Subgroups — C₁₉×#62863 #18068822

Order 4864.

7466 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3560	C₂	1	8	yes	maximal, complemented
2	C₁₉×#3558	C₂	1	8	yes	maximal, complemented
3	C₁₉×#3537	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3534	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3533	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3532	C₂	1	8	yes	maximal, complemented
7	C₁₉×#3505	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3496	C₂	1	4	yes	maximal, complemented
9	C₁₉×#3484	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₉×#538	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₉×#534	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	complemented
13	C₂³×D₄×C₁₉	C₂²	1	2	yes	complemented
14	C₁₉×#563	C₂²	1	8	yes	complemented
15	C₁₉×#562	C₂²	1	16	yes	complemented
16	C₁₉×H(3,𝔽₄)	C₂²	1	8	yes	complemented
17	C₁₉×#560	C₂²	1	16	yes	complemented
18	C₁₉×#560	C₂²	1	8	yes	complemented
19	C₁₉×#560	C₂²	1	8	yes	complemented
20	C₁₉×#559	C₂²	1	8	yes	complemented
21	C₁₉×#553	C₂²	1	16	yes	complemented
22	C₁₉×#553	C₂²	1	8	yes	complemented
23	C₁₉×#553	C₂²	1	16	yes	complemented
24	C₁₉×#552	C₂²	1	8	yes	complemented
25	C₁₉×#551	C₂²	1	16	yes	complemented
26	C₁₉×#551	C₂²	1	8	yes	complemented
27	C₁₉×#551	C₂²	1	8	yes	complemented
28	C₁₉×#548	C₂²	1	8	yes	complemented
29	C₁₉×#547	C₂²	1	8	yes	complemented
30	C₁₉×#547	C₂²	1	8	yes	complemented
31	C₁₉×#546	C₂²	1	8	yes	complemented
32	C₁₉×#546	C₂²	1	16	yes	complemented
33	C₁₉×#546	C₂²	1	16	yes	complemented
34	C₁₉×#546	C₂²	1	16	yes	complemented
35	C₁₉×#546	C₂²	1	16	yes	complemented
36	C₁₉×#546	C₂²	1	16	yes	complemented
37	D₄²×C₁₉	C₂²	1	8	yes	complemented
38	D₄²×C₁₉	C₂²	1	16	yes	complemented
39	D₄²×C₁₉	C₂²	1	16	yes	complemented
40	D₄²×C₁₉	C₂²	1	8	yes	complemented
41	D₄²×C₁₉	C₂²	1	8	yes	complemented
42	C₁₉×#542	C₂²	1	16	yes	complemented
43	C₁₉×#540	C₂²	1	16	yes	complemented
44	C₁₉×#539	C₂²	1	16	yes	complemented
45	C₁₉×#539	C₂²	1	8	yes	complemented
46	C₁₉×#538	C₂²	1	16	yes	complemented
47	C₁₉×#538	C₂²	1	8	yes	complemented
48	C₁₉×#538	C₂²	1	8	yes	complemented
49	C₁₉×#538	C₂²	1	16	yes	complemented
50	C₁₉×#538	C₂²	1	16	yes	complemented
51	C₁₉×#538	C₂²	1	16	yes	complemented
52	C₁₉×#538	C₂²	1	8	yes	complemented
53	C₁₉×#537	C₂²	1	8	yes	complemented
54	C₁₉×#535	C₂²	1	8	yes	complemented
55	C₁₉×#535	C₂²	1	16	yes	complemented
56	C₁₉×#534	C₂²	1	8	yes	complemented
57	C₁₉×#534	C₂²	1	8	yes	complemented
58	C₁₉×#534	C₂²	1	8	yes	complemented
59	C₁₉×#534	C₂²	1	8	yes	complemented
60	C₁₉×#534	C₂²	1	16	yes	complemented
61	C₁₉×#534	C₂²	1	8	yes	complemented
62	C₁₉×#532	C₂²	1	8	yes	complemented
63	C₁₉×#529	C₂²	1	8	yes	complemented
64	C₂×C₁₉×#126	C₂²	1	4	yes	complemented
65	C₂×C₁₉×#124	C₂²	1	4	yes	complemented
66	C₁₉×#525	C₂²	1	8	yes	complemented
67	C₁₉×#525	C₂²	1	8	yes	complemented
68	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
69	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
70	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
71	C₂×C₁₉×#121	C₂²	1	4	yes	complemented
72	C₂×C₁₉×#121	C₂²	1	4	yes	complemented
73	C₂×C₁₉×#121	C₂²	1	2	yes	complemented
74	C₂×C₁₉×#121	C₂²	1	8	yes	complemented
75	C₂×C₁₉×#120	C₂²	1	4	yes	complemented
76	C₂×C₁₉×#120	C₂²	1	4	yes	complemented
77	C₂×C₁₉×#120	C₂²	1	8	yes	complemented
78	C₁₉×#518	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	complemented
80	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
81	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
82	C₂⁵×C₁₉	C₂³	1	2	yes	—
83	C₁₉×H(5,𝔽₂)	—	4	16	no	—
84	C₂×#41×C₁₉	C₂³	1	8	yes	—
85	C₂×#41×C₁₉	C₂³	1	16	yes	complemented
86	C₂×#41×C₁₉	C₂³	1	8	yes	complemented
