Subgroups — C₂×C₁₉×#3484 #18068722

Order 4864.

14438 conjugacy classes of subgroups.

The subgroup lattice has 580 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, complemented
2	C₂⁴×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3484	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₁₉×#546	C₂	1	8	yes	maximal, complemented
5	C₂×D₄²×C₁₉	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₉×#535	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#534	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₉×#525	C₂	1	2	yes	maximal, complemented
9	C₂²×C₁₉×#120	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁶×C₁₉	C₂²	1	2	yes	complemented
12	C₂×C₁₉×H(5,𝔽₂)	—	2	16	no	—
13	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	16	yes	complemented
14	C₂²×#41×C₁₉	C₂²	1	2	yes	complemented
15	C₂²×#41×C₁₉	C₂²	1	4	yes	complemented
16	C₂³×D₄×C₁₉	—	2	16	no	—
17	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₉	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₁₉	C₂²	1	8	yes	complemented
21	C₂³×D₄×C₁₉	C₂²	1	4	yes	complemented
22	C₂³×D₄×C₁₉	C₂²	1	4	yes	complemented
23	C₂³×D₄×C₁₉	C₂²	1	16	yes	complemented
24	C₂³×D₄×C₁₉	C₂²	1	8	yes	complemented
25	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#546	C₂²	1	128	yes	complemented
27	D₄²×C₁₉	C₂²	1	128	yes	complemented
28	C₁₉×#535	C₂²	1	32	yes	complemented
29	C₁₉×#534	C₂²	1	64	yes	complemented
30	C₂×C₁₉×#127	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#124	C₂²	1	4	yes	complemented
32	C₁₉×#525	C₂²	1	32	yes	complemented
33	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
34	C₂×C₁₉×#123	C₂²	1	8	yes	complemented
35	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
36	C₂×C₁₉×#121	C₂²	1	4	yes	complemented
37	C₂×C₁₉×#121	C₂²	1	16	yes	complemented
38	C₂×C₁₉×#121	C₂²	1	8	yes	complemented
39	C₂×C₁₉×#120	C₂²	1	4	yes	complemented
40	C₂×C₁₉×#120	C₂²	1	8	yes	complemented
41	C₂×C₁₉×#120	C₂²	1	16	yes	complemented
42	C₂×C₁₉×#120	C₂²	1	8	yes	complemented
43	C₂×C₁₉×#120	C₂²	1	64	yes	complemented
44	C₁₉×#518	C₂²	1	16	yes	complemented
45	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
46	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
47	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
48	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
49	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	complemented
50	C₂⁵×C₁₉	—	2	16	no	—
51	C₂⁵×C₁₉	—	4	16	no	—
52	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
53	C₂⁵×C₁₉	C₂³	1	8	yes	—
54	C₂⁵×C₁₉	C₂³	1	2	yes	—
55	C₂⁵×C₁₉	C₂³	1	2	yes	—
56	C₂⁵×C₁₉	C₂³	1	16	yes	complemented
57	C₂⁵×C₁₉	C₂³	1	4	yes	complemented
58	C₁₉×H(5,𝔽₂)	—	2	128	no	—
59	C₂×#41×C₁₉	—	2	32	no	—
60	C₂×#41×C₁₉	—	2	16	no	—
61	C₂×#41×C₁₉	C₂³	1	16	yes	complemented
62	C₂×#41×C₁₉	C₂³	1	32	yes	complemented
63	C₂²×Q₈×C₁₉	C₂³	1	2	yes	complemented
64	C₂²×D₄×C₁₉	—	2	16	no	—
65	C₂²×D₄×C₁₉	—	2	32	no	—
66	C₂²×D₄×C₁₉	—	2	64	no	—
67	C₂²×D₄×C₁₉	—	2	128	no	—
68	C₂²×D₄×C₁₉	—	2	32	no	—
69	C₂²×D₄×C₁₉	—	2	8	no	—
70	C₂²×D₄×C₁₉	—	4	32	no	—
71	C₂²×D₄×C₁₉	D₄	1	16	yes	complemented
72	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
73	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
74	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
75	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
76	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
78	C₂²×D₄×C₁₉	C₂³	1	16	yes	complemented
79	C₂²×D₄×C₁₉	C₂³	1	8	yes	complemented
80	C₂²×D₄×C₁₉	C₂³	1	64	yes	complemented
81	C₂²×D₄×C₁₉	C₂³	1	8	yes	complemented
82	C₂²×D₄×C₁₉	C₂³	1	2	yes	complemented
83	C₂²×D₄×C₁₉	C₂³	1	16	yes	complemented
84	C₂²×D₄×C₁₉	C₂³	1	32	yes	complemented
85	C₂²×D₄×C₁₉	C₂³	1	32	yes	complemented
