Subgroups — C₂×C₁₉×#3512 #18068768

Order 4864.

7238 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3512	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₉×#553	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#553	C₂	1	8	yes	maximal, complemented
4	C₂×C₁₉×#552	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₉×#541	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#540	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#537	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#529	C₂	1	4	yes	maximal, complemented
10	C₂²×C₁₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#520	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₁₉	C₂²	1	2	yes	—
15	C₁₉×#553	C₂²	1	64	yes	complemented
16	C₁₉×#553	C₂²	1	128	yes	complemented
17	C₁₉×#552	C₂²	1	64	yes	complemented
18	C₁₉×#541	C₂²	1	32	yes	complemented
19	C₁₉×#540	C₂²	1	32	yes	complemented
20	C₁₉×#537	C₂²	1	32	yes	complemented
21	C₁₉×#532	C₂²	1	16	yes	complemented
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₁₉×#529	C₂²	1	64	yes	complemented
25	C₂×C₁₉×#126	C₂²	1	8	yes	—
26	C₂×C₁₉×#126	C₂²	1	8	yes	—
27	C₂×C₁₉×#125	C₂²	1	2	yes	—
28	C₂×C₁₉×#125	C₂²	1	2	yes	—
29	C₂×C₁₉×#125	C₂²	1	4	yes	—
30	C₂×C₁₉×#125	C₂²	1	8	yes	—
31	C₂×C₁₉×#125	C₂²	1	16	yes	complemented
32	C₂×C₁₉×#124	C₂²	1	2	yes	—
33	C₂×C₁₉×#123	C₂²	1	8	yes	—
34	C₂×C₁₉×#123	C₂²	1	8	yes	—
35	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
37	C₂×C₁₉×#121	C₂²	1	4	yes	—
38	C₂×C₁₉×#121	C₂²	1	4	yes	—
39	C₂×C₁₉×#121	C₂²	1	8	yes	—
40	C₂×C₁₉×#121	C₂²	1	4	yes	—
41	C₂×C₁₉×#121	C₂²	1	8	yes	—
42	C₁₉×#520	C₂²	1	32	yes	complemented
43	C₄×#41×C₁₉	C₂²	1	16	yes	complemented
44	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
46	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
47	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
49	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
50	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
51	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
52	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#117	C₂²	1	2	yes	—
54	C₂×C₁₉×#117	C₂²	1	4	yes	—
55	C₂×C₁₉×#117	C₂²	1	8	yes	—
56	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
57	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
58	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
59	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
60	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
61	C₂×#41×C₁₉	—	2	8	no	—
62	C₂×#41×C₁₉	—	2	16	no	—
63	C₂×#41×C₁₉	C₂³	1	8	yes	—
64	C₂×#41×C₁₉	C₂³	1	16	yes	—
65	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
72	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
73	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
79	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
81	C₁₉×#127	C₂³	1	8	yes	—
82	C₁₉×#126	C₂³	1	64	yes	—
83	C₁₉×#126	C₂³	1	64	yes	—
84	C₁₉×#125	C₂³	1	16	yes	—
85	C₁₉×#125	C₂³	1	16	yes	—
86	C₁₉×#125	C₂³	1	32	yes	—
87	C₁₉×#125	C₂³	1	64	yes	—
88	C₁₉×#124	C₂³	1	16	yes	—
89	C₁₉×#123	C₂³	1	64	yes	—
90	C₁₉×#123	C₂³	1	64	yes	—
91	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
92	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
93	C₁₉×#121	C₂³	1	32	yes	—
94	C₁₉×#121	C₂³	1	32	yes	—
95	C₁₉×#121	C₂³	1	64	yes	—
96	C₁₉×#121	C₂³	1	32	yes	—
97	C₁₉×#121	C₂³	1	64	yes	—
98	C₄×Q₈×C₁₉	C₂³	1	16	yes	—
99	C₄×Q₈×C₁₉	C₂³	1	32	yes	—
100	C₄×D₄×C₁₉	C₂³	1	32	yes	—
101	C₄×D₄×C₁₉	C₂³	1	16	yes	—
102	C₄×D₄×C₁₉	C₂³	1	32	yes	—
103	C₄×D₄×C₁₉	C₂³	1	64	yes	—
104	C₄×D₄×C₁₉	C₂³	1	64	yes	—
105	C₄×D₄×C₁₉	C₂³	1	32	yes	—
106	C₁₉×#117	C₂³	1	8	yes	—
107	C₁₉×#117	C₂³	1	16	yes	—
108	C₁₉×#117	C₂³	1	32	yes	—
109	C₁₉×#117	C₂³	1	64	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	32	yes	—
117	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
118	C₂×C₄⋊C₄×C₁₉	C₂³	1	32	yes	—
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
127	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
135	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
136	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
