semidirect
316. #382	C₂²×C₁₉	semidirect
317. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
318. #343	C₂²×C₁₉	semidirect
319. #339	C₂²×C₁₉	semidirect
320. #339	C₂²×C₁₉	semidirect
399. C₁₉	#32973	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×#3080	2
C₁₉×#2566	2
C₁₉×#1860	2
C₁₉×#1859	2
C₁₉×#1856	2
C₁₉×#1806	2
C₁₉×#1800	2
C₁₉×#1792	2
#32973	19

Subgroups — C19×#32973 #18038932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32973 #18038932