Subgroups — C₂×C₁₉×#3538 #18068684

Order 4864.

7162 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×#3538	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₉×#563	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#552	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#551	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×Q₈×C₁₉	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×#544	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#541	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#539	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₉×#536	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#525	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₉	C₂²	1	2	yes	complemented
15	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#563	C₂²	1	64	yes	complemented
17	C₁₉×#552	C₂²	1	64	yes	complemented
18	C₁₉×#551	C₂²	1	64	yes	complemented
19	D₄×Q₈×C₁₉	C₂²	1	64	yes	complemented
20	C₁₉×#544	C₂²	1	64	yes	complemented
21	C₁₉×#541	C₂²	1	32	yes	complemented
22	C₁₉×#539	C₂²	1	64	yes	complemented
23	C₁₉×#536	C₂²	1	32	yes	complemented
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	4	yes	complemented
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	8	yes	complemented
27	C₂×C₁₉×#126	C₂²	1	8	yes	—
28	C₂×C₁₉×#126	C₂²	1	8	yes	complemented
29	C₂×C₁₉×#125	C₂²	1	8	yes	complemented
30	C₂×C₁₉×#125	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#125	C₂²	1	8	yes	complemented
32	C₂×C₁₉×#124	C₂²	1	4	yes	—
33	C₁₉×#525	C₂²	1	16	yes	—
34	C₂×C₁₉×#123	C₂²	1	2	yes	—
35	C₂×C₁₉×#123	C₂²	1	4	yes	—
36	C₂×C₁₉×#123	C₂²	1	8	yes	—
37	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
38	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
39	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
40	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
41	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
42	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	—
44	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	32	yes	complemented
45	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
47	C₂×C₁₉×#121	C₂²	1	2	yes	—
48	C₂×C₁₉×#120	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
50	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
51	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
52	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
53	C₂×C₁₉×#117	C₂²	1	8	yes	—
54	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
55	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
56	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
57	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
58	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×#41×C₁₉	—	4	4	no	—
60	C₂×#41×C₁₉	C₂³	1	8	yes	—
61	C₂²×Q₈×C₁₉	—	4	8	no	—
62	C₂²×Q₈×C₁₉	—	4	8	no	—
63	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
64	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
65	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
66	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₉	C₂³	1	16	yes	—
68	C₂²×Q₈×C₁₉	C₂³	1	16	yes	complemented
69	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	—	4	4	no	—
73	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
82	C₁₉×C₄⋊Q₈	C₂³	1	32	yes	complemented
83	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	complemented
84	C₁₉×C₄⋊Q₈	C₂³	1	64	yes	complemented
85	C₁₉×#126	C₂³	1	64	yes	—
86	C₁₉×#126	C₂³	1	64	yes	complemented
87	C₁₉×#125	C₂³	1	64	yes	complemented
88	C₁₉×#125	C₂³	1	16	yes	complemented
89	C₁₉×#125	C₂³	1	64	yes	complemented
90	C₁₉×#124	C₂³	1	32	yes	—
91	C₁₉×#123	C₂³	1	16	yes	—
92	C₁₉×#123	C₂³	1	32	yes	—
93	C₁₉×#123	C₂³	1	64	yes	—
94	C₁₉×#123	C₂³	1	32	yes	complemented
95	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
96	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
97	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
98	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	—
99	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
100	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	—
101	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
102	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	complemented
103	C₁₉×#121	C₂³	1	16	yes	—
104	C₁₉×#120	C₂³	1	16	yes	—
105	C₄×Q₈×C₁₉	C₂³	1	32	yes	complemented
106	C₄×D₄×C₁₉	C₂³	1	32	yes	—
107	C₄×D₄×C₁₉	C₂³	1	64	yes	—
108	C₁₉×#117	C₂³	1	8	yes	—
109	C₁₉×#117	C₂³	1	64	yes	—
110	C₁₉×#117	C₂³	1	16	yes	complemented
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	8	yes	—
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	32	yes	—
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
