Subgroups — C₁₉×#36727 #18042686

Order 4864.

2214 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2847	C₂	1	2	yes	maximal, complemented
2	C₁₉×#2748	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2741	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2703	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2671	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2656	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2443	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2424	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2325	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
14	C₂×C₁₉×#121	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	4	yes	—
16	C₂×C₁₉×#121	C₂²	1	4	yes	—
17	C₂×C₁₉×#121	C₂²	1	2	yes	—
18	C₂×C₁₉×#121	C₂²	1	2	yes	—
19	C₂×C₁₉×#120	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#400	C₂²	1	4	yes	complemented
24	C₁₉×#399	C₂²	1	4	yes	complemented
25	C₁₉×#399	C₂²	1	4	yes	complemented
26	C₁₉×#398	C₂²	1	4	yes	complemented
27	C₁₉×#398	C₂²	1	4	yes	complemented
28	C₁₉×#397	C₂²	1	4	yes	complemented
29	C₁₉×#396	C₂²	1	4	yes	—
30	C₁₉×#394	C₂²	1	4	yes	—
31	C₁₉×#394	C₂²	1	4	yes	—
32	C₁₉×#394	C₂²	1	4	yes	complemented
33	C₁₉×#392	C₂²	1	4	yes	—
34	C₁₉×#392	C₂²	1	4	yes	complemented
35	C₁₉×#390	C₂²	1	4	yes	—
36	C₁₉×#388	C₂²	1	4	yes	—
37	C₁₉×#388	C₂²	1	4	yes	complemented
38	C₁₉×#388	C₂²	1	4	yes	complemented
39	C₁₉×#387	C₂²	1	4	yes	complemented
40	C₁₉×#387	C₂²	1	4	yes	complemented
41	C₁₉×#386	C₂²	1	4	yes	—
42	C₁₉×#386	C₂²	1	4	yes	—
43	C₁₉×#386	C₂²	1	4	yes	—
44	C₁₉×#386	C₂²	1	4	yes	—
45	C₁₉×#386	C₂²	1	4	yes	—
46	C₁₉×#386	C₂²	1	4	yes	complemented
47	C₁₉×#385	C₂²	1	4	yes	—
48	C₁₉×#385	C₂²	1	4	yes	complemented
49	C₁₉×#385	C₂²	1	4	yes	complemented
50	C₁₉×#380	C₂²	1	4	yes	—
51	C₁₉×#380	C₂²	1	4	yes	—
52	C₁₉×#380	C₂²	1	2	yes	—
53	C₁₉×#380	C₂²	1	2	yes	—
54	C₁₉×#380	C₂²	1	2	yes	—
55	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
57	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
61	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₉	—	2	4	no	—
64	C₂³×C₄×C₁₉	—	4	4	no	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×#123	—	4	8	no	—
73	C₁₉×#121	—	2	8	no	—
74	C₁₉×#121	—	4	4	no	—
75	C₁₉×#121	—	4	4	no	—
76	C₁₉×#121	—	4	8	no	—
77	C₁₉×#121	—	4	8	no	—
78	C₁₉×#120	—	4	8	no	—
79	C₄×D₄×C₁₉	—	4	8	no	—
80	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
91	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
104	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
105	C₁₉×#95	C₂³	1	4	yes	—
106	C₁₉×#95	C₂³	1	4	yes	—
107	C₁₉×#95	C₂³	1	4	yes	—
108	C₁₉×#95	C₂³	1	4	yes	—
109	C₁₉×#95	C₂³	1	4	yes	—
110	C₁₉×#95	C₂³	1	4	yes	—
111	C₁₉×#95	C₂³	1	4	yes	—
112	C₁₉×#95	C₂³	1	4	yes	—
113	C₁₉×#95	C₂³	1	4	yes	—
114	C₂⁴×C₁₉	—	2	2	no	—
115	C₂⁴×C₁₉	—	2	2	no	—
116	C₂⁴×C₁₉	—	2	2	no	—
117	C₂⁴×C₁₉	—	2	4	no	—
118	C₂⁴×C₁₉	—	4	2	no	—
119	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