87	C₂²×Q₈×C₁₉	C₂³	1	2	yes	complemented
88	C₂²×D₄×C₁₉	—	4	8	no	—
89	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
93	C₂²×D₄×C₁₉	C₂³	1	16	yes	—
94	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₉	C₂³	1	16	yes	complemented
98	C₂²×D₄×C₁₉	C₂³	1	16	yes	complemented
99	C₂²×D₄×C₁₉	C₂³	1	2	yes	complemented
100	C₂²×D₄×C₁₉	C₂³	1	8	yes	complemented
101	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₉	C₂³	1	4	yes	complemented
104	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	complemented
105	C₁₉×#127	C₂³	1	8	yes	—
106	C₁₉×#127	C₂³	1	8	yes	—
107	C₁₉×#127	C₂³	1	8	yes	complemented
108	C₁₉×#126	C₂³	1	16	yes	complemented
109	C₁₉×#126	C₂³	1	16	yes	complemented
110	C₁₉×#126	C₂³	1	16	yes	complemented
111	C₁₉×#126	C₂³	1	16	yes	complemented
112	C₁₉×#126	C₂³	1	16	yes	complemented
113	C₁₉×#125	C₂³	1	8	yes	complemented
114	C₁₉×#125	C₂³	1	16	yes	complemented
115	C₁₉×#124	C₂³	1	8	yes	—
116	C₁₉×#124	C₂³	1	8	yes	—
117	C₁₉×#124	C₂³	1	16	yes	complemented
118	C₁₉×#124	C₂³	1	16	yes	complemented
119	C₁₉×#124	C₂³	1	8	yes	complemented
120	C₁₉×#124	C₂³	1	16	yes	complemented
121	C₁₉×#124	C₂³	1	16	yes	complemented
122	C₁₉×#123	C₂³	1	16	yes	—
123	C₁₉×#123	C₂³	1	8	yes	—
124	C₁₉×#123	C₂³	1	8	yes	—
125	C₁₉×#123	C₂³	1	16	yes	—
126	C₁₉×#123	C₂³	1	8	yes	—
127	C₁₉×#123	C₂³	1	8	yes	—
128	C₁₉×#123	C₂³	1	16	yes	complemented
129	C₁₉×#123	C₂³	1	16	yes	complemented
130	C₁₉×#123	C₂³	1	16	yes	complemented
131	C₁₉×#123	C₂³	1	16	yes	complemented
132	C₁₉×#123	C₂³	1	16	yes	complemented
133	C₁₉×#123	C₂³	1	16	yes	complemented
134	C₁₉×#123	C₂³	1	16	yes	complemented
135	C₁₉×#123	C₂³	1	16	yes	complemented
136	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
137	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	complemented
138	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	complemented
139	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	complemented
140	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	complemented
141	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	complemented
142	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	complemented
143	C₁₉×#121	C₂³	1	8	yes	—
144	C₁₉×#121	C₂³	1	8	yes	—
145	C₁₉×#121	C₂³	1	8	yes	—
146	C₁₉×#121	C₂³	1	8	yes	—
147	C₁₉×#121	C₂³	1	8	yes	—
148	C₁₉×#121	C₂³	1	16	yes	—
149	C₁₉×#121	C₂³	1	16	yes	—
150	C₁₉×#121	C₂³	1	16	yes	—
151	C₁₉×#121	C₂³	1	16	yes	—
152	C₁₉×#121	C₂³	1	8	yes	complemented
153	C₁₉×#121	C₂³	1	16	yes	complemented
154	C₁₉×#121	C₂³	1	16	yes	complemented
155	C₁₉×#121	C₂³	1	16	yes	complemented
156	C₁₉×#121	C₂³	1	8	yes	complemented
157	C₁₉×#121	C₂³	1	16	yes	complemented
158	C₁₉×#121	C₂³	1	8	yes	complemented
159	C₁₉×#121	C₂³	1	8	yes	complemented
160	C₁₉×#121	C₂³	1	16	yes	complemented
161	C₁₉×#121	C₂³	1	16	yes	complemented
162	C₁₉×#121	C₂³	1	16	yes	complemented
163	C₁₉×#121	C₂³	1	16	yes	complemented
164	C₁₉×#121	C₂³	1	16	yes	complemented
165	C₁₉×#120	C₂³	1	16	yes	—
166	C₁₉×#120	C₂³	1	16	yes	—
167	C₁₉×#120	C₂³	1	8	yes	—
168	C₁₉×#120	C₂³	1	8	yes	—
169	C₁₉×#120	C₂³	1	16	yes	—
170	C₁₉×#120	C₂³	1	16	yes	—
171	C₁₉×#120	C₂³	1	8	yes	—
172	C₁₉×#120	C₂³	1	8	yes	—
173	C₁₉×#120	C₂³	1	16	yes	complemented
174	C₁₉×#120	C₂³	1	16	yes	complemented
175	C₁₉×#120	C₂³	1	16	yes	complemented
176	C₁₉×#120	C₂³	1	16	yes	complemented
177	C₁₉×#120	C₂³	1	16	yes	complemented
178	C₄×Q₈×C₁₉	C₂³	1	8	yes	complemented
179	C₄×D₄×C₁₉	C₂³	1	8	yes	—
180	C₄×D₄×C₁₉	C₂³	1	8	yes	—
181	C₄×D₄×C₁₉	C₂³	1	8	yes	complemented
182	C₄×D₄×C₁₉	C₂³	1	8	yes	complemented
183	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
184	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
