Subgroups — C₁₉×#62842 #18068801

Order 4864.

11770 conjugacy classes of subgroups.

The subgroup lattice has 368 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	2	yes	maximal, complemented
2	C₁₉×#3496	C₂	1	16	yes	maximal, complemented
3	C₁₉×#3485	C₂	1	16	yes	maximal, complemented
4	C₁₉×#3484	C₂	1	16	yes	maximal, complemented
5	C₁₉×#3449	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×#534	C₂	1	8	yes	maximal, complemented
7	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×H(5,𝔽₂)	—	2	32	no	—
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	16	yes	complemented
10	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	16	yes	complemented
11	C₂²×#41×C₁₉	C₂²	1	4	yes	complemented
12	C₂²×#41×C₁₉	C₂²	1	8	yes	complemented
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₉	C₂²	1	8	yes	complemented
15	C₂³×D₄×C₁₉	C₂²	1	8	yes	complemented
16	C₁₉×#547	C₂²	1	64	yes	complemented
17	C₁₉×#546	C₂²	1	128	yes	complemented
18	D₄²×C₁₉	C₂²	1	64	yes	complemented
19	C₁₉×#537	C₂²	1	16	yes	complemented
20	C₁₉×#536	C₂²	1	16	yes	complemented
21	C₁₉×#535	C₂²	1	16	yes	complemented
22	C₁₉×#534	C₂²	1	16	yes	complemented
23	C₁₉×#534	C₂²	1	64	yes	complemented
24	C₁₉×#534	C₂²	1	32	yes	complemented
25	C₁₉×#532	C₂²	1	16	yes	complemented
26	C₁₉×#525	C₂²	1	32	yes	complemented
27	C₂×C₁₉×#123	C₂²	1	32	yes	complemented
28	C₂×C₁₉×#121	C₂²	1	32	yes	complemented
29	C₂×C₁₉×#120	C₂²	1	32	yes	complemented
30	C₁₉×#518	C₂²	1	16	yes	complemented
31	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
32	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
34	C₂⁵×C₁₉	C₂³	1	2	yes	—
35	C₂⁵×C₁₉	C₂³	1	8	yes	complemented
36	C₁₉×H(5,𝔽₂)	—	2	128	no	—
37	C₁₉×H(5,𝔽₂)	—	2	128	no	—
38	C₂×#41×C₁₉	—	2	64	no	—
39	C₂×#41×C₁₉	—	2	32	no	—
40	C₂×#41×C₁₉	C₂³	1	16	yes	—
41	C₂×#41×C₁₉	C₂³	1	16	yes	complemented
42	C₂×#41×C₁₉	C₂³	1	64	yes	complemented
43	C₂²×Q₈×C₁₉	C₂³	1	4	yes	complemented
44	C₂²×D₄×C₁₉	—	2	64	no	—
45	C₂²×D₄×C₁₉	—	2	64	no	—
46	C₂²×D₄×C₁₉	D₄	1	16	yes	complemented
47	C₂²×D₄×C₁₉	C₂³	1	32	yes	—
48	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
49	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
50	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	32	yes	complemented
52	C₂²×D₄×C₁₉	C₂³	1	16	yes	complemented
53	C₂²×D₄×C₁₉	C₂³	1	4	yes	complemented
54	C₂²×D₄×C₁₉	C₂³	1	64	yes	complemented
55	C₂²×D₄×C₁₉	C₂³	1	32	yes	complemented
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₉	C₂³	1	8	yes	complemented
58	C₂³×C₄×C₁₉	C₂³	1	8	yes	complemented
59	C₂³×C₄×C₁₉	C₂³	1	8	yes	complemented
60	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	complemented
61	C₁₉×#127	C₂³	1	16	yes	complemented
62	C₁₉×#124	C₂³	1	32	yes	complemented
63	C₁₉×#123	C₂³	1	64	yes	complemented
64	C₁₉×#123	C₂³	1	128	yes	complemented
65	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	complemented
66	C₁₉×#121	C₂³	1	64	yes	complemented
67	C₁₉×#121	C₂³	1	128	yes	complemented
68	C₁₉×#121	C₂³	1	64	yes	complemented
69	C₁₉×#120	C₂³	1	64	yes	complemented
70	C₁₉×#120	C₂³	1	128	yes	complemented
71	C₄×D₄×C₁₉	C₂³	1	64	yes	complemented
72	C₄×D₄×C₁₉	C₂³	1	64	yes	complemented
