Subgroups — C₁₉×#62894 #18068853

Order 4864.

7294 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	6	yes	maximal, complemented
2	C₁₉×#3536	C₂	1	12	yes	maximal, complemented
3	C₁₉×#3536	C₂	1	6	yes	maximal, complemented
4	C₁₉×#3535	C₂	1	12	yes	maximal, complemented
5	C₁₉×#3520	C₂	1	6	yes	maximal, complemented
6	C₁₉×#3501	C₂	1	3	yes	maximal, complemented
7	C₁₉×#3490	C₂	1	6	yes	maximal, complemented
8	C₁₉×#3489	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₉×#546	C₂	1	3	yes	maximal, complemented
10	C₁₉×#3459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#543	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	complemented
13	C₂²×#41×C₁₉	C₂²	1	3	yes	complemented
14	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#563	C₂²	1	12	yes	complemented
16	C₁₉×#562	C₂²	1	24	yes	complemented
17	C₁₉×#562	C₂²	1	12	yes	complemented
18	C₁₉×#556	C₂²	1	6	yes	complemented
19	C₁₉×#554	C₂²	1	12	yes	complemented
20	C₁₉×#554	C₂²	1	24	yes	complemented
21	C₁₉×#552	C₂²	1	12	yes	complemented
22	C₁₉×#551	C₂²	1	24	yes	complemented
23	C₁₉×#551	C₂²	1	24	yes	complemented
24	D₄×Q₈×C₁₉	C₂²	1	12	yes	complemented
25	D₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
26	C₁₉×#548	C₂²	1	12	yes	complemented
27	C₁₉×#548	C₂²	1	12	yes	complemented
28	C₁₉×#547	C₂²	1	6	yes	complemented
29	C₁₉×#547	C₂²	1	6	yes	complemented
30	C₁₉×#547	C₂²	1	24	yes	complemented
31	C₁₉×#546	C₂²	1	12	yes	complemented
32	C₁₉×#546	C₂²	1	24	yes	complemented
33	C₁₉×#546	C₂²	1	12	yes	complemented
34	C₁₉×#546	C₂²	1	24	yes	complemented
35	C₁₉×#546	C₂²	1	24	yes	complemented
36	C₁₉×#544	C₂²	1	6	yes	complemented
37	C₁₉×#543	C₂²	1	1	yes	characteristic
38	C₁₉×#543	C₂²	1	6	yes	—
39	C₁₉×#543	C₂²	1	12	yes	complemented
40	C₁₉×#543	C₂²	1	12	yes	complemented
41	C₁₉×#543	C₂²	1	6	yes	complemented
42	C₁₉×#542	C₂²	1	12	yes	complemented
43	C₁₉×#542	C₂²	1	24	yes	complemented
44	C₁₉×#539	C₂²	1	6	yes	complemented
45	C₁₉×#539	C₂²	1	24	yes	complemented
46	C₁₉×#539	C₂²	1	12	yes	complemented
47	C₁₉×#538	C₂²	1	6	yes	complemented
48	C₁₉×#538	C₂²	1	12	yes	complemented
49	C₁₉×#538	C₂²	1	12	yes	complemented
50	C₁₉×#537	C₂²	1	12	yes	complemented
51	C₁₉×#537	C₂²	1	12	yes	complemented
52	C₁₉×#537	C₂²	1	6	yes	complemented
53	C₁₉×#536	C₂²	1	12	yes	complemented
54	C₁₉×#536	C₂²	1	6	yes	complemented
55	C₁₉×#534	C₂²	1	3	yes	—
56	C₁₉×#533	C₂²	1	6	yes	complemented
57	C₁₉×#529	C₂²	1	6	yes	complemented
58	C₂×C₁₉×#124	C₂²	1	3	yes	complemented
59	C₁₉×#525	C₂²	1	6	yes	complemented
60	C₁₉×#525	C₂²	1	12	yes	complemented
61	C₁₉×#525	C₂²	1	12	yes	complemented
62	C₂×C₁₉×#123	C₂²	1	6	yes	complemented
63	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
64	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	12	yes	complemented
65	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	12	yes	complemented
66	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
67	C₂×C₁₉×#121	C₂²	1	3	yes	complemented
68	C₂×C₁₉×#121	C₂²	1	6	yes	complemented
69	C₂×C₁₉×#120	C₂²	1	6	yes	—
70	C₁₉×#520	C₂²	1	6	yes	complemented
71	C₁₉×#518	C₂²	1	6	yes	—
72	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
73	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	complemented
74	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
75	C₂⁵×C₁₉	C₂³	1	2	yes	—
76	C₁₉×2₋¹⁺⁴	—	4	8	no	—
77	C₂×#41×C₁₉	—	4	12	no	—
78	C₂×#41×C₁₉	C₂³	1	6	yes	—
79	C₂×#41×C₁₉	C₂³	1	12	yes	—
80	C₂×#41×C₁₉	C₂³	1	6	yes	—
81	C₂×#41×C₁₉	C₂³	1	2	yes	complemented
82	C₂×#41×C₁₉	C₂³	1	12	yes	complemented
83	C₂×#41×C₁₉	C₂³	1	12	yes	complemented
84	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
85	C₂²×Q₈×C₁₉	C₂³	1	4	yes	complemented
86	C₂²×Q₈×C₁₉	C₂³	1	6	yes	complemented
87	C₂²×Q₈×C₁₉	C₂³	1	4	yes	complemented
88	C₂²×D₄×C₁₉	—	4	4	no	—
89	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
90	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
91	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
92	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
93	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
94	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
95	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
96	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
98	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
99	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
100	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
101	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	complemented
102	C₁₉×#126	C₂³	1	12	yes	complemented
103	C₁₉×#126	C₂³	1	24	yes	complemented
104	C₁₉×#126	C₂³	1	24	yes	complemented
105	C₁₉×#125	C₂³	1	6	yes	complemented
106	C₁₉×#125	C₂³	1	12	yes	complemented
107	C₁₉×#125	C₂³	1	24	yes	complemented
108	C₁₉×#124	C₂³	1	12	yes	—
