Subgroups — C₂×C₁₉×#1792 #18026572

Order 4864.

4114 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#104	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#417	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1792	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₁₉×H(5,𝔽₂)	—	2	8	no	—
8	C₂×C₁₉×H(5,𝔽₂)	—	2	4	no	—
9	C₂×C₁₉×H(5,𝔽₂)	—	2	4	no	—
10	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
11	C₂×C₁₉×H(5,𝔽₂)	C₄	1	8	yes	complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	—
13	C₂²×#41×C₁₉	—	2	2	no	—
14	C₂²×#41×C₁₉	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₉	—	2	2	no	—
16	C₂³×D₄×C₁₉	—	2	2	no	—
17	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₉×#104	—	2	8	no	—
23	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
24	C₁₉×#417	—	2	4	no	—
25	C₁₉×#417	C₂²	1	8	yes	complemented
26	C₂×C₁₉×#103	—	2	2	no	—
27	C₂×C₁₉×#102	—	2	2	no	—
28	C₂×C₁₉×#100	—	2	4	no	—
29	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
30	C₁₉×#390	—	2	2	no	—
31	C₁₉×#390	C₂²	1	4	yes	complemented
32	C₂⁵×C₁₉	—	2	2	no	—
33	C₂⁵×C₁₉	D₄	1	2	yes	—
34	C₁₉×H(5,𝔽₂)	—	2	16	no	—
35	C₁₉×H(5,𝔽₂)	—	2	32	no	—
36	C₁₉×H(5,𝔽₂)	—	2	32	no	—
37	C₁₉×H(5,𝔽₂)	—	2	16	no	—
38	C₁₉×H(5,𝔽₂)	—	2	16	no	—
39	C₁₉×H(5,𝔽₂)	—	2	8	no	—
40	C₁₉×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
41	C₂×#41×C₁₉	—	2	8	no	—
42	C₂×#41×C₁₉	—	2	16	no	—
43	C₂×#41×C₁₉	—	2	16	no	—
44	C₂×#41×C₁₉	—	2	8	no	—
45	C₂×#41×C₁₉	—	2	4	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	4	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
50	C₂×#41×C₁₉	D₄	1	8	yes	—
51	C₂×#41×C₁₉	D₄	1	4	yes	—
52	C₂×#41×C₁₉	C₂³	1	4	yes	—
53	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
54	C₂²×D₄×C₁₉	—	2	4	no	—
55	C₂²×D₄×C₁₉	—	2	8	no	—
56	C₂²×D₄×C₁₉	—	2	16	no	—
57	C₂²×D₄×C₁₉	—	2	8	no	—
58	C₂²×D₄×C₁₉	—	2	16	no	—
59	C₂²×D₄×C₁₉	—	2	16	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	—	2	8	no	—
62	C₂²×D₄×C₁₉	—	2	16	no	—
63	C₂²×D₄×C₁₉	—	2	8	no	—
64	C₂²×D₄×C₁₉	—	2	2	no	—
65	C₂²×D₄×C₁₉	—	2	4	no	—
66	C₂²×D₄×C₁₉	—	2	2	no	—
67	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
68	C₂²×D₄×C₁₉	D₄	1	2	yes	—
69	C₂²×D₄×C₁₉	D₄	1	4	yes	—
70	C₂²×D₄×C₁₉	D₄	1	2	yes	—
71	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₉	—	2	2	no	—
73	C₂³×C₄×C₁₉	—	2	2	no	—
74	C₂³×C₄×C₁₉	—	2	1	no	—
75	C₂³×C₄×C₁₉	—	2	1	no	—
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₁₉	—	2	2	no	—
78	C₂×M₁₆×C₁₉	—	2	4	no	—
79	C₂×M₁₆×C₁₉	—	2	4	no	—
80	C₂×M₁₆×C₁₉	C₂³	1	4	yes	complemented
81	C₂²×C₈×C₁₉	—	2	2	no	—
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	C₂³	1	2	yes	complemented
86	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
88	C₂×C₄²×C₁₉	—	2	4	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	C₂³	1	2	yes	complemented
91	C₁₉×#104	—	2	16	no	—
92	C₁₉×#103	—	2	8	no	—
93	C₁₉×#102	—	2	8	no	—
94	C₁₉×#100	—	2	8	no	—
95	C₂⁴×C₁₉	—	2	8	no	—