185	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
186	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
187	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
188	C₄×D₄×C₁₉	C₂³	1	8	yes	complemented
189	C₄×D₄×C₁₉	C₂³	1	8	yes	complemented
190	C₄×D₄×C₁₉	C₂³	1	8	yes	complemented
191	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
192	C₁₉×#117	C₂³	1	8	yes	—
193	C₁₉×#117	C₂³	1	8	yes	complemented
194	C₁₉×#117	C₂³	1	16	yes	complemented
195	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	complemented
197	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	complemented
198	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
199	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	complemented
200	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
201	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
204	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
206	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
207	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
209	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	complemented
210	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	complemented
211	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	complemented
212	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	complemented
213	C₂×C₄²×C₁₉	C₂³	1	4	yes	complemented
214	C₂⁴×C₁₉	—	2	4	no	—
215	C₂⁴×C₁₉	—	4	4	no	—
216	C₂⁴×C₁₉	—	8	2	no	—
217	C₂⁴×C₁₉	—	8	4	no	—
218	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
219	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
220	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
221	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
222	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
223	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
224	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
225	#41×C₁₉	—	4	16	no	—
226	#41×C₁₉	—	4	32	no	—
227	#41×C₁₉	—	8	8	no	—
228	C₂×Q₈×C₁₉	—	8	2	no	—
229	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
230	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
231	C₂×D₄×C₁₉	—	2	16	no	—
232	C₂×D₄×C₁₉	—	2	16	no	—
233	C₂×D₄×C₁₉	—	4	8	no	—
234	C₂×D₄×C₁₉	—	4	32	no	—
235	C₂×D₄×C₁₉	—	4	16	no	—
236	C₂×D₄×C₁₉	—	4	32	no	—
237	C₂×D₄×C₁₉	—	8	4	no	—
238	C₂×D₄×C₁₉	—	8	4	no	—
239	C₂×D₄×C₁₉	—	8	4	no	—
240	C₂×D₄×C₁₉	—	8	2	no	—
241	C₂×D₄×C₁₉	—	8	8	no	—
242	C₂×D₄×C₁₉	—	8	16	no	—
243	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
244	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
245	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
246	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
247	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
248	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
249	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
250	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
251	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
252	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
253	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
254	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
255	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
256	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
257	C₂²×C₄×C₁₉	—	4	4	no	—
258	C₂²×C₄×C₁₉	—	8	2	no	—
259	C₂²×C₄×C₁₉	—	8	4	no	—
260	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
262	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
269	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
270	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
272	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
273	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