117	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
123	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
124	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
125	C₂×C₂²⋊C₄×C₁₉	C₂³	1	32	yes	—
126	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
131	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
134	C₂⁴×C₁₉	—	2	8	no	—
135	C₂⁴×C₁₉	—	4	2	no	—
136	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
138	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
139	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
140	#41×C₁₉	—	4	16	no	—
141	C₂×Q₈×C₁₉	—	2	16	no	—
142	C₂×Q₈×C₁₉	—	4	8	no	—
143	C₂×Q₈×C₁₉	—	4	8	no	—
144	C₂×Q₈×C₁₉	—	4	2	no	—
145	C₂×Q₈×C₁₉	—	4	32	no	—
146	C₂×Q₈×C₁₉	—	4	32	no	—
147	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
148	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
149	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
150	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
151	C₂×D₄×C₁₉	—	2	16	no	—
152	C₂×D₄×C₁₉	—	4	2	no	—
153	C₂×D₄×C₁₉	—	4	4	no	—
154	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
155	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
156	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₉	—	2	16	no	—
158	C₂²×C₄×C₁₉	—	2	8	no	—
159	C₂²×C₄×C₁₉	—	2	4	no	—
160	C₂²×C₄×C₁₉	—	2	8	no	—
161	C₂²×C₄×C₁₉	—	4	16	no	—
162	C₂²×C₄×C₁₉	—	4	4	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	4	8	no	—
165	C₂²×C₄×C₁₉	—	4	8	no	—
166	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
167	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
168	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
170	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
177	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
178	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
182	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
183	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
184	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
185	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
186	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
187	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
188	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
189	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
190	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
191	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
192	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
193	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
194	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
195	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
196	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
197	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
198	C₄²×C₁₉	C₂⁴	1	16	yes	—
199	C₄²×C₁₉	C₂⁴	1	8	yes	—
200	C₄²×C₁₉	C₂⁴	1	32	yes	—
201	C₂×#3538	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₁₉	—	2	4	no	—
203	C₂³×C₁₉	—	2	4	no	—
204	C₂³×C₁₉	—	2	4	no	—
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	2	8	no	—
207	C₂³×C₁₉	—	2	16	no	—
208	C₂³×C₁₉	—	2	4	no	—
209	C₂³×C₁₉	—	4	4	no	—
210	C₂³×C₁₉	—	4	16	no	—
211	C₂³×C₁₉	2₋¹⁺⁴	1	8	yes	—
212	C₂³×C₁₉	C₂⁵	1	2	yes	—
213	C₂³×C₁₉	C₂⁵	1	4	yes	—
214	C₂³×C₁₉	C₂⁵	1	4	yes	—
215	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
216	Q₈×C₁₉	—	2	32	no	—
217	Q₈×C₁₉	—	4	16	no	—
218	Q₈×C₁₉	—	4	16	no	—
219	Q₈×C₁₉	—	4	4	no	—
220	D₄×C₁₉	—	2	32	no	—
221	D₄×C₁₉	—	4	4	no	—
222	D₄×C₁₉	—	4	8	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	16	no	—
227	C₂×C₄×C₁₉	—	2	32	no	—
228	C₂×C₄×C₁₉	—	2	16	no	—
229	C₂×C₄×C₁₉	—	2	8	no	—
230	C₂×C₄×C₁₉	—	2	16	no	—
231	C₂×C₄×C₁₉	—	2	8	no	—
232	C₂×C₄×C₁₉	—	2	16	no	—
233	C₂×C₄×C₁₉	—	4	8	no	—
234	C₂×C₄×C₁₉	—	4	4	no	—
235	C₂×C₄×C₁₉	—	4	16	no	—
236	C₂×C₄×C₁₉	—	4	16	no	—
237	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
238	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
239	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
240	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
241	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
242	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
243	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
244	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
245	#3538	C₂×C₁₉	1	32	yes	direct product factor
246	C₂×#563	C₂×C₁₉	1	4	yes	complemented
247	C₂×#552	C₂×C₁₉	1	4	yes	complemented
248	C₂×#551	C₂×C₁₉	1	4	yes	complemented
249	C₂×D₄×Q₈	C₂×C₁₉	1	4	yes	complemented
250	C₂×#544	C₂×C₁₉	1	4	yes	complemented
251	C₂×#541	C₂×C₁₉	1	2	yes	complemented
252	C₂×#539	C₂×C₁₉	1	4	yes	complemented
253	C₂×#536	C₂×C₁₉	1	2	yes	complemented
254	C₂×#525	C₂×C₁₉	1	1	yes	characteristic