86	C₂²×D₄×C₁₉	C₂³	1	64	yes	complemented
87	C₂³×C₄×C₁₉	—	2	8	no	—
88	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
89	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₉	C₂³	1	8	yes	complemented
92	C₂³×C₄×C₁₉	C₂³	1	4	yes	complemented
93	C₂³×C₄×C₁₉	C₂³	1	4	yes	complemented
94	C₂³×C₄×C₁₉	C₂³	1	8	yes	complemented
95	C₁₉×#127	C₂³	1	32	yes	complemented
96	C₁₉×#124	C₂³	1	32	yes	complemented
97	C₁₉×#123	C₂³	1	32	yes	complemented
98	C₁₉×#123	C₂³	1	64	yes	complemented
99	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
100	C₁₉×#121	C₂³	1	32	yes	complemented
101	C₁₉×#121	C₂³	1	128	yes	complemented
102	C₁₉×#121	C₂³	1	64	yes	complemented
103	C₁₉×#120	C₂³	1	32	yes	complemented
104	C₁₉×#120	C₂³	1	64	yes	complemented
105	C₁₉×#120	C₂³	1	128	yes	complemented
106	C₁₉×#120	C₂³	1	64	yes	complemented
107	C₄×D₄×C₁₉	C₂³	1	64	yes	complemented
108	C₄×D₄×C₁₉	C₂³	1	64	yes	complemented
109	C₁₉×#117	C₂³	1	16	yes	complemented
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	complemented
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	complemented
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	32	yes	complemented
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	64	yes	complemented
116	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	complemented
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	complemented
118	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	complemented
119	C₂×C₄²×C₁₉	C₂³	1	4	yes	complemented
120	C₂⁴×C₁₉	—	2	4	no	—
121	C₂⁴×C₁₉	—	2	8	no	—
122	C₂⁴×C₁₉	—	2	32	no	—
123	C₂⁴×C₁₉	—	2	8	no	—
124	C₂⁴×C₁₉	—	2	64	no	—
125	C₂⁴×C₁₉	—	2	32	no	—
126	C₂⁴×C₁₉	—	2	16	no	—
127	C₂⁴×C₁₉	—	4	8	no	—
128	C₂⁴×C₁₉	—	4	16	no	—
129	C₂⁴×C₁₉	—	4	8	no	—
130	C₂⁴×C₁₉	—	4	64	no	—
131	C₂⁴×C₁₉	—	4	16	no	—
132	C₂⁴×C₁₉	—	4	128	no	—
133	C₂⁴×C₁₉	C₂×D₄	1	16	yes	complemented
134	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
135	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
136	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
137	C₂⁴×C₁₉	C₂⁴	1	32	yes	—
138	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
139	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
140	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
141	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
142	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
143	C₂⁴×C₁₉	C₂⁴	1	16	yes	complemented
144	#41×C₁₉	—	2	128	no	—
145	#41×C₁₉	—	2	64	no	—
146	C₂×Q₈×C₁₉	—	2	8	no	—
147	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	complemented
148	C₂×D₄×C₁₉	—	2	32	no	—
149	C₂×D₄×C₁₉	—	2	16	no	—
150	C₂×D₄×C₁₉	—	2	32	no	—
151	C₂×D₄×C₁₉	—	2	64	no	—
152	C₂×D₄×C₁₉	—	2	128	no	—
153	C₂×D₄×C₁₉	—	2	32	no	—
154	C₂×D₄×C₁₉	—	2	256	no	—
155	C₂×D₄×C₁₉	—	2	128	no	—
156	C₂×D₄×C₁₉	—	2	16	no	—
157	C₂×D₄×C₁₉	—	2	8	no	—
158	C₂×D₄×C₁₉	—	2	32	no	—
159	C₂×D₄×C₁₉	—	4	32	no	—
160	C₂×D₄×C₁₉	—	4	128	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	32	yes	complemented
162	C₂×D₄×C₁₉	C₂×D₄	1	64	yes	complemented
163	C₂×D₄×C₁₉	C₂⁴	1	32	yes	—
164	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
165	C₂×D₄×C₁₉	C₂⁴	1	32	yes	—
166	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
167	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
168	C₂×D₄×C₁₉	C₂⁴	1	32	yes	complemented
169	C₂×D₄×C₁₉	C₂⁴	1	8	yes	complemented
170	C₂×D₄×C₁₉	C₂⁴	1	64	yes	complemented
171	C₂²×C₄×C₁₉	—	2	4	no	—
172	C₂²×C₄×C₁₉	—	2	16	no	—
173	C₂²×C₄×C₁₉	—	2	16	no	—
174	C₂²×C₄×C₁₉	—	2	16	no	—
175	C₂²×C₄×C₁₉	—	2	32	no	—
176	C₂²×C₄×C₁₉	—	4	16	no	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	complemented
178	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
181	C₂²×C₄×C₁₉	C₂⁴	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	4	yes	—