73	C₁₉×#117	C₂³	1	16	yes	complemented
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	complemented
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	32	yes	complemented
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	complemented
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	32	yes	complemented
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	64	yes	complemented
80	C₂×C₄²×C₁₉	C₂³	1	4	yes	complemented
81	C₂⁴×C₁₉	—	2	32	no	—
82	C₂⁴×C₁₉	—	8	4	no	—
83	C₂⁴×C₁₉	—	8	16	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	16	yes	complemented
85	C₂⁴×C₁₉	C₂⁴	1	32	yes	—
86	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
87	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
88	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
89	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
90	#41×C₁₉	—	2	256	no	—
91	#41×C₁₉	—	2	64	no	—
92	#41×C₁₉	—	2	64	no	—
93	C₂×Q₈×C₁₉	—	2	16	no	—
94	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
95	C₂×D₄×C₁₉	—	2	32	no	—
96	C₂×D₄×C₁₉	—	2	64	no	—
97	C₂×D₄×C₁₉	—	2	128	no	—
98	C₂×D₄×C₁₉	—	2	128	no	—
99	C₂×D₄×C₁₉	—	2	256	no	—
100	C₂×D₄×C₁₉	—	2	16	no	—
101	C₂×D₄×C₁₉	—	8	32	no	—
102	C₂×D₄×C₁₉	C₂×D₄	1	64	yes	complemented
103	C₂×D₄×C₁₉	C₂×D₄	1	32	yes	complemented
104	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
105	C₂×D₄×C₁₉	C₂⁴	1	64	yes	—
106	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
107	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
108	C₂×D₄×C₁₉	C₂⁴	1	64	yes	—
109	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
110	C₂²×C₄×C₁₉	—	2	32	no	—
111	C₂²×C₄×C₁₉	—	2	32	no	—
112	C₂²×C₄×C₁₉	—	8	8	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	complemented
114	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
121	C₄⋊C₄×C₁₉	C₂⁴	1	64	yes	—
122	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
123	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
124	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
125	C₂²⋊C₄×C₁₉	C₂⁴	1	128	yes	—
126	C₄²×C₁₉	C₂⁴	1	16	yes	—
127	#62842	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₁₉	—	2	16	no	—
129	C₂³×C₁₉	—	2	64	no	—
130	C₂³×C₁₉	—	4	8	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	16	no	—
133	C₂³×C₁₉	—	4	16	no	—
134	C₂³×C₁₉	—	4	64	no	—
135	C₂³×C₁₉	—	8	16	no	—
136	C₂³×C₁₉	—	8	64	no	—
137	C₂³×C₁₉	C₂²×D₄	1	32	yes	—
138	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
139	C₂³×C₁₉	C₂²×D₄	1	16	yes	—
140	C₂³×C₁₉	C₂⁵	1	16	yes	—
141	C₂³×C₁₉	C₂⁵	1	2	yes	—
142	C₂³×C₁₉	C₂⁵	1	8	yes	—
143	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
144	Q₈×C₁₉	—	2	32	no	—
145	D₄×C₁₉	—	2	32	no	—
146	D₄×C₁₉	—	2	128	no	—
147	D₄×C₁₉	—	2	32	no	—
148	D₄×C₁₉	—	2	32	no	—
149	D₄×C₁₉	—	4	64	no	—
150	D₄×C₁₉	C₂²×D₄	1	64	yes	—
151	C₂×C₄×C₁₉	—	2	16	no	—
152	C₂×C₄×C₁₉	—	2	64	no	—
153	C₂×C₄×C₁₉	—	2	64	no	—
154	C₂×C₄×C₁₉	—	4	8	no	—
155	C₂×C₄×C₁₉	—	4	32	no	—
156	C₂×C₄×C₁₉	C₂²×D₄	1	16	yes	—
157	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
158	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
159	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
160	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