109	C₁₉×#124	C₂³	1	12	yes	—
110	C₁₉×#124	C₂³	1	6	yes	complemented
111	C₁₉×#124	C₂³	1	24	yes	complemented
112	C₁₉×#124	C₂³	1	24	yes	complemented
113	C₁₉×#123	C₂³	1	24	yes	—
114	C₁₉×#123	C₂³	1	24	yes	—
115	C₁₉×#123	C₂³	1	12	yes	—
116	C₁₉×#123	C₂³	1	24	yes	complemented
117	C₁₉×#123	C₂³	1	12	yes	complemented
118	C₁₉×#123	C₂³	1	24	yes	complemented
119	C₁₉×#123	C₂³	1	24	yes	complemented
120	C₁₉×#123	C₂³	1	24	yes	complemented
121	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
122	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
123	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
124	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
125	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
126	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
127	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
128	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
129	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
130	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
131	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
132	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	complemented
133	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
134	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	complemented
135	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
136	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
137	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	complemented
138	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
139	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
140	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	complemented
141	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	complemented
142	C₁₉×#121	C₂³	1	24	yes	—
143	C₁₉×#121	C₂³	1	12	yes	—
144	C₁₉×#121	C₂³	1	12	yes	—
145	C₁₉×#121	C₂³	1	24	yes	—
146	C₁₉×#121	C₂³	1	6	yes	—
147	C₁₉×#121	C₂³	1	6	yes	—
148	C₁₉×#121	C₂³	1	6	yes	complemented
149	C₁₉×#121	C₂³	1	12	yes	complemented
150	C₁₉×#121	C₂³	1	12	yes	complemented
151	C₁₉×#121	C₂³	1	24	yes	complemented
152	C₁₉×#121	C₂³	1	24	yes	complemented
153	C₁₉×#120	C₂³	1	24	yes	—
154	C₁₉×#120	C₂³	1	24	yes	—
155	C₁₉×#120	C₂³	1	12	yes	—
156	C₄×Q₈×C₁₉	C₂³	1	12	yes	complemented
157	C₄×Q₈×C₁₉	C₂³	1	2	yes	complemented
158	C₄×Q₈×C₁₉	C₂³	1	12	yes	complemented
159	C₄×D₄×C₁₉	C₂³	1	12	yes	—
160	C₄×D₄×C₁₉	C₂³	1	12	yes	—
161	C₄×D₄×C₁₉	C₂³	1	6	yes	—
162	C₄×D₄×C₁₉	C₂³	1	12	yes	—
163	C₄×D₄×C₁₉	C₂³	1	6	yes	—
164	C₄×D₄×C₁₉	C₂³	1	24	yes	—
165	C₄×D₄×C₁₉	C₂³	1	24	yes	—
166	C₄×D₄×C₁₉	C₂³	1	24	yes	complemented
167	C₄×D₄×C₁₉	C₂³	1	6	yes	complemented
168	C₄×D₄×C₁₉	C₂³	1	24	yes	complemented
169	C₁₉×#117	C₂³	1	12	yes	—
170	C₁₉×#117	C₂³	1	6	yes	complemented
171	C₁₉×#117	C₂³	1	12	yes	complemented
172	C₁₉×#117	C₂³	1	12	yes	complemented
173	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
174	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
175	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
176	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	complemented
177	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	complemented
178	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	complemented
179	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	complemented
180	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
181	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
182	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
183	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
184	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	—
185	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	—
186	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
187	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
188	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
189	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
190	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
191	C₂⁴×C₁₉	—	2	8	no	—
192	C₂⁴×C₁₉	—	4	4	no	—
193	C₂⁴×C₁₉	—	8	2	no	—
194	C₂⁴×C₁₉	C₂⁴	1	6	yes	—
195	C₂⁴×C₁₉	C₂⁴	1	6	yes	—
196	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
197	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
198	#41×C₁₉	—	2	24	no	—
199	#41×C₁₉	—	4	4	no	—
200	#41×C₁₉	—	4	24	no	—
201	#41×C₁₉	—	4	24	no	—
202	#41×C₁₉	—	4	12	no	—
203	#41×C₁₉	—	8	12	no	—
204	C₂×Q₈×C₁₉	—	4	8	no	—
205	C₂×Q₈×C₁₉	—	4	6	no	—
206	C₂×Q₈×C₁₉	—	4	12	no	—
207	C₂×Q₈×C₁₉	—	8	4	no	—
208	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
209	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
211	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
213	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
214	C₂×D₄×C₁₉	—	2	12	no	—
215	C₂×D₄×C₁₉	—	2	12	no	—
216	C₂×D₄×C₁₉	—	4	6	no	—
