Subgroups — C₂×C₄×C₁₉×H(5,𝔽₂) #18068608

Order 4864.

12378 conjugacy classes of subgroups.

The subgroup lattice has 248 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	C₄×C₁₉×H(5,𝔽₂)	C₂	1	32	yes	maximal, direct product factor
3	C₂×C₁₉×#520	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₉×#518	C₂	1	9	yes	maximal, complemented
5	C₂×C₄×#41×C₁₉	C₂	1	6	yes	maximal, complemented
6	C₂²×C₄×D₄×C₁₉	C₂	1	9	yes	maximal, complemented
7	C₂×C₁₉×H(5,𝔽₂)	C₄	1	32	yes	direct product factor
8	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	16	yes	—
9	C₂²×#41×C₁₉	C₂²	1	6	yes	—
10	C₂³×D₄×C₁₉	C₂²	1	9	yes	—
11	C₂⁴×C₄×C₁₉	C₂²	1	6	yes	complemented
12	C₁₉×#520	C₂²	1	96	yes	complemented
13	C₁₉×#518	C₂²	1	144	yes	complemented
14	C₄×#41×C₁₉	C₂²	1	96	yes	complemented
15	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
16	C₂×C₄×Q₈×C₁₉	C₂²	1	6	yes	complemented
17	C₂×C₄×D₄×C₁₉	C₂²	1	18	yes	complemented
18	C₂×C₄×D₄×C₁₉	C₂²	1	18	yes	complemented
19	C₂×C₄×D₄×C₁₉	C₂²	1	36	yes	complemented
20	C₂×C₄×D₄×C₁₉	C₂²	1	144	yes	complemented
21	C₂×C₁₉×#117	C₂²	1	18	yes	complemented
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	9	yes	complemented
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	18	yes	complemented
24	C₂²×C₄²×C₁₉	C₂²	1	9	yes	complemented
25	C₂⁵×C₁₉	C₂³	1	6	yes	—
26	C₁₉×H(5,𝔽₂)	C₂×C₄	1	256	yes	direct product factor
27	C₂×#41×C₁₉	C₂×C₄	1	96	yes	complemented
28	C₂×#41×C₁₉	C₂³	1	48	yes	—
29	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
30	C₂²×D₄×C₁₉	C₂×C₄	1	144	yes	complemented
31	C₂²×D₄×C₁₉	C₂³	1	18	yes	—
32	C₂²×D₄×C₁₉	C₂³	1	72	yes	—
33	C₂³×C₄×C₁₉	—	4	24	no	—
34	C₂³×C₄×C₁₉	C₂³	1	9	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	9	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	18	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	9	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	48	yes	complemented
39	C₄×Q₈×C₁₉	C₂³	1	16	yes	complemented
40	C₄×Q₈×C₁₉	C₂³	1	48	yes	complemented
41	C₄×D₄×C₁₉	C₂³	1	144	yes	complemented
42	C₄×D₄×C₁₉	C₂³	1	288	yes	complemented
43	C₄×D₄×C₁₉	C₂³	1	144	yes	complemented
44	C₁₉×#117	C₂³	1	144	yes	complemented
45	C₂×C₄⋊C₄×C₁₉	C₂³	1	18	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂³	1	72	yes	complemented
48	C₂×C₂²⋊C₄×C₁₉	C₂³	1	36	yes	—
49	C₂×C₂²⋊C₄×C₁₉	C₂³	1	144	yes	complemented
50	C₂×C₄²×C₁₉	C₂³	1	18	yes	—
51	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
52	C₂×C₄²×C₁₉	C₂³	1	72	yes	complemented
53	C₂⁴×C₁₉	—	4	12	no	—
54	C₂⁴×C₁₉	—	4	12	no	—
55	C₂⁴×C₁₉	C₂²×C₄	1	48	yes	complemented
56	C₂⁴×C₁₉	C₂⁴	1	9	yes	—
57	C₂⁴×C₁₉	C₂⁴	1	24	yes	—
58	#41×C₁₉	C₂²×C₄	1	384	yes	complemented
59	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	complemented
60	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