161	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	2	yes	complemented
162	#3496	C₂×C₁₉	1	16	yes	complemented
163	#3485	C₂×C₁₉	1	16	yes	complemented
164	#3484	C₂×C₁₉	1	16	yes	complemented
165	#3449	C₂×C₁₉	1	4	yes	complemented
166	C₂×#534	C₂×C₁₉	1	8	yes	complemented
167	C₂×#518	C₂×C₁₉	1	1	yes	characteristic, complemented
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	16	no	—
170	C₂²×C₁₉	—	2	4	no	—
171	C₂²×C₁₉	—	2	16	no	—
172	C₂²×C₁₉	—	2	32	no	—
173	C₂²×C₁₉	—	4	4	no	—
174	C₂²×C₁₉	—	4	32	no	—
175	C₂²×C₁₉	—	4	16	no	—
176	C₂²×C₁₉	—	4	32	no	—
177	C₂²×C₁₉	—	8	64	no	—
178	C₂²×C₁₉	C₂³×D₄	1	4	yes	—
179	C₂²×C₁₉	C₂³×D₄	1	16	yes	—
180	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
181	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
182	C₄×C₁₉	—	2	16	no	—
183	C₄×C₁₉	—	2	16	no	—
184	C₄×C₁₉	C₂³×D₄	1	8	yes	—
185	C₂×H(5,𝔽₂)	—	2	32	no	—
186	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	16	yes	complemented
187	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	16	yes	complemented
188	C₂²×#41	C₂²×C₁₉	1	4	yes	complemented
189	C₂²×#41	C₂²×C₁₉	1	8	yes	complemented
190	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
191	C₂³×D₄	C₂²×C₁₉	1	8	yes	complemented
192	C₂³×D₄	C₂²×C₁₉	1	8	yes	complemented
193	#547	C₂²×C₁₉	1	64	yes	complemented
194	#546	C₂²×C₁₉	1	128	yes	complemented
195	D₄²	C₂²×C₁₉	1	64	yes	complemented
196	#537	C₂²×C₁₉	1	16	yes	complemented
197	#536	C₂²×C₁₉	1	16	yes	complemented
198	#535	C₂²×C₁₉	1	16	yes	complemented
199	#534	C₂²×C₁₉	1	16	yes	complemented
200	#534	C₂²×C₁₉	1	64	yes	complemented
201	#534	C₂²×C₁₉	1	32	yes	complemented
202	#532	C₂²×C₁₉	1	16	yes	complemented
203	#525	C₂²×C₁₉	1	32	yes	complemented
204	C₂×#123	C₂²×C₁₉	1	32	yes	complemented
205	C₂×#121	C₂²×C₁₉	1	32	yes	complemented
206	C₂×#120	C₂²×C₁₉	1	32	yes	complemented
207	#518	C₂²×C₁₉	1	16	yes	complemented
208	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
209	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
210	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
211	C₂×C₁₉	—	2	4	no	—
212	C₂×C₁₉	—	2	2	no	—
213	C₂×C₁₉	—	2	16	no	—
214	C₂×C₁₉	—	4	16	no	—
215	C₂×C₁₉	C₂⁴×D₄	1	1	yes	characteristic
216	C₂×C₁₉	H(7,𝔽₂)	1	2	yes	—
217	C₂⁵	C₂³×C₁₉	1	2	yes	—
218	C₂⁵	C₂³×C₁₉	1	8	yes	complemented
219	H(5,𝔽₂)	—	2	128	no	—
220	H(5,𝔽₂)	—	2	128	no	—
221	C₂×#41	—	2	64	no	—
222	C₂×#41	—	2	32	no	—
223	C₂×#41	C₂³×C₁₉	1	16	yes	—
224	C₂×#41	C₂³×C₁₉	1	16	yes	complemented
225	C₂×#41	C₂³×C₁₉	1	64	yes	complemented
226	C₂²×Q₈	C₂³×C₁₉	1	4	yes	complemented
227	C₂²×D₄	—	2	64	no	—
228	C₂²×D₄	—	2	64	no	—
229	C₂²×D₄	D₄×C₁₉	1	16	yes	complemented
230	C₂²×D₄	C₂³×C₁₉	1	32	yes	—
231	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
232	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
233	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
234	C₂²×D₄	C₂³×C₁₉	1	32	yes	complemented
235	C₂²×D₄	C₂³×C₁₉	1	16	yes	complemented
236	C₂²×D₄	C₂³×C₁₉	1	4	yes	complemented
237	C₂²×D₄	C₂³×C₁₉	1	64	yes	complemented
238	C₂²×D₄	C₂³×C₁₉	1	32	yes	complemented
239	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₉	1	8	yes	complemented
241	C₂³×C₄	C₂³×C₁₉	1	8	yes	complemented