120	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₂×D₄×C₁₉	—	2	8	no	—
124	C₂×D₄×C₁₉	—	2	8	no	—
125	C₂×D₄×C₁₉	—	2	8	no	—
126	C₂×D₄×C₁₉	—	2	8	no	—
127	C₂×D₄×C₁₉	—	2	8	no	—
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	4	4	no	—
130	C₂×D₄×C₁₉	—	4	4	no	—
131	C₂×D₄×C₁₉	—	4	2	no	—
132	C₂×D₄×C₁₉	—	4	2	no	—
133	C₂×D₄×C₁₉	—	4	4	no	—
134	C₂×D₄×C₁₉	—	4	4	no	—
135	C₂×D₄×C₁₉	—	4	4	no	—
136	C₂×D₄×C₁₉	—	4	4	no	—
137	C₂×D₄×C₁₉	—	4	4	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	4	no	—
142	C₂²×C₄×C₁₉	—	2	4	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	4	2	no	—
147	C₂²×C₄×C₁₉	—	4	2	no	—
148	C₂²×C₄×C₁₉	—	4	2	no	—
149	C₂²×C₄×C₁₉	—	4	2	no	—
150	C₂²×C₄×C₁₉	—	4	2	no	—
151	C₂²×C₄×C₁₉	—	4	2	no	—
152	C₂²×C₄×C₁₉	—	4	2	no	—
153	C₂²×C₄×C₁₉	—	4	4	no	—
154	C₂²×C₄×C₁₉	—	4	4	no	—
155	C₂²×C₄×C₁₉	—	4	4	no	—
156	C₂²×C₄×C₁₉	—	4	16	no	—
157	C₂²×C₄×C₁₉	#41	1	4	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
165	C₄⋊C₄×C₁₉	—	2	4	no	—
166	C₄⋊C₄×C₁₉	—	2	8	no	—
167	C₄⋊C₄×C₁₉	—	4	4	no	—
168	C₄⋊C₄×C₁₉	—	4	4	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	—	4	2	no	—
171	C₄⋊C₄×C₁₉	—	4	4	no	—
172	C₄⋊C₄×C₁₉	—	4	4	no	—
173	C₄⋊C₄×C₁₉	—	4	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	8	no	—
175	C₂²⋊C₄×C₁₉	—	2	8	no	—
176	C₂²⋊C₄×C₁₉	—	2	8	no	—
177	C₂²⋊C₄×C₁₉	—	2	8	no	—
178	C₂²⋊C₄×C₁₉	—	2	8	no	—
179	C₂²⋊C₄×C₁₉	—	4	4	no	—
180	C₂²⋊C₄×C₁₉	—	4	4	no	—
181	C₂²⋊C₄×C₁₉	—	4	4	no	—
182	C₂²⋊C₄×C₁₉	—	4	4	no	—
183	C₂²⋊C₄×C₁₉	—	4	4	no	—
184	C₂²⋊C₄×C₁₉	—	4	4	no	—
185	C₂²⋊C₄×C₁₉	—	4	4	no	—
186	C₂²⋊C₄×C₁₉	—	4	4	no	—
187	C₄²×C₁₉	—	4	4	no	—
188	#36727	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	1	no	—
191	C₂³×C₁₉	—	2	1	no	—
192	C₂³×C₁₉	—	2	8	no	—
193	C₂³×C₁₉	—	2	1	no	—
194	C₂³×C₁₉	—	2	1	no	—
195	C₂³×C₁₉	—	2	1	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	—	2	2	no	—
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	—	2	4	no	—
202	C₂³×C₁₉	—	2	4	no	—
203	C₂³×C₁₉	—	2	4	no	—
204	C₂³×C₁₉	—	2	4	no	—
205	C₂³×C₁₉	—	2	4	no	—
206	C₂³×C₁₉	—	2	4	no	—
207	C₂³×C₁₉	—	2	4	no	—
208	C₂³×C₁₉	—	4	8	no	—
209	C₂³×C₁₉	—	4	8	no	—
210	C₂³×C₁₉	—	4	4	no	—
211	C₂³×C₁₉	—	4	4	no	—
212	C₂³×C₁₉	C₂×#41	1	2	yes	—
213	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
214	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
215	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
216	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
217	D₄×C₁₉	—	4	16	no	—
218	D₄×C₁₉	—	8	4	no	—
219	D₄×C₁₉	—	8	8	no	—
220	D₄×C₁₉	—	8	8	no	—
221	D₄×C₁₉	—	8	8	no	—
222	C₂×C₄×C₁₉	—	2	8	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	4	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	4	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	4	4	no	—
243	C₂×C₄×C₁₉	—	4	8	no	—
244	C₂×C₄×C₁₉	—	4	8	no	—
245	C₂×C₄×C₁₉	—	8	4	no	—
246	C₂×C₄×C₁₉	—	8	4	no	—
247	C₂×C₄×C₁₉	—	8	8	no	—
248	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
250	#2847	C₂×C₁₉	1	2	yes	complemented
