Subgroups — C₂×C₁₉×#2584 #18040851

Order 4864.

2574 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2584	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₉×#398	C₂	1	2	yes	maximal
5	C₂×C₁₉×#395	C₂	1	2	yes	maximal
6	C₂×C₁₉×#389	C₂	1	2	yes	maximal
7	C₂×C₁₉×#389	C₂	1	4	yes	maximal
8	C₂×C₁₉×#389	C₂	1	2	yes	maximal
9	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#125	—	2	8	no	—
12	C₂×C₁₉×#125	C₂²	1	8	yes	—
13	C₂×C₄×Q₈×C₁₉	—	2	8	no	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	8	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#398	C₂²	1	16	yes	—
28	C₁₉×#395	C₂²	1	16	yes	—
29	C₁₉×#389	C₂²	1	16	yes	—
30	C₁₉×#389	C₂²	1	16	yes	—
31	C₁₉×#389	C₂²	1	32	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
33	C₂×C₁₉×#95	C₂²	1	2	yes	—
34	C₂×C₁₉×#95	C₂²	1	4	yes	—
35	C₂×C₁₉×#95	C₂²	1	4	yes	—
36	C₂²×Q₈×C₁₉	—	2	4	no	—
37	C₂²×Q₈×C₁₉	—	2	8	no	—
38	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₁₉×#125	—	2	32	no	—
48	C₄×Q₈×C₁₉	—	2	32	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
56	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
57	C₂×C₄⋊C₄×C₁₉	Q₈	1	16	yes	complemented
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
67	C₂×C₄²×C₁₉	—	2	8	no	—
68	C₂×C₄²×C₁₉	—	4	4	no	—
69	C₂×C₄²×C₁₉	D₄	1	8	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
73	C₁₉×#95	C₂³	1	8	yes	—
74	C₁₉×#95	C₂³	1	16	yes	—
75	C₁₉×#95	C₂³	1	16	yes	—
76	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
77	C₂×Q₈×C₁₉	—	2	32	no	—
78	C₂×Q₈×C₁₉	—	2	8	no	—
79	C₂×Q₈×C₁₉	—	2	16	no	—
80	C₂²×C₄×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	—	2	8	no	—
82	C₂²×C₄×C₁₉	—	2	4	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	8	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	8	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₉	C₂×Q₈	1	16	yes	—
99	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
100	C₂²×C₄×C₁₉	#41	1	8	yes	—
101	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
109	C₄⋊C₄×C₁₉	—	2	16	no	—
110	C₄⋊C₄×C₁₉	—	2	8	no	—
111	C₄⋊C₄×C₁₉	—	2	16	no	—
112	C₄⋊C₄×C₁₉	—	2	16	no	—
113	C₄⋊C₄×C₁₉	—	2	8	no	—
114	C₄⋊C₄×C₁₉	—	2	8	no	—
115	C₄⋊C₄×C₁₉	—	2	32	no	—
116	C₄⋊C₄×C₁₉	—	4	16	no	—
117	C₄⋊C₄×C₁₉	C₂×Q₈	1	32	yes	complemented
118	C₄²×C₁₉	—	2	16	no	—
119	C₄²×C₁₉	—	4	8	no	—
120	C₄²×C₁₉	C₂×D₄	1	16	yes	—
121	C₂×#2584	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
123	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
124	C₂³×C₁₉	C₂×#41	1	4	yes	—
125	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
126	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
127	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
128	Q₈×C₁₉	—	2	32	no	—
129	C₂×C₄×C₁₉	—	2	8	no	—
130	C₂×C₄×C₁₉	—	2	16	no	—
131	C₂×C₄×C₁₉	—	2	8	no	—
132	C₂×C₄×C₁₉	—	2	32	no	—
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	2	8	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	8	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	4	no	—
141	C₂×C₄×C₁₉	—	2	4	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	8	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	4	8	no	—
149	C₂×C₄×C₁₉	—	4	8	no	—
150	C₂×C₄×C₁₉	—	4	8	no	—
151	C₂×C₄×C₁₉	C₄⋊Q₈	1	16	yes	—
152	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₁₉	C₂²×Q₈	1	16	yes	—
156	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
157	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
158	C₂²×#125	C₂×C₁₉	1	1	yes	characteristic
159	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
160	#2584	C₂×C₁₉	1	16	yes	direct product factor
161	C₂×#398	C₂×C₁₉	1	2	yes	—
162	C₂×#395	C₂×C₁₉	1	2	yes	—
163	C₂×#389	C₂×C₁₉	1	2	yes	—
164	C₂×#389	C₂×C₁₉	1	4	yes	—
165	C₂×#389	C₂×C₁₉	1	2	yes	—
166	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
167	C₂²×C₁₉	#525	1	4	yes	—
168	C₂²×C₁₉	C₂×C₄⋊Q₈	1	4	yes	—
169	C₂²×C₁₉	#537	1	4	yes	—
170	C₂²×C₁₉	#554	1	8	yes	—
171	C₂²×C₁₉	#557	1	8	yes	—
172	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
173	C₂²×C₁₉	C₂³×Q₈	1	2	yes	—
174	C₂²×C₁₉	C₂²×#41	1	2	yes	—
175	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
176	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
177	C₄×C₁₉	—	2	4	no	—
178	C₄×C₁₉	—	2	8	no	—
179	C₄×C₁₉	—	2	4	no	—
180	C₄×C₁₉	—	2	16	no	—
181	C₄×C₁₉	—	4	4	no	—
182	C₄×C₁₉	—	4	4	no	—
183	C₄×C₁₉	—	4	4	no	—
184	C₄×C₁₉	C₂×C₄⋊Q₈	1	8	yes	—
185	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
186	C₂×#125	—	2	8	no	—
187	C₂×#125	C₂²×C₁₉	1	8	yes	—
188	C₂×C₄×Q₈	—	2	8	no	—
189	C₂×C₄×Q₈	C₂²×C₁₉	1	8	yes	—
190	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
191	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
192	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
193	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
199	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
200	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
201	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
202	#398	C₂²×C₁₉	1	16	yes	—
203	#395	C₂²×C₁₉	1	16	yes	—
204	#389	C₂²×C₁₉	1	16	yes	—