274	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
275	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
276	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
277	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
278	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
279	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
280	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
281	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
282	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
283	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
284	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
285	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
286	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
287	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
288	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
289	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
290	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
291	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
292	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
293	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
294	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
295	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
296	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
297	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
298	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
299	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
300	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
301	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
302	C₄²×C₁₉	C₂⁴	1	8	yes	—
303	C₄²×C₁₉	C₂⁴	1	8	yes	—
304	C₄²×C₁₉	C₂⁴	1	8	yes	—
305	C₄²×C₁₉	C₂⁴	1	8	yes	—
306	#62863	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂³×C₁₉	—	2	4	no	—
308	C₂³×C₁₉	—	2	8	no	—
309	C₂³×C₁₉	—	2	8	no	—
310	C₂³×C₁₉	—	2	8	no	—
311	C₂³×C₁₉	—	4	2	no	—
312	C₂³×C₁₉	—	4	4	no	—
313	C₂³×C₁₉	—	4	4	no	—
314	C₂³×C₁₉	—	4	8	no	—
315	C₂³×C₁₉	—	4	4	no	—
316	C₂³×C₁₉	—	4	4	no	—
317	C₂³×C₁₉	—	4	4	no	—
318	C₂³×C₁₉	—	4	8	no	—
319	C₂³×C₁₉	—	4	16	no	—
320	C₂³×C₁₉	—	4	8	no	—
321	C₂³×C₁₉	—	4	16	no	—
322	C₂³×C₁₉	—	8	8	no	—
323	C₂³×C₁₉	—	8	16	no	—
324	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
325	C₂³×C₁₉	C₂⁵	1	4	yes	—
326	C₂³×C₁₉	C₂⁵	1	8	yes	—
327	C₂³×C₁₉	C₂⁵	1	8	yes	—
328	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
329	C₂³×C₁₉	C₂⁵	1	2	yes	—
330	Q₈×C₁₉	—	4	8	no	—
331	Q₈×C₁₉	—	4	8	no	—
332	D₄×C₁₉	—	2	32	no	—
333	D₄×C₁₉	—	2	16	no	—
334	D₄×C₁₉	—	2	16	no	—
335	D₄×C₁₉	—	4	8	no	—
336	D₄×C₁₉	—	4	8	no	—
337	D₄×C₁₉	—	4	8	no	—
338	D₄×C₁₉	—	4	16	no	—
339	D₄×C₁₉	—	4	16	no	—
340	D₄×C₁₉	—	4	8	no	—
341	D₄×C₁₉	—	4	16	no	—
342	D₄×C₁₉	—	4	8	no	—
343	D₄×C₁₉	—	4	16	no	—
344	D₄×C₁₉	—	4	8	no	—
345	D₄×C₁₉	—	4	16	no	—
346	C₂×C₄×C₁₉	—	2	8	no	—
347	C₂×C₄×C₁₉	—	2	8	no	—
348	C₂×C₄×C₁₉	—	4	8	no	—
349	C₂×C₄×C₁₉	—	4	4	no	—
350	C₂×C₄×C₁₉	—	4	2	no	—
351	C₂×C₄×C₁₉	—	4	4	no	—
352	C₂×C₄×C₁₉	—	4	8	no	—
353	C₂×C₄×C₁₉	—	4	4	no	—
354	C₂×C₄×C₁₉	—	4	2	no	—
355	C₂×C₄×C₁₉	—	4	8	no	—
356	C₂×C₄×C₁₉	—	4	16	no	—
357	C₂×C₄×C₁₉	—	4	8	no	—
358	C₂×C₄×C₁₉	—	4	4	no	—
359	C₂×C₄×C₁₉	—	4	16	no	—
360	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
361	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
362	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
363	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
364	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
365	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
366	#3560	C₂×C₁₉	1	8	yes	complemented
367	#3558	C₂×C₁₉	1	8	yes	complemented
368	#3537	C₂×C₁₉	1	8	yes	complemented
