Subgroups — C₁₉×#34963 #18040922

Order 4864.

3270 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2598	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2580	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2535	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2487	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2482	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2408	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2404	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2398	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2397	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₉×#121	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₉×#120	C₂	1	4	yes	maximal, complemented
14	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉×#121	C₂²	1	4	yes	—
19	C₂×C₁₉×#120	C₂²	1	4	yes	—
20	C₄×#41×C₁₉	—	2	8	no	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄×D₄×C₁₉	—	2	8	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
33	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
35	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₉	C₂²	1	2	yes	complemented
39	C₁₉×#400	C₂²	1	4	yes	complemented
40	C₁₉×#399	C₂²	1	4	yes	complemented
41	C₁₉×#399	C₂²	1	4	yes	complemented
42	C₁₉×#397	C₂²	1	4	yes	complemented
43	C₁₉×#394	C₂²	1	4	yes	—
44	C₁₉×#393	C₂²	1	4	yes	complemented
45	C₁₉×#392	C₂²	1	4	yes	—
46	C₁₉×#392	C₂²	1	4	yes	complemented
47	C₁₉×#390	C₂²	1	4	yes	—
48	C₁₉×#389	C₂²	1	4	yes	complemented
49	C₁₉×#388	C₂²	1	8	yes	complemented
50	C₁₉×#386	C₂²	1	4	yes	—
51	C₁₉×#386	C₂²	1	8	yes	complemented
52	C₁₉×#386	C₂²	1	8	yes	complemented
53	C₁₉×#385	C₂²	1	4	yes	—
54	C₁₉×#385	C₂²	1	8	yes	complemented
55	C₁₉×#383	C₂²	1	2	yes	complemented
56	C₁₉×#382	C₂²	1	2	yes	complemented
57	C₁₉×#381	C₂²	1	2	yes	—
58	C₁₉×#380	C₂²	1	2	yes	—
59	C₁₉×#380	C₂²	1	4	yes	complemented
60	C₁₉×#379	C₂²	1	4	yes	—
61	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	complemented
64	C₁₉×#376	C₂²	1	2	yes	complemented
65	C₂⁵×C₁₉	C₂³	1	2	yes	—
66	C₂×#41×C₁₉	—	2	8	no	—
67	C₂×#41×C₁₉	—	2	4	no	—
68	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₉	—	2	8	no	—
70	C₂²×D₄×C₁₉	—	2	4	no	—
71	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
74	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₉	—	2	8	no	—
77	C₂³×C₄×C₁₉	—	4	8	no	—
78	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
87	C₁₉×#121	—	2	16	no	—
88	C₁₉×#120	—	2	16	no	—
89	C₄×Q₈×C₁₉	—	2	4	no	—
90	C₄×Q₈×C₁₉	—	2	4	no	—
91	C₄×D₄×C₁₉	—	2	8	no	—
92	C₄×D₄×C₁₉	—	2	8	no	—
93	C₄×D₄×C₁₉	—	2	8	no	—
94	C₄×D₄×C₁₉	—	2	8	no	—
95	C₄×D₄×C₁₉	—	2	8	no	—
96	C₄×D₄×C₁₉	—	2	8	no	—
97	C₄×D₄×C₁₉	—	2	4	no	—
98	C₄×D₄×C₁₉	—	2	4	no	—
99	C₄×D₄×C₁₉	—	4	16	no	—
100	C₁₉×#117	—	2	4	no	—
101	C₁₉×#117	—	2	8	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
112	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
122	C₂×C₄²×C₁₉	—	2	8	no	—
123	C₂×C₄²×C₁₉	D₄	1	8	yes	complemented
124	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
127	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
132	C₁₉×#95	C₂³	1	4	yes	—
133	C₁₉×#95	C₂³	1	4	yes	—
134	C₁₉×#95	C₂³	1	4	yes	—