217	C₂×D₄×C₁₉	—	4	12	no	—
218	C₂×D₄×C₁₉	—	4	12	no	—
219	C₂×D₄×C₁₉	—	8	6	no	—
220	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
221	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
222	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
223	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
224	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
225	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
226	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
227	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
228	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
229	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₉	—	4	2	no	—
231	C₂²×C₄×C₁₉	—	4	6	no	—
232	C₂²×C₄×C₁₉	—	4	12	no	—
233	C₂²×C₄×C₁₉	—	8	6	no	—
234	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
235	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
236	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
237	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
238	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
239	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
240	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
241	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
242	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
243	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
244	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
245	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
246	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
247	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
248	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
249	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
250	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
251	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
252	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
253	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
254	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
255	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
256	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
257	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
258	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
259	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
260	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
261	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
262	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
263	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
264	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
265	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
266	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
267	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
268	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
269	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
270	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
271	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
272	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
273	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
274	C₄²×C₁₉	C₂⁴	1	6	yes	—
275	C₄²×C₁₉	C₂⁴	1	6	yes	—
276	C₄²×C₁₉	C₂⁴	1	24	yes	—
277	#62894	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₁₉	—	2	12	no	—
279	C₂³×C₁₉	—	2	12	no	—
280	C₂³×C₁₉	—	2	6	no	—
281	C₂³×C₁₉	—	2	12	no	—
282	C₂³×C₁₉	—	4	1	no	—
283	C₂³×C₁₉	—	4	6	no	—
284	C₂³×C₁₉	—	4	1	no	—
285	C₂³×C₁₉	—	4	3	no	—
286	C₂³×C₁₉	—	4	6	no	—
287	C₂³×C₁₉	—	4	3	no	—
288	C₂³×C₁₉	—	4	6	no	—
289	C₂³×C₁₉	—	8	16	no	—
290	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	complemented
291	C₂³×C₁₉	C₂⁵	1	6	yes	—
292	C₂³×C₁₉	C₂⁵	1	6	yes	—
293	C₂³×C₁₉	C₂⁵	1	2	yes	—
294	C₂³×C₁₉	C₂⁵	1	3	yes	—
295	Q₈×C₁₉	—	2	12	no	—
296	Q₈×C₁₉	—	4	2	no	—
297	Q₈×C₁₉	—	4	12	no	—
298	Q₈×C₁₉	—	4	6	no	—
299	Q₈×C₁₉	—	4	2	no	—
300	Q₈×C₁₉	—	4	12	no	—
301	D₄×C₁₉	—	2	12	no	—
302	D₄×C₁₉	—	2	24	no	—
303	D₄×C₁₉	—	2	24	no	—
304	D₄×C₁₉	—	2	6	no	—
305	D₄×C₁₉	—	4	6	no	—
306	D₄×C₁₉	—	4	12	no	—
307	D₄×C₁₉	—	4	24	no	—
308	D₄×C₁₉	—	4	6	no	—
309	D₄×C₁₉	—	4	6	no	—
310	D₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
311	C₂×C₄×C₁₉	—	2	24	no	—
312	C₂×C₄×C₁₉	—	2	6	no	—
313	C₂×C₄×C₁₉	—	2	6	no	—
314	C₂×C₄×C₁₉	—	2	12	no	—
315	C₂×C₄×C₁₉	—	4	3	no	—
316	C₂×C₄×C₁₉	—	4	3	no	—
317	C₂×C₄×C₁₉	—	4	6	no	—
318	C₂×C₄×C₁₉	—	4	6	no	—
319	C₂×C₄×C₁₉	—	4	12	no	—
320	C₂×C₄×C₁₉	—	4	3	no	—
321	C₂×C₄×C₁₉	—	4	6	no	—
322	C₂×C₄×C₁₉	—	4	12	no	—
323	C₂×C₄×C₁₉	—	4	12	no	—
324	C₂×C₄×C₁₉	—	4	12	no	—
325	C₂×C₄×C₁₉	—	4	12	no	—
326	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
327	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
328	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