137	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
138	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
139	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
140	#41×C₁₉	—	2	32	no	—
141	#41×C₁₉	—	2	64	no	—
142	C₂×Q₈×C₁₉	—	2	4	no	—
143	C₂×Q₈×C₁₉	—	2	8	no	—
144	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
145	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
146	C₂×D₄×C₁₉	—	2	8	no	—
147	C₂×D₄×C₁₉	—	2	16	no	—
148	C₂×D₄×C₁₉	—	2	4	no	—
149	C₂×D₄×C₁₉	—	2	8	no	—
150	C₂×D₄×C₁₉	—	4	16	no	—
151	C₂×D₄×C₁₉	—	4	8	no	—
152	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
153	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
154	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
155	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
156	C₂×D₄×C₁₉	C₂⁴	1	32	yes	—
157	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
158	C₂²×C₄×C₁₉	—	2	16	no	—
159	C₂²×C₄×C₁₉	—	2	8	no	—
160	C₂²×C₄×C₁₉	—	4	8	no	—
161	C₂²×C₄×C₁₉	—	4	16	no	—
162	C₂²×C₄×C₁₉	—	4	4	no	—
163	C₂²×C₄×C₁₉	—	4	8	no	—
164	C₂²×C₄×C₁₉	#41	1	8	yes	—
165	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
166	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
167	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
173	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
175	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
176	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
177	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
181	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
182	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
183	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
184	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
185	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
186	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
187	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
188	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
189	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
190	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
191	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
192	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
193	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
194	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
195	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
196	C₄²×C₁₉	C₂⁴	1	4	yes	—
197	C₄²×C₁₉	C₂⁴	1	8	yes	—
198	C₄²×C₁₉	C₂⁴	1	16	yes	—
199	C₄²×C₁₉	C₂⁴	1	4	yes	—
200	C₄²×C₁₉	C₂⁴	1	8	yes	—
201	C₄²×C₁₉	C₂⁴	1	32	yes	—
202	C₂×#3512	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂³×C₁₉	—	2	4	no	—
204	C₂³×C₁₉	—	2	8	no	—
205	C₂³×C₁₉	—	2	4	no	—
206	C₂³×C₁₉	—	2	8	no	—
207	C₂³×C₁₉	—	2	8	no	—
208	C₂³×C₁₉	—	2	8	no	—
209	C₂³×C₁₉	C₂×#41	1	4	yes	—
210	C₂³×C₁₉	C₂⁵	1	8	yes	—
211	C₂³×C₁₉	C₂⁵	1	4	yes	—
212	C₂³×C₁₉	C₂⁵	1	2	yes	—
213	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
214	Q₈×C₁₉	—	2	8	no	—
215	Q₈×C₁₉	—	2	16	no	—
216	D₄×C₁₉	—	2	16	no	—
217	D₄×C₁₉	—	2	32	no	—
218	D₄×C₁₉	—	2	8	no	—
219	D₄×C₁₉	—	2	16	no	—
220	D₄×C₁₉	—	4	32	no	—
221	D₄×C₁₉	—	4	16	no	—
222	C₂×C₄×C₁₉	—	2	8	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	8	no	—
226	C₂×C₄×C₁₉	—	2	16	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	32	no	—
229	C₂×C₄×C₁₉	—	2	16	no	—
230	C₂×C₄×C₁₉	—	4	16	no	—
231	C₂×C₄×C₁₉	—	4	32	no	—
232	C₂×C₄×C₁₉	—	4	8	no	—
233	C₂×C₄×C₁₉	—	4	16	no	—
234	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
235	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
236	C₂×C₄×C₁₉	C₂×#41	1	16	yes	—
237	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
238	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
239	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
240	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
241	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
242	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
243	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
244	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