255	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	2	yes	complemented
256	C₂²×C₁₉	—	2	4	no	—
257	C₂²×C₁₉	—	2	4	no	—
258	C₂²×C₁₉	—	2	16	no	—
259	C₂²×C₁₉	—	2	4	no	—
260	C₂²×C₁₉	—	2	2	no	—
261	C₂²×C₁₉	—	2	8	no	—
262	C₂²×C₁₉	—	2	4	no	—
263	C₂²×C₁₉	—	4	16	no	—
264	C₂²×C₁₉	—	4	8	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
267	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	8	yes	—
268	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	4	yes	—
269	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
270	C₄×C₁₉	—	2	2	no	—
271	C₄×C₁₉	—	2	4	no	—
272	C₄×C₁₉	—	2	4	no	—
273	C₄×C₁₉	—	2	16	no	—
274	C₄×C₁₉	—	2	16	no	—
275	C₄×C₁₉	—	2	8	no	—
276	C₄×C₁₉	C₂×H(5,𝔽₂)	1	4	yes	—
277	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
278	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
279	C₂³×Q₈	C₂²×C₁₉	1	2	yes	complemented
280	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
281	#563	C₂²×C₁₉	1	64	yes	complemented
282	#552	C₂²×C₁₉	1	64	yes	complemented
283	#551	C₂²×C₁₉	1	64	yes	complemented
284	D₄×Q₈	C₂²×C₁₉	1	64	yes	complemented
285	#544	C₂²×C₁₉	1	64	yes	complemented
286	#541	C₂²×C₁₉	1	32	yes	complemented
287	#539	C₂²×C₁₉	1	64	yes	complemented
288	#536	C₂²×C₁₉	1	32	yes	complemented
289	C₂×C₄⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
290	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
291	C₂×C₄⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
292	C₂×#126	C₂²×C₁₉	1	8	yes	—
293	C₂×#126	C₂²×C₁₉	1	8	yes	complemented
294	C₂×#125	C₂²×C₁₉	1	8	yes	complemented
295	C₂×#125	C₂²×C₁₉	1	2	yes	complemented
296	C₂×#125	C₂²×C₁₉	1	8	yes	complemented
297	C₂×#124	C₂²×C₁₉	1	4	yes	—
298	#525	C₂²×C₁₉	1	16	yes	—
299	C₂×#123	C₂²×C₁₉	1	2	yes	—
300	C₂×#123	C₂²×C₁₉	1	4	yes	—
301	C₂×#123	C₂²×C₁₉	1	8	yes	—
302	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
303	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
304	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
305	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
306	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
307	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
308	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	—
309	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	32	yes	complemented
310	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
311	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
312	C₂×#121	C₂²×C₁₉	1	2	yes	—
313	C₂×#120	C₂²×C₁₉	1	2	yes	—
314	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
315	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
316	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
317	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#117	C₂²×C₁₉	1	8	yes	—
319	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
320	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
321	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
322	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
323	C₂×C₁₉	—	2	8	no	—
324	C₂×C₁₉	—	4	4	no	—
325	C₂×C₁₉	—	4	2	no	—
326	C₂×C₁₉	#3538	1	4	yes	direct product factor
327	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×C₁₉	C₂²×2₋¹⁺⁴	1	2	yes	—
329	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
330	C₂×#41	—	4	4	no	—
331	C₂×#41	C₂³×C₁₉	1	8	yes	—
332	C₂²×Q₈	—	4	8	no	—
333	C₂²×Q₈	—	4	8	no	—
334	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
335	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
336	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
337	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₁₉	1	16	yes	—
339	C₂²×Q₈	C₂³×C₁₉	1	16	yes	complemented
340	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
341	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
342	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂³×C₄	—	4	4	no	—
344	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
345	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
346	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
349	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
350	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
351	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
353	C₄⋊Q₈	C₂³×C₁₉	1	32	yes	complemented
354	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
355	C₄⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
356	#126	C₂³×C₁₉	1	64	yes	—
357	#126	C₂³×C₁₉	1	64	yes	complemented
358	#125	C₂³×C₁₉	1	64	yes	complemented
359	#125	C₂³×C₁₉	1	16	yes	complemented
360	#125	C₂³×C₁₉	1	64	yes	complemented
361	#124	C₂³×C₁₉	1	32	yes	—
362	#123	C₂³×C₁₉	1	16	yes	—
363	#123	C₂³×C₁₉	1	32	yes	—
364	#123	C₂³×C₁₉	1	64	yes	—