329	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
330	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
331	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
332	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
333	#3561	C₂×C₁₉	1	6	yes	complemented
334	#3536	C₂×C₁₉	1	12	yes	complemented
335	#3536	C₂×C₁₉	1	6	yes	complemented
336	#3535	C₂×C₁₉	1	12	yes	complemented
337	#3520	C₂×C₁₉	1	6	yes	complemented
338	#3501	C₂×C₁₉	1	3	yes	complemented
339	#3490	C₂×C₁₉	1	6	yes	complemented
340	#3489	C₂×C₁₉	1	6	yes	complemented
341	C₂×#546	C₂×C₁₉	1	3	yes	complemented
342	#3459	C₂×C₁₉	1	1	yes	characteristic, complemented
343	C₂×#543	C₂×C₁₉	1	2	yes	complemented
344	C₂²×C₁₉	—	2	3	no	—
345	C₂²×C₁₉	—	2	2	no	—
346	C₂²×C₁₉	—	2	2	no	—
347	C₂²×C₁₉	—	2	3	no	—
348	C₂²×C₁₉	—	2	6	no	—
349	C₂²×C₁₉	—	2	6	no	—
350	C₂²×C₁₉	—	2	6	no	—
351	C₂²×C₁₉	—	2	6	no	—
352	C₂²×C₁₉	—	2	6	no	—
353	C₂²×C₁₉	—	2	6	no	—
354	C₂²×C₁₉	—	4	4	no	—
355	C₂²×C₁₉	—	4	24	no	—
356	C₂²×C₁₉	—	8	6	no	—
357	C₂²×C₁₉	—	8	12	no	—
358	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	4	yes	—
359	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	6	yes	—
360	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
361	C₄×C₁₉	—	2	6	no	—
362	C₄×C₁₉	—	2	3	no	—
363	C₄×C₁₉	—	2	12	no	—
364	C₄×C₁₉	—	2	6	no	—
365	C₄×C₁₉	—	2	12	no	—
366	C₄×C₁₉	—	2	6	no	—
367	C₄×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
368	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	complemented
369	C₂²×#41	C₂²×C₁₉	1	3	yes	complemented
370	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
371	#563	C₂²×C₁₉	1	12	yes	complemented
372	#562	C₂²×C₁₉	1	24	yes	complemented
373	#562	C₂²×C₁₉	1	12	yes	complemented
374	#556	C₂²×C₁₉	1	6	yes	complemented
375	#554	C₂²×C₁₉	1	12	yes	complemented
376	#554	C₂²×C₁₉	1	24	yes	complemented
377	#552	C₂²×C₁₉	1	12	yes	complemented
378	#551	C₂²×C₁₉	1	24	yes	complemented
379	#551	C₂²×C₁₉	1	24	yes	complemented
380	D₄×Q₈	C₂²×C₁₉	1	12	yes	complemented
381	D₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
382	#548	C₂²×C₁₉	1	12	yes	complemented
383	#548	C₂²×C₁₉	1	12	yes	complemented
384	#547	C₂²×C₁₉	1	6	yes	complemented
385	#547	C₂²×C₁₉	1	6	yes	complemented
386	#547	C₂²×C₁₉	1	24	yes	complemented
387	#546	C₂²×C₁₉	1	12	yes	complemented
388	#546	C₂²×C₁₉	1	24	yes	complemented
389	#546	C₂²×C₁₉	1	12	yes	complemented
390	#546	C₂²×C₁₉	1	24	yes	complemented
391	#546	C₂²×C₁₉	1	24	yes	complemented
392	#544	C₂²×C₁₉	1	6	yes	complemented
393	#543	C₂²×C₁₉	1	1	yes	characteristic
394	#543	C₂²×C₁₉	1	6	yes	—
395	#543	C₂²×C₁₉	1	12	yes	complemented
396	#543	C₂²×C₁₉	1	12	yes	complemented
397	#543	C₂²×C₁₉	1	6	yes	complemented
398	#542	C₂²×C₁₉	1	12	yes	complemented
399	#542	C₂²×C₁₉	1	24	yes	complemented
400	#539	C₂²×C₁₉	1	6	yes	complemented
401	#539	C₂²×C₁₉	1	24	yes	complemented
402	#539	C₂²×C₁₉	1	12	yes	complemented
403	#538	C₂²×C₁₉	1	6	yes	complemented
404	#538	C₂²×C₁₉	1	12	yes	complemented
405	#538	C₂²×C₁₉	1	12	yes	complemented
406	#537	C₂²×C₁₉	1	12	yes	complemented
407	#537	C₂²×C₁₉	1	12	yes	complemented
408	#537	C₂²×C₁₉	1	6	yes	complemented
409	#536	C₂²×C₁₉	1	12	yes	complemented
410	#536	C₂²×C₁₉	1	6	yes	complemented
411	#534	C₂²×C₁₉	1	3	yes	—
412	#533	C₂²×C₁₉	1	6	yes	complemented
413	#529	C₂²×C₁₉	1	6	yes	complemented
414	C₂×#124	C₂²×C₁₉	1	3	yes	complemented
415	#525	C₂²×C₁₉	1	6	yes	complemented
416	#525	C₂²×C₁₉	1	12	yes	complemented
417	#525	C₂²×C₁₉	1	12	yes	complemented
418	C₂×#123	C₂²×C₁₉	1	6	yes	complemented
419	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
420	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	12	yes	complemented
421	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	12	yes	complemented
422	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
423	C₂×#121	C₂²×C₁₉	1	3	yes	complemented
424	C₂×#121	C₂²×C₁₉	1	6	yes	complemented
425	C₂×#120	C₂²×C₁₉	1	6	yes	—
426	#520	C₂²×C₁₉	1	6	yes	complemented
427	#518	C₂²×C₁₉	1	6	yes	—
428	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
429	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	complemented
430	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
431	C₂×C₁₉	—	2	6	no	—
432	C₂×C₁₉	—	2	4	no	—
433	C₂×C₁₉	—	4	6	no	—
434	C₂×C₁₉	—	4	6	no	—
435	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×C₁₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
437	C₂×C₁₉	H(7,𝔽₂)	1	1	yes	characteristic
438	C₂⁵	C₂³×C₁₉	1	2	yes	—
439	2₋¹⁺⁴	—	4	8	no	—
440	C₂×#41	—	4	12	no	—
441	C₂×#41	C₂³×C₁₉	1	6	yes	—
442	C₂×#41	C₂³×C₁₉	1	12	yes	—
443	C₂×#41	C₂³×C₁₉	1	6	yes	—
444	C₂×#41	C₂³×C₁₉	1	2	yes	complemented
445	C₂×#41	C₂³×C₁₉	1	12	yes	complemented
446	C₂×#41	C₂³×C₁₉	1	12	yes	complemented
447	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