96	C₂⁴×C₁₉	—	2	16	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	4	no	—
101	C₂⁴×C₁₉	—	4	4	no	—
102	C₂⁴×C₁₉	—	4	4	no	—
103	C₂⁴×C₁₉	—	8	4	no	—
104	C₂⁴×C₁₉	—	8	4	no	—
105	C₂⁴×C₁₉	C₂²⋊C₄	1	8	yes	—
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
108	#41×C₁₉	—	2	32	no	—
109	#41×C₁₉	—	2	64	no	—
110	#41×C₁₉	—	2	32	no	—
111	#41×C₁₉	—	2	8	no	—
112	#41×C₁₉	—	2	8	no	—
113	#41×C₁₉	—	2	8	no	—
114	#41×C₁₉	—	2	8	no	—
115	#41×C₁₉	—	2	8	no	—
116	#41×C₁₉	—	2	4	no	—
117	#41×C₁₉	—	2	4	no	—
118	#41×C₁₉	C₂²⋊C₄	1	16	yes	complemented
119	#41×C₁₉	C₂²×C₄	1	8	yes	—
120	#41×C₁₉	C₂×D₄	1	8	yes	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	4	no	—
123	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
124	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₁₉	—	2	16	no	—
126	C₂×D₄×C₁₉	—	2	32	no	—
127	C₂×D₄×C₁₉	—	2	32	no	—
128	C₂×D₄×C₁₉	—	2	64	no	—
129	C₂×D₄×C₁₉	—	2	32	no	—
130	C₂×D₄×C₁₉	—	2	64	no	—
131	C₂×D₄×C₁₉	—	2	8	no	—
132	C₂×D₄×C₁₉	—	2	32	no	—
133	C₂×D₄×C₁₉	—	2	4	no	—
134	C₂×D₄×C₁₉	—	2	8	no	—
135	C₂×D₄×C₁₉	—	2	4	no	—
136	C₂×D₄×C₁₉	—	2	32	no	—
137	C₂×D₄×C₁₉	—	2	8	no	—
138	C₂×D₄×C₁₉	—	2	8	no	—
139	C₂×D₄×C₁₉	—	2	8	no	—
140	C₂×D₄×C₁₉	—	2	4	no	—
141	C₂×D₄×C₁₉	—	2	4	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	8	no	—
144	C₂×D₄×C₁₉	—	2	4	no	—
145	C₂×D₄×C₁₉	—	2	4	no	—
146	C₂×D₄×C₁₉	—	2	4	no	—
147	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	—
148	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	complemented
149	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
150	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₉	—	2	8	no	—
153	C₂²×C₄×C₁₉	—	2	16	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	8	no	—
156	C₂²×C₄×C₁₉	—	2	4	no	—
157	C₂²×C₄×C₁₉	—	2	8	no	—
158	C₂²×C₄×C₁₉	—	2	4	no	—
159	C₂²×C₄×C₁₉	—	2	4	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	4	2	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	4	4	no	—
165	C₂²×C₄×C₁₉	—	4	1	no	—
166	C₂²×C₄×C₁₉	—	4	1	no	—
167	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₁₉	—	2	4	no	—
175	M₁₆×C₁₉	—	2	4	no	—
176	M₁₆×C₁₉	—	4	4	no	—
177	C₂×C₈×C₁₉	—	2	4	no	—
178	C₂×C₈×C₁₉	—	4	4	no	—
179	C₄⋊C₄×C₁₉	—	2	4	no	—
180	C₄⋊C₄×C₁₉	—	4	2	no	—
181	C₂²⋊C₄×C₁₉	—	4	16	no	—
182	C₄²×C₁₉	—	2	4	no	—
183	C₄²×C₁₉	—	4	2	no	—
184	C₂×#1792	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	2	2	no	—
187	C₂³×C₁₉	—	2	32	no	—
188	C₂³×C₁₉	—	2	4	no	—
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	2	8	no	—
191	C₂³×C₁₉	—	2	8	no	—
192	C₂³×C₁₉	—	2	4	no	—
193	C₂³×C₁₉	—	2	8	no	—
194	C₂³×C₁₉	—	4	4	no	—
195	C₂³×C₁₉	—	4	16	no	—
196	C₂³×C₁₉	—	4	4	no	—
197	C₂³×C₁₉	—	4	4	no	—
198	C₂³×C₁₉	—	4	4	no	—
199	C₂³×C₁₉	—	4	4	no	—
200	C₂³×C₁₉	—	4	4	no	—
201	C₂³×C₁₉	—	8	8	no	—
202	C₂³×C₁₉	—	8	2	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	—	8	32	no	—
205	C₂³×C₁₉	—	8	8	no	—
206	C₂³×C₁₉	—	8	8	no	—