251	#2748	C₂×C₁₉	1	4	yes	complemented
252	#2741	C₂×C₁₉	1	4	yes	complemented
253	#2703	C₂×C₁₉	1	4	yes	complemented
254	#2671	C₂×C₁₉	1	4	yes	complemented
255	#2656	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2646	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2443	C₂×C₁₉	1	4	yes	complemented
258	#2424	C₂×C₁₉	1	4	yes	complemented
259	#2325	C₂×C₁₉	1	2	yes	complemented
260	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
261	C₂²×C₁₉	—	2	2	no	—
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	2	4	no	—
264	C₂²×C₁₉	—	2	4	no	—
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	2	2	no	—
267	C₂²×C₁₉	—	2	4	no	—
268	C₂²×C₁₉	—	2	4	no	—
269	C₂²×C₁₉	—	4	16	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	2	no	—
275	C₂²×C₁₉	—	4	2	no	—
276	C₂²×C₁₉	—	4	4	no	—
277	C₂²×C₁₉	—	4	4	no	—
278	C₂²×C₁₉	—	4	4	no	—
279	C₂²×C₁₉	—	4	4	no	—
280	C₂²×C₁₉	—	4	4	no	—
281	C₂²×C₁₉	—	4	4	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	#540	1	4	yes	—
284	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
285	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
286	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
287	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
289	C₄×C₁₉	—	2	4	no	—
290	C₄×C₁₉	—	2	4	no	—
291	C₄×C₁₉	—	4	4	no	—
292	C₄×C₁₉	—	4	4	no	—
293	C₄×C₁₉	—	4	4	no	—
294	C₄×C₁₉	—	4	4	no	—
295	C₄×C₁₉	—	4	4	no	—
296	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
298	C₂×#121	C₂²×C₁₉	1	2	yes	—
299	C₂×#121	C₂²×C₁₉	1	2	yes	—
300	C₂×#121	C₂²×C₁₉	1	2	yes	—
301	C₂×#121	C₂²×C₁₉	1	4	yes	—
302	C₂×#121	C₂²×C₁₉	1	4	yes	—
303	C₂×#120	C₂²×C₁₉	1	4	yes	—
304	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
305	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
306	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
307	#400	C₂²×C₁₉	1	4	yes	complemented
308	#399	C₂²×C₁₉	1	4	yes	complemented
309	#399	C₂²×C₁₉	1	4	yes	complemented
310	#398	C₂²×C₁₉	1	4	yes	complemented
311	#398	C₂²×C₁₉	1	4	yes	complemented
312	#397	C₂²×C₁₉	1	4	yes	complemented
313	#396	C₂²×C₁₉	1	4	yes	—
314	#394	C₂²×C₁₉	1	4	yes	—
315	#394	C₂²×C₁₉	1	4	yes	—
316	#394	C₂²×C₁₉	1	4	yes	complemented
317	#392	C₂²×C₁₉	1	4	yes	—
318	#392	C₂²×C₁₉	1	4	yes	complemented
319	#390	C₂²×C₁₉	1	4	yes	—
320	#388	C₂²×C₁₉	1	4	yes	—
321	#388	C₂²×C₁₉	1	4	yes	complemented
322	#388	C₂²×C₁₉	1	4	yes	complemented
323	#387	C₂²×C₁₉	1	4	yes	complemented
324	#387	C₂²×C₁₉	1	4	yes	complemented
325	#386	C₂²×C₁₉	1	4	yes	—
326	#386	C₂²×C₁₉	1	4	yes	—
327	#386	C₂²×C₁₉	1	4	yes	—
328	#386	C₂²×C₁₉	1	4	yes	—
329	#386	C₂²×C₁₉	1	4	yes	—
330	#386	C₂²×C₁₉	1	4	yes	complemented
331	#385	C₂²×C₁₉	1	4	yes	—
332	#385	C₂²×C₁₉	1	4	yes	complemented
333	#385	C₂²×C₁₉	1	4	yes	complemented
334	#380	C₂²×C₁₉	1	2	yes	—
335	#380	C₂²×C₁₉	1	2	yes	—
336	#380	C₂²×C₁₉	1	2	yes	—
337	#380	C₂²×C₁₉	1	4	yes	—
338	#380	C₂²×C₁₉	1	4	yes	—
339	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×C₁₉	—	2	4	no	—