448	C₂²×Q₈	C₂³×C₁₉	1	4	yes	complemented
449	C₂²×Q₈	C₂³×C₁₉	1	6	yes	complemented
450	C₂²×Q₈	C₂³×C₁₉	1	4	yes	complemented
451	C₂²×D₄	—	4	4	no	—
452	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
453	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
454	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
455	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
456	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
457	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
458	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
459	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
461	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
462	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
463	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
464	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	complemented
465	#126	C₂³×C₁₉	1	12	yes	complemented
466	#126	C₂³×C₁₉	1	24	yes	complemented
467	#126	C₂³×C₁₉	1	24	yes	complemented
468	#125	C₂³×C₁₉	1	6	yes	complemented
469	#125	C₂³×C₁₉	1	12	yes	complemented
470	#125	C₂³×C₁₉	1	24	yes	complemented
471	#124	C₂³×C₁₉	1	12	yes	—
472	#124	C₂³×C₁₉	1	12	yes	—
473	#124	C₂³×C₁₉	1	6	yes	complemented
474	#124	C₂³×C₁₉	1	24	yes	complemented
475	#124	C₂³×C₁₉	1	24	yes	complemented
476	#123	C₂³×C₁₉	1	24	yes	—
477	#123	C₂³×C₁₉	1	24	yes	—
478	#123	C₂³×C₁₉	1	12	yes	—
479	#123	C₂³×C₁₉	1	24	yes	complemented
480	#123	C₂³×C₁₉	1	12	yes	complemented
481	#123	C₂³×C₁₉	1	24	yes	complemented
482	#123	C₂³×C₁₉	1	24	yes	complemented
483	#123	C₂³×C₁₉	1	24	yes	complemented
484	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
485	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
486	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
487	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
488	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
489	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
490	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
491	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
492	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
493	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
494	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
495	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	complemented
496	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
497	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	complemented
498	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
499	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
500	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
501	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
502	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
503	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	complemented
504	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	complemented
505	#121	C₂³×C₁₉	1	24	yes	—
506	#121	C₂³×C₁₉	1	12	yes	—
507	#121	C₂³×C₁₉	1	12	yes	—
508	#121	C₂³×C₁₉	1	24	yes	—
509	#121	C₂³×C₁₉	1	6	yes	—
510	#121	C₂³×C₁₉	1	6	yes	—
511	#121	C₂³×C₁₉	1	6	yes	complemented
512	#121	C₂³×C₁₉	1	12	yes	complemented
513	#121	C₂³×C₁₉	1	12	yes	complemented
514	#121	C₂³×C₁₉	1	24	yes	complemented
515	#121	C₂³×C₁₉	1	24	yes	complemented
516	#120	C₂³×C₁₉	1	24	yes	—
517	#120	C₂³×C₁₉	1	24	yes	—
518	#120	C₂³×C₁₉	1	12	yes	—
519	C₄×Q₈	C₂³×C₁₉	1	12	yes	complemented
520	C₄×Q₈	C₂³×C₁₉	1	2	yes	complemented
521	C₄×Q₈	C₂³×C₁₉	1	12	yes	complemented
522	C₄×D₄	C₂³×C₁₉	1	12	yes	—
523	C₄×D₄	C₂³×C₁₉	1	12	yes	—
524	C₄×D₄	C₂³×C₁₉	1	6	yes	—
525	C₄×D₄	C₂³×C₁₉	1	12	yes	—
526	C₄×D₄	C₂³×C₁₉	1	6	yes	—
527	C₄×D₄	C₂³×C₁₉	1	24	yes	—
528	C₄×D₄	C₂³×C₁₉	1	24	yes	—
529	C₄×D₄	C₂³×C₁₉	1	24	yes	complemented
530	C₄×D₄	C₂³×C₁₉	1	6	yes	complemented
531	C₄×D₄	C₂³×C₁₉	1	24	yes	complemented
532	#117	C₂³×C₁₉	1	12	yes	—
533	#117	C₂³×C₁₉	1	6	yes	complemented
534	#117	C₂³×C₁₉	1	12	yes	complemented
535	#117	C₂³×C₁₉	1	12	yes	complemented
536	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	complemented
540	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	complemented
541	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	complemented
542	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	complemented
543	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
553	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
554	C₁₉	#62894	1	1	yes	characteristic, direct product factor, Sylow
555	C₂⁴	—	2	8	no	—
556	C₂⁴	—	4	4	no	—
557	C₂⁴	—	8	2	no	—
558	C₂⁴	C₂⁴×C₁₉	1	6	yes	—
559	C₂⁴	C₂⁴×C₁₉	1	6	yes	—
560	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
561	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
562	#41	—	2	24	no	—
563	#41	—	4	4	no	—
564	#41	—	4	24	no	—