207	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂³×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
209	C₂³×C₁₉	#120	1	2	yes	—
210	C₂³×C₁₉	#120	1	1	yes	characteristic
211	C₂³×C₁₉	#120	1	1	yes	characteristic
212	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₉	—	2	4	no	—
214	Q₈×C₁₉	—	2	8	no	—
215	Q₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	complemented
216	D₄×C₁₉	—	2	64	no	—
217	D₄×C₁₉	—	2	8	no	—
218	D₄×C₁₉	—	2	8	no	—
219	D₄×C₁₉	—	2	16	no	—
220	D₄×C₁₉	—	2	8	no	—
221	D₄×C₁₉	—	2	8	no	—
222	D₄×C₁₉	—	2	4	no	—
223	D₄×C₁₉	—	2	16	no	—
224	D₄×C₁₉	—	2	8	no	—
225	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	complemented
226	C₂×C₄×C₁₉	—	2	32	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	8	no	—
229	C₂×C₄×C₁₉	—	2	8	no	—
230	C₂×C₄×C₁₉	—	2	8	no	—
231	C₂×C₄×C₁₉	—	2	16	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	4	8	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	4	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
241	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
242	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
243	C₂×C₄×C₁₉	#120	1	4	yes	—
244	C₂×C₄×C₁₉	#120	1	4	yes	—
245	C₂×C₄×C₁₉	#120	1	2	yes	—
246	C₂×C₄×C₁₉	#120	1	2	yes	—
247	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
251	C₈×C₁₉	—	4	4	no	—
252	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
253	C₂²×#104	C₂×C₁₉	1	2	yes	complemented
254	C₂×#417	C₂×C₁₉	1	2	yes	complemented
255	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
256	C₂×#390	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1792	C₂×C₁₉	1	8	yes	direct product factor
258	C₂²×C₁₉	—	2	4	no	—
259	C₂²×C₁₉	—	2	4	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	8	no	—
265	C₂²×C₁₉	—	2	8	no	—
266	C₂²×C₁₉	—	4	8	no	—
267	C₂²×C₁₉	—	4	16	no	—
268	C₂²×C₁₉	—	4	16	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	—	4	4	no	—
273	C₂²×C₁₉	—	8	4	no	—
274	C₂²×C₁₉	—	8	8	no	—
275	C₂²×C₁₉	—	8	32	no	—
276	C₂²×C₁₉	#379	1	2	yes	—
277	C₂²×C₁₉	#379	1	2	yes	—
278	C₂²×C₁₉	#453	1	2	yes	—
279	C₂²×C₁₉	#455	1	2	yes	—
280	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
281	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
282	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
283	C₄×C₁₉	—	2	8	no	—
284	C₄×C₁₉	—	4	4	no	—
285	C₄×C₁₉	—	8	2	no	—
286	C₄×C₁₉	#379	1	4	yes	—
287	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
288	C₄×C₁₉	C₂×#120	1	2	yes	—
289	C₂×H(5,𝔽₂)	—	2	8	no	—
290	C₂×H(5,𝔽₂)	—	2	4	no	—
291	C₂×H(5,𝔽₂)	—	2	4	no	—
292	C₂×H(5,𝔽₂)	—	2	2	no	—
293	C₂×H(5,𝔽₂)	C₄×C₁₉	1	8	yes	complemented
294	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	—
295	C₂²×#41	—	2	2	no	—
296	C₂²×#41	C₂²×C₁₉	1	2	yes	—
297	C₂³×D₄	—	2	2	no	—
298	C₂³×D₄	—	2	2	no	—
299	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
300	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
301	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
302	C₂²×C₂²⋊C₄	—	2	2	no	—
