Subgroups — C₂×C₁₉×#3518 #18068750

Order 4864.

7118 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3518	C₂	1	32	yes	maximal, direct product factor
2	C₂×Q₈²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#556	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₉×#556	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₉×#555	C₂	1	3	yes	maximal, complemented
6	C₂×D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#548	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#542	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₉×#533	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₉×#529	C₂	1	3	yes	maximal, complemented
11	C₂×C₁₉×#519	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	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
15	Q₈²×C₁₉	C₂²	1	16	yes	complemented
16	C₁₉×#556	C₂²	1	96	yes	complemented
17	C₁₉×#556	C₂²	1	48	yes	complemented
18	C₁₉×#555	C₂²	1	48	yes	complemented
19	D₄×Q₈×C₁₉	C₂²	1	16	yes	complemented
20	C₁₉×#548	C₂²	1	32	yes	complemented
21	C₁₉×#542	C₂²	1	96	yes	complemented
22	C₁₉×#533	C₂²	1	48	yes	complemented
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	6	yes	—
26	C₁₉×#529	C₂²	1	48	yes	complemented
27	C₂×C₁₉×#126	C₂²	1	6	yes	—
28	C₂×C₁₉×#126	C₂²	1	12	yes	—
29	C₂×C₁₉×#125	C₂²	1	3	yes	—
30	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#124	C₂²	1	6	yes	—
32	C₂×C₁₉×#124	C₂²	1	12	yes	—
33	C₂×C₁₉×#123	C₂²	1	6	yes	—
34	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
35	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
36	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
37	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
38	C₂×C₁₉×#121	C₂²	1	3	yes	—
39	C₂×C₁₉×#121	C₂²	1	6	yes	—
40	C₁₉×#519	C₂²	1	32	yes	complemented
41	C₄×#41×C₁₉	C₂²	1	16	yes	complemented
42	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₉	C₂²	1	6	yes	—
45	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₁₉	C₂²	1	6	yes	—
47	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
48	C₂×C₄×Q₈×C₁₉	C₂²	1	6	yes	—
49	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
50	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
51	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
52	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
53	C₂×C₁₉×#117	C₂²	1	3	yes	—
54	C₂×C₁₉×#117	C₂²	1	6	yes	—
55	C₂×C₁₉×#117	C₂²	1	6	yes	—
56	C₂×C₁₉×#117	C₂²	1	6	yes	—
57	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
58	C₂×#41×C₁₉	—	2	8	no	—
59	C₂×#41×C₁₉	C₂³	1	8	yes	—
60	C₂²×Q₈×C₁₉	—	2	16	no	—
61	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
63	C₂²×Q₈×C₁₉	C₂³	1	16	yes	—
64	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
65	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
68	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
69	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
70	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
71	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
72	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
73	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
74	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
75	C₁₉×C₄⋊Q₈	C₂³	1	48	yes	—
76	C₁₉×#126	C₂³	1	48	yes	—
77	C₁₉×#126	C₂³	1	96	yes	—
78	C₁₉×#125	C₂³	1	24	yes	—
79	C₁₉×#124	C₂³	1	8	yes	—
80	C₁₉×#124	C₂³	1	48	yes	—
81	C₁₉×#124	C₂³	1	96	yes	—
82	C₁₉×#123	C₂³	1	48	yes	—
83	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
84	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
85	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
86	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
87	C₁₉×#121	C₂³	1	24	yes	—
88	C₁₉×#121	C₂³	1	48	yes	—
89	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
90	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
91	C₄×Q₈×C₁₉	C₂³	1	48	yes	—
92	C₄×Q₈×C₁₉	C₂³	1	16	yes	—
93	C₄×Q₈×C₁₉	C₂³	1	48	yes	—
94	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
95	C₄×Q₈×C₁₉	C₂³	1	48	yes	—
96	C₄×D₄×C₁₉	C₂³	1	24	yes	—
97	C₄×D₄×C₁₉	C₂³	1	24	yes	—
98	C₄×D₄×C₁₉	C₂³	1	48	yes	—
99	C₄×D₄×C₁₉	C₂³	1	24	yes	—
100	C₁₉×#117	C₂³	1	24	yes	—
101	C₁₉×#117	C₂³	1	48	yes	—
