Subgroups — C₂×C₁₉×#3485 #18068733

Order 4864.

11686 conjugacy classes of subgroups.

The subgroup lattice has 532 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	C₂³×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3485	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₁₉×#547	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₉×#546	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₉×#536	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×#123	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×H(5,𝔽₂)	—	2	16	no	—
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	16	yes	complemented
13	C₂²×#41×C₁₉	—	2	16	no	—
14	C₂²×#41×C₁₉	C₂²	1	2	yes	—
15	C₂²×#41×C₁₉	C₂²	1	8	yes	complemented
16	C₂²×#41×C₁₉	C₂²	1	4	yes	complemented
17	C₂²×#41×C₁₉	C₂²	1	16	yes	complemented
18	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
20	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₁₉	C₂²	1	2	yes	complemented
22	C₂³×D₄×C₁₉	C₂²	1	4	yes	complemented
23	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	complemented
24	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#547	C₂²	1	128	yes	complemented
26	C₁₉×#546	C₂²	1	128	yes	complemented
27	C₁₉×#536	C₂²	1	32	yes	complemented
28	C₁₉×#534	C₂²	1	64	yes	complemented
29	C₂×C₁₉×C₄⋊Q₈	C₂²	1	4	yes	complemented
30	C₂×C₁₉×#124	C₂²	1	4	yes	complemented
31	C₁₉×#525	C₂²	1	32	yes	complemented
32	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
33	C₂×C₁₉×#123	C₂²	1	8	yes	complemented
34	C₂×C₁₉×#123	C₂²	1	16	yes	complemented
35	C₂×C₁₉×#123	C₂²	1	8	yes	complemented
36	C₂×C₁₉×#123	C₂²	1	64	yes	complemented
37	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
38	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
39	C₂×C₁₉×#121	C₂²	1	4	yes	complemented
40	C₂×C₁₉×#121	C₂²	1	16	yes	complemented
41	C₂×C₁₉×#120	C₂²	1	4	yes	complemented
42	C₂×C₁₉×#120	C₂²	1	8	yes	complemented
43	C₁₉×#518	C₂²	1	16	yes	complemented
44	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
45	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
46	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
47	C₂²×C₄⋊C₄×C₁₉	C₂²	1	8	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	C₂³	1	4	yes	—
51	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
52	C₂⁵×C₁₉	C₂³	1	2	yes	—
53	C₁₉×H(5,𝔽₂)	—	2	128	no	—
54	C₂×#41×C₁₉	—	2	64	no	—
55	C₂×#41×C₁₉	—	2	32	no	—
56	C₂×#41×C₁₉	—	2	128	no	—
57	C₂×#41×C₁₉	—	2	16	no	—
58	C₂×#41×C₁₉	C₂³	1	16	yes	—
59	C₂×#41×C₁₉	C₂³	1	64	yes	complemented
60	C₂×#41×C₁₉	C₂³	1	32	yes	complemented
61	C₂²×Q₈×C₁₉	—	2	8	no	—
62	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
63	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
64	C₂²×Q₈×C₁₉	C₂³	1	8	yes	complemented
65	C₂²×D₄×C₁₉	—	2	32	no	—
66	C₂²×D₄×C₁₉	—	2	16	no	—
67	C₂²×D₄×C₁₉	—	2	32	no	—
68	C₂²×D₄×C₁₉	D₄	1	16	yes	complemented
69	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
72	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₉	C₂³	1	32	yes	—
74	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