369	#3534	C₂×C₁₉	1	8	yes	complemented
370	#3533	C₂×C₁₉	1	8	yes	complemented
371	#3532	C₂×C₁₉	1	8	yes	complemented
372	#3505	C₂×C₁₉	1	4	yes	complemented
373	#3496	C₂×C₁₉	1	4	yes	complemented
374	#3484	C₂×C₁₉	1	4	yes	complemented
375	C₂×#538	C₂×C₁₉	1	2	yes	complemented
376	C₂×#534	C₂×C₁₉	1	1	yes	characteristic, complemented
377	C₂²×C₁₉	—	2	2	no	—
378	C₂²×C₁₉	—	2	2	no	—
379	C₂²×C₁₉	—	2	2	no	—
380	C₂²×C₁₉	—	2	8	no	—
381	C₂²×C₁₉	—	2	4	no	—
382	C₂²×C₁₉	—	2	8	no	—
383	C₂²×C₁₉	—	2	8	no	—
384	C₂²×C₁₉	—	2	16	no	—
385	C₂²×C₁₉	—	2	8	no	—
386	C₂²×C₁₉	—	2	8	no	—
387	C₂²×C₁₉	—	4	4	no	—
388	C₂²×C₁₉	—	4	8	no	—
389	C₂²×C₁₉	—	8	8	no	—
390	C₂²×C₁₉	—	8	8	no	—
391	C₂²×C₁₉	—	8	8	no	—
392	C₂²×C₁₉	—	8	16	no	—
393	C₂²×C₁₉	—	16	8	no	—
394	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
395	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	4	yes	—
396	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
397	C₄×C₁₉	—	2	8	no	—
398	C₄×C₁₉	—	2	8	no	—
399	C₄×C₁₉	—	2	4	no	—
400	C₄×C₁₉	—	2	8	no	—
401	C₄×C₁₉	—	2	4	no	—
402	C₄×C₁₉	—	2	8	no	—
403	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	complemented
404	C₂³×D₄	C₂²×C₁₉	1	2	yes	complemented
405	#563	C₂²×C₁₉	1	8	yes	complemented
406	#562	C₂²×C₁₉	1	16	yes	complemented
407	H(3,𝔽₄)	C₂²×C₁₉	1	8	yes	complemented
408	#560	C₂²×C₁₉	1	16	yes	complemented
409	#560	C₂²×C₁₉	1	8	yes	complemented
410	#560	C₂²×C₁₉	1	8	yes	complemented
411	#559	C₂²×C₁₉	1	8	yes	complemented
412	#553	C₂²×C₁₉	1	16	yes	complemented
413	#553	C₂²×C₁₉	1	8	yes	complemented
414	#553	C₂²×C₁₉	1	16	yes	complemented
415	#552	C₂²×C₁₉	1	8	yes	complemented
416	#551	C₂²×C₁₉	1	16	yes	complemented
417	#551	C₂²×C₁₉	1	8	yes	complemented
418	#551	C₂²×C₁₉	1	8	yes	complemented
419	#548	C₂²×C₁₉	1	8	yes	complemented
420	#547	C₂²×C₁₉	1	8	yes	complemented
421	#547	C₂²×C₁₉	1	8	yes	complemented
422	#546	C₂²×C₁₉	1	8	yes	complemented
423	#546	C₂²×C₁₉	1	16	yes	complemented
424	#546	C₂²×C₁₉	1	16	yes	complemented
425	#546	C₂²×C₁₉	1	16	yes	complemented
426	#546	C₂²×C₁₉	1	16	yes	complemented
427	#546	C₂²×C₁₉	1	16	yes	complemented
428	D₄²	C₂²×C₁₉	1	8	yes	complemented
429	D₄²	C₂²×C₁₉	1	16	yes	complemented
430	D₄²	C₂²×C₁₉	1	16	yes	complemented
431	D₄²	C₂²×C₁₉	1	8	yes	complemented
432	D₄²	C₂²×C₁₉	1	8	yes	complemented
433	#542	C₂²×C₁₉	1	16	yes	complemented
434	#540	C₂²×C₁₉	1	16	yes	complemented
435	#539	C₂²×C₁₉	1	16	yes	complemented
436	#539	C₂²×C₁₉	1	8	yes	complemented
437	#538	C₂²×C₁₉	1	16	yes	complemented
438	#538	C₂²×C₁₉	1	8	yes	complemented
439	#538	C₂²×C₁₉	1	8	yes	complemented
440	#538	C₂²×C₁₉	1	16	yes	complemented
441	#538	C₂²×C₁₉	1	16	yes	complemented
442	#538	C₂²×C₁₉	1	16	yes	complemented
443	#538	C₂²×C₁₉	1	8	yes	complemented
444	#537	C₂²×C₁₉	1	8	yes	complemented
445	#535	C₂²×C₁₉	1	8	yes	complemented
446	#535	C₂²×C₁₉	1	16	yes	complemented
447	#534	C₂²×C₁₉	1	8	yes	complemented
448	#534	C₂²×C₁₉	1	8	yes	complemented
449	#534	C₂²×C₁₉	1	8	yes	complemented
450	#534	C₂²×C₁₉	1	8	yes	complemented
451	#534	C₂²×C₁₉	1	16	yes	complemented
452	#534	C₂²×C₁₉	1	8	yes	complemented
453	#532	C₂²×C₁₉	1	8	yes	complemented
454	#529	C₂²×C₁₉	1	8	yes	complemented
455	C₂×#126	C₂²×C₁₉	1	4	yes	complemented
456	C₂×#124	C₂²×C₁₉	1	4	yes	complemented
457	#525	C₂²×C₁₉	1	8	yes	complemented
458	#525	C₂²×C₁₉	1	8	yes	complemented
459	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
460	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
461	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	complemented
462	C₂×#121	C₂²×C₁₉	1	4	yes	complemented
463	C₂×#121	C₂²×C₁₉	1	4	yes	complemented
464	C₂×#121	C₂²×C₁₉	1	2	yes	complemented