185	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	complemented
186	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	complemented
187	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	complemented
188	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	complemented
189	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	complemented
190	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
191	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
192	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	complemented
193	C₂²⋊C₄×C₁₉	C₂⁴	1	64	yes	complemented
194	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	complemented
195	C₄²×C₁₉	C₂⁴	1	16	yes	complemented
196	C₂×#3484	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₁₉	—	2	32	no	—
198	C₂³×C₁₉	—	2	8	no	—
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	—	2	16	no	—
201	C₂³×C₁₉	—	2	4	no	—
202	C₂³×C₁₉	—	2	4	no	—
203	C₂³×C₁₉	—	2	16	no	—
204	C₂³×C₁₉	—	2	8	no	—
205	C₂³×C₁₉	—	2	64	no	—
206	C₂³×C₁₉	—	2	16	no	—
207	C₂³×C₁₉	—	2	8	no	—
208	C₂³×C₁₉	—	2	16	no	—
209	C₂³×C₁₉	—	2	16	no	—
210	C₂³×C₁₉	—	2	64	no	—
211	C₂³×C₁₉	—	2	32	no	—
212	C₂³×C₁₉	—	4	32	no	—
213	C₂³×C₁₉	—	4	16	no	—
214	C₂³×C₁₉	—	4	32	no	—
215	C₂³×C₁₉	—	4	16	no	—
216	C₂³×C₁₉	—	4	32	no	—
217	C₂³×C₁₉	—	4	128	no	—
218	C₂³×C₁₉	—	4	256	no	—
219	C₂³×C₁₉	—	4	32	no	—
220	C₂³×C₁₉	—	8	32	no	—
221	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
222	C₂³×C₁₉	C₂²×D₄	1	16	yes	—
223	C₂³×C₁₉	C₂²×D₄	1	32	yes	complemented
224	C₂³×C₁₉	H(5,𝔽₂)	1	8	yes	complemented
225	C₂³×C₁₉	C₂⁵	1	8	yes	—
226	C₂³×C₁₉	C₂⁵	1	8	yes	—
227	C₂³×C₁₉	C₂⁵	1	2	yes	—
228	C₂³×C₁₉	C₂⁵	1	8	yes	—
229	C₂³×C₁₉	C₂⁵	1	4	yes	—
230	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
231	Q₈×C₁₉	—	2	16	no	—
232	D₄×C₁₉	—	2	64	no	—
233	D₄×C₁₉	—	2	32	no	—
234	D₄×C₁₉	—	2	64	no	—
235	D₄×C₁₉	—	2	64	no	—
236	D₄×C₁₉	—	2	32	no	—
237	D₄×C₁₉	—	2	16	no	—
238	D₄×C₁₉	—	4	64	no	—
239	D₄×C₁₉	C₂²×D₄	1	64	yes	complemented
240	C₂×C₄×C₁₉	—	2	8	no	—
241	C₂×C₄×C₁₉	—	2	4	no	—
242	C₂×C₄×C₁₉	—	2	8	no	—
243	C₂×C₄×C₁₉	—	2	32	no	—
244	C₂×C₄×C₁₉	—	2	16	no	—
245	C₂×C₄×C₁₉	—	2	32	no	—
246	C₂×C₄×C₁₉	—	2	32	no	—
247	C₂×C₄×C₁₉	—	4	32	no	—
248	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
249	C₂×C₄×C₁₉	C₂²×D₄	1	16	yes	complemented
250	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
251	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
252	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
253	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
254	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
255	C₂⁴×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#3484	C₂×C₁₉	1	32	yes	direct product factor
257	C₂×#546	C₂×C₁₉	1	8	yes	complemented
258	C₂×D₄²	C₂×C₁₉	1	8	yes	complemented
259	C₂×#535	C₂×C₁₉	1	2	yes	complemented
260	C₂×#534	C₂×C₁₉	1	4	yes	complemented
261	C₂×#525	C₂×C₁₉	1	2	yes	complemented
262	C₂²×#120	C₂×C₁₉	1	4	yes	complemented
263	C₂×#518	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂²×C₁₉	—	2	32	no	—
265	C₂²×C₁₉	—	2	4	no	—
266	C₂²×C₁₉	—	2	16	no	—
267	C₂²×C₁₉	—	2	4	no	—
268	C₂²×C₁₉	—	2	4	no	—
269	C₂²×C₁₉	—	2	8	no	—
270	C₂²×C₁₉	—	2	16	no	—
271	C₂²×C₁₉	—	2	32	no	—
272	C₂²×C₁₉	—	2	8	no	—
273	C₂²×C₁₉	—	2	8	no	—
274	C₂²×C₁₉	—	2	16	no	—
275	C₂²×C₁₉	—	2	16	no	—
276	C₂²×C₁₉	—	4	32	no	—
277	C₂²×C₁₉	—	4	128	no	—
278	C₂²×C₁₉	—	4	32	no	—
279	C₂²×C₁₉	—	4	16	no	—
280	C₂²×C₁₉	—	4	16	no	—
281	C₂²×C₁₉	—	8	32	no	—
282	C₂²×C₁₉	C₂³×D₄	1	4	yes	—
283	C₂²×C₁₉	C₂³×D₄	1	16	yes	—
284	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
285	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	4	yes	—
286	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	8	yes	complemented