75	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
76	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
77	C₂²×D₄×C₁₉	C₂³	1	16	yes	complemented
78	C₂²×D₄×C₁₉	C₂³	1	32	yes	complemented
79	C₂³×C₄×C₁₉	—	2	16	no	—
80	C₂³×C₄×C₁₉	—	2	8	no	—
81	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
82	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
83	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
88	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₉	C₂³	1	16	yes	complemented
90	C₂³×C₄×C₁₉	C₂³	1	8	yes	complemented
91	C₁₉×C₄⋊Q₈	C₂³	1	32	yes	complemented
92	C₁₉×#124	C₂³	1	32	yes	complemented
93	C₁₉×#123	C₂³	1	32	yes	complemented
94	C₁₉×#123	C₂³	1	64	yes	complemented
95	C₁₉×#123	C₂³	1	128	yes	complemented
96	C₁₉×#123	C₂³	1	64	yes	complemented
97	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
98	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	complemented
99	C₁₉×#121	C₂³	1	32	yes	complemented
100	C₁₉×#121	C₂³	1	128	yes	complemented
101	C₁₉×#120	C₂³	1	32	yes	complemented
102	C₁₉×#120	C₂³	1	64	yes	complemented
103	C₄×D₄×C₁₉	C₂³	1	64	yes	complemented
104	C₄×D₄×C₁₉	C₂³	1	64	yes	complemented
105	C₁₉×#117	C₂³	1	16	yes	complemented
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	64	yes	complemented
110	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
112	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
114	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	32	yes	complemented
116	C₂×C₂²⋊C₄×C₁₉	C₂³	1	64	yes	complemented
117	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
118	C₂⁴×C₁₉	—	2	4	no	—
119	C₂⁴×C₁₉	—	2	16	no	—
120	C₂⁴×C₁₉	—	4	8	no	—
121	C₂⁴×C₁₉	—	4	4	no	—
122	C₂⁴×C₁₉	—	4	16	no	—
123	C₂⁴×C₁₉	C₂×D₄	1	16	yes	—
124	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
125	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
126	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
128	C₂⁴×C₁₉	C₂⁴	1	16	yes	—
129	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
130	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
131	#41×C₁₉	—	2	256	no	—
132	#41×C₁₉	—	2	128	no	—
133	#41×C₁₉	—	2	64	no	—
134	C₂×Q₈×C₁₉	—	2	16	no	—
135	C₂×Q₈×C₁₉	—	2	32	no	—
136	C₂×Q₈×C₁₉	—	2	8	no	—
137	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
138	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
139	C₂×D₄×C₁₉	—	2	16	no	—
140	C₂×D₄×C₁₉	—	2	32	no	—
141	C₂×D₄×C₁₉	—	2	32	no	—
142	C₂×D₄×C₁₉	—	2	128	no	—
143	C₂×D₄×C₁₉	—	2	64	no	—
144	C₂×D₄×C₁₉	—	2	128	no	—
145	C₂×D₄×C₁₉	—	2	8	no	—
146	C₂×D₄×C₁₉	—	4	16	no	—
147	C₂×D₄×C₁₉	C₂×D₄	1	32	yes	—
148	C₂×D₄×C₁₉	C₂×D₄	1	64	yes	complemented
149	C₂×D₄×C₁₉	C₂⁴	1	32	yes	—
150	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
151	C₂×D₄×C₁₉	C₂⁴	1	32	yes	—
152	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
153	C₂×D₄×C₁₉	C₂⁴	1	32	yes	—
154	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	8	no	—
157	C₂²×C₄×C₁₉	—	2	32	no	—
158	C₂²×C₄×C₁₉	—	2	64	no	—
159	C₂²×C₄×C₁₉	—	2	16	no	—
160	C₂²×C₄×C₁₉	—	2	16	no	—
161	C₂²×C₄×C₁₉	—	2	32	no	—