465	C₂×#121	C₂²×C₁₉	1	8	yes	complemented
466	C₂×#120	C₂²×C₁₉	1	4	yes	complemented
467	C₂×#120	C₂²×C₁₉	1	4	yes	complemented
468	C₂×#120	C₂²×C₁₉	1	8	yes	complemented
469	#518	C₂²×C₁₉	1	4	yes	complemented
470	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	complemented
471	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
472	C₂×C₁₉	—	2	2	no	—
473	C₂×C₁₉	—	2	4	no	—
474	C₂×C₁₉	—	4	4	no	—
475	C₂×C₁₉	—	4	8	no	—
476	C₂×C₁₉	—	4	8	no	—
477	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₁₉	H(7,𝔽₂)	1	2	yes	—
479	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
480	C₂⁵	C₂³×C₁₉	1	2	yes	—
481	H(5,𝔽₂)	—	4	16	no	—
482	C₂×#41	C₂³×C₁₉	1	8	yes	—
483	C₂×#41	C₂³×C₁₉	1	16	yes	complemented
484	C₂×#41	C₂³×C₁₉	1	8	yes	complemented
485	C₂²×Q₈	C₂³×C₁₉	1	2	yes	complemented
486	C₂²×D₄	—	4	8	no	—
487	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
488	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
489	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
490	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
491	C₂²×D₄	C₂³×C₁₉	1	16	yes	—
492	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
493	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
494	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
495	C₂²×D₄	C₂³×C₁₉	1	16	yes	complemented
496	C₂²×D₄	C₂³×C₁₉	1	16	yes	complemented
497	C₂²×D₄	C₂³×C₁₉	1	2	yes	complemented
498	C₂²×D₄	C₂³×C₁₉	1	8	yes	complemented
499	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
501	C₂³×C₄	C₂³×C₁₉	1	4	yes	complemented
502	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	complemented
503	#127	C₂³×C₁₉	1	8	yes	—
504	#127	C₂³×C₁₉	1	8	yes	—
505	#127	C₂³×C₁₉	1	8	yes	complemented
506	#126	C₂³×C₁₉	1	16	yes	complemented
507	#126	C₂³×C₁₉	1	16	yes	complemented
508	#126	C₂³×C₁₉	1	16	yes	complemented
509	#126	C₂³×C₁₉	1	16	yes	complemented
510	#126	C₂³×C₁₉	1	16	yes	complemented
511	#125	C₂³×C₁₉	1	8	yes	complemented
512	#125	C₂³×C₁₉	1	16	yes	complemented
513	#124	C₂³×C₁₉	1	8	yes	—
514	#124	C₂³×C₁₉	1	8	yes	—
515	#124	C₂³×C₁₉	1	16	yes	complemented
516	#124	C₂³×C₁₉	1	16	yes	complemented
517	#124	C₂³×C₁₉	1	8	yes	complemented
518	#124	C₂³×C₁₉	1	16	yes	complemented
519	#124	C₂³×C₁₉	1	16	yes	complemented
520	#123	C₂³×C₁₉	1	16	yes	—
521	#123	C₂³×C₁₉	1	8	yes	—
522	#123	C₂³×C₁₉	1	8	yes	—
523	#123	C₂³×C₁₉	1	16	yes	—
524	#123	C₂³×C₁₉	1	8	yes	—
525	#123	C₂³×C₁₉	1	8	yes	—
526	#123	C₂³×C₁₉	1	16	yes	complemented
527	#123	C₂³×C₁₉	1	16	yes	complemented
528	#123	C₂³×C₁₉	1	16	yes	complemented
529	#123	C₂³×C₁₉	1	16	yes	complemented
530	#123	C₂³×C₁₉	1	16	yes	complemented
531	#123	C₂³×C₁₉	1	16	yes	complemented
532	#123	C₂³×C₁₉	1	16	yes	complemented
533	#123	C₂³×C₁₉	1	16	yes	complemented
534	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
535	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	complemented
536	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	complemented
537	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
538	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
539	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
540	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
541	#121	C₂³×C₁₉	1	8	yes	—
542	#121	C₂³×C₁₉	1	8	yes	—
543	#121	C₂³×C₁₉	1	8	yes	—
544	#121	C₂³×C₁₉	1	8	yes	—
545	#121	C₂³×C₁₉	1	8	yes	—
546	#121	C₂³×C₁₉	1	16	yes	—
547	#121	C₂³×C₁₉	1	16	yes	—
548	#121	C₂³×C₁₉	1	16	yes	—
549	#121	C₂³×C₁₉	1	16	yes	—
550	#121	C₂³×C₁₉	1	8	yes	complemented
551	#121	C₂³×C₁₉	1	16	yes	complemented
552	#121	C₂³×C₁₉	1	16	yes	complemented
553	#121	C₂³×C₁₉	1	16	yes	complemented
554	#121	C₂³×C₁₉	1	8	yes	complemented
555	#121	C₂³×C₁₉	1	16	yes	complemented