61	C₂×D₄×C₁₉	C₂²×C₄	1	144	yes	complemented
62	C₂×D₄×C₁₉	C₂²×C₄	1	576	yes	complemented
63	C₂×D₄×C₁₉	C₂⁴	1	72	yes	—
64	C₂²×C₄×C₁₉	—	2	36	no	—
65	C₂²×C₄×C₁₉	—	4	96	no	—
66	C₂²×C₄×C₁₉	—	4	36	no	—
67	C₂²×C₄×C₁₉	—	4	18	no	—
68	C₂²×C₄×C₁₉	C₂²×C₄	1	72	yes	complemented
69	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
70	C₂²×C₄×C₁₉	C₂⁴	1	9	yes	—
71	C₂²×C₄×C₁₉	C₂⁴	1	36	yes	—
72	C₂²×C₄×C₁₉	C₂⁴	1	36	yes	—
73	C₂²×C₄×C₁₉	C₂⁴	1	72	yes	—
74	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
75	C₂²×C₄×C₁₉	C₂⁴	1	36	yes	—
76	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
77	C₄⋊C₄×C₁₉	C₂⁴	1	72	yes	—
78	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
79	C₂²⋊C₄×C₁₉	C₂⁴	1	144	yes	—
80	C₄²×C₁₉	C₂⁴	1	24	yes	—
81	C₄²×C₁₉	C₂⁴	1	72	yes	—
82	C₂×C₄×H(5,𝔽₂)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂³×C₁₉	—	2	18	no	—
84	C₂³×C₁₉	—	2	18	no	—
85	C₂³×C₁₉	—	4	24	no	—
86	C₂³×C₁₉	—	4	96	no	—
87	C₂³×C₁₉	—	4	24	no	—
88	C₂³×C₁₉	C₂³×C₄	1	36	yes	—
89	C₂³×C₁₉	C₂³×C₄	1	96	yes	complemented
90	C₂³×C₁₉	C₂⁵	1	18	yes	—
91	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
92	Q₈×C₁₉	C₂³×C₄	1	32	yes	complemented
93	D₄×C₁₉	C₂³×C₄	1	288	yes	complemented
94	C₂×C₄×C₁₉	—	2	18	no	—
95	C₂×C₄×C₁₉	—	2	12	no	—
96	C₂×C₄×C₁₉	—	2	72	no	—
97	C₂×C₄×C₁₉	—	4	72	no	—
98	C₂×C₄×C₁₉	—	4	36	no	—
99	C₂×C₄×C₁₉	C₂³×C₄	1	24	yes	—
100	C₂×C₄×C₁₉	C₂³×C₄	1	144	yes	complemented
101	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	direct product factor
102	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
103	C₂×C₄×C₁₉	C₂⁵	1	18	yes	—
104	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
105	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
106	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
107	C₄×H(5,𝔽₂)	C₂×C₁₉	1	32	yes	direct product factor
108	C₂×#520	C₂×C₁₉	1	6	yes	complemented
109	C₂×#518	C₂×C₁₉	1	9	yes	complemented
110	C₂×C₄×#41	C₂×C₁₉	1	6	yes	complemented
111	C₂²×C₄×D₄	C₂×C₁₉	1	9	yes	complemented
112	C₂²×C₁₉	—	2	18	no	—
113	C₂²×C₁₉	—	2	18	no	—
114	C₂²×C₁₉	—	2	72	no	—
115	C₂²×C₁₉	—	4	96	no	—
116	C₂²×C₁₉	C₂⁴×C₄	1	36	yes	—
117	C₂²×C₁₉	C₂⁴×C₄	1	2	yes	—
118	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
119	C₂²×C₁₉	#585	1	2	yes	—
120	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
121	C₄×C₁₉	—	2	18	no	—
122	C₄×C₁₉	—	2	12	no	—
123	C₄×C₁₉	C₂⁴×C₄	1	24	yes	—
124	C₄×C₁₉	C₂×H(5,𝔽₂)	1	4	yes	direct product factor
125	C₂×H(5,𝔽₂)	C₄×C₁₉	1	32	yes	direct product factor
126	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	16	yes	—
127	C₂²×#41	C₂²×C₁₉	1	6	yes	—
128	C₂³×D₄	C₂²×C₁₉	1	9	yes	—
129	C₂⁴×C₄	C₂²×C₁₉	1	6	yes	complemented
130	#520	C₂²×C₁₉	1	96	yes	complemented
131	#518	C₂²×C₁₉	1	144	yes	complemented
132	C₄×#41	C₂²×C₁₉	1	96	yes	complemented