287	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
288	C₄×C₁₉	—	2	4	no	—
289	C₄×C₁₉	—	2	8	no	—
290	C₄×C₁₉	—	2	16	no	—
291	C₄×C₁₉	C₂³×D₄	1	8	yes	—
292	C₂⁶	C₂²×C₁₉	1	2	yes	complemented
293	C₂×H(5,𝔽₂)	—	2	16	no	—
294	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	16	yes	complemented
295	C₂²×#41	C₂²×C₁₉	1	2	yes	complemented
296	C₂²×#41	C₂²×C₁₉	1	4	yes	complemented
297	C₂³×D₄	—	2	16	no	—
298	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
299	C₂³×D₄	C₂²×C₁₉	1	2	yes	complemented
300	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
301	C₂³×D₄	C₂²×C₁₉	1	8	yes	complemented
302	C₂³×D₄	C₂²×C₁₉	1	4	yes	complemented
303	C₂³×D₄	C₂²×C₁₉	1	16	yes	complemented
304	C₂³×D₄	C₂²×C₁₉	1	4	yes	complemented
305	C₂³×D₄	C₂²×C₁₉	1	8	yes	complemented
306	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
307	#546	C₂²×C₁₉	1	128	yes	complemented
308	D₄²	C₂²×C₁₉	1	128	yes	complemented
309	#535	C₂²×C₁₉	1	32	yes	complemented
310	#534	C₂²×C₁₉	1	64	yes	complemented
311	C₂×#127	C₂²×C₁₉	1	4	yes	complemented
312	C₂×#124	C₂²×C₁₉	1	4	yes	complemented
313	#525	C₂²×C₁₉	1	32	yes	complemented
314	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
315	C₂×#123	C₂²×C₁₉	1	8	yes	complemented
316	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
317	C₂×#121	C₂²×C₁₉	1	4	yes	complemented
318	C₂×#121	C₂²×C₁₉	1	16	yes	complemented
319	C₂×#121	C₂²×C₁₉	1	8	yes	complemented
320	C₂×#120	C₂²×C₁₉	1	4	yes	complemented
321	C₂×#120	C₂²×C₁₉	1	8	yes	complemented
322	C₂×#120	C₂²×C₁₉	1	16	yes	complemented
323	C₂×#120	C₂²×C₁₉	1	8	yes	complemented
324	C₂×#120	C₂²×C₁₉	1	64	yes	complemented
325	#518	C₂²×C₁₉	1	16	yes	complemented
326	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
327	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
328	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
329	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
330	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
331	C₂×C₁₉	—	2	4	no	—
332	C₂×C₁₉	—	2	8	no	—
333	C₂×C₁₉	—	2	16	no	—
334	C₂×C₁₉	—	4	8	no	—
335	C₂×C₁₉	—	4	8	no	—
336	C₂×C₁₉	#3484	1	4	yes	direct product factor
337	C₂×C₁₉	C₂⁴×D₄	1	1	yes	characteristic
338	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	2	yes	—
339	C₂⁵	—	2	16	no	—
340	C₂⁵	—	4	16	no	—
341	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
342	C₂⁵	C₂³×C₁₉	1	8	yes	—
343	C₂⁵	C₂³×C₁₉	1	2	yes	—
344	C₂⁵	C₂³×C₁₉	1	2	yes	—
345	C₂⁵	C₂³×C₁₉	1	16	yes	complemented
346	C₂⁵	C₂³×C₁₉	1	4	yes	complemented
347	H(5,𝔽₂)	—	2	128	no	—
348	C₂×#41	—	2	32	no	—
349	C₂×#41	—	2	16	no	—
350	C₂×#41	C₂³×C₁₉	1	16	yes	complemented
351	C₂×#41	C₂³×C₁₉	1	32	yes	complemented
352	C₂²×Q₈	C₂³×C₁₉	1	2	yes	complemented
353	C₂²×D₄	—	2	16	no	—
354	C₂²×D₄	—	2	32	no	—
355	C₂²×D₄	—	2	64	no	—
356	C₂²×D₄	—	2	128	no	—
357	C₂²×D₄	—	2	32	no	—
358	C₂²×D₄	—	2	8	no	—
359	C₂²×D₄	—	4	32	no	—
360	C₂²×D₄	D₄×C₁₉	1	16	yes	complemented
361	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
362	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
363	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
364	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
365	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
366	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
367	C₂²×D₄	C₂³×C₁₉	1	16	yes	complemented
368	C₂²×D₄	C₂³×C₁₉	1	8	yes	complemented
369	C₂²×D₄	C₂³×C₁₉	1	64	yes	complemented
370	C₂²×D₄	C₂³×C₁₉	1	8	yes	complemented
371	C₂²×D₄	C₂³×C₁₉	1	2	yes	complemented
372	C₂²×D₄	C₂³×C₁₉	1	16	yes	complemented
373	C₂²×D₄	C₂³×C₁₉	1	32	yes	complemented
374	C₂²×D₄	C₂³×C₁₉	1	32	yes	complemented
375	C₂²×D₄	C₂³×C₁₉	1	64	yes	complemented
376	C₂³×C₄	—	2	8	no	—
377	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