245	#3512	C₂×C₁₉	1	32	yes	direct product factor
246	C₂×#553	C₂×C₁₉	1	4	yes	complemented
247	C₂×#553	C₂×C₁₉	1	8	yes	complemented
248	C₂×#552	C₂×C₁₉	1	4	yes	complemented
249	C₂×#541	C₂×C₁₉	1	2	yes	complemented
250	C₂×#540	C₂×C₁₉	1	2	yes	complemented
251	C₂×#537	C₂×C₁₉	1	2	yes	complemented
252	C₂×#532	C₂×C₁₉	1	1	yes	characteristic, complemented
253	C₂×#529	C₂×C₁₉	1	4	yes	complemented
254	C₂²×#125	C₂×C₁₉	1	1	yes	characteristic, complemented
255	C₂×#520	C₂×C₁₉	1	2	yes	complemented
256	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
257	C₂²×C₁₉	—	2	4	no	—
258	C₂²×C₁₉	—	2	8	no	—
259	C₂²×C₁₉	—	2	8	no	—
260	C₂²×C₁₉	—	2	4	no	—
261	C₂²×C₁₉	—	2	8	no	—
262	C₂²×C₁₉	—	2	8	no	—
263	C₂²×C₁₉	—	2	8	no	—
264	C₂²×C₁₉	—	4	16	no	—
265	C₂²×C₁₉	—	4	8	no	—
266	C₂²×C₁₉	C₂²×#41	1	4	yes	—
267	C₂²×C₁₉	C₂²×#41	1	2	yes	—
268	C₂²×C₁₉	#585	1	4	yes	—
269	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
270	C₄×C₁₉	—	2	8	no	—
271	C₄×C₁₉	—	2	4	no	—
272	C₄×C₁₉	—	2	4	no	—
273	C₄×C₁₉	—	2	8	no	—
274	C₄×C₁₉	—	2	16	no	—
275	C₄×C₁₉	—	2	4	no	—
276	C₄×C₁₉	C₂²×#41	1	4	yes	—
277	C₄×C₁₉	C₂²×#41	1	4	yes	—
278	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×#41	C₂²×C₁₉	1	2	yes	—
280	#553	C₂²×C₁₉	1	64	yes	complemented
281	#553	C₂²×C₁₉	1	128	yes	complemented
282	#552	C₂²×C₁₉	1	64	yes	complemented
283	#541	C₂²×C₁₉	1	32	yes	complemented
284	#540	C₂²×C₁₉	1	32	yes	complemented
285	#537	C₂²×C₁₉	1	32	yes	complemented
286	#532	C₂²×C₁₉	1	16	yes	complemented
287	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
289	#529	C₂²×C₁₉	1	64	yes	complemented
290	C₂×#126	C₂²×C₁₉	1	8	yes	—
291	C₂×#126	C₂²×C₁₉	1	8	yes	—
292	C₂×#125	C₂²×C₁₉	1	2	yes	—
293	C₂×#125	C₂²×C₁₉	1	2	yes	—
294	C₂×#125	C₂²×C₁₉	1	4	yes	—
295	C₂×#125	C₂²×C₁₉	1	8	yes	—
296	C₂×#125	C₂²×C₁₉	1	16	yes	complemented
297	C₂×#124	C₂²×C₁₉	1	2	yes	—
298	C₂×#123	C₂²×C₁₉	1	8	yes	—
299	C₂×#123	C₂²×C₁₉	1	8	yes	—
300	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
301	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
302	C₂×#121	C₂²×C₁₉	1	4	yes	—
303	C₂×#121	C₂²×C₁₉	1	4	yes	—
304	C₂×#121	C₂²×C₁₉	1	8	yes	—
305	C₂×#121	C₂²×C₁₉	1	4	yes	—
306	C₂×#121	C₂²×C₁₉	1	8	yes	—
307	#520	C₂²×C₁₉	1	32	yes	complemented
308	C₄×#41	C₂²×C₁₉	1	16	yes	complemented
309	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
310	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
311	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
312	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
313	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
314	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
315	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
316	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
317	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#117	C₂²×C₁₉	1	2	yes	—
319	C₂×#117	C₂²×C₁₉	1	4	yes	—
320	C₂×#117	C₂²×C₁₉	1	8	yes	—
321	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
322	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
323	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
324	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
325	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
326	C₂×C₁₉	—	2	4	no	—
327	C₂×C₁₉	—	4	8	no	—
328	C₂×C₁₉	—	4	4	no	—
329	C₂×C₁₉	#3512	1	4	yes	direct product factor
330	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
331	C₂×C₁₉	C₂×#585	1	2	yes	—
332	C₂×#41	—	2	8	no	—
333	C₂×#41	—	2	16	no	—
334	C₂×#41	C₂³×C₁₉	1	8	yes	—
335	C₂×#41	C₂³×C₁₉	1	16	yes	—
336	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
338	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
339	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
340	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
342	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
343	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
344	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
345	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
346	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