135	C₁₉×#95	C₂³	1	8	yes	—
136	C₁₉×#95	C₂³	1	8	yes	—
137	C₁₉×#95	C₂³	1	4	yes	—
138	C₂⁴×C₁₉	—	2	4	no	—
139	C₂⁴×C₁₉	—	2	8	no	—
140	C₂⁴×C₁₉	—	2	8	no	—
141	C₂⁴×C₁₉	—	4	4	no	—
142	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
143	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
144	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
145	#41×C₁₉	—	2	32	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	4	no	—
148	C₂×D₄×C₁₉	—	2	32	no	—
149	C₂×D₄×C₁₉	—	2	4	no	—
150	C₂×D₄×C₁₉	—	2	8	no	—
151	C₂×D₄×C₁₉	—	2	4	no	—
152	C₂×D₄×C₁₉	—	2	4	no	—
153	C₂×D₄×C₁₉	—	2	16	no	—
154	C₂×D₄×C₁₉	—	2	16	no	—
155	C₂×D₄×C₁₉	—	2	4	no	—
156	C₂×D₄×C₁₉	—	2	4	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	4	no	—
159	C₂×D₄×C₁₉	—	4	8	no	—
160	C₂×D₄×C₁₉	#41	1	8	yes	—
161	C₂×D₄×C₁₉	#41	1	8	yes	complemented
162	C₂²×C₄×C₁₉	—	2	4	no	—
163	C₂²×C₄×C₁₉	—	2	4	no	—
164	C₂²×C₄×C₁₉	—	2	4	no	—
165	C₂²×C₄×C₁₉	—	2	4	no	—
166	C₂²×C₄×C₁₉	—	2	4	no	—
167	C₂²×C₄×C₁₉	—	2	4	no	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	4	no	—
170	C₂²×C₄×C₁₉	—	2	4	no	—
171	C₂²×C₄×C₁₉	—	2	8	no	—
172	C₂²×C₄×C₁₉	—	2	8	no	—
173	C₂²×C₄×C₁₉	—	2	8	no	—
174	C₂²×C₄×C₁₉	—	2	8	no	—
175	C₂²×C₄×C₁₉	—	2	16	no	—
176	C₂²×C₄×C₁₉	—	4	8	no	—
177	C₂²×C₄×C₁₉	—	4	4	no	—
178	C₂²×C₄×C₁₉	—	4	32	no	—
179	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
185	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
193	C₄⋊C₄×C₁₉	—	2	4	no	—
194	C₄⋊C₄×C₁₉	—	2	4	no	—
195	C₄⋊C₄×C₁₉	—	2	4	no	—
196	C₄⋊C₄×C₁₉	—	2	4	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	8	no	—
200	C₄⋊C₄×C₁₉	—	4	8	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	8	no	—
203	C₂²⋊C₄×C₁₉	—	2	16	no	—
204	C₂²⋊C₄×C₁₉	—	2	8	no	—
205	C₂²⋊C₄×C₁₉	—	2	8	no	—
206	C₂²⋊C₄×C₁₉	—	2	4	no	—
207	C₂²⋊C₄×C₁₉	—	2	4	no	—
208	C₂²⋊C₄×C₁₉	—	2	16	no	—
209	C₂²⋊C₄×C₁₉	—	4	8	no	—
210	C₂²⋊C₄×C₁₉	—	4	8	no	—
211	C₄²×C₁₉	—	2	4	no	—
212	C₄²×C₁₉	—	2	4	no	—
213	C₄²×C₁₉	—	2	4	no	—
214	C₄²×C₁₉	—	2	8	no	—
215	C₄²×C₁₉	C₂×D₄	1	4	yes	—
216	C₄²×C₁₉	C₂×D₄	1	4	yes	—
217	C₄²×C₁₉	C₂×D₄	1	4	yes	—
218	C₄²×C₁₉	C₂×D₄	1	4	yes	—
219	#34963	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	2	2	no	—
222	C₂³×C₁₉	—	2	16	no	—
223	C₂³×C₁₉	—	2	2	no	—
224	C₂³×C₁₉	—	2	4	no	—
225	C₂³×C₁₉	—	2	8	no	—
226	C₂³×C₁₉	—	2	2	no	—
227	C₂³×C₁₉	—	2	4	no	—
228	C₂³×C₁₉	—	2	4	no	—
229	C₂³×C₁₉	—	2	4	no	—
230	C₂³×C₁₉	—	2	8	no	—
231	C₂³×C₁₉	—	4	32	no	—
232	C₂³×C₁₉	—	4	8	no	—
233	C₂³×C₁₉	—	4	8	no	—
234	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
235	C₂³×C₁₉	C₂×#41	1	8	yes	—
236	C₂³×C₁₉	C₂×#41	1	4	yes	—
237	C₂³×C₁₉	C₂×#41	1	4	yes	—
238	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
239	Q₈×C₁₉	—	2	8	no	—
240	D₄×C₁₉	—	2	16	no	—
241	D₄×C₁₉	—	2	8	no	—
242	D₄×C₁₉	—	2	16	no	—
243	D₄×C₁₉	—	2	16	no	—
244	D₄×C₁₉	—	4	32	no	—
245	C₂×C₄×C₁₉	—	2	16	no	—
246	C₂×C₄×C₁₉	—	2	8	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	8	no	—
254	C₂×C₄×C₁₉	—	2	8	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	4	no	—
258	C₂×C₄×C₁₉	—	2	4	no	—
259	C₂×C₄×C₁₉	—	2	8	no	—
260	C₂×C₄×C₁₉	—	2	8	no	—
261	C₂×C₄×C₁₉	—	2	8	no	—
262	C₂×C₄×C₁₉	—	2	4	no	—
263	C₂×C₄×C₁₉	—	2	8	no	—
264	C₂×C₄×C₁₉	—	4	16	no	—