556	#121	C₂³×C₁₉	1	8	yes	complemented
557	#121	C₂³×C₁₉	1	8	yes	complemented
558	#121	C₂³×C₁₉	1	16	yes	complemented
559	#121	C₂³×C₁₉	1	16	yes	complemented
560	#121	C₂³×C₁₉	1	16	yes	complemented
561	#121	C₂³×C₁₉	1	16	yes	complemented
562	#121	C₂³×C₁₉	1	16	yes	complemented
563	#120	C₂³×C₁₉	1	16	yes	—
564	#120	C₂³×C₁₉	1	16	yes	—
565	#120	C₂³×C₁₉	1	8	yes	—
566	#120	C₂³×C₁₉	1	8	yes	—
567	#120	C₂³×C₁₉	1	16	yes	—
568	#120	C₂³×C₁₉	1	16	yes	—
569	#120	C₂³×C₁₉	1	8	yes	—
570	#120	C₂³×C₁₉	1	8	yes	—
571	#120	C₂³×C₁₉	1	16	yes	complemented
572	#120	C₂³×C₁₉	1	16	yes	complemented
573	#120	C₂³×C₁₉	1	16	yes	complemented
574	#120	C₂³×C₁₉	1	16	yes	complemented
575	#120	C₂³×C₁₉	1	16	yes	complemented
576	C₄×Q₈	C₂³×C₁₉	1	8	yes	complemented
577	C₄×D₄	C₂³×C₁₉	1	8	yes	—
578	C₄×D₄	C₂³×C₁₉	1	8	yes	—
579	C₄×D₄	C₂³×C₁₉	1	8	yes	complemented
580	C₄×D₄	C₂³×C₁₉	1	8	yes	complemented
581	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
582	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
583	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
584	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
585	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
586	C₄×D₄	C₂³×C₁₉	1	8	yes	complemented
587	C₄×D₄	C₂³×C₁₉	1	8	yes	complemented
588	C₄×D₄	C₂³×C₁₉	1	8	yes	complemented
589	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
590	#117	C₂³×C₁₉	1	8	yes	—
591	#117	C₂³×C₁₉	1	8	yes	complemented
592	#117	C₂³×C₁₉	1	16	yes	complemented
593	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	complemented
595	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	complemented
596	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	complemented
597	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	complemented
598	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	complemented
599	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	complemented
608	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	complemented
609	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	complemented
610	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	complemented
611	C₂×C₄²	C₂³×C₁₉	1	4	yes	complemented
612	C₁₉	#62863	1	1	yes	characteristic, direct product factor, Sylow
613	C₂⁴	—	2	4	no	—
614	C₂⁴	—	4	4	no	—
615	C₂⁴	—	8	2	no	—
616	C₂⁴	—	8	4	no	—
617	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
618	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
619	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
620	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
621	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
622	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
623	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
624	#41	—	4	16	no	—
625	#41	—	4	32	no	—
626	#41	—	8	8	no	—
627	C₂×Q₈	—	8	2	no	—
628	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
629	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
630	C₂×D₄	—	2	16	no	—
631	C₂×D₄	—	2	16	no	—
632	C₂×D₄	—	4	8	no	—
633	C₂×D₄	—	4	32	no	—
634	C₂×D₄	—	4	16	no	—
635	C₂×D₄	—	4	32	no	—
636	C₂×D₄	—	8	4	no	—
637	C₂×D₄	—	8	4	no	—
638	C₂×D₄	—	8	4	no	—
639	C₂×D₄	—	8	2	no	—
640	C₂×D₄	—	8	8	no	—
641	C₂×D₄	—	8	16	no	—
642	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
643	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
644	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
645	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
646	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
647	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
648	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
649	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