242	C₂³×C₄	C₂³×C₁₉	1	8	yes	complemented
243	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
244	#127	C₂³×C₁₉	1	16	yes	complemented
245	#124	C₂³×C₁₉	1	32	yes	complemented
246	#123	C₂³×C₁₉	1	64	yes	complemented
247	#123	C₂³×C₁₉	1	128	yes	complemented
248	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
249	#121	C₂³×C₁₉	1	64	yes	complemented
250	#121	C₂³×C₁₉	1	128	yes	complemented
251	#121	C₂³×C₁₉	1	64	yes	complemented
252	#120	C₂³×C₁₉	1	64	yes	complemented
253	#120	C₂³×C₁₉	1	128	yes	complemented
254	C₄×D₄	C₂³×C₁₉	1	64	yes	complemented
255	C₄×D₄	C₂³×C₁₉	1	64	yes	complemented
256	#117	C₂³×C₁₉	1	16	yes	complemented
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	complemented
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	32	yes	complemented
259	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
260	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	complemented
261	C₂×C₂²⋊C₄	C₂³×C₁₉	1	32	yes	complemented
262	C₂×C₂²⋊C₄	C₂³×C₁₉	1	64	yes	complemented
263	C₂×C₄²	C₂³×C₁₉	1	4	yes	complemented
264	C₁₉	#62842	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	—	2	32	no	—
266	C₂⁴	—	8	4	no	—
267	C₂⁴	—	8	16	no	—
268	C₂⁴	C₂×D₄×C₁₉	1	16	yes	complemented
269	C₂⁴	C₂⁴×C₁₉	1	32	yes	—
270	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
271	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
272	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
273	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
274	#41	—	2	256	no	—
275	#41	—	2	64	no	—
276	#41	—	2	64	no	—
277	C₂×Q₈	—	2	16	no	—
278	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
279	C₂×D₄	—	2	32	no	—
280	C₂×D₄	—	2	64	no	—
281	C₂×D₄	—	2	128	no	—
282	C₂×D₄	—	2	128	no	—
283	C₂×D₄	—	2	256	no	—
284	C₂×D₄	—	2	16	no	—
285	C₂×D₄	—	8	32	no	—
286	C₂×D₄	C₂×D₄×C₁₉	1	64	yes	complemented
287	C₂×D₄	C₂×D₄×C₁₉	1	32	yes	complemented
288	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
289	C₂×D₄	C₂⁴×C₁₉	1	64	yes	—
290	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
291	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
292	C₂×D₄	C₂⁴×C₁₉	1	64	yes	—
293	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
294	C₂²×C₄	—	2	32	no	—
295	C₂²×C₄	—	2	32	no	—
296	C₂²×C₄	—	8	8	no	—
297	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	complemented
298	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
299	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
300	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
301	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
302	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
303	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
305	C₄⋊C₄	C₂⁴×C₁₉	1	64	yes	—
306	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
307	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
308	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
309	C₂²⋊C₄	C₂⁴×C₁₉	1	128	yes	—
310	C₄²	C₂⁴×C₁₉	1	16	yes	—
311	C₂³	—	2	16	no	—
312	C₂³	—	2	64	no	—
313	C₂³	—	4	8	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	16	no	—
316	C₂³	—	4	16	no	—
317	C₂³	—	4	64	no	—
318	C₂³	—	8	16	no	—
319	C₂³	—	8	64	no	—
320	C₂³	C₂²×D₄×C₁₉	1	32	yes	—