265	C₂×C₄×C₁₉	—	4	8	no	—
266	C₂×C₄×C₁₉	—	4	8	no	—
267	C₂×C₄×C₁₉	—	4	8	no	—
268	C₂×C₄×C₁₉	—	4	16	no	—
269	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
276	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
277	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
278	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
279	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#2598	C₂×C₁₉	1	4	yes	complemented
281	#2580	C₂×C₁₉	1	2	yes	complemented
282	#2535	C₂×C₁₉	1	2	yes	complemented
283	#2487	C₂×C₁₉	1	2	yes	complemented
284	#2482	C₂×C₁₉	1	2	yes	complemented
285	#2408	C₂×C₁₉	1	2	yes	complemented
286	#2404	C₂×C₁₉	1	2	yes	complemented
287	#2398	C₂×C₁₉	1	2	yes	complemented
288	#2397	C₂×C₁₉	1	2	yes	complemented
289	C₄×#121	C₂×C₁₉	1	4	yes	complemented
290	C₄×#120	C₂×C₁₉	1	4	yes	complemented
291	#2283	C₂×C₁₉	1	1	yes	characteristic, complemented
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	8	no	—
295	C₂²×C₁₉	—	2	4	no	—
296	C₂²×C₁₉	—	2	8	no	—
297	C₂²×C₁₉	—	2	8	no	—
298	C₂²×C₁₉	—	2	16	no	—
299	C₂²×C₁₉	—	4	32	no	—
300	C₂²×C₁₉	—	4	2	no	—
301	C₂²×C₁₉	—	4	4	no	—
302	C₂²×C₁₉	—	4	4	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	4	4	no	—
305	C₂²×C₁₉	—	4	8	no	—
306	C₂²×C₁₉	#525	1	4	yes	—
307	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
308	C₂²×C₁₉	C₂²×#41	1	2	yes	—
309	C₂²×C₁₉	C₂²×#41	1	2	yes	—
310	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
311	C₄×C₁₉	—	2	2	no	—
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	2	4	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	4	no	—
319	C₄×C₁₉	—	4	8	no	—
320	C₄×C₁₉	#525	1	4	yes	—
321	C₄×C₁₉	#535	1	4	yes	—
322	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
323	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
324	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
325	C₂×#121	C₂²×C₁₉	1	4	yes	—
326	C₂×#120	C₂²×C₁₉	1	4	yes	—
327	C₄×#41	—	2	8	no	—
328	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
329	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
330	C₂×C₄×D₄	—	2	8	no	—
331	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
332	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
333	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
334	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
335	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
336	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
337	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
338	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
339	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
340	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
342	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
343	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
344	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
345	C₂²×C₄²	C₂²×C₁₉	1	2	yes	complemented
346	#400	C₂²×C₁₉	1	4	yes	complemented
347	#399	C₂²×C₁₉	1	4	yes	complemented
348	#399	C₂²×C₁₉	1	4	yes	complemented
349	#397	C₂²×C₁₉	1	4	yes	complemented
350	#394	C₂²×C₁₉	1	4	yes	—
351	#393	C₂²×C₁₉	1	4	yes	complemented
352	#392	C₂²×C₁₉	1	4	yes	—
353	#392	C₂²×C₁₉	1	4	yes	complemented