565	#41	—	4	24	no	—
566	#41	—	4	12	no	—
567	#41	—	8	12	no	—
568	C₂×Q₈	—	4	8	no	—
569	C₂×Q₈	—	4	6	no	—
570	C₂×Q₈	—	4	12	no	—
571	C₂×Q₈	—	8	4	no	—
572	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
573	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
574	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
575	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
577	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
578	C₂×D₄	—	2	12	no	—
579	C₂×D₄	—	2	12	no	—
580	C₂×D₄	—	4	6	no	—
581	C₂×D₄	—	4	12	no	—
582	C₂×D₄	—	4	12	no	—
583	C₂×D₄	—	8	6	no	—
584	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
585	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
586	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
587	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
588	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
589	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
590	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
591	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
592	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
593	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	6	no	—
596	C₂²×C₄	—	4	12	no	—
597	C₂²×C₄	—	8	6	no	—
598	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
599	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
600	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
601	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
602	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
603	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
604	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
605	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
606	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
607	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
608	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
609	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
610	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
611	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
612	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
613	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
614	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
615	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
616	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
617	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
618	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
619	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
620	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
621	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
622	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
623	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
624	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
625	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
626	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
627	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
628	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
629	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
630	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
631	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
632	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
633	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
634	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
635	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
636	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
637	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
638	C₄²	C₂⁴×C₁₉	1	6	yes	—
639	C₄²	C₂⁴×C₁₉	1	6	yes	—
640	C₄²	C₂⁴×C₁₉	1	24	yes	—
641	C₂³	—	2	12	no	—
642	C₂³	—	2	12	no	—
643	C₂³	—	2	6	no	—
644	C₂³	—	2	12	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	6	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	3	no	—
649	C₂³	—	4	6	no	—
650	C₂³	—	4	3	no	—
651	C₂³	—	4	6	no	—
652	C₂³	—	8	16	no	—
653	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	complemented
654	C₂³	C₂⁵×C₁₉	1	6	yes	—
655	C₂³	C₂⁵×C₁₉	1	6	yes	—
656	C₂³	C₂⁵×C₁₉	1	2	yes	—
657	C₂³	C₂⁵×C₁₉	1	3	yes	—
658	Q₈	—	2	12	no	—
659	Q₈	—	4	2	no	—
660	Q₈	—	4	12	no	—
661	Q₈	—	4	6	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	12	no	—
664	D₄	—	2	12	no	—
665	D₄	—	2	24	no	—
666	D₄	—	2	24	no	—
667	D₄	—	2	6	no	—
668	D₄	—	4	6	no	—
669	D₄	—	4	12	no	—
670	D₄	—	4	24	no	—
671	D₄	—	4	6	no	—
672	D₄	—	4	6	no	—
673	D₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
674	C₂×C₄	—	2	24	no	—
675	C₂×C₄	—	2	6	no	—
676	C₂×C₄	—	2	6	no	—
677	C₂×C₄	—	2	12	no	—
678	C₂×C₄	—	4	3	no	—
679	C₂×C₄	—	4	3	no	—
680	C₂×C₄	—	4	6	no	—
681	C₂×C₄	—	4	6	no	—
682	C₂×C₄	—	4	12	no	—
683	C₂×C₄	—	4	3	no	—