321	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
322	C₂³	C₂²×D₄×C₁₉	1	16	yes	—
323	C₂³	C₂⁵×C₁₉	1	16	yes	—
324	C₂³	C₂⁵×C₁₉	1	2	yes	—
325	C₂³	C₂⁵×C₁₉	1	8	yes	—
326	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
327	Q₈	—	2	32	no	—
328	D₄	—	2	32	no	—
329	D₄	—	2	128	no	—
330	D₄	—	2	32	no	—
331	D₄	—	2	32	no	—
332	D₄	—	4	64	no	—
333	D₄	C₂²×D₄×C₁₉	1	64	yes	—
334	C₂×C₄	—	2	16	no	—
335	C₂×C₄	—	2	64	no	—
336	C₂×C₄	—	2	64	no	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	32	no	—
339	C₂×C₄	C₂²×D₄×C₁₉	1	16	yes	—
340	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
341	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
342	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
343	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	16	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	2	16	no	—
348	C₂²	—	2	32	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	32	no	—
351	C₂²	—	4	16	no	—
352	C₂²	—	4	32	no	—
353	C₂²	—	8	64	no	—
354	C₂²	C₂³×D₄×C₁₉	1	4	yes	—
355	C₂²	C₂³×D₄×C₁₉	1	16	yes	—
356	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
357	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
358	C₄	—	2	16	no	—
359	C₄	—	2	16	no	—
360	C₄	C₂³×D₄×C₁₉	1	8	yes	—
361	C₂	—	2	4	no	—
362	C₂	—	2	2	no	—
363	C₂	—	2	16	no	—
364	C₂	—	4	16	no	—
365	C₂	C₂⁴×D₄×C₁₉	1	1	yes	characteristic
366	C₂	C₁₉×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×H(5,𝔽₂)	C₂	semidirect
2. C₁₉×#3496	C₂	semidirect
3. C₁₉×#3485	C₂	semidirect
4. C₁₉×#3484	C₂	semidirect
5. C₁₉×#3449	C₂	semidirect
6. C₂×C₁₉×#534	C₂	semidirect
7. C₂×C₁₉×#518	C₂	semidirect
9. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
10. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
11. C₂²×#41×C₁₉	C₂²	semidirect
12. C₂²×#41×C₁₉	C₂²	semidirect
14. C₂³×D₄×C₁₉	C₂²	semidirect
15. C₂³×D₄×C₁₉	C₂²	semidirect
16. C₁₉×#547	C₂²	semidirect
17. C₁₉×#546	C₂²	semidirect
18. D₄²×C₁₉	C₂²	semidirect
19. C₁₉×#537	C₂²	semidirect
20. C₁₉×#536	C₂²	semidirect
21. C₁₉×#535	C₂²	semidirect
22. C₁₉×#534	C₂²	semidirect
23. C₁₉×#534	C₂²	semidirect
24. C₁₉×#534	C₂²	semidirect
25. C₁₉×#532	C₂²	semidirect
26. C₁₉×#525	C₂²	semidirect
27. C₂×C₁₉×#123	C₂²	semidirect
28. C₂×C₁₉×#121	C₂²	semidirect
29. C₂×C₁₉×#120	C₂²	semidirect
30. C₁₉×#518	C₂²	semidirect
31. C₂×C₄×D₄×C₁₉	C₂²	semidirect
32. C₂×C₁₉×#117	C₂²	semidirect
33. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
35. C₂⁵×C₁₉	C₂³	semidirect
41. C₂×#41×C₁₉	C₂³	semidirect
42. C₂×#41×C₁₉	C₂³	semidirect
43. C₂²×Q₈×C₁₉	C₂³	semidirect
46. C₂²×D₄×C₁₉	D₄	semidirect
51. C₂²×D₄×C₁₉	C₂³	semidirect
52. C₂²×D₄×C₁₉	C₂³	semidirect
53. C₂²×D₄×C₁₉	C₂³	semidirect
54. C₂²×D₄×C₁₉	C₂³	semidirect
55. C₂²×D₄×C₁₉	C₂³	semidirect
57. C₂³×C₄×C₁₉	C₂³	semidirect
58. C₂³×C₄×C₁₉	C₂³	semidirect
59. C₂³×C₄×C₁₉	C₂³	semidirect
60. C₁₉×C₄⋊Q₈	C₂³	semidirect
61. C₁₉×#127	C₂³	semidirect
62. C₁₉×#124	C₂³	semidirect
63. C₁₉×#123	C₂³	semidirect
64. C₁₉×#123	C₂³	semidirect
65. C₁₉×C₂²⋊Q₈	C₂³	semidirect
66. C₁₉×#121	C₂³	semidirect
67. C₁₉×#121	C₂³	semidirect
68. C₁₉×#121	C₂³	semidirect
69. C₁₉×#120	C₂³	semidirect
70. C₁₉×#120	C₂³	semidirect
71. C₄×D₄×C₁₉	C₂³	semidirect