303	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
304	C₂×#104	—	2	8	no	—
305	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
306	#417	—	2	4	no	—
307	#417	C₂²×C₁₉	1	8	yes	complemented
308	C₂×#103	—	2	2	no	—
309	C₂×#102	—	2	2	no	—
310	C₂×#100	—	2	4	no	—
311	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
312	#390	—	2	2	no	—
313	#390	C₂²×C₁₉	1	4	yes	complemented
314	C₂×C₁₉	—	2	1	no	—
315	C₂×C₁₉	—	2	1	no	—
316	C₂×C₁₉	—	2	2	no	—
317	C₂×C₁₉	—	4	8	no	—
318	C₂×C₁₉	—	4	8	no	—
319	C₂×C₁₉	#1792	1	4	yes	direct product factor
320	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
321	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
322	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
323	C₂⁵	—	2	2	no	—
324	C₂⁵	D₄×C₁₉	1	2	yes	—
325	H(5,𝔽₂)	—	2	32	no	—
326	H(5,𝔽₂)	—	2	16	no	—
327	H(5,𝔽₂)	—	2	32	no	—
328	H(5,𝔽₂)	—	2	16	no	—
329	H(5,𝔽₂)	—	2	16	no	—
330	H(5,𝔽₂)	—	2	8	no	—
331	H(5,𝔽₂)	C₂×C₄×C₁₉	1	16	yes	complemented
332	C₂×#41	—	2	16	no	—
333	C₂×#41	—	2	8	no	—
334	C₂×#41	—	2	16	no	—
335	C₂×#41	—	2	8	no	—
336	C₂×#41	—	2	4	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	4	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
341	C₂×#41	D₄×C₁₉	1	8	yes	—
342	C₂×#41	D₄×C₁₉	1	4	yes	—
343	C₂×#41	C₂³×C₁₉	1	4	yes	—
344	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
345	C₂²×D₄	—	2	4	no	—
346	C₂²×D₄	—	2	16	no	—
347	C₂²×D₄	—	2	8	no	—
348	C₂²×D₄	—	2	16	no	—
349	C₂²×D₄	—	2	8	no	—
350	C₂²×D₄	—	2	16	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	8	no	—
353	C₂²×D₄	—	2	16	no	—
354	C₂²×D₄	—	2	8	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	4	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
359	C₂²×D₄	D₄×C₁₉	1	2	yes	—
360	C₂²×D₄	D₄×C₁₉	1	4	yes	—
361	C₂²×D₄	D₄×C₁₉	1	2	yes	—
362	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
363	C₂³×C₄	—	2	2	no	—
364	C₂³×C₄	—	2	2	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	—	2	4	no	—
370	C₂×M₁₆	—	2	4	no	—
371	C₂×M₁₆	C₂³×C₁₉	1	4	yes	complemented
372	C₂²×C₈	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	complemented
377	C₂×C₂²⋊C₄	—	2	8	no	—
378	C₂×C₂²⋊C₄	—	4	8	no	—
379	C₂×C₄²	—	2	4	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	C₂³×C₁₉	1	2	yes	complemented
382	#104	—	2	16	no	—
383	#103	—	2	8	no	—
384	#102	—	2	8	no	—
385	#100	—	2	8	no	—
386	C₁₉	C₂×#1792	1	1	yes	characteristic, direct product factor, Sylow
387	C₂⁴	—	2	16	no	—
388	C₂⁴	—	2	8	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	4	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	4	4	no	—
394	C₂⁴	—	4	4	no	—
395	C₂⁴	—	8	4	no	—
396	C₂⁴	—	8	4	no	—
397	C₂⁴	C₂²⋊C₄×C₁₉	1	8	yes	—
398	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
400	#41	—	2	64	no	—
401	#41	—	2	32	no	—
402	#41	—	2	32	no	—
403	#41	—	2	8	no	—
404	#41	—	2	8	no	—
405	#41	—	2	8	no	—
406	#41	—	2	8	no	—
407	#41	—	2	8	no	—
408	#41	—	2	4	no	—
409	#41	—	2	4	no	—