342	C₂×C₁₉	—	4	2	no	—
343	C₂×C₁₉	—	4	2	no	—
344	C₂×C₁₉	—	8	4	no	—
345	C₂×C₁₉	C₂×#540	1	1	yes	characteristic
346	C₂×C₁₉	#3490	1	1	yes	characteristic
347	C₂×C₁₉	#3492	1	1	yes	characteristic
348	C₂×C₁₉	#3536	1	2	yes	—
349	C₂×C₁₉	#3537	1	2	yes	—
350	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
351	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
352	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
353	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
354	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
355	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
356	C₂³×C₄	—	2	4	no	—
357	C₂³×C₄	—	4	4	no	—
358	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
360	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
361	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
365	#123	—	4	8	no	—
366	#121	—	2	8	no	—
367	#121	—	4	4	no	—
368	#121	—	4	4	no	—
369	#121	—	4	8	no	—
370	#121	—	4	8	no	—
371	#120	—	4	8	no	—
372	C₄×D₄	—	4	8	no	—
373	C₂×C₄⋊C₄	—	4	4	no	—
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
383	C₂×C₂²⋊C₄	—	4	4	no	—
384	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
397	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
398	#95	C₂³×C₁₉	1	4	yes	—
399	#95	C₂³×C₁₉	1	4	yes	—
400	#95	C₂³×C₁₉	1	4	yes	—
401	#95	C₂³×C₁₉	1	4	yes	—
402	#95	C₂³×C₁₉	1	4	yes	—
403	#95	C₂³×C₁₉	1	4	yes	—
404	#95	C₂³×C₁₉	1	4	yes	—
405	#95	C₂³×C₁₉	1	4	yes	—
406	#95	C₂³×C₁₉	1	4	yes	—
407	C₁₉	#36727	1	1	yes	characteristic, direct product factor, Sylow
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	2	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	4	2	no	—
413	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
414	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
415	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
416	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	4	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	16	no	—
451	C₂²×C₄	#41×C₁₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	4	4	no	—
462	C₄⋊C₄	—	4	4	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	4	no	—
466	C₄⋊C₄	—	4	4	no	—
467	C₄⋊C₄	—	4	4	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	4	4	no	—
474	C₂²⋊C₄	—	4	4	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	4	4	no	—
477	C₂²⋊C₄	—	4	4	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	4	no	—
480	C₂²⋊C₄	—	4	4	no	—
481	C₄²	—	4	4	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	8	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	4	8	no	—
502	C₂³	—	4	8	no	—
503	C₂³	—	4	4	no	—
504	C₂³	—	4	4	no	—
505	C₂³	C₂×#41×C₁₉	1	2	yes	—
506	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
507	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
508	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
509	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
510	D₄	—	4	16	no	—
511	D₄	—	8	4	no	—
512	D₄	—	8	8	no	—