205	#389	C₂²×C₁₉	1	32	yes	—
206	#389	C₂²×C₁₉	1	16	yes	—
207	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
208	C₂×#95	C₂²×C₁₉	1	2	yes	—
209	C₂×#95	C₂²×C₁₉	1	4	yes	—
210	C₂×#95	C₂²×C₁₉	1	4	yes	—
211	C₂×C₁₉	#2584	1	8	yes	direct product factor
212	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
213	C₂×C₁₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic
214	C₂×C₁₉	C₂×#537	1	1	yes	characteristic
215	C₂×C₁₉	C₂×#554	1	2	yes	—
216	C₂×C₁₉	C₂×#557	1	2	yes	—
217	C₂²×Q₈	—	2	4	no	—
218	C₂²×Q₈	—	2	8	no	—
219	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
220	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
221	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
222	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
223	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
224	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
226	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
227	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
228	#125	—	2	32	no	—
229	C₄×Q₈	—	2	32	no	—
230	C₂×C₄⋊C₄	—	2	8	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	—	2	8	no	—
233	C₂×C₄⋊C₄	—	2	8	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	16	no	—
237	C₂×C₄⋊C₄	—	4	8	no	—
238	C₂×C₄⋊C₄	Q₈×C₁₉	1	16	yes	complemented
239	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
245	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
248	C₂×C₄²	—	2	8	no	—
249	C₂×C₄²	—	4	4	no	—
250	C₂×C₄²	D₄×C₁₉	1	8	yes	—
251	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
252	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
253	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
254	#95	C₂³×C₁₉	1	8	yes	—
255	#95	C₂³×C₁₉	1	16	yes	—
256	#95	C₂³×C₁₉	1	16	yes	—
257	C₁₉	C₂×#2584	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
259	C₂×Q₈	—	2	32	no	—
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	—	2	16	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
278	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
279	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
280	C₂²×C₄	C₂×Q₈×C₁₉	1	16	yes	—
281	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
282	C₂²×C₄	#41×C₁₉	1	8	yes	—
283	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
284	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
288	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
289	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
290	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	2	16	no	—
294	C₄⋊C₄	—	2	16	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	32	no	—
298	C₄⋊C₄	—	4	16	no	—
299	C₄⋊C₄	C₂×Q₈×C₁₉	1	32	yes	complemented
300	C₄²	—	2	16	no	—
301	C₄²	—	4	8	no	—
302	C₄²	C₂×D₄×C₁₉	1	16	yes	—
303	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
304	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
305	C₂³	C₂×#41×C₁₉	1	4	yes	—
306	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
307	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
308	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
309	Q₈	—	2	32	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	16	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	32	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	C₁₉×C₄⋊Q₈	1	16	yes	—
333	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
334	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
335	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
336	C₂×C₄	C₂²×Q₈×C₁₉	1	16	yes	—
337	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
338	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
339	C₂²	C₁₉×#525	1	4	yes	—
340	C₂²	C₂×C₁₉×C₄⋊Q₈	1	4	yes	—
341	C₂²	C₁₉×#537	1	4	yes	—
342	C₂²	C₁₉×#554	1	8	yes	—
343	C₂²	C₁₉×#557	1	8	yes	—
344	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
345	C₂²	C₂³×Q₈×C₁₉	1	2	yes	—
346	C₂²	C₂²×#41×C₁₉	1	2	yes	—
347	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	2	8	no	—
351	C₄	—	2	4	no	—
352	C₄	—	2	16	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	—	4	4	no	—
356	C₄	C₂×C₁₉×C₄⋊Q₈	1	8	yes	—
357	C₂	C₁₉×#2584	1	8	yes	direct product factor
358	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
359	C₂	C₂²×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
360	C₂	C₂×C₁₉×#537	1	1	yes	characteristic
361	C₂	C₂×C₁₉×#554	1	2	yes	—
362	C₂	C₂×C₁₉×#557	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₉×#2584	C₂	direct (N × H)
57. C₂×C₄⋊C₄×C₁₉	Q₈	semidirect
117. C₄⋊C₄×C₁₉	C₂×Q₈	semidirect
121. C₂×#2584	C₁₉	direct (N × H)
160. #2584	C₂×C₁₉	direct (N × H)
211. C₂×C₁₉	#2584	direct (N × H)
238. C₂×C₄⋊C₄	Q₈×C₁₉	semidirect
257. C₁₉	C₂×#2584	direct (N × H)
299. C₄⋊C₄	C₂×Q₈×C₁₉	semidirect
357. C₂	C₁₉×#2584	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×#125	2
C₂²×C₄×Q₈×C₁₉	2
C₁₉×#2584	2
C₂×C₁₉×#398	2
C₂×C₁₉×#395	2
C₂×C₁₉×#389	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₂×#2584	19

Subgroups — C2×C19×#2584 #18040851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2584 #18040851