133	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
134	C₂×C₄×Q₈	C₂²×C₁₉	1	6	yes	complemented
135	C₂×C₄×D₄	C₂²×C₁₉	1	18	yes	complemented
136	C₂×C₄×D₄	C₂²×C₁₉	1	36	yes	complemented
137	C₂×C₄×D₄	C₂²×C₁₉	1	18	yes	complemented
138	C₂×C₄×D₄	C₂²×C₁₉	1	144	yes	complemented
139	C₂×#117	C₂²×C₁₉	1	18	yes	complemented
140	C₂²×C₄⋊C₄	C₂²×C₁₉	1	9	yes	complemented
141	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	18	yes	complemented
142	C₂²×C₄²	C₂²×C₁₉	1	9	yes	complemented
143	C₂×C₁₉	—	2	36	no	—
144	C₂×C₁₉	C₄×H(5,𝔽₂)	1	4	yes	direct product factor
145	C₂×C₁₉	C₂⁵×C₄	1	1	yes	characteristic
146	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
147	C₂×C₁₉	C₂×#585	1	1	yes	characteristic
148	C₂⁵	C₂³×C₁₉	1	6	yes	—
149	H(5,𝔽₂)	C₂×C₄×C₁₉	1	256	yes	direct product factor
150	C₂×#41	C₂×C₄×C₁₉	1	96	yes	complemented
151	C₂×#41	C₂³×C₁₉	1	48	yes	—
152	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
153	C₂²×D₄	C₂×C₄×C₁₉	1	144	yes	complemented
154	C₂²×D₄	C₂³×C₁₉	1	18	yes	—
155	C₂²×D₄	C₂³×C₁₉	1	72	yes	—
156	C₂³×C₄	—	4	24	no	—
157	C₂³×C₄	C₂³×C₁₉	1	9	yes	—
158	C₂³×C₄	C₂³×C₁₉	1	9	yes	—
159	C₂³×C₄	C₂³×C₁₉	1	18	yes	—
160	C₂³×C₄	C₂³×C₁₉	1	9	yes	—
161	C₂³×C₄	C₂³×C₁₉	1	48	yes	complemented
162	C₄×Q₈	C₂³×C₁₉	1	16	yes	complemented
163	C₄×Q₈	C₂³×C₁₉	1	48	yes	complemented
164	C₄×D₄	C₂³×C₁₉	1	144	yes	complemented
165	C₄×D₄	C₂³×C₁₉	1	288	yes	complemented
166	C₄×D₄	C₂³×C₁₉	1	144	yes	complemented
167	#117	C₂³×C₁₉	1	144	yes	complemented
168	C₂×C₄⋊C₄	C₂³×C₁₉	1	18	yes	—
169	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
170	C₂×C₄⋊C₄	C₂³×C₁₉	1	72	yes	complemented
171	C₂×C₂²⋊C₄	C₂³×C₁₉	1	36	yes	—
172	C₂×C₂²⋊C₄	C₂³×C₁₉	1	144	yes	complemented
173	C₂×C₄²	C₂³×C₁₉	1	18	yes	—
174	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
175	C₂×C₄²	C₂³×C₁₉	1	72	yes	complemented
176	C₁₉	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, direct product factor, Sylow
177	C₂⁴	—	4	12	no	—
178	C₂⁴	—	4	12	no	—
179	C₂⁴	C₂²×C₄×C₁₉	1	48	yes	complemented
180	C₂⁴	C₂⁴×C₁₉	1	9	yes	—
181	C₂⁴	C₂⁴×C₁₉	1	24	yes	—
182	#41	C₂²×C₄×C₁₉	1	384	yes	complemented
183	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	complemented
184	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
185	C₂×D₄	C₂²×C₄×C₁₉	1	144	yes	complemented
186	C₂×D₄	C₂²×C₄×C₁₉	1	576	yes	complemented
187	C₂×D₄	C₂⁴×C₁₉	1	72	yes	—
188	C₂²×C₄	—	2	36	no	—
189	C₂²×C₄	—	4	96	no	—
190	C₂²×C₄	—	4	36	no	—
191	C₂²×C₄	—	4	18	no	—
192	C₂²×C₄	C₂²×C₄×C₁₉	1	72	yes	complemented
193	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
194	C₂²×C₄	C₂⁴×C₁₉	1	9	yes	—
195	C₂²×C₄	C₂⁴×C₁₉	1	36	yes	—
196	C₂²×C₄	C₂⁴×C₁₉	1	36	yes	—
197	C₂²×C₄	C₂⁴×C₁₉	1	72	yes	—
198	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