684	C₂×C₄	—	4	6	no	—
685	C₂×C₄	—	4	12	no	—
686	C₂×C₄	—	4	12	no	—
687	C₂×C₄	—	4	12	no	—
688	C₂×C₄	—	4	12	no	—
689	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
690	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
691	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
692	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
693	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
694	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
695	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
696	C₂²	—	2	3	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	3	no	—
700	C₂²	—	2	6	no	—
701	C₂²	—	2	6	no	—
702	C₂²	—	2	6	no	—
703	C₂²	—	2	6	no	—
704	C₂²	—	2	6	no	—
705	C₂²	—	2	6	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	4	24	no	—
708	C₂²	—	8	12	no	—
709	C₂²	—	8	6	no	—
710	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	4	yes	—
711	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	6	yes	—
712	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
713	C₄	—	2	6	no	—
714	C₄	—	2	3	no	—
715	C₄	—	2	12	no	—
716	C₄	—	2	6	no	—
717	C₄	—	2	12	no	—
718	C₄	—	2	6	no	—
719	C₄	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
720	C₂	—	2	6	no	—
721	C₂	—	2	4	no	—
722	C₂	—	4	6	no	—
723	C₂	—	4	6	no	—
724	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
725	C₂	C₂²×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
726	C₂	C₁₉×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉×#3561	C₂	semidirect
2. C₁₉×#3536	C₂	semidirect
3. C₁₉×#3536	C₂	semidirect
4. C₁₉×#3535	C₂	semidirect
5. C₁₉×#3520	C₂	semidirect
6. C₁₉×#3501	C₂	semidirect
7. C₁₉×#3490	C₂	semidirect
8. C₁₉×#3489	C₂	semidirect
9. C₂×C₁₉×#546	C₂	semidirect
10. C₁₉×#3459	C₂	semidirect
11. C₂×C₁₉×#543	C₂	semidirect
12. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
13. C₂²×#41×C₁₉	C₂²	semidirect
15. C₁₉×#563	C₂²	semidirect
16. C₁₉×#562	C₂²	semidirect
17. C₁₉×#562	C₂²	semidirect
18. C₁₉×#556	C₂²	semidirect
19. C₁₉×#554	C₂²	semidirect
20. C₁₉×#554	C₂²	semidirect
21. C₁₉×#552	C₂²	semidirect
22. C₁₉×#551	C₂²	semidirect
23. C₁₉×#551	C₂²	semidirect
24. D₄×Q₈×C₁₉	C₂²	semidirect
25. D₄×Q₈×C₁₉	C₂²	semidirect
26. C₁₉×#548	C₂²	semidirect
27. C₁₉×#548	C₂²	semidirect
28. C₁₉×#547	C₂²	semidirect
29. C₁₉×#547	C₂²	semidirect
30. C₁₉×#547	C₂²	semidirect
31. C₁₉×#546	C₂²	semidirect
32. C₁₉×#546	C₂²	semidirect
33. C₁₉×#546	C₂²	semidirect
34. C₁₉×#546	C₂²	semidirect
35. C₁₉×#546	C₂²	semidirect
36. C₁₉×#544	C₂²	semidirect
39. C₁₉×#543	C₂²	semidirect
40. C₁₉×#543	C₂²	semidirect
41. C₁₉×#543	C₂²	semidirect
42. C₁₉×#542	C₂²	semidirect
43. C₁₉×#542	C₂²	semidirect
44. C₁₉×#539	C₂²	semidirect
45. C₁₉×#539	C₂²	semidirect
46. C₁₉×#539	C₂²	semidirect
47. C₁₉×#538	C₂²	semidirect
48. C₁₉×#538	C₂²	semidirect
49. C₁₉×#538	C₂²	semidirect
50. C₁₉×#537	C₂²	semidirect
51. C₁₉×#537	C₂²	semidirect
52. C₁₉×#537	C₂²	semidirect
53. C₁₉×#536	C₂²	semidirect
54. C₁₉×#536	C₂²	semidirect
56. C₁₉×#533	C₂²	semidirect
57. C₁₉×#529	C₂²	semidirect
58. C₂×C₁₉×#124	C₂²	semidirect
59. C₁₉×#525	C₂²	semidirect
60. C₁₉×#525	C₂²	semidirect
61. C₁₉×#525	C₂²	semidirect
62. C₂×C₁₉×#123	C₂²	semidirect
64. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
65. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
66. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
67. C₂×C₁₉×#121	C₂²	semidirect
68. C₂×C₁₉×#121	C₂²	semidirect
70. C₁₉×#520	C₂²	semidirect
73. C₂×C₄×D₄×C₁₉	C₂²	semidirect
81. C₂×#41×C₁₉	C₂³	semidirect
82. C₂×#41×C₁₉	C₂³	semidirect
83. C₂×#41×C₁₉	C₂³	semidirect
85. C₂²×Q₈×C₁₉	C₂³	semidirect
86. C₂²×Q₈×C₁₉	C₂³	semidirect
87. C₂²×Q₈×C₁₉	C₂³	semidirect
99. C₁₉×C₄⋊Q₈	C₂³	semidirect
100. C₁₉×C₄⋊Q₈	C₂³	semidirect
101. C₁₉×C₄⋊Q₈	C₂³	semidirect
102. C₁₉×#126	C₂³	semidirect
103. C₁₉×#126	C₂³	semidirect
104. C₁₉×#126	C₂³	semidirect
105. C₁₉×#125	C₂³	semidirect
106. C₁₉×#125	C₂³	semidirect
107. C₁₉×#125	C₂³	semidirect
110. C₁₉×#124	C₂³	semidirect
111. C₁₉×#124	C₂³	semidirect
112. C₁₉×#124	C₂³	semidirect
116. C₁₉×#123	C₂³	semidirect
117. C₁₉×#123	C₂³	semidirect
118. C₁₉×#123	C₂³	semidirect
119. C₁₉×#123	C₂³	semidirect
120. C₁₉×#123	C₂³	semidirect
129. C₁₉×C₂²⋊Q₈	C₂³	semidirect
130. C₁₉×C₂²⋊Q₈	C₂³	semidirect
131. C₁₉×C₂²⋊Q₈	C₂³	semidirect
132. C₁₉×C₂²⋊Q₈	C₂³	semidirect
133. C₁₉×C₂²⋊Q₈	C₂³	semidirect
134. C₁₉×C₂²⋊Q₈	C₂³	semidirect
135. C₁₉×C₂²⋊Q₈	C₂³	semidirect
136. C₁₉×C₂²⋊Q₈	C₂³	semidirect
137. C₁₉×C₂²⋊Q₈	C₂³	semidirect
138. C₁₉×C₂²⋊Q₈	C₂³	semidirect
139. C₁₉×C₂²⋊Q₈	C₂³	semidirect
140. C₁₉×C₂²⋊Q₈	C₂³	semidirect
141. C₁₉×C₂²⋊Q₈	C₂³	semidirect
148. C₁₉×#121	C₂³	semidirect
149. C₁₉×#121	C₂³	semidirect
150. C₁₉×#121	C₂³	semidirect
151. C₁₉×#121	C₂³	semidirect
152. C₁₉×#121	C₂³	semidirect
156. C₄×Q₈×C₁₉	C₂³	semidirect