513	D₄	—	8	8	no	—
514	D₄	—	8	8	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	8	4	no	—
539	C₂×C₄	—	8	4	no	—
540	C₂×C₄	—	8	8	no	—
541	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
542	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	4	16	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	C₁₉×#540	1	4	yes	—
566	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
567	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
568	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
569	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
571	C₄	—	2	4	no	—
572	C₄	—	2	4	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	4	no	—
576	C₄	—	4	4	no	—
577	C₄	—	4	4	no	—
578	C₂	—	2	4	no	—
579	C₂	—	4	2	no	—
580	C₂	—	4	2	no	—
581	C₂	—	8	4	no	—
582	C₂	C₂×C₁₉×#540	1	1	yes	characteristic
583	C₂	C₁₉×#3490	1	1	yes	characteristic
584	C₂	C₁₉×#3492	1	1	yes	characteristic
585	C₂	C₁₉×#3536	1	2	yes	—
586	C₂	C₁₉×#3537	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2847	C₂	semidirect
2. C₁₉×#2748	C₂	semidirect
3. C₁₉×#2741	C₂	semidirect
4. C₁₉×#2703	C₂	semidirect
5. C₁₉×#2671	C₂	semidirect
6. C₁₉×#2656	C₂	semidirect
7. C₁₉×#2646	C₂	semidirect
8. C₁₉×#2443	C₂	semidirect
9. C₁₉×#2424	C₂	semidirect
10. C₁₉×#2325	C₂	semidirect
11. C₂×C₁₉×#380	C₂	semidirect
13. C₂×C₁₉×#123	C₂²	semidirect
23. C₁₉×#400	C₂²	semidirect
24. C₁₉×#399	C₂²	semidirect
25. C₁₉×#399	C₂²	semidirect
26. C₁₉×#398	C₂²	semidirect
27. C₁₉×#398	C₂²	semidirect
28. C₁₉×#397	C₂²	semidirect
32. C₁₉×#394	C₂²	semidirect
34. C₁₉×#392	C₂²	semidirect
37. C₁₉×#388	C₂²	semidirect
38. C₁₉×#388	C₂²	semidirect
39. C₁₉×#387	C₂²	semidirect
40. C₁₉×#387	C₂²	semidirect
46. C₁₉×#386	C₂²	semidirect
48. C₁₉×#385	C₂²	semidirect
49. C₁₉×#385	C₂²	semidirect
188. #36727	C₁₉	direct (N × H)
250. #2847	C₂×C₁₉	semidirect
251. #2748	C₂×C₁₉	semidirect
252. #2741	C₂×C₁₉	semidirect
253. #2703	C₂×C₁₉	semidirect
254. #2671	C₂×C₁₉	semidirect
255. #2656	C₂×C₁₉	semidirect
256. #2646	C₂×C₁₉	semidirect
257. #2443	C₂×C₁₉	semidirect
258. #2424	C₂×C₁₉	semidirect
259. #2325	C₂×C₁₉	semidirect
260. C₂×#380	C₂×C₁₉	semidirect
297. C₂×#123	C₂²×C₁₉	semidirect
307. #400	C₂²×C₁₉	semidirect
308. #399	C₂²×C₁₉	semidirect
309. #399	C₂²×C₁₉	semidirect
310. #398	C₂²×C₁₉	semidirect
311. #398	C₂²×C₁₉	semidirect
312. #397	C₂²×C₁₉	semidirect
316. #394	C₂²×C₁₉	semidirect
318. #392	C₂²×C₁₉	semidirect
321. #388	C₂²×C₁₉	semidirect
322. #388	C₂²×C₁₉	semidirect
323. #387	C₂²×C₁₉	semidirect
324. #387	C₂²×C₁₉	semidirect
330. #386	C₂²×C₁₉	semidirect
332. #385	C₂²×C₁₉	semidirect
333. #385	C₂²×C₁₉	semidirect
407. C₁₉	#36727	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×#2847	2
C₁₉×#2748	2
C₁₉×#2741	2
C₁₉×#2703	2
C₁₉×#2671	2
C₁₉×#2656	2
C₁₉×#2646	2
C₁₉×#2443	2
C₁₉×#2424	2
C₁₉×#2325	2
C₂×C₁₉×#380	2
#36727	19

Subgroups — C19×#36727 #18042686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#36727 #18042686