347	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
349	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
350	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
352	#127	C₂³×C₁₉	1	8	yes	—
353	#126	C₂³×C₁₉	1	64	yes	—
354	#126	C₂³×C₁₉	1	64	yes	—
355	#125	C₂³×C₁₉	1	16	yes	—
356	#125	C₂³×C₁₉	1	16	yes	—
357	#125	C₂³×C₁₉	1	32	yes	—
358	#125	C₂³×C₁₉	1	64	yes	—
359	#124	C₂³×C₁₉	1	16	yes	—
360	#123	C₂³×C₁₉	1	64	yes	—
361	#123	C₂³×C₁₉	1	64	yes	—
362	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
363	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
364	#121	C₂³×C₁₉	1	32	yes	—
365	#121	C₂³×C₁₉	1	32	yes	—
366	#121	C₂³×C₁₉	1	64	yes	—
367	#121	C₂³×C₁₉	1	32	yes	—
368	#121	C₂³×C₁₉	1	64	yes	—
369	C₄×Q₈	C₂³×C₁₉	1	16	yes	—
370	C₄×Q₈	C₂³×C₁₉	1	32	yes	—
371	C₄×D₄	C₂³×C₁₉	1	32	yes	—
372	C₄×D₄	C₂³×C₁₉	1	16	yes	—
373	C₄×D₄	C₂³×C₁₉	1	32	yes	—
374	C₄×D₄	C₂³×C₁₉	1	64	yes	—
375	C₄×D₄	C₂³×C₁₉	1	64	yes	—
376	C₄×D₄	C₂³×C₁₉	1	32	yes	—
377	#117	C₂³×C₁₉	1	8	yes	—
378	#117	C₂³×C₁₉	1	16	yes	—
379	#117	C₂³×C₁₉	1	32	yes	—
380	#117	C₂³×C₁₉	1	64	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₉	1	32	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₉	1	32	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
400	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
401	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
402	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
403	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
405	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
406	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
407	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
408	C₁₉	C₂×#3512	1	1	yes	characteristic, direct product factor, Sylow
409	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
410	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
411	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
412	#41	—	2	32	no	—
413	#41	—	2	64	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	8	no	—
416	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
417	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	16	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	4	16	no	—
423	C₂×D₄	—	4	8	no	—
424	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
425	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
426	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
427	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
428	C₂×D₄	C₂⁴×C₁₉	1	32	yes	—
429	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
430	C₂²×C₄	—	2	16	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	4	8	no	—
433	C₂²×C₄	—	4	16	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	#41×C₁₉	1	8	yes	—
437	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
443	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
444	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
445	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
446	C₂²×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	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
452	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
453	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
454	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
455	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
456	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
457	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
458	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
459	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
460	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
461	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
462	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
463	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
464	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
465	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
466	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
467	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