162	C₂²×C₄×C₁₉	—	2	16	no	—
163	C₂²×C₄×C₁₉	—	4	16	no	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
165	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
166	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
167	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
169	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
176	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
178	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
179	C₄⋊C₄×C₁₉	C₂⁴	1	64	yes	—
180	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
181	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
182	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
183	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
184	C₂²⋊C₄×C₁₉	C₂⁴	1	64	yes	—
185	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
186	C₄²×C₁₉	C₂⁴	1	16	yes	—
187	C₂×#3485	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₁₉	—	2	16	no	—
189	C₂³×C₁₉	—	2	4	no	—
190	C₂³×C₁₉	—	2	8	no	—
191	C₂³×C₁₉	—	2	4	no	—
192	C₂³×C₁₉	—	2	8	no	—
193	C₂³×C₁₉	—	2	8	no	—
194	C₂³×C₁₉	—	2	16	no	—
195	C₂³×C₁₉	—	2	32	no	—
196	C₂³×C₁₉	—	4	32	no	—
197	C₂³×C₁₉	—	4	16	no	—
198	C₂³×C₁₉	—	4	8	no	—
199	C₂³×C₁₉	—	4	32	no	—
200	C₂³×C₁₉	—	4	16	no	—
201	C₂³×C₁₉	—	8	32	no	—
202	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
203	C₂³×C₁₉	C₂²×D₄	1	16	yes	—
204	C₂³×C₁₉	C₂²×D₄	1	32	yes	—
205	C₂³×C₁₉	C₂⁵	1	8	yes	—
206	C₂³×C₁₉	C₂⁵	1	4	yes	—
207	C₂³×C₁₉	C₂⁵	1	2	yes	—
208	C₂³×C₁₉	C₂⁵	1	8	yes	—
209	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
210	Q₈×C₁₉	—	2	32	no	—
211	Q₈×C₁₉	—	2	16	no	—
212	D₄×C₁₉	—	2	32	no	—
213	D₄×C₁₉	—	2	64	no	—
214	D₄×C₁₉	—	2	64	no	—
215	D₄×C₁₉	—	2	16	no	—
216	D₄×C₁₉	—	4	32	no	—
217	D₄×C₁₉	C₂²×D₄	1	64	yes	—
218	C₂×C₄×C₁₉	—	2	8	no	—
219	C₂×C₄×C₁₉	—	2	4	no	—
220	C₂×C₄×C₁₉	—	2	8	no	—
221	C₂×C₄×C₁₉	—	2	16	no	—
222	C₂×C₄×C₁₉	—	2	8	no	—
223	C₂×C₄×C₁₉	—	2	64	no	—
224	C₂×C₄×C₁₉	—	2	32	no	—
225	C₂×C₄×C₁₉	—	2	16	no	—
226	C₂×C₄×C₁₉	—	2	32	no	—
227	C₂×C₄×C₁₉	—	2	32	no	—
228	C₂×C₄×C₁₉	—	4	32	no	—
229	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
230	C₂×C₄×C₁₉	C₂²×D₄	1	16	yes	—
231	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
232	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
233	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
234	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
235	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
236	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
237	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#3485	C₂×C₁₉	1	32	yes	direct product factor
239	C₂×#547	C₂×C₁₉	1	8	yes	complemented
240	C₂×#546	C₂×C₁₉	1	8	yes	complemented
241	C₂×#536	C₂×C₁₉	1	2	yes	complemented
242	C₂×#534	C₂×C₁₉	1	4	yes	complemented
243	C₂×#525	C₂×C₁₉	1	2	yes	complemented
244	C₂²×#123	C₂×C₁₉	1	4	yes	complemented
245	C₂×#518	C₂×C₁₉	1	1	yes	characteristic, complemented
246	C₂²×C₁₉	—	2	16	no	—
247	C₂²×C₁₉	—	2	4	no	—
248	C₂²×C₁₉	—	2	8	no	—
249	C₂²×C₁₉	—	2	32	no	—
250	C₂²×C₁₉	—	2	4	no	—
251	C₂²×C₁₉	—	2	8	no	—