378	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
379	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₁₉	1	8	yes	complemented
381	C₂³×C₄	C₂³×C₁₉	1	4	yes	complemented
382	C₂³×C₄	C₂³×C₁₉	1	4	yes	complemented
383	C₂³×C₄	C₂³×C₁₉	1	8	yes	complemented
384	#127	C₂³×C₁₉	1	32	yes	complemented
385	#124	C₂³×C₁₉	1	32	yes	complemented
386	#123	C₂³×C₁₉	1	32	yes	complemented
387	#123	C₂³×C₁₉	1	64	yes	complemented
388	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	complemented
389	#121	C₂³×C₁₉	1	32	yes	complemented
390	#121	C₂³×C₁₉	1	128	yes	complemented
391	#121	C₂³×C₁₉	1	64	yes	complemented
392	#120	C₂³×C₁₉	1	32	yes	complemented
393	#120	C₂³×C₁₉	1	64	yes	complemented
394	#120	C₂³×C₁₉	1	128	yes	complemented
395	#120	C₂³×C₁₉	1	64	yes	complemented
396	C₄×D₄	C₂³×C₁₉	1	64	yes	complemented
397	C₄×D₄	C₂³×C₁₉	1	64	yes	complemented
398	#117	C₂³×C₁₉	1	16	yes	complemented
399	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	complemented
400	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	complemented
401	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₉	1	32	yes	complemented
404	C₂×C₂²⋊C₄	C₂³×C₁₉	1	64	yes	complemented
405	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	complemented
406	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	complemented
407	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	complemented
408	C₂×C₄²	C₂³×C₁₉	1	4	yes	complemented
409	C₁₉	C₂×#3484	1	1	yes	characteristic, direct product factor, Sylow
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	8	no	—
412	C₂⁴	—	2	32	no	—
413	C₂⁴	—	2	8	no	—
414	C₂⁴	—	2	64	no	—
415	C₂⁴	—	2	32	no	—
416	C₂⁴	—	2	16	no	—
417	C₂⁴	—	4	8	no	—
418	C₂⁴	—	4	16	no	—
419	C₂⁴	—	4	8	no	—
420	C₂⁴	—	4	64	no	—
421	C₂⁴	—	4	16	no	—
422	C₂⁴	—	4	128	no	—
423	C₂⁴	C₂×D₄×C₁₉	1	16	yes	complemented
424	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
425	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
426	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
427	C₂⁴	C₂⁴×C₁₉	1	32	yes	—
428	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
429	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
430	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
431	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
432	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
433	C₂⁴	C₂⁴×C₁₉	1	16	yes	complemented
434	#41	—	2	128	no	—
435	#41	—	2	64	no	—
436	C₂×Q₈	—	2	8	no	—
437	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	complemented
438	C₂×D₄	—	2	32	no	—
439	C₂×D₄	—	2	16	no	—
440	C₂×D₄	—	2	32	no	—
441	C₂×D₄	—	2	64	no	—
442	C₂×D₄	—	2	128	no	—
443	C₂×D₄	—	2	32	no	—
444	C₂×D₄	—	2	256	no	—
445	C₂×D₄	—	2	128	no	—
446	C₂×D₄	—	2	16	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	32	no	—
449	C₂×D₄	—	4	32	no	—
450	C₂×D₄	—	4	128	no	—
451	C₂×D₄	C₂×D₄×C₁₉	1	32	yes	complemented
452	C₂×D₄	C₂×D₄×C₁₉	1	64	yes	complemented
453	C₂×D₄	C₂⁴×C₁₉	1	32	yes	—
454	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
455	C₂×D₄	C₂⁴×C₁₉	1	32	yes	—
456	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
457	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
458	C₂×D₄	C₂⁴×C₁₉	1	32	yes	complemented
459	C₂×D₄	C₂⁴×C₁₉	1	8	yes	complemented
460	C₂×D₄	C₂⁴×C₁₉	1	64	yes	complemented
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	16	no	—
463	C₂²×C₄	—	2	16	no	—
464	C₂²×C₄	—	2	16	no	—
465	C₂²×C₄	—	2	32	no	—
466	C₂²×C₄	—	4	16	no	—
467	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	complemented
468	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
469	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
472	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	complemented