468	C₄²	C₂⁴×C₁₉	1	4	yes	—
469	C₄²	C₂⁴×C₁₉	1	8	yes	—
470	C₄²	C₂⁴×C₁₉	1	16	yes	—
471	C₄²	C₂⁴×C₁₉	1	4	yes	—
472	C₄²	C₂⁴×C₁₉	1	8	yes	—
473	C₄²	C₂⁴×C₁₉	1	32	yes	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	8	no	—
480	C₂³	C₂×#41×C₁₉	1	4	yes	—
481	C₂³	C₂⁵×C₁₉	1	8	yes	—
482	C₂³	C₂⁵×C₁₉	1	4	yes	—
483	C₂³	C₂⁵×C₁₉	1	2	yes	—
484	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
485	Q₈	—	2	8	no	—
486	Q₈	—	2	16	no	—
487	D₄	—	2	16	no	—
488	D₄	—	2	32	no	—
489	D₄	—	2	8	no	—
490	D₄	—	2	16	no	—
491	D₄	—	4	32	no	—
492	D₄	—	4	16	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	16	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	32	no	—
500	C₂×C₄	—	2	16	no	—
501	C₂×C₄	—	4	16	no	—
502	C₂×C₄	—	4	32	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	—	4	16	no	—
505	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
506	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
507	C₂×C₄	C₂×#41×C₁₉	1	16	yes	—
508	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
509	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
510	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
511	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
512	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
513	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
514	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
515	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
516	C₂²	—	2	8	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	8	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	8	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	4	16	no	—
524	C₂²	—	4	8	no	—
525	C₂²	C₂²×#41×C₁₉	1	4	yes	—
526	C₂²	C₂²×#41×C₁₉	1	2	yes	—
527	C₂²	C₁₉×#585	1	4	yes	—
528	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
529	C₄	—	2	8	no	—
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	8	no	—
533	C₄	—	2	16	no	—
534	C₄	—	2	4	no	—
535	C₄	C₂²×#41×C₁₉	1	4	yes	—
536	C₄	C₂²×#41×C₁₉	1	4	yes	—
537	C₂	—	2	4	no	—
538	C₂	—	4	8	no	—
539	C₂	—	4	4	no	—
540	C₂	C₁₉×#3512	1	4	yes	direct product factor
541	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
542	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. C₁₉×#3512	C₂	direct (N × H)
2. C₂×C₁₉×#553	C₂	semidirect
3. C₂×C₁₉×#553	C₂	semidirect
4. C₂×C₁₉×#552	C₂	semidirect
5. C₂×C₁₉×#541	C₂	semidirect
6. C₂×C₁₉×#540	C₂	semidirect
7. C₂×C₁₉×#537	C₂	semidirect
8. C₂×C₁₉×#532	C₂	semidirect
9. C₂×C₁₉×#529	C₂	semidirect
10. C₂²×C₁₉×#125	C₂	semidirect
11. C₂×C₁₉×#520	C₂	semidirect
12. C₂×C₄×#41×C₁₉	C₂	semidirect
15. C₁₉×#553	C₂²	semidirect
16. C₁₉×#553	C₂²	semidirect
17. C₁₉×#552	C₂²	semidirect
18. C₁₉×#541	C₂²	semidirect
19. C₁₉×#540	C₂²	semidirect
20. C₁₉×#537	C₂²	semidirect
21. C₁₉×#532	C₂²	semidirect
24. C₁₉×#529	C₂²	semidirect
31. C₂×C₁₉×#125	C₂²	semidirect
42. C₁₉×#520	C₂²	semidirect
43. C₄×#41×C₁₉	C₂²	semidirect
202. C₂×#3512	C₁₉	direct (N × H)
245. #3512	C₂×C₁₉	direct (N × H)
246. C₂×#553	C₂×C₁₉	semidirect
247. C₂×#553	C₂×C₁₉	semidirect
248. C₂×#552	C₂×C₁₉	semidirect
249. C₂×#541	C₂×C₁₉	semidirect
250. C₂×#540	C₂×C₁₉	semidirect
251. C₂×#537	C₂×C₁₉	semidirect
252. C₂×#532	C₂×C₁₉	semidirect
253. C₂×#529	C₂×C₁₉	semidirect
254. C₂²×#125	C₂×C₁₉	semidirect
255. C₂×#520	C₂×C₁₉	semidirect
256. C₂×C₄×#41	C₂×C₁₉	semidirect
280. #553	C₂²×C₁₉	semidirect
281. #553	C₂²×C₁₉	semidirect
282. #552	C₂²×C₁₉	semidirect
283. #541	C₂²×C₁₉	semidirect
284. #540	C₂²×C₁₉	semidirect
285. #537	C₂²×C₁₉	semidirect
286. #532	C₂²×C₁₉	semidirect
289. #529	C₂²×C₁₉	semidirect
296. C₂×#125	C₂²×C₁₉	semidirect
307. #520	C₂²×C₁₉	semidirect
308. C₄×#41	C₂²×C₁₉	semidirect
329. C₂×C₁₉	#3512	direct (N × H)
408. C₁₉	C₂×#3512	direct (N × H)
540. C₂	C₁₉×#3512	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#3512	2
C₂×C₁₉×#553	2
C₂×C₁₉×#552	2
C₂×C₁₉×#541	2
C₂×C₁₉×#540	2
C₂×C₁₉×#537	2
C₂×C₁₉×#532	2
C₂×C₁₉×#529	2
C₂²×C₁₉×#125	2
C₂×C₁₉×#520	2
C₂×C₄×#41×C₁₉	2
C₂×#3512	19

Subgroups — C2×C19×#3512 #18068768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3512 #18068768