410	#41	C₂²⋊C₄×C₁₉	1	16	yes	complemented
411	#41	C₂²×C₄×C₁₉	1	8	yes	—
412	#41	C₂×D₄×C₁₉	1	8	yes	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	complemented
416	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
417	C₂×D₄	—	2	32	no	—
418	C₂×D₄	—	2	16	no	—
419	C₂×D₄	—	2	64	no	—
420	C₂×D₄	—	2	32	no	—
421	C₂×D₄	—	2	64	no	—
422	C₂×D₄	—	2	32	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	32	no	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	32	no	—
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
440	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
441	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
442	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
443	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
444	C₂²×C₄	—	2	16	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	8	no	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
462	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
466	M₁₆	—	2	4	no	—
467	M₁₆	—	2	4	no	—
468	M₁₆	—	4	4	no	—
469	C₂×C₈	—	2	4	no	—
470	C₂×C₈	—	4	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	16	no	—
474	C₄²	—	2	4	no	—
475	C₄²	—	4	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	32	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	2	8	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	8	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	16	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	8	2	no	—
493	C₂³	—	8	2	no	—
494	C₂³	—	8	8	no	—
495	C₂³	—	8	8	no	—
496	C₂³	—	8	8	no	—
497	C₂³	—	8	32	no	—
498	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
499	C₂³	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
500	C₂³	C₁₉×#120	1	1	yes	characteristic
501	C₂³	C₁₉×#120	1	2	yes	—
502	C₂³	C₁₉×#120	1	1	yes	characteristic
503	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	Q₈	—	2	8	no	—
505	Q₈	—	2	4	no	—
506	Q₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	complemented
507	D₄	—	2	64	no	—
508	D₄	—	2	16	no	—
509	D₄	—	2	8	no	—
510	D₄	—	2	8	no	—
511	D₄	—	2	16	no	—
512	D₄	—	2	8	no	—
513	D₄	—	2	8	no	—
514	D₄	—	2	8	no	—
515	D₄	—	2	4	no	—
516	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	complemented
517	C₂×C₄	—	2	32	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	16	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
532	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
533	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
534	C₂×C₄	C₁₉×#120	1	2	yes	—
535	C₂×C₄	C₁₉×#120	1	2	yes	—
536	C₂×C₄	C₁₉×#120	1	4	yes	—
537	C₂×C₄	C₁₉×#120	1	4	yes	—
538	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
540	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
541	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
542	C₈	—	4	4	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	8	no	—
550	C₂²	—	2	8	no	—
551	C₂²	—	4	8	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	16	no	—