365	#123	C₂³×C₁₉	1	32	yes	complemented
366	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
367	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
368	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
369	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	—
370	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
371	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	—
372	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	complemented
373	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
374	#121	C₂³×C₁₉	1	16	yes	—
375	#120	C₂³×C₁₉	1	16	yes	—
376	C₄×Q₈	C₂³×C₁₉	1	32	yes	complemented
377	C₄×D₄	C₂³×C₁₉	1	32	yes	—
378	C₄×D₄	C₂³×C₁₉	1	64	yes	—
379	#117	C₂³×C₁₉	1	8	yes	—
380	#117	C₂³×C₁₉	1	64	yes	—
381	#117	C₂³×C₁₉	1	16	yes	complemented
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	8	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	32	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₉	1	32	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
402	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
403	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
405	C₁₉	C₂×#3538	1	1	yes	characteristic, direct product factor, Sylow
406	C₂⁴	—	2	8	no	—
407	C₂⁴	—	4	2	no	—
408	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
409	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
410	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
411	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
412	#41	—	4	16	no	—
413	C₂×Q₈	—	2	16	no	—
414	C₂×Q₈	—	4	8	no	—
415	C₂×Q₈	—	4	8	no	—
416	C₂×Q₈	—	4	2	no	—
417	C₂×Q₈	—	4	32	no	—
418	C₂×Q₈	—	4	32	no	—
419	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
420	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
421	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
422	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
423	C₂×D₄	—	2	16	no	—
424	C₂×D₄	—	4	2	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
427	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
428	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
429	C₂²×C₄	—	2	16	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	8	no	—
433	C₂²×C₄	—	4	16	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	8	no	—
437	C₂²×C₄	—	4	8	no	—
438	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
440	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
442	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
444	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
446	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
448	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
449	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
450	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
451	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
453	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
454	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
455	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
456	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
457	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
458	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
459	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
460	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
461	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
462	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
463	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
464	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
465	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
466	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
467	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
468	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
469	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
470	C₄²	C₂⁴×C₁₉	1	16	yes	—
471	C₄²	C₂⁴×C₁₉	1	8	yes	—
472	C₄²	C₂⁴×C₁₉	1	32	yes	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	16	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	4	16	no	—
482	C₂³	C₁₉×2₋¹⁺⁴	1	8	yes	—
483	C₂³	C₂⁵×C₁₉	1	2	yes	—
484	C₂³	C₂⁵×C₁₉	1	4	yes	—
485	C₂³	C₂⁵×C₁₉	1	4	yes	—
486	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
487	Q₈	—	2	32	no	—
488	Q₈	—	4	16	no	—
489	Q₈	—	4	16	no	—
490	Q₈	—	4	4	no	—
491	D₄	—	2	32	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	8	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	16	no	—
498	C₂×C₄	—	2	32	no	—
499	C₂×C₄	—	2	16	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	16	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	16	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	16	no	—
507	C₂×C₄	—	4	16	no	—
508	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