102	C₁₉×#117	C₂³	1	48	yes	—
103	C₁₉×#117	C₂³	1	48	yes	—
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
114	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
118	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
120	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
121	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
123	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
124	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
125	C₂×C₄²×C₁₉	C₂³	1	24	yes	—
126	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
127	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
128	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
129	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
130	#41×C₁₉	—	2	32	no	—
131	C₂×Q₈×C₁₉	—	2	64	no	—
132	C₂×Q₈×C₁₉	—	2	24	no	—
133	C₂×Q₈×C₁₉	—	2	4	no	—
134	C₂×Q₈×C₁₉	—	4	12	no	—
135	C₂×Q₈×C₁₉	#41	1	8	yes	—
136	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
137	C₂×Q₈×C₁₉	C₂⁴	1	24	yes	—
138	C₂×Q₈×C₁₉	C₂⁴	1	24	yes	—
139	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
140	C₂×D₄×C₁₉	—	2	12	no	—
141	C₂×D₄×C₁₉	—	2	4	no	—
142	C₂×D₄×C₁₉	—	4	12	no	—
143	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
144	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
145	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
146	C₂²×C₄×C₁₉	—	2	24	no	—
147	C₂²×C₄×C₁₉	—	2	12	no	—
148	C₂²×C₄×C₁₉	—	2	12	no	—
149	C₂²×C₄×C₁₉	—	4	6	no	—
150	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
152	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
153	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
154	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
159	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
160	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
161	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
162	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
164	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
165	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
166	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
167	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
168	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
169	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
170	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
171	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
172	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
173	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
174	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
175	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
176	C₂²⋊C₄×C₁₉	C₂⁴	1	48	yes	—
177	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
178	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
179	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
180	C₄²×C₁₉	C₂⁴	1	4	yes	—
181	C₄²×C₁₉	C₂⁴	1	12	yes	—
182	C₄²×C₁₉	C₂⁴	1	12	yes	—
183	C₄²×C₁₉	C₂⁴	1	12	yes	—
184	C₄²×C₁₉	C₂⁴	1	48	yes	—
185	C₄²×C₁₉	C₂⁴	1	24	yes	—
186	C₂×#3518	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₁₉	—	2	4	no	—
188	C₂³×C₁₉	—	2	6	no	—
189	C₂³×C₁₉	—	2	6	no	—
190	C₂³×C₁₉	—	2	4	no	—
191	C₂³×C₁₉	—	2	6	no	—
192	C₂³×C₁₉	—	2	4	no	—
193	C₂³×C₁₉	C₂⁵	1	4	yes	—
194	C₂³×C₁₉	C₂⁵	1	6	yes	—
195	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
196	Q₈×C₁₉	—	2	48	no	—
197	Q₈×C₁₉	—	2	8	no	—
198	Q₈×C₁₉	—	4	24	no	—
199	Q₈×C₁₉	C₂×#41	1	16	yes	—
200	D₄×C₁₉	—	2	24	no	—
201	D₄×C₁₉	—	2	8	no	—
202	D₄×C₁₉	—	4	24	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	12	no	—
205	C₂×C₄×C₁₉	—	2	6	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	6	no	—
209	C₂×C₄×C₁₉	—	2	12	no	—
210	C₂×C₄×C₁₉	—	2	48	no	—
211	C₂×C₄×C₁₉	—	2	24	no	—
212	C₂×C₄×C₁₉	—	2	24	no	—
213	C₂×C₄×C₁₉	—	4	12	no	—
214	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
215	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
216	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
217	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
218	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
219	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