199	C₂²×C₄	C₂⁴×C₁₉	1	36	yes	—
200	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
201	C₄⋊C₄	C₂⁴×C₁₉	1	72	yes	—
202	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
203	C₂²⋊C₄	C₂⁴×C₁₉	1	144	yes	—
204	C₄²	C₂⁴×C₁₉	1	24	yes	—
205	C₄²	C₂⁴×C₁₉	1	72	yes	—
206	C₂³	—	2	18	no	—
207	C₂³	—	2	18	no	—
208	C₂³	—	4	24	no	—
209	C₂³	—	4	96	no	—
210	C₂³	—	4	24	no	—
211	C₂³	C₂³×C₄×C₁₉	1	36	yes	—
212	C₂³	C₂³×C₄×C₁₉	1	96	yes	complemented
213	C₂³	C₂⁵×C₁₉	1	18	yes	—
214	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
215	Q₈	C₂³×C₄×C₁₉	1	32	yes	complemented
216	D₄	C₂³×C₄×C₁₉	1	288	yes	complemented
217	C₂×C₄	—	2	18	no	—
218	C₂×C₄	—	2	12	no	—
219	C₂×C₄	—	2	72	no	—
220	C₂×C₄	—	4	72	no	—
221	C₂×C₄	—	4	36	no	—
222	C₂×C₄	C₂³×C₄×C₁₉	1	24	yes	—
223	C₂×C₄	C₂³×C₄×C₁₉	1	144	yes	complemented
224	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	direct product factor
225	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
226	C₂×C₄	C₂⁵×C₁₉	1	18	yes	—
227	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
228	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
229	C₂²	—	2	72	no	—
230	C₂²	—	2	18	no	—
231	C₂²	—	2	18	no	—
232	C₂²	—	4	96	no	—
233	C₂²	C₂⁴×C₄×C₁₉	1	36	yes	—
234	C₂²	C₂⁴×C₄×C₁₉	1	2	yes	—
235	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
236	C₂²	C₁₉×#585	1	2	yes	—
237	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
238	C₄	—	2	18	no	—
239	C₄	—	2	12	no	—
240	C₄	C₂⁴×C₄×C₁₉	1	24	yes	—
241	C₄	C₂×C₁₉×H(5,𝔽₂)	1	4	yes	direct product factor
242	C₂	—	2	36	no	—
243	C₂	C₄×C₁₉×H(5,𝔽₂)	1	4	yes	direct product factor
244	C₂	C₂⁵×C₄×C₁₉	1	1	yes	characteristic
245	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂	C₂×C₁₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂	C₂⁵×C₄×C₁₉
Frattini, cosocle	C₂²	C₂⁶×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂²×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₉×H(5,𝔽₂)	C₂	direct (N × H)
3. C₂×C₁₉×#520	C₂	semidirect
4. C₂×C₁₉×#518	C₂	semidirect
5. C₂×C₄×#41×C₁₉	C₂	semidirect
6. C₂²×C₄×D₄×C₁₉	C₂	semidirect
7. C₂×C₁₉×H(5,𝔽₂)	C₄	direct (N × H)
11. C₂⁴×C₄×C₁₉	C₂²	semidirect
12. C₁₉×#520	C₂²	semidirect
13. C₁₉×#518	C₂²	semidirect
14. C₄×#41×C₁₉	C₂²	semidirect
15. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
16. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
17. C₂×C₄×D₄×C₁₉	C₂²	semidirect
18. C₂×C₄×D₄×C₁₉	C₂²	semidirect
19. C₂×C₄×D₄×C₁₉	C₂²	semidirect
20. C₂×C₄×D₄×C₁₉	C₂²	semidirect
21. C₂×C₁₉×#117	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
23. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
24. C₂²×C₄²×C₁₉	C₂²	semidirect
26. C₁₉×H(5,𝔽₂)	C₂×C₄	direct (N × H)
27. C₂×#41×C₁₉	C₂×C₄	semidirect
30. C₂²×D₄×C₁₉	C₂×C₄	semidirect
38. C₂³×C₄×C₁₉	C₂³	semidirect
39. C₄×Q₈×C₁₉	C₂³	semidirect