157. C₄×Q₈×C₁₉	C₂³	semidirect
158. C₄×Q₈×C₁₉	C₂³	semidirect
166. C₄×D₄×C₁₉	C₂³	semidirect
167. C₄×D₄×C₁₉	C₂³	semidirect
168. C₄×D₄×C₁₉	C₂³	semidirect
170. C₁₉×#117	C₂³	semidirect
171. C₁₉×#117	C₂³	semidirect
172. C₁₉×#117	C₂³	semidirect
176. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
177. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
178. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
179. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
277. #62894	C₁₉	direct (N × H)
290. C₂³×C₁₉	2₋¹⁺⁴	semidirect
333. #3561	C₂×C₁₉	semidirect
334. #3536	C₂×C₁₉	semidirect
335. #3536	C₂×C₁₉	semidirect
336. #3535	C₂×C₁₉	semidirect
337. #3520	C₂×C₁₉	semidirect
338. #3501	C₂×C₁₉	semidirect
339. #3490	C₂×C₁₉	semidirect
340. #3489	C₂×C₁₉	semidirect
341. C₂×#546	C₂×C₁₉	semidirect
342. #3459	C₂×C₁₉	semidirect
343. C₂×#543	C₂×C₁₉	semidirect
368. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
369. C₂²×#41	C₂²×C₁₉	semidirect
371. #563	C₂²×C₁₉	semidirect
372. #562	C₂²×C₁₉	semidirect
373. #562	C₂²×C₁₉	semidirect
374. #556	C₂²×C₁₉	semidirect
375. #554	C₂²×C₁₉	semidirect
376. #554	C₂²×C₁₉	semidirect
377. #552	C₂²×C₁₉	semidirect
378. #551	C₂²×C₁₉	semidirect
379. #551	C₂²×C₁₉	semidirect
380. D₄×Q₈	C₂²×C₁₉	semidirect
381. D₄×Q₈	C₂²×C₁₉	semidirect
382. #548	C₂²×C₁₉	semidirect
383. #548	C₂²×C₁₉	semidirect
384. #547	C₂²×C₁₉	semidirect
385. #547	C₂²×C₁₉	semidirect
386. #547	C₂²×C₁₉	semidirect
387. #546	C₂²×C₁₉	semidirect
388. #546	C₂²×C₁₉	semidirect
389. #546	C₂²×C₁₉	semidirect
390. #546	C₂²×C₁₉	semidirect
391. #546	C₂²×C₁₉	semidirect
392. #544	C₂²×C₁₉	semidirect
395. #543	C₂²×C₁₉	semidirect
396. #543	C₂²×C₁₉	semidirect
397. #543	C₂²×C₁₉	semidirect
398. #542	C₂²×C₁₉	semidirect
399. #542	C₂²×C₁₉	semidirect
400. #539	C₂²×C₁₉	semidirect
401. #539	C₂²×C₁₉	semidirect
402. #539	C₂²×C₁₉	semidirect
403. #538	C₂²×C₁₉	semidirect
404. #538	C₂²×C₁₉	semidirect
405. #538	C₂²×C₁₉	semidirect
406. #537	C₂²×C₁₉	semidirect
407. #537	C₂²×C₁₉	semidirect
408. #537	C₂²×C₁₉	semidirect
409. #536	C₂²×C₁₉	semidirect
410. #536	C₂²×C₁₉	semidirect
412. #533	C₂²×C₁₉	semidirect
413. #529	C₂²×C₁₉	semidirect
414. C₂×#124	C₂²×C₁₉	semidirect
415. #525	C₂²×C₁₉	semidirect
416. #525	C₂²×C₁₉	semidirect
417. #525	C₂²×C₁₉	semidirect
418. C₂×#123	C₂²×C₁₉	semidirect
420. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
421. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
422. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
423. C₂×#121	C₂²×C₁₉	semidirect
424. C₂×#121	C₂²×C₁₉	semidirect
426. #520	C₂²×C₁₉	semidirect
429. C₂×C₄×D₄	C₂²×C₁₉	semidirect
444. C₂×#41	C₂³×C₁₉	semidirect
445. C₂×#41	C₂³×C₁₉	semidirect
446. C₂×#41	C₂³×C₁₉	semidirect
448. C₂²×Q₈	C₂³×C₁₉	semidirect
449. C₂²×Q₈	C₂³×C₁₉	semidirect
450. C₂²×Q₈	C₂³×C₁₉	semidirect
462. C₄⋊Q₈	C₂³×C₁₉	semidirect
463. C₄⋊Q₈	C₂³×C₁₉	semidirect
464. C₄⋊Q₈	C₂³×C₁₉	semidirect
465. #126	C₂³×C₁₉	semidirect
466. #126	C₂³×C₁₉	semidirect
467. #126	C₂³×C₁₉	semidirect
468. #125	C₂³×C₁₉	semidirect
469. #125	C₂³×C₁₉	semidirect
470. #125	C₂³×C₁₉	semidirect
473. #124	C₂³×C₁₉	semidirect
474. #124	C₂³×C₁₉	semidirect
475. #124	C₂³×C₁₉	semidirect
479. #123	C₂³×C₁₉	semidirect
480. #123	C₂³×C₁₉	semidirect
481. #123	C₂³×C₁₉	semidirect
482. #123	C₂³×C₁₉	semidirect
483. #123	C₂³×C₁₉	semidirect
492. C₂²⋊Q₈	C₂³×C₁₉	semidirect
493. C₂²⋊Q₈	C₂³×C₁₉	semidirect
494. C₂²⋊Q₈	C₂³×C₁₉	semidirect
495. C₂²⋊Q₈	C₂³×C₁₉	semidirect
496. C₂²⋊Q₈	C₂³×C₁₉	semidirect
497. C₂²⋊Q₈	C₂³×C₁₉	semidirect
498. C₂²⋊Q₈	C₂³×C₁₉	semidirect
499. C₂²⋊Q₈	C₂³×C₁₉	semidirect
500. C₂²⋊Q₈	C₂³×C₁₉	semidirect
501. C₂²⋊Q₈	C₂³×C₁₉	semidirect
502. C₂²⋊Q₈	C₂³×C₁₉	semidirect
503. C₂²⋊Q₈	C₂³×C₁₉	semidirect
504. C₂²⋊Q₈	C₂³×C₁₉	semidirect
511. #121	C₂³×C₁₉	semidirect
512. #121	C₂³×C₁₉	semidirect
513. #121	C₂³×C₁₉	semidirect
514. #121	C₂³×C₁₉	semidirect
515. #121	C₂³×C₁₉	semidirect
519. C₄×Q₈	C₂³×C₁₉	semidirect
520. C₄×Q₈	C₂³×C₁₉	semidirect
521. C₄×Q₈	C₂³×C₁₉	semidirect
529. C₄×D₄	C₂³×C₁₉	semidirect
530. C₄×D₄	C₂³×C₁₉	semidirect
531. C₄×D₄	C₂³×C₁₉	semidirect
533. #117	C₂³×C₁₉	semidirect
534. #117	C₂³×C₁₉	semidirect
535. #117	C₂³×C₁₉	semidirect
539. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
540. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
541. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
542. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
554. C₁₉	#62894	direct (N × H)
653. C₂³	C₁₉×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3561	2
C₁₉×#3536	2
C₁₉×#3535	2
C₁₉×#3520	2
C₁₉×#3501	2
C₁₉×#3490	2
C₁₉×#3489	2
C₂×C₁₉×#546	2
C₁₉×#3459	2
C₂×C₁₉×#543	2
#62894	19

Subgroups — C19×#62894 #18068853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62894 #18068853