252	C₂²×C₁₉	—	2	8	no	—
253	C₂²×C₁₉	—	2	16	no	—
254	C₂²×C₁₉	—	4	32	no	—
255	C₂²×C₁₉	—	4	16	no	—
256	C₂²×C₁₉	—	4	8	no	—
257	C₂²×C₁₉	—	4	16	no	—
258	C₂²×C₁₉	—	8	32	no	—
259	C₂²×C₁₉	C₂³×D₄	1	4	yes	—
260	C₂²×C₁₉	C₂³×D₄	1	16	yes	—
261	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
262	C₂²×C₁₉	#585	1	4	yes	—
263	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
264	C₄×C₁₉	—	2	4	no	—
265	C₄×C₁₉	—	2	8	no	—
266	C₄×C₁₉	—	2	8	no	—
267	C₄×C₁₉	—	2	16	no	—
268	C₄×C₁₉	C₂³×D₄	1	8	yes	—
269	C₂×H(5,𝔽₂)	—	2	16	no	—
270	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	16	yes	complemented
271	C₂²×#41	—	2	16	no	—
272	C₂²×#41	C₂²×C₁₉	1	2	yes	—
273	C₂²×#41	C₂²×C₁₉	1	8	yes	complemented
274	C₂²×#41	C₂²×C₁₉	1	4	yes	complemented
275	C₂²×#41	C₂²×C₁₉	1	16	yes	complemented
276	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
277	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
278	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
279	C₂³×D₄	C₂²×C₁₉	1	2	yes	complemented
280	C₂³×D₄	C₂²×C₁₉	1	4	yes	complemented
281	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	complemented
282	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
283	#547	C₂²×C₁₉	1	128	yes	complemented
284	#546	C₂²×C₁₉	1	128	yes	complemented
285	#536	C₂²×C₁₉	1	32	yes	complemented
286	#534	C₂²×C₁₉	1	64	yes	complemented
287	C₂×C₄⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
288	C₂×#124	C₂²×C₁₉	1	4	yes	complemented
289	#525	C₂²×C₁₉	1	32	yes	complemented
290	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
291	C₂×#123	C₂²×C₁₉	1	8	yes	complemented
292	C₂×#123	C₂²×C₁₉	1	16	yes	complemented
293	C₂×#123	C₂²×C₁₉	1	8	yes	complemented
294	C₂×#123	C₂²×C₁₉	1	64	yes	complemented
295	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
296	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
297	C₂×#121	C₂²×C₁₉	1	4	yes	complemented
298	C₂×#121	C₂²×C₁₉	1	16	yes	complemented
299	C₂×#120	C₂²×C₁₉	1	4	yes	complemented
300	C₂×#120	C₂²×C₁₉	1	8	yes	complemented
301	#518	C₂²×C₁₉	1	16	yes	complemented
302	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
303	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
304	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
305	C₂²×C₄⋊C₄	C₂²×C₁₉	1	8	yes	complemented
306	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
307	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
308	C₂×C₁₉	—	2	4	no	—
309	C₂×C₁₉	—	2	16	no	—
310	C₂×C₁₉	—	4	4	no	—
311	C₂×C₁₉	—	4	8	no	—
312	C₂×C₁₉	#3485	1	4	yes	direct product factor
313	C₂×C₁₉	C₂⁴×D₄	1	1	yes	characteristic
314	C₂×C₁₉	C₂×#585	1	2	yes	—
315	C₂⁵	C₂³×C₁₉	1	4	yes	—
316	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
317	C₂⁵	C₂³×C₁₉	1	2	yes	—
318	H(5,𝔽₂)	—	2	128	no	—
319	C₂×#41	—	2	64	no	—
320	C₂×#41	—	2	32	no	—
321	C₂×#41	—	2	128	no	—
322	C₂×#41	—	2	16	no	—
323	C₂×#41	C₂³×C₁₉	1	16	yes	—
324	C₂×#41	C₂³×C₁₉	1	64	yes	complemented
325	C₂×#41	C₂³×C₁₉	1	32	yes	complemented
326	C₂²×Q₈	—	2	8	no	—
327	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