476	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	complemented
477	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	complemented
478	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	complemented
479	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	complemented
480	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
481	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
482	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	complemented
483	C₂²⋊C₄	C₂⁴×C₁₉	1	64	yes	complemented
484	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	complemented
485	C₄²	C₂⁴×C₁₉	1	16	yes	complemented
486	C₂³	—	2	32	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	16	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	16	no	—
493	C₂³	—	2	8	no	—
494	C₂³	—	2	64	no	—
495	C₂³	—	2	16	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	16	no	—
498	C₂³	—	2	16	no	—
499	C₂³	—	2	64	no	—
500	C₂³	—	2	32	no	—
501	C₂³	—	4	32	no	—
502	C₂³	—	4	16	no	—
503	C₂³	—	4	32	no	—
504	C₂³	—	4	16	no	—
505	C₂³	—	4	32	no	—
506	C₂³	—	4	128	no	—
507	C₂³	—	4	256	no	—
508	C₂³	—	4	32	no	—
509	C₂³	—	8	32	no	—
510	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
511	C₂³	C₂²×D₄×C₁₉	1	16	yes	—
512	C₂³	C₂²×D₄×C₁₉	1	32	yes	complemented
513	C₂³	C₁₉×H(5,𝔽₂)	1	8	yes	complemented
514	C₂³	C₂⁵×C₁₉	1	8	yes	—
515	C₂³	C₂⁵×C₁₉	1	8	yes	—
516	C₂³	C₂⁵×C₁₉	1	2	yes	—
517	C₂³	C₂⁵×C₁₉	1	8	yes	—
518	C₂³	C₂⁵×C₁₉	1	4	yes	—
519	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
520	Q₈	—	2	16	no	—
521	D₄	—	2	64	no	—
522	D₄	—	2	32	no	—
523	D₄	—	2	64	no	—
524	D₄	—	2	64	no	—
525	D₄	—	2	32	no	—
526	D₄	—	2	16	no	—
527	D₄	—	4	64	no	—
528	D₄	C₂²×D₄×C₁₉	1	64	yes	complemented
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	32	no	—
533	C₂×C₄	—	2	16	no	—
534	C₂×C₄	—	2	32	no	—
535	C₂×C₄	—	2	32	no	—
536	C₂×C₄	—	4	32	no	—
537	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
538	C₂×C₄	C₂²×D₄×C₁₉	1	16	yes	complemented
539	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
540	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
541	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
542	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
543	C₂²	—	2	32	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	2	16	no	—
546	C₂²	—	2	32	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	16	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	16	no	—
554	C₂²	—	2	16	no	—
555	C₂²	—	4	32	no	—
556	C₂²	—	4	128	no	—
557	C₂²	—	4	32	no	—
558	C₂²	—	4	16	no	—
559	C₂²	—	4	16	no	—
560	C₂²	—	8	32	no	—
561	C₂²	C₂³×D₄×C₁₉	1	4	yes	—
562	C₂²	C₂³×D₄×C₁₉	1	16	yes	—
563	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
564	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	4	yes	—
565	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	8	yes	complemented
566	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
567	C₄	—	2	4	no	—
568	C₄	—	2	8	no	—
569	C₄	—	2	16	no	—
570	C₄	C₂³×D₄×C₁₉	1	8	yes	—
571	C₂	—	2	4	no	—
572	C₂	—	2	8	no	—
573	C₂	—	2	16	no	—
574	C₂	—	4	8	no	—
575	C₂	—	4	8	no	—
576	C₂	C₁₉×#3484	1	4	yes	direct product factor
577	C₂	C₂⁴×D₄×C₁₉	1	1	yes	characteristic
578	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×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. C₂⁴×D₄×C₁₉	C₂	semidirect
3. C₁₉×#3484	C₂	direct (N × H)
4. C₂×C₁₉×#546	C₂	semidirect
5. C₂×D₄²×C₁₉	C₂	semidirect
6. C₂×C₁₉×#535	C₂	semidirect
7. C₂×C₁₉×#534	C₂	semidirect
8. C₂×C₁₉×#525	C₂	semidirect
9. C₂²×C₁₉×#120	C₂	semidirect
10. C₂×C₁₉×#518	C₂	semidirect
11. C₂⁶×C₁₉	C₂²	semidirect
13. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
14. C₂²×#41×C₁₉	C₂²	semidirect
15. C₂²×#41×C₁₉	C₂²	semidirect