40. C₄×Q₈×C₁₉	C₂³	semidirect
41. C₄×D₄×C₁₉	C₂³	semidirect
42. C₄×D₄×C₁₉	C₂³	semidirect
43. C₄×D₄×C₁₉	C₂³	semidirect
44. C₁₉×#117	C₂³	semidirect
47. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
49. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
52. C₂×C₄²×C₁₉	C₂³	semidirect
55. C₂⁴×C₁₉	C₂²×C₄	semidirect
58. #41×C₁₉	C₂²×C₄	semidirect
59. C₂×Q₈×C₁₉	C₂²×C₄	semidirect
61. C₂×D₄×C₁₉	C₂²×C₄	semidirect
62. C₂×D₄×C₁₉	C₂²×C₄	semidirect
68. C₂²×C₄×C₁₉	C₂²×C₄	semidirect
82. C₂×C₄×H(5,𝔽₂)	C₁₉	direct (N × H)
89. C₂³×C₁₉	C₂³×C₄	semidirect
92. Q₈×C₁₉	C₂³×C₄	semidirect
93. D₄×C₁₉	C₂³×C₄	semidirect
100. C₂×C₄×C₁₉	C₂³×C₄	semidirect
101. C₂×C₄×C₁₉	H(5,𝔽₂)	direct (N × H)
107. C₄×H(5,𝔽₂)	C₂×C₁₉	direct (N × H)
108. C₂×#520	C₂×C₁₉	semidirect
109. C₂×#518	C₂×C₁₉	semidirect
110. C₂×C₄×#41	C₂×C₁₉	semidirect
111. C₂²×C₄×D₄	C₂×C₁₉	semidirect
124. C₄×C₁₉	C₂×H(5,𝔽₂)	direct (N × H)
125. C₂×H(5,𝔽₂)	C₄×C₁₉	direct (N × H)
129. C₂⁴×C₄	C₂²×C₁₉	semidirect
130. #520	C₂²×C₁₉	semidirect
131. #518	C₂²×C₁₉	semidirect
132. C₄×#41	C₂²×C₁₉	semidirect
133. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
134. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
135. C₂×C₄×D₄	C₂²×C₁₉	semidirect
136. C₂×C₄×D₄	C₂²×C₁₉	semidirect
137. C₂×C₄×D₄	C₂²×C₁₉	semidirect
138. C₂×C₄×D₄	C₂²×C₁₉	semidirect
139. C₂×#117	C₂²×C₁₉	semidirect
140. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
141. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
142. C₂²×C₄²	C₂²×C₁₉	semidirect
144. C₂×C₁₉	C₄×H(5,𝔽₂)	direct (N × H)
149. H(5,𝔽₂)	C₂×C₄×C₁₉	direct (N × H)
150. C₂×#41	C₂×C₄×C₁₉	semidirect
153. C₂²×D₄	C₂×C₄×C₁₉	semidirect
161. C₂³×C₄	C₂³×C₁₉	semidirect
162. C₄×Q₈	C₂³×C₁₉	semidirect
163. C₄×Q₈	C₂³×C₁₉	semidirect
164. C₄×D₄	C₂³×C₁₉	semidirect
165. C₄×D₄	C₂³×C₁₉	semidirect
166. C₄×D₄	C₂³×C₁₉	semidirect
167. #117	C₂³×C₁₉	semidirect
170. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
172. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
175. C₂×C₄²	C₂³×C₁₉	semidirect
176. C₁₉	C₂×C₄×H(5,𝔽₂)	direct (N × H)
179. C₂⁴	C₂²×C₄×C₁₉	semidirect
182. #41	C₂²×C₄×C₁₉	semidirect
183. C₂×Q₈	C₂²×C₄×C₁₉	semidirect
185. C₂×D₄	C₂²×C₄×C₁₉	semidirect
186. C₂×D₄	C₂²×C₄×C₁₉	semidirect
192. C₂²×C₄	C₂²×C₄×C₁₉	semidirect
212. C₂³	C₂³×C₄×C₁₉	semidirect
215. Q₈	C₂³×C₄×C₁₉	semidirect
216. D₄	C₂³×C₄×C₁₉	semidirect
223. C₂×C₄	C₂³×C₄×C₁₉	semidirect
224. C₂×C₄	C₁₉×H(5,𝔽₂)	direct (N × H)
241. C₄	C₂×C₁₉×H(5,𝔽₂)	direct (N × H)
243. C₂	C₄×C₁₉×H(5,𝔽₂)	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
C₄×C₁₉×H(5,𝔽₂)	2
C₂×C₁₉×#520	2
C₂×C₁₉×#518	2
C₂×C₄×#41×C₁₉	2
C₂²×C₄×D₄×C₁₉	2
C₂×C₄×H(5,𝔽₂)	19

Subgroups — C2×C4×C19×H(5,𝔽2) #18068608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₉×H(5,𝔽₂) #18068608