328	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
329	C₂²×Q₈	C₂³×C₁₉	1	8	yes	complemented
330	C₂²×D₄	—	2	32	no	—
331	C₂²×D₄	—	2	16	no	—
332	C₂²×D₄	—	2	32	no	—
333	C₂²×D₄	D₄×C₁₉	1	16	yes	complemented
334	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
335	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
336	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
337	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
338	C₂²×D₄	C₂³×C₁₉	1	32	yes	—
339	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
340	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
341	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
342	C₂²×D₄	C₂³×C₁₉	1	16	yes	complemented
343	C₂²×D₄	C₂³×C₁₉	1	32	yes	complemented
344	C₂³×C₄	—	2	16	no	—
345	C₂³×C₄	—	2	8	no	—
346	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
347	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
348	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
349	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
350	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
352	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
353	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₁₉	1	16	yes	complemented
355	C₂³×C₄	C₂³×C₁₉	1	8	yes	complemented
356	C₄⋊Q₈	C₂³×C₁₉	1	32	yes	complemented
357	#124	C₂³×C₁₉	1	32	yes	complemented
358	#123	C₂³×C₁₉	1	32	yes	complemented
359	#123	C₂³×C₁₉	1	64	yes	complemented
360	#123	C₂³×C₁₉	1	128	yes	complemented
361	#123	C₂³×C₁₉	1	64	yes	complemented
362	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	complemented
363	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
364	#121	C₂³×C₁₉	1	32	yes	complemented
365	#121	C₂³×C₁₉	1	128	yes	complemented
366	#120	C₂³×C₁₉	1	32	yes	complemented
367	#120	C₂³×C₁₉	1	64	yes	complemented
368	C₄×D₄	C₂³×C₁₉	1	64	yes	complemented
369	C₄×D₄	C₂³×C₁₉	1	64	yes	complemented
370	#117	C₂³×C₁₉	1	16	yes	complemented
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	64	yes	complemented
375	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₉	1	32	yes	complemented
381	C₂×C₂²⋊C₄	C₂³×C₁₉	1	64	yes	complemented
382	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
383	C₁₉	C₂×#3485	1	1	yes	characteristic, direct product factor, Sylow
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	2	16	no	—
386	C₂⁴	—	4	8	no	—
387	C₂⁴	—	4	4	no	—
388	C₂⁴	—	4	16	no	—
389	C₂⁴	C₂×D₄×C₁₉	1	16	yes	—
390	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
391	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
392	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
393	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
394	C₂⁴	C₂⁴×C₁₉	1	16	yes	—
395	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
396	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
397	#41	—	2	256	no	—
398	#41	—	2	128	no	—
399	#41	—	2	64	no	—
400	C₂×Q₈	—	2	16	no	—
401	C₂×Q₈	—	2	32	no	—
402	C₂×Q₈	—	2	8	no	—
403	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
404	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