18. C₂³×D₄×C₁₉	C₂²	semidirect
19. C₂³×D₄×C₁₉	C₂²	semidirect
20. C₂³×D₄×C₁₉	C₂²	semidirect
21. C₂³×D₄×C₁₉	C₂²	semidirect
22. C₂³×D₄×C₁₉	C₂²	semidirect
23. C₂³×D₄×C₁₉	C₂²	semidirect
24. C₂³×D₄×C₁₉	C₂²	semidirect
25. C₂⁴×C₄×C₁₉	C₂²	semidirect
26. C₁₉×#546	C₂²	semidirect
27. D₄²×C₁₉	C₂²	semidirect
28. C₁₉×#535	C₂²	semidirect
29. C₁₉×#534	C₂²	semidirect
30. C₂×C₁₉×#127	C₂²	semidirect
31. C₂×C₁₉×#124	C₂²	semidirect
32. C₁₉×#525	C₂²	semidirect
33. C₂×C₁₉×#123	C₂²	semidirect
34. C₂×C₁₉×#123	C₂²	semidirect
35. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₁₉×#121	C₂²	semidirect
37. C₂×C₁₉×#121	C₂²	semidirect
38. C₂×C₁₉×#121	C₂²	semidirect
39. C₂×C₁₉×#120	C₂²	semidirect
40. C₂×C₁₉×#120	C₂²	semidirect
41. C₂×C₁₉×#120	C₂²	semidirect
42. C₂×C₁₉×#120	C₂²	semidirect
43. C₂×C₁₉×#120	C₂²	semidirect
44. C₁₉×#518	C₂²	semidirect
45. C₂×C₄×D₄×C₁₉	C₂²	semidirect
46. C₂×C₄×D₄×C₁₉	C₂²	semidirect
47. C₂×C₁₉×#117	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
56. C₂⁵×C₁₉	C₂³	semidirect
57. C₂⁵×C₁₉	C₂³	semidirect
61. C₂×#41×C₁₉	C₂³	semidirect
62. C₂×#41×C₁₉	C₂³	semidirect
63. C₂²×Q₈×C₁₉	C₂³	semidirect
71. C₂²×D₄×C₁₉	D₄	semidirect
78. C₂²×D₄×C₁₉	C₂³	semidirect
79. C₂²×D₄×C₁₉	C₂³	semidirect
80. C₂²×D₄×C₁₉	C₂³	semidirect
81. C₂²×D₄×C₁₉	C₂³	semidirect
82. C₂²×D₄×C₁₉	C₂³	semidirect
83. C₂²×D₄×C₁₉	C₂³	semidirect
84. C₂²×D₄×C₁₉	C₂³	semidirect
85. C₂²×D₄×C₁₉	C₂³	semidirect
86. C₂²×D₄×C₁₉	C₂³	semidirect
91. C₂³×C₄×C₁₉	C₂³	semidirect
92. C₂³×C₄×C₁₉	C₂³	semidirect
93. C₂³×C₄×C₁₉	C₂³	semidirect
94. C₂³×C₄×C₁₉	C₂³	semidirect
95. C₁₉×#127	C₂³	semidirect
96. C₁₉×#124	C₂³	semidirect
97. C₁₉×#123	C₂³	semidirect
98. C₁₉×#123	C₂³	semidirect
99. C₁₉×C₂²⋊Q₈	C₂³	semidirect
100. C₁₉×#121	C₂³	semidirect
101. C₁₉×#121	C₂³	semidirect
102. C₁₉×#121	C₂³	semidirect
103. C₁₉×#120	C₂³	semidirect
104. C₁₉×#120	C₂³	semidirect
105. C₁₉×#120	C₂³	semidirect
106. C₁₉×#120	C₂³	semidirect
107. C₄×D₄×C₁₉	C₂³	semidirect
108. C₄×D₄×C₁₉	C₂³	semidirect
109. C₁₉×#117	C₂³	semidirect
110. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
111. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
114. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
115. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
116. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
117. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
118. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
119. C₂×C₄²×C₁₉	C₂³	semidirect
133. C₂⁴×C₁₉	C₂×D₄	semidirect
143. C₂⁴×C₁₉	C₂⁴	semidirect
147. C₂×Q₈×C₁₉	C₂⁴	semidirect
161. C₂×D₄×C₁₉	C₂×D₄	semidirect
162. C₂×D₄×C₁₉	C₂×D₄	semidirect
168. C₂×D₄×C₁₉	C₂⁴	semidirect
169. C₂×D₄×C₁₉	C₂⁴	semidirect
170. C₂×D₄×C₁₉	C₂⁴	semidirect
177. C₂²×C₄×C₁₉	C₂×D₄	semidirect
185. C₂²×C₄×C₁₉	C₂⁴	semidirect
186. C₂²×C₄×C₁₉	C₂⁴	semidirect
187. C₂²×C₄×C₁₉	C₂⁴	semidirect
188. C₄⋊C₄×C₁₉	C₂⁴	semidirect
189. C₄⋊C₄×C₁₉	C₂⁴	semidirect
192. C₂²⋊C₄×C₁₉	C₂⁴	semidirect
193. C₂²⋊C₄×C₁₉	C₂⁴	semidirect
194. C₂²⋊C₄×C₁₉	C₂⁴	semidirect
195. C₄²×C₁₉	C₂⁴	semidirect
196. C₂×#3484	C₁₉	direct (N × H)
223. C₂³×C₁₉	C₂²×D₄	semidirect
224. C₂³×C₁₉	H(5,𝔽₂)	semidirect
239. D₄×C₁₉	C₂²×D₄	semidirect
249. C₂×C₄×C₁₉	C₂²×D₄	semidirect
254. C₂²×H(5,𝔽₂)	C₂×C₁₉	semidirect
255. C₂⁴×D₄	C₂×C₁₉	semidirect
256. #3484	C₂×C₁₉	direct (N × H)
257. C₂×#546	C₂×C₁₉	semidirect
258. C₂×D₄²	C₂×C₁₉	semidirect
259. C₂×#535	C₂×C₁₉	semidirect
260. C₂×#534	C₂×C₁₉	semidirect
261. C₂×#525	C₂×C₁₉	semidirect
262. C₂²×#120	C₂×C₁₉	semidirect
263. C₂×#518	C₂×C₁₉	semidirect
286. C₂²×C₁₉	C₂×H(5,𝔽₂)	semidirect
292. C₂⁶	C₂²×C₁₉	semidirect
294. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
295. C₂²×#41	C₂²×C₁₉	semidirect
296. C₂²×#41	C₂²×C₁₉	semidirect