220	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
221	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
222	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
223	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
224	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
225	#3518	C₂×C₁₉	1	32	yes	direct product factor
226	C₂×Q₈²	C₂×C₁₉	1	1	yes	characteristic, complemented
227	C₂×#556	C₂×C₁₉	1	6	yes	complemented
228	C₂×#556	C₂×C₁₉	1	3	yes	complemented
229	C₂×#555	C₂×C₁₉	1	3	yes	complemented
230	C₂×D₄×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂×#548	C₂×C₁₉	1	2	yes	complemented
232	C₂×#542	C₂×C₁₉	1	6	yes	complemented
233	C₂×#533	C₂×C₁₉	1	3	yes	complemented
234	C₂×#529	C₂×C₁₉	1	3	yes	complemented
235	C₂×#519	C₂×C₁₉	1	2	yes	complemented
236	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
237	C₂²×C₁₉	—	2	4	no	—
238	C₂²×C₁₉	—	2	6	no	—
239	C₂²×C₁₉	—	2	6	no	—
240	C₂²×C₁₉	—	2	4	no	—
241	C₂²×C₁₉	—	2	6	no	—
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	4	8	no	—
244	C₂²×C₁₉	—	4	12	no	—
245	C₂²×C₁₉	C₂²×#41	1	2	yes	—
246	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
247	C₂²×C₁₉	#585	1	2	yes	—
248	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
249	C₄×C₁₉	—	2	2	no	—
250	C₄×C₁₉	—	2	12	no	—
251	C₄×C₁₉	—	2	6	no	—
252	C₄×C₁₉	—	2	4	no	—
253	C₄×C₁₉	—	2	2	no	—
254	C₄×C₁₉	—	2	6	no	—
255	C₄×C₁₉	—	2	12	no	—
256	C₄×C₁₉	C₂²×#41	1	12	yes	—
257	C₄×C₁₉	C₂×2₋¹⁺⁴	1	4	yes	—
258	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
259	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
260	Q₈²	C₂²×C₁₉	1	16	yes	complemented
261	#556	C₂²×C₁₉	1	96	yes	complemented
262	#556	C₂²×C₁₉	1	48	yes	complemented
263	#555	C₂²×C₁₉	1	48	yes	complemented
264	D₄×Q₈	C₂²×C₁₉	1	16	yes	complemented
265	#548	C₂²×C₁₉	1	32	yes	complemented
266	#542	C₂²×C₁₉	1	96	yes	complemented
267	#533	C₂²×C₁₉	1	48	yes	complemented
268	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
269	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
270	C₂×C₄⋊Q₈	C₂²×C₁₉	1	6	yes	—
271	#529	C₂²×C₁₉	1	48	yes	complemented
272	C₂×#126	C₂²×C₁₉	1	6	yes	—
273	C₂×#126	C₂²×C₁₉	1	12	yes	—
274	C₂×#125	C₂²×C₁₉	1	3	yes	—
275	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#124	C₂²×C₁₉	1	6	yes	—
277	C₂×#124	C₂²×C₁₉	1	12	yes	—
278	C₂×#123	C₂²×C₁₉	1	6	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
280	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
281	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
282	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
283	C₂×#121	C₂²×C₁₉	1	3	yes	—
284	C₂×#121	C₂²×C₁₉	1	6	yes	—
285	#519	C₂²×C₁₉	1	32	yes	complemented
286	C₄×#41	C₂²×C₁₉	1	16	yes	complemented
287	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₄×Q₈	C₂²×C₁₉	1	6	yes	—
290	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
291	C₂×C₄×Q₈	C₂²×C₁₉	1	6	yes	—
292	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
293	C₂×C₄×Q₈	C₂²×C₁₉	1	6	yes	—
294	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
295	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
296	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
297	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
298	C₂×#117	C₂²×C₁₉	1	3	yes	—
299	C₂×#117	C₂²×C₁₉	1	6	yes	—
300	C₂×#117	C₂²×C₁₉	1	6	yes	—
301	C₂×#117	C₂²×C₁₉	1	6	yes	—
302	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
303	C₂×C₁₉	—	4	4	no	—
304	C₂×C₁₉	—	4	6	no	—
305	C₂×C₁₉	#3518	1	4	yes	direct product factor
306	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
307	C₂×C₁₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
308	C₂×C₁₉	C₂×#585	1	1	yes	characteristic
309	C₂×#41	—	2	8	no	—
310	C₂×#41	C₂³×C₁₉	1	8	yes	—
311	C₂²×Q₈	—	2	16	no	—
312	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
314	C₂²×Q₈	C₂³×C₁₉	1	16	yes	—
315	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
316	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
319	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
320	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
321	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
322	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