557	C₂²	—	4	16	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	8	no	—
560	C₂²	—	8	32	no	—
561	C₂²	C₁₉×#379	1	2	yes	—
562	C₂²	C₁₉×#379	1	2	yes	—
563	C₂²	C₁₉×#453	1	2	yes	—
564	C₂²	C₁₉×#455	1	2	yes	—
565	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
566	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
567	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
568	C₄	—	2	8	no	—
569	C₄	—	4	4	no	—
570	C₄	—	8	2	no	—
571	C₄	C₁₉×#379	1	4	yes	—
572	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
573	C₄	C₂×C₁₉×#120	1	2	yes	—
574	C₂	—	2	1	no	—
575	C₂	—	2	1	no	—
576	C₂	—	2	2	no	—
577	C₂	—	4	8	no	—
578	C₂	—	4	8	no	—
579	C₂	C₁₉×#1792	1	4	yes	direct product factor
580	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
581	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
582	C₂	C₂×C₁₉×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#104	C₂	semidirect
3. C₂×C₁₉×#417	C₂	semidirect
4. C₂²×C₁₉×#100	C₂	semidirect
5. C₂×C₁₉×#390	C₂	semidirect
6. C₁₉×#1792	C₂	direct (N × H)
11. C₂×C₁₉×H(5,𝔽₂)	C₄	semidirect
18. C₂²×M₁₆×C₁₉	C₂²	semidirect
19. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
21. C₂²×C₄²×C₁₉	C₂²	semidirect
23. C₂×C₁₉×#104	C₂²	semidirect
25. C₁₉×#417	C₂²	semidirect
29. C₂×C₁₉×#100	C₂²	semidirect
31. C₁₉×#390	C₂²	semidirect
40. C₁₉×H(5,𝔽₂)	C₂×C₄	semidirect
80. C₂×M₁₆×C₁₉	C₂³	semidirect
85. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
90. C₂×C₄²×C₁₉	C₂³	semidirect
118. #41×C₁₉	C₂²⋊C₄	semidirect
123. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
148. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
184. C₂×#1792	C₁₉	direct (N × H)
215. Q₈×C₁₉	C₂×C₂²⋊C₄	semidirect
225. D₄×C₁₉	C₂×C₂²⋊C₄	semidirect
253. C₂²×#104	C₂×C₁₉	semidirect
254. C₂×#417	C₂×C₁₉	semidirect
255. C₂²×#100	C₂×C₁₉	semidirect
256. C₂×#390	C₂×C₁₉	semidirect
257. #1792	C₂×C₁₉	direct (N × H)
293. C₂×H(5,𝔽₂)	C₄×C₁₉	semidirect
300. C₂²×M₁₆	C₂²×C₁₉	semidirect
301. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
303. C₂²×C₄²	C₂²×C₁₉	semidirect
305. C₂×#104	C₂²×C₁₉	semidirect
307. #417	C₂²×C₁₉	semidirect
311. C₂×#100	C₂²×C₁₉	semidirect
313. #390	C₂²×C₁₉	semidirect
319. C₂×C₁₉	#1792	direct (N × H)
331. H(5,𝔽₂)	C₂×C₄×C₁₉	semidirect
371. C₂×M₁₆	C₂³×C₁₉	semidirect
376. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
381. C₂×C₄²	C₂³×C₁₉	semidirect
386. C₁₉	C₂×#1792	direct (N × H)
410. #41	C₂²⋊C₄×C₁₉	semidirect
415. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
440. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
506. Q₈	C₂×C₂²⋊C₄×C₁₉	semidirect
516. D₄	C₂×C₂²⋊C₄×C₁₉	semidirect
579. C₂	C₁₉×#1792	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×H(5,𝔽₂)	2
C₂²×C₁₉×#104	2
C₂×C₁₉×#417	2
C₂²×C₁₉×#100	2
C₂×C₁₉×#390	2
C₁₉×#1792	2
C₂×#1792	19

Subgroups — C2×C19×#1792 #18026572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1792 #18026572