299. C₂³×D₄	C₂²×C₁₉	semidirect
300. C₂³×D₄	C₂²×C₁₉	semidirect
301. C₂³×D₄	C₂²×C₁₉	semidirect
302. C₂³×D₄	C₂²×C₁₉	semidirect
303. C₂³×D₄	C₂²×C₁₉	semidirect
304. C₂³×D₄	C₂²×C₁₉	semidirect
305. C₂³×D₄	C₂²×C₁₉	semidirect
306. C₂⁴×C₄	C₂²×C₁₉	semidirect
307. #546	C₂²×C₁₉	semidirect
308. D₄²	C₂²×C₁₉	semidirect
309. #535	C₂²×C₁₉	semidirect
310. #534	C₂²×C₁₉	semidirect
311. C₂×#127	C₂²×C₁₉	semidirect
312. C₂×#124	C₂²×C₁₉	semidirect
313. #525	C₂²×C₁₉	semidirect
314. C₂×#123	C₂²×C₁₉	semidirect
315. C₂×#123	C₂²×C₁₉	semidirect
316. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
317. C₂×#121	C₂²×C₁₉	semidirect
318. C₂×#121	C₂²×C₁₉	semidirect
319. C₂×#121	C₂²×C₁₉	semidirect
320. C₂×#120	C₂²×C₁₉	semidirect
321. C₂×#120	C₂²×C₁₉	semidirect
322. C₂×#120	C₂²×C₁₉	semidirect
323. C₂×#120	C₂²×C₁₉	semidirect
324. C₂×#120	C₂²×C₁₉	semidirect
325. #518	C₂²×C₁₉	semidirect
326. C₂×C₄×D₄	C₂²×C₁₉	semidirect
327. C₂×C₄×D₄	C₂²×C₁₉	semidirect
328. C₂×#117	C₂²×C₁₉	semidirect
329. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
330. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
336. C₂×C₁₉	#3484	direct (N × H)
345. C₂⁵	C₂³×C₁₉	semidirect
346. C₂⁵	C₂³×C₁₉	semidirect
350. C₂×#41	C₂³×C₁₉	semidirect
351. C₂×#41	C₂³×C₁₉	semidirect
352. C₂²×Q₈	C₂³×C₁₉	semidirect
360. C₂²×D₄	D₄×C₁₉	semidirect
367. C₂²×D₄	C₂³×C₁₉	semidirect
368. C₂²×D₄	C₂³×C₁₉	semidirect
369. C₂²×D₄	C₂³×C₁₉	semidirect
370. C₂²×D₄	C₂³×C₁₉	semidirect
371. C₂²×D₄	C₂³×C₁₉	semidirect
372. C₂²×D₄	C₂³×C₁₉	semidirect
373. C₂²×D₄	C₂³×C₁₉	semidirect
374. C₂²×D₄	C₂³×C₁₉	semidirect
375. C₂²×D₄	C₂³×C₁₉	semidirect
380. C₂³×C₄	C₂³×C₁₉	semidirect
381. C₂³×C₄	C₂³×C₁₉	semidirect
382. C₂³×C₄	C₂³×C₁₉	semidirect
383. C₂³×C₄	C₂³×C₁₉	semidirect
384. #127	C₂³×C₁₉	semidirect
385. #124	C₂³×C₁₉	semidirect
386. #123	C₂³×C₁₉	semidirect
387. #123	C₂³×C₁₉	semidirect
388. C₂²⋊Q₈	C₂³×C₁₉	semidirect
389. #121	C₂³×C₁₉	semidirect
390. #121	C₂³×C₁₉	semidirect
391. #121	C₂³×C₁₉	semidirect
392. #120	C₂³×C₁₉	semidirect
393. #120	C₂³×C₁₉	semidirect
394. #120	C₂³×C₁₉	semidirect
395. #120	C₂³×C₁₉	semidirect
396. C₄×D₄	C₂³×C₁₉	semidirect
397. C₄×D₄	C₂³×C₁₉	semidirect
398. #117	C₂³×C₁₉	semidirect
399. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
400. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
403. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
404. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
405. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
406. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
407. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
408. C₂×C₄²	C₂³×C₁₉	semidirect
409. C₁₉	C₂×#3484	direct (N × H)
423. C₂⁴	C₂×D₄×C₁₉	semidirect
433. C₂⁴	C₂⁴×C₁₉	semidirect
437. C₂×Q₈	C₂⁴×C₁₉	semidirect
451. C₂×D₄	C₂×D₄×C₁₉	semidirect
452. C₂×D₄	C₂×D₄×C₁₉	semidirect
458. C₂×D₄	C₂⁴×C₁₉	semidirect
459. C₂×D₄	C₂⁴×C₁₉	semidirect
460. C₂×D₄	C₂⁴×C₁₉	semidirect
467. C₂²×C₄	C₂×D₄×C₁₉	semidirect
475. C₂²×C₄	C₂⁴×C₁₉	semidirect
476. C₂²×C₄	C₂⁴×C₁₉	semidirect
477. C₂²×C₄	C₂⁴×C₁₉	semidirect
478. C₄⋊C₄	C₂⁴×C₁₉	semidirect
479. C₄⋊C₄	C₂⁴×C₁₉	semidirect
482. C₂²⋊C₄	C₂⁴×C₁₉	semidirect
483. C₂²⋊C₄	C₂⁴×C₁₉	semidirect
484. C₂²⋊C₄	C₂⁴×C₁₉	semidirect
485. C₄²	C₂⁴×C₁₉	semidirect
512. C₂³	C₂²×D₄×C₁₉	semidirect
513. C₂³	C₁₉×H(5,𝔽₂)	semidirect
528. D₄	C₂²×D₄×C₁₉	semidirect
538. C₂×C₄	C₂²×D₄×C₁₉	semidirect
565. C₂²	C₂×C₁₉×H(5,𝔽₂)	semidirect
576. C₂	C₁₉×#3484	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
C₂⁴×D₄×C₁₉	2
C₁₉×#3484	2
C₂×C₁₉×#546	2
C₂×D₄²×C₁₉	2
C₂×C₁₉×#535	2
C₂×C₁₉×#534	2
C₂×C₁₉×#525	2
C₂²×C₁₉×#120	2
C₂×C₁₉×#518	2
C₂×#3484	19

Subgroups — C2×C19×#3484 #18068722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3484 #18068722