509	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
510	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
511	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
512	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
513	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
514	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
515	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
516	C₂²	—	2	16	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	4	16	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	8	no	—
526	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
527	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	8	yes	—
528	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	4	yes	—
529	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
530	C₄	—	2	2	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	16	no	—
534	C₄	—	2	16	no	—
535	C₄	—	2	8	no	—
536	C₄	C₂×C₁₉×H(5,𝔽₂)	1	4	yes	—
537	C₂	—	2	8	no	—
538	C₂	—	4	2	no	—
539	C₂	—	4	4	no	—
540	C₂	C₁₉×#3538	1	4	yes	direct product factor
541	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
542	C₂	C₂²×C₁₉×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
prime radical	C₂×C₁₉×#525	C₂
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×#3538	C₂	direct (N × H)
2. C₂×C₁₉×#563	C₂	semidirect
3. C₂×C₁₉×#552	C₂	semidirect
4. C₂×C₁₉×#551	C₂	semidirect
5. C₂×D₄×Q₈×C₁₉	C₂	semidirect
6. C₂×C₁₉×#544	C₂	semidirect
7. C₂×C₁₉×#541	C₂	semidirect
8. C₂×C₁₉×#539	C₂	semidirect
9. C₂×C₁₉×#536	C₂	semidirect
11. C₂²×C₁₉×C₂²⋊Q₈	C₂	semidirect
14. C₂³×Q₈×C₁₉	C₂²	semidirect
16. C₁₉×#563	C₂²	semidirect
17. C₁₉×#552	C₂²	semidirect
18. C₁₉×#551	C₂²	semidirect
19. D₄×Q₈×C₁₉	C₂²	semidirect
20. C₁₉×#544	C₂²	semidirect
21. C₁₉×#541	C₂²	semidirect
22. C₁₉×#539	C₂²	semidirect
23. C₁₉×#536	C₂²	semidirect
24. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₁₉×#126	C₂²	semidirect
29. C₂×C₁₉×#125	C₂²	semidirect
30. C₂×C₁₉×#125	C₂²	semidirect
31. C₂×C₁₉×#125	C₂²	semidirect
37. C₂×C₁₉×#123	C₂²	semidirect
44. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
46. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
54. C₂×C₁₉×#117	C₂²	semidirect
68. C₂²×Q₈×C₁₉	C₂³	semidirect
82. C₁₉×C₄⋊Q₈	C₂³	semidirect
83. C₁₉×C₄⋊Q₈	C₂³	semidirect
84. C₁₉×C₄⋊Q₈	C₂³	semidirect
86. C₁₉×#126	C₂³	semidirect
87. C₁₉×#125	C₂³	semidirect
88. C₁₉×#125	C₂³	semidirect
89. C₁₉×#125	C₂³	semidirect
94. C₁₉×#123	C₂³	semidirect
101. C₁₉×C₂²⋊Q₈	C₂³	semidirect
102. C₁₉×C₂²⋊Q₈	C₂³	semidirect
105. C₄×Q₈×C₁₉	C₂³	semidirect
110. C₁₉×#117	C₂³	semidirect
201. C₂×#3538	C₁₉	direct (N × H)
245. #3538	C₂×C₁₉	direct (N × H)
246. C₂×#563	C₂×C₁₉	semidirect
247. C₂×#552	C₂×C₁₉	semidirect
248. C₂×#551	C₂×C₁₉	semidirect
249. C₂×D₄×Q₈	C₂×C₁₉	semidirect
250. C₂×#544	C₂×C₁₉	semidirect
251. C₂×#541	C₂×C₁₉	semidirect
252. C₂×#539	C₂×C₁₉	semidirect
253. C₂×#536	C₂×C₁₉	semidirect
255. C₂²×C₂²⋊Q₈	C₂×C₁₉	semidirect
279. C₂³×Q₈	C₂²×C₁₉	semidirect
281. #563	C₂²×C₁₉	semidirect
282. #552	C₂²×C₁₉	semidirect
283. #551	C₂²×C₁₉	semidirect
284. D₄×Q₈	C₂²×C₁₉	semidirect
285. #544	C₂²×C₁₉	semidirect
286. #541	C₂²×C₁₉	semidirect
287. #539	C₂²×C₁₉	semidirect
288. #536	C₂²×C₁₉	semidirect
289. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
290. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
291. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
293. C₂×#126	C₂²×C₁₉	semidirect
294. C₂×#125	C₂²×C₁₉	semidirect
295. C₂×#125	C₂²×C₁₉	semidirect
296. C₂×#125	C₂²×C₁₉	semidirect
302. C₂×#123	C₂²×C₁₉	semidirect
309. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
310. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
311. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
314. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
319. C₂×#117	C₂²×C₁₉	semidirect
326. C₂×C₁₉	#3538	direct (N × H)
339. C₂²×Q₈	C₂³×C₁₉	semidirect
353. C₄⋊Q₈	C₂³×C₁₉	semidirect
354. C₄⋊Q₈	C₂³×C₁₉	semidirect
355. C₄⋊Q₈	C₂³×C₁₉	semidirect
357. #126	C₂³×C₁₉	semidirect
358. #125	C₂³×C₁₉	semidirect
359. #125	C₂³×C₁₉	semidirect
360. #125	C₂³×C₁₉	semidirect
365. #123	C₂³×C₁₉	semidirect
372. C₂²⋊Q₈	C₂³×C₁₉	semidirect
373. C₂²⋊Q₈	C₂³×C₁₉	semidirect
376. C₄×Q₈	C₂³×C₁₉	semidirect
381. #117	C₂³×C₁₉	semidirect
405. C₁₉	C₂×#3538	direct (N × H)
540. C₂	C₁₉×#3538	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×#3538	2
C₂×C₁₉×#563	2
C₂×C₁₉×#552	2
C₂×C₁₉×#551	2
C₂×D₄×Q₈×C₁₉	2
C₂×C₁₉×#544	2
C₂×C₁₉×#541	2
C₂×C₁₉×#539	2
C₂×C₁₉×#536	2
C₂×C₁₉×#525	2
C₂²×C₁₉×C₂²⋊Q₈	2
C₂×#3538	19

Subgroups — C2×C19×#3538 #18068684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3538 #18068684