323	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
324	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
325	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
326	C₄⋊Q₈	C₂³×C₁₉	1	48	yes	—
327	#126	C₂³×C₁₉	1	48	yes	—
328	#126	C₂³×C₁₉	1	96	yes	—
329	#125	C₂³×C₁₉	1	24	yes	—
330	#124	C₂³×C₁₉	1	8	yes	—
331	#124	C₂³×C₁₉	1	48	yes	—
332	#124	C₂³×C₁₉	1	96	yes	—
333	#123	C₂³×C₁₉	1	48	yes	—
334	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
335	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
336	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
337	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
338	#121	C₂³×C₁₉	1	24	yes	—
339	#121	C₂³×C₁₉	1	48	yes	—
340	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
341	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
342	C₄×Q₈	C₂³×C₁₉	1	48	yes	—
343	C₄×Q₈	C₂³×C₁₉	1	16	yes	—
344	C₄×Q₈	C₂³×C₁₉	1	48	yes	—
345	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
346	C₄×Q₈	C₂³×C₁₉	1	48	yes	—
347	C₄×D₄	C₂³×C₁₉	1	24	yes	—
348	C₄×D₄	C₂³×C₁₉	1	24	yes	—
349	C₄×D₄	C₂³×C₁₉	1	48	yes	—
350	C₄×D₄	C₂³×C₁₉	1	24	yes	—
351	#117	C₂³×C₁₉	1	24	yes	—
352	#117	C₂³×C₁₉	1	48	yes	—
353	#117	C₂³×C₁₉	1	48	yes	—
354	#117	C₂³×C₁₉	1	48	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
372	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
373	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
374	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
375	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
376	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
377	C₂×C₄²	C₂³×C₁₉	1	24	yes	—
378	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
379	C₁₉	C₂×#3518	1	1	yes	characteristic, direct product factor, Sylow
380	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
381	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
382	#41	—	2	32	no	—
383	C₂×Q₈	—	2	64	no	—
384	C₂×Q₈	—	2	24	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	4	12	no	—
387	C₂×Q₈	#41×C₁₉	1	8	yes	—
388	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
389	C₂×Q₈	C₂⁴×C₁₉	1	24	yes	—
390	C₂×Q₈	C₂⁴×C₁₉	1	24	yes	—
391	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
392	C₂×D₄	—	2	12	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	4	12	no	—
395	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
396	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
397	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
398	C₂²×C₄	—	2	24	no	—
399	C₂²×C₄	—	2	12	no	—
400	C₂²×C₄	—	2	12	no	—
401	C₂²×C₄	—	4	6	no	—
402	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
403	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
407	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
408	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
409	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
410	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
411	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
412	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
413	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
414	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
415	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
416	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
417	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
418	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
419	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
420	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
421	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
422	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
423	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
424	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
425	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
426	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
427	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
428	C₂²⋊C₄	C₂⁴×C₁₉	1	48	yes	—
429	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
430	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
431	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