354	#390	C₂²×C₁₉	1	4	yes	—
355	#389	C₂²×C₁₉	1	4	yes	complemented
356	#388	C₂²×C₁₉	1	8	yes	complemented
357	#386	C₂²×C₁₉	1	4	yes	—
358	#386	C₂²×C₁₉	1	8	yes	complemented
359	#386	C₂²×C₁₉	1	8	yes	complemented
360	#385	C₂²×C₁₉	1	4	yes	—
361	#385	C₂²×C₁₉	1	8	yes	complemented
362	#383	C₂²×C₁₉	1	2	yes	complemented
363	#382	C₂²×C₁₉	1	2	yes	complemented
364	#381	C₂²×C₁₉	1	2	yes	—
365	#380	C₂²×C₁₉	1	2	yes	—
366	#380	C₂²×C₁₉	1	4	yes	complemented
367	#379	C₂²×C₁₉	1	4	yes	—
368	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
369	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
370	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
371	#376	C₂²×C₁₉	1	2	yes	complemented
372	C₂×C₁₉	—	2	4	no	—
373	C₂×C₁₉	—	4	4	no	—
374	C₂×C₁₉	—	4	8	no	—
375	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
376	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
377	C₂×C₁₉	C₂×#535	1	1	yes	characteristic
378	C₂×C₁₉	#3481	1	4	yes	—
379	C₂⁵	C₂³×C₁₉	1	2	yes	—
380	C₂×#41	—	2	8	no	—
381	C₂×#41	—	2	4	no	—
382	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
383	C₂²×D₄	—	2	8	no	—
384	C₂²×D₄	—	2	4	no	—
385	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
386	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
388	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
389	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
390	C₂³×C₄	—	2	8	no	—
391	C₂³×C₄	—	4	8	no	—
392	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
393	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
394	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
395	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
396	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
400	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
401	#121	—	2	16	no	—
402	#120	—	2	16	no	—
403	C₄×Q₈	—	2	4	no	—
404	C₄×Q₈	—	2	4	no	—
405	C₄×D₄	—	2	8	no	—
406	C₄×D₄	—	2	8	no	—
407	C₄×D₄	—	2	8	no	—
408	C₄×D₄	—	2	8	no	—
409	C₄×D₄	—	2	8	no	—
410	C₄×D₄	—	2	8	no	—
411	C₄×D₄	—	2	4	no	—
412	C₄×D₄	—	2	4	no	—
413	C₄×D₄	—	4	16	no	—
414	#117	—	2	4	no	—
415	#117	—	2	8	no	—
416	C₂×C₄⋊C₄	—	2	4	no	—
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
425	C₂×C₂²⋊C₄	—	2	8	no	—
426	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
436	C₂×C₄²	—	2	8	no	—
437	C₂×C₄²	D₄×C₁₉	1	8	yes	complemented
438	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
439	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
440	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
441	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
442	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
446	#95	C₂³×C₁₉	1	4	yes	—
447	#95	C₂³×C₁₉	1	4	yes	—
448	#95	C₂³×C₁₉	1	4	yes	—
449	#95	C₂³×C₁₉	1	8	yes	—
450	#95	C₂³×C₁₉	1	8	yes	—
451	#95	C₂³×C₁₉	1	4	yes	—
452	C₁₉	#34963	1	1	yes	characteristic, direct product factor, Sylow
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	2	8	no	—
455	C₂⁴	—	2	8	no	—
456	C₂⁴	—	4	4	no	—
457	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
458	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
459	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