405	C₂×D₄	—	2	16	no	—
406	C₂×D₄	—	2	32	no	—
407	C₂×D₄	—	2	32	no	—
408	C₂×D₄	—	2	128	no	—
409	C₂×D₄	—	2	64	no	—
410	C₂×D₄	—	2	128	no	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	4	16	no	—
413	C₂×D₄	C₂×D₄×C₁₉	1	32	yes	—
414	C₂×D₄	C₂×D₄×C₁₉	1	64	yes	complemented
415	C₂×D₄	C₂⁴×C₁₉	1	32	yes	—
416	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
417	C₂×D₄	C₂⁴×C₁₉	1	32	yes	—
418	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
419	C₂×D₄	C₂⁴×C₁₉	1	32	yes	—
420	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	2	32	no	—
424	C₂²×C₄	—	2	64	no	—
425	C₂²×C₄	—	2	16	no	—
426	C₂²×C₄	—	2	16	no	—
427	C₂²×C₄	—	2	32	no	—
428	C₂²×C₄	—	2	16	no	—
429	C₂²×C₄	—	4	16	no	—
430	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
431	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
432	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
434	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
436	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
437	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
438	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
439	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
441	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
442	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
444	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
445	C₄⋊C₄	C₂⁴×C₁₉	1	64	yes	—
446	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
447	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
448	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
449	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
450	C₂²⋊C₄	C₂⁴×C₁₉	1	64	yes	—
451	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
452	C₄²	C₂⁴×C₁₉	1	16	yes	—
453	C₂³	—	2	16	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	8	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	8	no	—
458	C₂³	—	2	8	no	—
459	C₂³	—	2	16	no	—
460	C₂³	—	2	32	no	—
461	C₂³	—	4	32	no	—
462	C₂³	—	4	16	no	—
463	C₂³	—	4	8	no	—
464	C₂³	—	4	32	no	—
465	C₂³	—	4	16	no	—
466	C₂³	—	8	32	no	—
467	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
468	C₂³	C₂²×D₄×C₁₉	1	16	yes	—
469	C₂³	C₂²×D₄×C₁₉	1	32	yes	—
470	C₂³	C₂⁵×C₁₉	1	8	yes	—
471	C₂³	C₂⁵×C₁₉	1	4	yes	—
472	C₂³	C₂⁵×C₁₉	1	2	yes	—
473	C₂³	C₂⁵×C₁₉	1	8	yes	—
474	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
475	Q₈	—	2	32	no	—
476	Q₈	—	2	16	no	—
477	D₄	—	2	32	no	—
478	D₄	—	2	64	no	—
479	D₄	—	2	64	no	—
480	D₄	—	2	16	no	—
481	D₄	—	4	32	no	—
482	D₄	C₂²×D₄×C₁₉	1	64	yes	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	16	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	64	no	—
489	C₂×C₄	—	2	32	no	—
490	C₂×C₄	—	2	16	no	—
491	C₂×C₄	—	2	32	no	—
492	C₂×C₄	—	2	32	no	—
493	C₂×C₄	—	4	32	no	—
494	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
495	C₂×C₄	C₂²×D₄×C₁₉	1	16	yes	—
496	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
497	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
498	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