72. C₄×D₄×C₁₉	C₂³	semidirect
73. C₁₉×#117	C₂³	semidirect
74. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
75. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
77. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
78. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
79. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
80. C₂×C₄²×C₁₉	C₂³	semidirect
84. C₂⁴×C₁₉	C₂×D₄	semidirect
102. C₂×D₄×C₁₉	C₂×D₄	semidirect
103. C₂×D₄×C₁₉	C₂×D₄	semidirect
113. C₂²×C₄×C₁₉	C₂×D₄	semidirect
127. #62842	C₁₉	direct (N × H)
161. C₂²×H(5,𝔽₂)	C₂×C₁₉	semidirect
162. #3496	C₂×C₁₉	semidirect
163. #3485	C₂×C₁₉	semidirect
164. #3484	C₂×C₁₉	semidirect
165. #3449	C₂×C₁₉	semidirect
166. C₂×#534	C₂×C₁₉	semidirect
167. C₂×#518	C₂×C₁₉	semidirect
186. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
187. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
188. C₂²×#41	C₂²×C₁₉	semidirect
189. C₂²×#41	C₂²×C₁₉	semidirect
191. C₂³×D₄	C₂²×C₁₉	semidirect
192. C₂³×D₄	C₂²×C₁₉	semidirect
193. #547	C₂²×C₁₉	semidirect
194. #546	C₂²×C₁₉	semidirect
195. D₄²	C₂²×C₁₉	semidirect
196. #537	C₂²×C₁₉	semidirect
197. #536	C₂²×C₁₉	semidirect
198. #535	C₂²×C₁₉	semidirect
199. #534	C₂²×C₁₉	semidirect
200. #534	C₂²×C₁₉	semidirect
201. #534	C₂²×C₁₉	semidirect
202. #532	C₂²×C₁₉	semidirect
203. #525	C₂²×C₁₉	semidirect
204. C₂×#123	C₂²×C₁₉	semidirect
205. C₂×#121	C₂²×C₁₉	semidirect
206. C₂×#120	C₂²×C₁₉	semidirect
207. #518	C₂²×C₁₉	semidirect
208. C₂×C₄×D₄	C₂²×C₁₉	semidirect
209. C₂×#117	C₂²×C₁₉	semidirect
210. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
218. C₂⁵	C₂³×C₁₉	semidirect
224. C₂×#41	C₂³×C₁₉	semidirect
225. C₂×#41	C₂³×C₁₉	semidirect
226. C₂²×Q₈	C₂³×C₁₉	semidirect
229. C₂²×D₄	D₄×C₁₉	semidirect
234. C₂²×D₄	C₂³×C₁₉	semidirect
235. C₂²×D₄	C₂³×C₁₉	semidirect
236. C₂²×D₄	C₂³×C₁₉	semidirect
237. C₂²×D₄	C₂³×C₁₉	semidirect
238. C₂²×D₄	C₂³×C₁₉	semidirect
240. C₂³×C₄	C₂³×C₁₉	semidirect
241. C₂³×C₄	C₂³×C₁₉	semidirect
242. C₂³×C₄	C₂³×C₁₉	semidirect
243. C₄⋊Q₈	C₂³×C₁₉	semidirect
244. #127	C₂³×C₁₉	semidirect
245. #124	C₂³×C₁₉	semidirect
246. #123	C₂³×C₁₉	semidirect
247. #123	C₂³×C₁₉	semidirect
248. C₂²⋊Q₈	C₂³×C₁₉	semidirect
249. #121	C₂³×C₁₉	semidirect
250. #121	C₂³×C₁₉	semidirect
251. #121	C₂³×C₁₉	semidirect
252. #120	C₂³×C₁₉	semidirect
253. #120	C₂³×C₁₉	semidirect
254. C₄×D₄	C₂³×C₁₉	semidirect
255. C₄×D₄	C₂³×C₁₉	semidirect
256. #117	C₂³×C₁₉	semidirect
257. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
258. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
260. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
261. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
262. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
263. C₂×C₄²	C₂³×C₁₉	semidirect
264. C₁₉	#62842	direct (N × H)
268. C₂⁴	C₂×D₄×C₁₉	semidirect
286. C₂×D₄	C₂×D₄×C₁₉	semidirect
287. C₂×D₄	C₂×D₄×C₁₉	semidirect
297. C₂²×C₄	C₂×D₄×C₁₉	semidirect

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
C₁₉×#3496	2
C₁₉×#3485	2
C₁₉×#3484	2
C₁₉×#3449	2
C₂×C₁₉×#534	2
C₂×C₁₉×#518	2
#62842	19

Subgroups — C19×#62842 #18068801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62842 #18068801