460	#41	—	2	32	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	4	no	—
463	C₂×D₄	—	2	32	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	16	no	—
469	C₂×D₄	—	2	16	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	4	8	no	—
475	C₂×D₄	#41×C₁₉	1	8	yes	—
476	C₂×D₄	#41×C₁₉	1	8	yes	complemented
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	2	8	no	—
490	C₂²×C₄	—	2	16	no	—
491	C₂²×C₄	—	4	8	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	—	4	32	no	—
494	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
495	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
496	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
498	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
507	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	8	no	—
515	C₄⋊C₄	—	4	8	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	16	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	8	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	16	no	—
524	C₂²⋊C₄	—	4	8	no	—
525	C₂²⋊C₄	—	4	8	no	—
526	C₄²	—	2	4	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	2	8	no	—
530	C₄²	C₂×D₄×C₁₉	1	4	yes	—
531	C₄²	C₂×D₄×C₁₉	1	4	yes	—
532	C₄²	C₂×D₄×C₁₉	1	4	yes	—
533	C₄²	C₂×D₄×C₁₉	1	4	yes	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	16	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	8	no	—
545	C₂³	—	4	32	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	4	8	no	—
548	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
549	C₂³	C₂×#41×C₁₉	1	8	yes	—
550	C₂³	C₂×#41×C₁₉	1	4	yes	—
551	C₂³	C₂×#41×C₁₉	1	4	yes	—
552	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
553	Q₈	—	2	8	no	—
554	D₄	—	2	16	no	—
555	D₄	—	2	8	no	—
556	D₄	—	2	16	no	—
557	D₄	—	2	16	no	—
558	D₄	—	4	32	no	—
559	C₂×C₄	—	2	16	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	8	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	4	16	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	—	4	8	no	—
581	C₂×C₄	—	4	16	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
584	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
585	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
587	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
588	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
589	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
590	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
591	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	8	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	8	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	2	16	no	—
599	C₂²	—	4	32	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	8	no	—
605	C₂²	—	4	4	no	—
606	C₂²	C₁₉×#525	1	4	yes	—
607	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
608	C₂²	C₂²×#41×C₁₉	1	2	yes	—
609	C₂²	C₂²×#41×C₁₉	1	2	yes	—
610	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	4	no	—
615	C₄	—	2	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	4	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	8	no	—
620	C₄	C₁₉×#525	1	4	yes	—
621	C₄	C₁₉×#535	1	4	yes	—
622	C₂	—	2	4	no	—
623	C₂	—	4	8	no	—
624	C₂	—	4	4	no	—
625	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