499	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
500	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
501	C₂²	—	2	8	no	—
502	C₂²	—	2	32	no	—
503	C₂²	—	2	16	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	2	16	no	—
509	C₂²	—	4	32	no	—
510	C₂²	—	4	16	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	16	no	—
513	C₂²	—	8	32	no	—
514	C₂²	C₂³×D₄×C₁₉	1	4	yes	—
515	C₂²	C₂³×D₄×C₁₉	1	16	yes	—
516	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
517	C₂²	C₁₉×#585	1	4	yes	—
518	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
519	C₄	—	2	4	no	—
520	C₄	—	2	8	no	—
521	C₄	—	2	8	no	—
522	C₄	—	2	16	no	—
523	C₄	C₂³×D₄×C₁₉	1	8	yes	—
524	C₂	—	2	4	no	—
525	C₂	—	2	16	no	—
526	C₂	—	4	4	no	—
527	C₂	—	4	8	no	—
528	C₂	C₁₉×#3485	1	4	yes	direct product factor
529	C₂	C₂⁴×D₄×C₁₉	1	1	yes	characteristic
530	C₂	C₂×C₁₉×#585	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. C₂³×#41×C₁₉	C₂	semidirect
3. C₁₉×#3485	C₂	direct (N × H)
4. C₂×C₁₉×#547	C₂	semidirect
5. C₂×C₁₉×#546	C₂	semidirect
6. C₂×C₁₉×#536	C₂	semidirect
7. C₂×C₁₉×#534	C₂	semidirect
8. C₂×C₁₉×#525	C₂	semidirect
9. C₂²×C₁₉×#123	C₂	semidirect
10. C₂×C₁₉×#518	C₂	semidirect
12. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
15. C₂²×#41×C₁₉	C₂²	semidirect
16. C₂²×#41×C₁₉	C₂²	semidirect
17. C₂²×#41×C₁₉	C₂²	semidirect
18. C₂³×Q₈×C₁₉	C₂²	semidirect
21. C₂³×D₄×C₁₉	C₂²	semidirect
22. C₂³×D₄×C₁₉	C₂²	semidirect
23. C₂⁴×C₄×C₁₉	C₂²	semidirect
24. C₂⁴×C₄×C₁₉	C₂²	semidirect
25. C₁₉×#547	C₂²	semidirect
26. C₁₉×#546	C₂²	semidirect
27. C₁₉×#536	C₂²	semidirect
28. C₁₉×#534	C₂²	semidirect
29. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₁₉×#124	C₂²	semidirect
31. C₁₉×#525	C₂²	semidirect
32. C₂×C₁₉×#123	C₂²	semidirect
33. C₂×C₁₉×#123	C₂²	semidirect
34. C₂×C₁₉×#123	C₂²	semidirect
35. C₂×C₁₉×#123	C₂²	semidirect
36. C₂×C₁₉×#123	C₂²	semidirect
37. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₁₉×#121	C₂²	semidirect
40. C₂×C₁₉×#121	C₂²	semidirect
41. C₂×C₁₉×#120	C₂²	semidirect
42. C₂×C₁₉×#120	C₂²	semidirect
43. C₁₉×#518	C₂²	semidirect
44. C₂×C₄×D₄×C₁₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₉	C₂²	semidirect
46. C₂×C₁₉×#117	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
59. C₂×#41×C₁₉	C₂³	semidirect
60. C₂×#41×C₁₉	C₂³	semidirect
64. C₂²×Q₈×C₁₉	C₂³	semidirect
68. C₂²×D₄×C₁₉	D₄	semidirect
77. C₂²×D₄×C₁₉	C₂³	semidirect
78. C₂²×D₄×C₁₉	C₂³	semidirect
89. C₂³×C₄×C₁₉	C₂³	semidirect
90. C₂³×C₄×C₁₉	C₂³	semidirect
91. C₁₉×C₄⋊Q₈	C₂³	semidirect
92. C₁₉×#124	C₂³	semidirect
93. C₁₉×#123	C₂³	semidirect
94. C₁₉×#123	C₂³	semidirect
95. C₁₉×#123	C₂³	semidirect
96. C₁₉×#123	C₂³	semidirect
97. C₁₉×C₂²⋊Q₈	C₂³	semidirect
98. C₁₉×C₂²⋊Q₈	C₂³	semidirect
99. C₁₉×#121	C₂³	semidirect
100. C₁₉×#121	C₂³	semidirect
101. C₁₉×#120	C₂³	semidirect
102. C₁₉×#120	C₂³	semidirect
103. C₄×D₄×C₁₉	C₂³	semidirect
104. C₄×D₄×C₁₉	C₂³	semidirect
105. C₁₉×#117	C₂³	semidirect
109. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
115. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
116. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
148. C₂×D₄×C₁₉	C₂×D₄	semidirect
187. C₂×#3485	C₁₉	direct (N × H)
236. C₂²×H(5,𝔽₂)	C₂×C₁₉	semidirect
237. C₂³×#41	C₂×C₁₉	semidirect
238. #3485	C₂×C₁₉	direct (N × H)
239. C₂×#547	C₂×C₁₉	semidirect
240. C₂×#546	C₂×C₁₉	semidirect
241. C₂×#536	C₂×C₁₉	semidirect
242. C₂×#534	C₂×C₁₉	semidirect
243. C₂×#525	C₂×C₁₉	semidirect
244. C₂²×#123	C₂×C₁₉	semidirect
245. C₂×#518	C₂×C₁₉	semidirect
270. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
273. C₂²×#41	C₂²×C₁₉	semidirect
274. C₂²×#41	C₂²×C₁₉	semidirect
275. C₂²×#41	C₂²×C₁₉	semidirect
276. C₂³×Q₈	C₂²×C₁₉	semidirect
279. C₂³×D₄	C₂²×C₁₉	semidirect
280. C₂³×D₄	C₂²×C₁₉	semidirect
281. C₂⁴×C₄	C₂²×C₁₉	semidirect
282. C₂⁴×C₄	C₂²×C₁₉	semidirect
283. #547	C₂²×C₁₉	semidirect
284. #546	C₂²×C₁₉	semidirect
285. #536	C₂²×C₁₉	semidirect
286. #534	C₂²×C₁₉	semidirect
287. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
288. C₂×#124	C₂²×C₁₉	semidirect
289. #525	C₂²×C₁₉	semidirect
290. C₂×#123	C₂²×C₁₉	semidirect
291. C₂×#123	C₂²×C₁₉	semidirect
292. C₂×#123	C₂²×C₁₉	semidirect
293. C₂×#123	C₂²×C₁₉	semidirect
294. C₂×#123	C₂²×C₁₉	semidirect
295. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
296. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
297. C₂×#121	C₂²×C₁₉	semidirect
298. C₂×#121	C₂²×C₁₉	semidirect
299. C₂×#120	C₂²×C₁₉	semidirect
300. C₂×#120	C₂²×C₁₉	semidirect
301. #518	C₂²×C₁₉	semidirect
302. C₂×C₄×D₄	C₂²×C₁₉	semidirect
303. C₂×C₄×D₄	C₂²×C₁₉	semidirect
304. C₂×#117	C₂²×C₁₉	semidirect
305. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
306. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
307. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
312. C₂×C₁₉	#3485	direct (N × H)
324. C₂×#41	C₂³×C₁₉	semidirect
325. C₂×#41	C₂³×C₁₉	semidirect
329. C₂²×Q₈	C₂³×C₁₉	semidirect
333. C₂²×D₄	D₄×C₁₉	semidirect
342. C₂²×D₄	C₂³×C₁₉	semidirect
343. C₂²×D₄	C₂³×C₁₉	semidirect
354. C₂³×C₄	C₂³×C₁₉	semidirect
355. C₂³×C₄	C₂³×C₁₉	semidirect
356. C₄⋊Q₈	C₂³×C₁₉	semidirect
357. #124	C₂³×C₁₉	semidirect
358. #123	C₂³×C₁₉	semidirect
359. #123	C₂³×C₁₉	semidirect
360. #123	C₂³×C₁₉	semidirect
361. #123	C₂³×C₁₉	semidirect
362. C₂²⋊Q₈	C₂³×C₁₉	semidirect
363. C₂²⋊Q₈	C₂³×C₁₉	semidirect
364. #121	C₂³×C₁₉	semidirect
365. #121	C₂³×C₁₉	semidirect
366. #120	C₂³×C₁₉	semidirect
367. #120	C₂³×C₁₉	semidirect
368. C₄×D₄	C₂³×C₁₉	semidirect
369. C₄×D₄	C₂³×C₁₉	semidirect
370. #117	C₂³×C₁₉	semidirect
374. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
380. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
381. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
383. C₁₉	C₂×#3485	direct (N × H)
414. C₂×D₄	C₂×D₄×C₁₉	semidirect
528. C₂	C₁₉×#3485	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
C₂³×#41×C₁₉	2
C₁₉×#3485	2
C₂×C₁₉×#547	2
C₂×C₁₉×#546	2
C₂×C₁₉×#536	2
C₂×C₁₉×#534	2
C₂×C₁₉×#525	2
C₂²×C₁₉×#123	2
C₂×C₁₉×#518	2
C₂×#3485	19

Subgroups — C2×C19×#3485 #18068733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3485 #18068733