432	C₄²	C₂⁴×C₁₉	1	4	yes	—
433	C₄²	C₂⁴×C₁₉	1	12	yes	—
434	C₄²	C₂⁴×C₁₉	1	12	yes	—
435	C₄²	C₂⁴×C₁₉	1	12	yes	—
436	C₄²	C₂⁴×C₁₉	1	48	yes	—
437	C₄²	C₂⁴×C₁₉	1	24	yes	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	6	no	—
440	C₂³	—	2	6	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	6	no	—
443	C₂³	—	2	4	no	—
444	C₂³	C₂⁵×C₁₉	1	4	yes	—
445	C₂³	C₂⁵×C₁₉	1	6	yes	—
446	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
447	Q₈	—	2	48	no	—
448	Q₈	—	2	8	no	—
449	Q₈	—	4	24	no	—
450	Q₈	C₂×#41×C₁₉	1	16	yes	—
451	D₄	—	2	24	no	—
452	D₄	—	2	8	no	—
453	D₄	—	4	24	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	12	no	—
456	C₂×C₄	—	2	6	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	2	12	no	—
461	C₂×C₄	—	2	48	no	—
462	C₂×C₄	—	2	24	no	—
463	C₂×C₄	—	2	24	no	—
464	C₂×C₄	—	4	12	no	—
465	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
466	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
467	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
468	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
469	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
470	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
471	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
472	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
473	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
474	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
475	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	6	no	—
478	C₂²	—	2	6	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	6	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	4	8	no	—
483	C₂²	—	4	12	no	—
484	C₂²	C₂²×#41×C₁₉	1	2	yes	—
485	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
486	C₂²	C₁₉×#585	1	2	yes	—
487	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	12	no	—
490	C₄	—	2	6	no	—
491	C₄	—	2	4	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	6	no	—
494	C₄	—	2	12	no	—
495	C₄	C₂²×#41×C₁₉	1	12	yes	—
496	C₄	C₂×C₁₉×2₋¹⁺⁴	1	4	yes	—
497	C₂	—	4	4	no	—
498	C₂	—	4	6	no	—
499	C₂	C₁₉×#3518	1	4	yes	direct product factor
500	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
501	C₂	C₂²×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
502	C₂	C₂×C₁₉×#585	1	1	yes	characteristic

	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×#3518	C₂	direct (N × H)
2. C₂×Q₈²×C₁₉	C₂	semidirect
3. C₂×C₁₉×#556	C₂	semidirect
4. C₂×C₁₉×#556	C₂	semidirect
5. C₂×C₁₉×#555	C₂	semidirect
6. C₂×D₄×Q₈×C₁₉	C₂	semidirect
7. C₂×C₁₉×#548	C₂	semidirect
8. C₂×C₁₉×#542	C₂	semidirect
9. C₂×C₁₉×#533	C₂	semidirect
10. C₂×C₁₉×#529	C₂	semidirect
11. C₂×C₁₉×#519	C₂	semidirect
12. C₂×C₄×#41×C₁₉	C₂	semidirect
15. Q₈²×C₁₉	C₂²	semidirect
16. C₁₉×#556	C₂²	semidirect
17. C₁₉×#556	C₂²	semidirect
18. C₁₉×#555	C₂²	semidirect
19. D₄×Q₈×C₁₉	C₂²	semidirect
20. C₁₉×#548	C₂²	semidirect
21. C₁₉×#542	C₂²	semidirect
22. C₁₉×#533	C₂²	semidirect
26. C₁₉×#529	C₂²	semidirect
40. C₁₉×#519	C₂²	semidirect
41. C₄×#41×C₁₉	C₂²	semidirect
186. C₂×#3518	C₁₉	direct (N × H)
225. #3518	C₂×C₁₉	direct (N × H)
226. C₂×Q₈²	C₂×C₁₉	semidirect
227. C₂×#556	C₂×C₁₉	semidirect
228. C₂×#556	C₂×C₁₉	semidirect
229. C₂×#555	C₂×C₁₉	semidirect
230. C₂×D₄×Q₈	C₂×C₁₉	semidirect
231. C₂×#548	C₂×C₁₉	semidirect
232. C₂×#542	C₂×C₁₉	semidirect
233. C₂×#533	C₂×C₁₉	semidirect
234. C₂×#529	C₂×C₁₉	semidirect
235. C₂×#519	C₂×C₁₉	semidirect
236. C₂×C₄×#41	C₂×C₁₉	semidirect
260. Q₈²	C₂²×C₁₉	semidirect
261. #556	C₂²×C₁₉	semidirect
262. #556	C₂²×C₁₉	semidirect
263. #555	C₂²×C₁₉	semidirect
264. D₄×Q₈	C₂²×C₁₉	semidirect
265. #548	C₂²×C₁₉	semidirect
266. #542	C₂²×C₁₉	semidirect
267. #533	C₂²×C₁₉	semidirect
271. #529	C₂²×C₁₉	semidirect
285. #519	C₂²×C₁₉	semidirect
286. C₄×#41	C₂²×C₁₉	semidirect
305. C₂×C₁₉	#3518	direct (N × H)
379. C₁₉	C₂×#3518	direct (N × H)
499. C₂	C₁₉×#3518	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×#3518	2
C₂×Q₈²×C₁₉	2
C₂×C₁₉×#556	2
C₂×C₁₉×#555	2
C₂×D₄×Q₈×C₁₉	2
C₂×C₁₉×#548	2
C₂×C₁₉×#542	2
C₂×C₁₉×#533	2
C₂×C₁₉×#529	2
C₂×C₁₉×#519	2
C₂×C₄×#41×C₁₉	2
C₂×#3518	19

Subgroups — C2×C19×#3518 #18068750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3518 #18068750