626	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
627	C₂	C₂×C₁₉×#535	1	1	yes	characteristic
628	C₂	C₁₉×#3481	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#41×C₁₉	C₂	semidirect
2. C₂²×C₄×D₄×C₁₉	C₂	semidirect
3. C₁₉×#2598	C₂	semidirect
4. C₁₉×#2580	C₂	semidirect
5. C₁₉×#2535	C₂	semidirect
6. C₁₉×#2487	C₂	semidirect
7. C₁₉×#2482	C₂	semidirect
8. C₁₉×#2408	C₂	semidirect
9. C₁₉×#2404	C₂	semidirect
10. C₁₉×#2398	C₂	semidirect
11. C₁₉×#2397	C₂	semidirect
12. C₄×C₁₉×#121	C₂	semidirect
13. C₄×C₁₉×#120	C₂	semidirect
14. C₁₉×#2283	C₂	semidirect
21. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
22. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
30. C₂×C₄×D₄×C₁₉	C₂²	semidirect
31. C₂×C₄×D₄×C₁₉	C₂²	semidirect
32. C₂×C₄×D₄×C₁₉	C₂²	semidirect
34. C₂×C₁₉×#117	C₂²	semidirect
38. C₂²×C₄²×C₁₉	C₂²	semidirect
39. C₁₉×#400	C₂²	semidirect
40. C₁₉×#399	C₂²	semidirect
41. C₁₉×#399	C₂²	semidirect
42. C₁₉×#397	C₂²	semidirect
44. C₁₉×#393	C₂²	semidirect
46. C₁₉×#392	C₂²	semidirect
48. C₁₉×#389	C₂²	semidirect
49. C₁₉×#388	C₂²	semidirect
51. C₁₉×#386	C₂²	semidirect
52. C₁₉×#386	C₂²	semidirect
54. C₁₉×#385	C₂²	semidirect
55. C₁₉×#383	C₂²	semidirect
56. C₁₉×#382	C₂²	semidirect
59. C₁₉×#380	C₂²	semidirect
61. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
64. C₁₉×#376	C₂²	semidirect
123. C₂×C₄²×C₁₉	D₄	semidirect
161. C₂×D₄×C₁₉	#41	semidirect
219. #34963	C₁₉	direct (N × H)
278. C₂×C₄×#41	C₂×C₁₉	semidirect
279. C₂²×C₄×D₄	C₂×C₁₉	semidirect
280. #2598	C₂×C₁₉	semidirect
281. #2580	C₂×C₁₉	semidirect
282. #2535	C₂×C₁₉	semidirect
283. #2487	C₂×C₁₉	semidirect
284. #2482	C₂×C₁₉	semidirect
285. #2408	C₂×C₁₉	semidirect
286. #2404	C₂×C₁₉	semidirect
287. #2398	C₂×C₁₉	semidirect
288. #2397	C₂×C₁₉	semidirect
289. C₄×#121	C₂×C₁₉	semidirect
290. C₄×#120	C₂×C₁₉	semidirect
291. #2283	C₂×C₁₉	semidirect
328. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
329. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
337. C₂×C₄×D₄	C₂²×C₁₉	semidirect
338. C₂×C₄×D₄	C₂²×C₁₉	semidirect
339. C₂×C₄×D₄	C₂²×C₁₉	semidirect
341. C₂×#117	C₂²×C₁₉	semidirect
345. C₂²×C₄²	C₂²×C₁₉	semidirect
346. #400	C₂²×C₁₉	semidirect
347. #399	C₂²×C₁₉	semidirect
348. #399	C₂²×C₁₉	semidirect
349. #397	C₂²×C₁₉	semidirect
351. #393	C₂²×C₁₉	semidirect
353. #392	C₂²×C₁₉	semidirect
355. #389	C₂²×C₁₉	semidirect
356. #388	C₂²×C₁₉	semidirect
358. #386	C₂²×C₁₉	semidirect
359. #386	C₂²×C₁₉	semidirect
361. #385	C₂²×C₁₉	semidirect
362. #383	C₂²×C₁₉	semidirect
363. #382	C₂²×C₁₉	semidirect
366. #380	C₂²×C₁₉	semidirect
368. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
370. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
371. #376	C₂²×C₁₉	semidirect
437. C₂×C₄²	D₄×C₁₉	semidirect
452. C₁₉	#34963	direct (N × H)
476. C₂×D₄	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₂²×C₄×D₄×C₁₉	2
C₁₉×#2598	2
C₁₉×#2580	2
C₁₉×#2535	2
C₁₉×#2487	2
C₁₉×#2482	2
C₁₉×#2408	2
C₁₉×#2404	2
C₁₉×#2398	2
C₁₉×#2397	2
C₄×C₁₉×#121	2
C₄×C₁₉×#120	2
C₁₉×#2283	2
#34963	19

Subgroups — C19×#34963 #18040922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34963 #18040922