650	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
651	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
652	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
653	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
654	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
655	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	8	2	no	—
658	C₂²×C₄	—	8	4	no	—
659	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
660	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
663	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
664	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
667	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
668	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
669	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
670	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
671	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
672	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
673	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
674	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
675	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
676	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
677	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
678	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
679	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
680	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
681	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
682	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
683	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
684	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
685	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
686	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
687	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
688	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
689	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
690	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
691	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
692	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
693	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
694	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
695	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
696	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
697	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
698	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
699	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
700	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
701	C₄²	C₂⁴×C₁₉	1	8	yes	—
702	C₄²	C₂⁴×C₁₉	1	8	yes	—
703	C₄²	C₂⁴×C₁₉	1	8	yes	—
704	C₄²	C₂⁴×C₁₉	1	8	yes	—
705	C₂³	—	2	4	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	8	no	—
708	C₂³	—	2	8	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	4	no	—
711	C₂³	—	4	4	no	—
712	C₂³	—	4	8	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	8	no	—
717	C₂³	—	4	16	no	—
718	C₂³	—	4	8	no	—
719	C₂³	—	4	16	no	—
720	C₂³	—	8	8	no	—
721	C₂³	—	8	16	no	—
722	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
723	C₂³	C₂⁵×C₁₉	1	4	yes	—
724	C₂³	C₂⁵×C₁₉	1	8	yes	—
725	C₂³	C₂⁵×C₁₉	1	8	yes	—
726	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
727	C₂³	C₂⁵×C₁₉	1	2	yes	—
728	Q₈	—	4	8	no	—
729	Q₈	—	4	8	no	—
730	D₄	—	2	32	no	—
731	D₄	—	2	16	no	—
732	D₄	—	2	16	no	—
733	D₄	—	4	8	no	—
734	D₄	—	4	8	no	—
735	D₄	—	4	8	no	—
736	D₄	—	4	16	no	—
737	D₄	—	4	16	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	16	no	—
740	D₄	—	4	8	no	—
741	D₄	—	4	16	no	—
742	D₄	—	4	8	no	—
743	D₄	—	4	16	no	—
744	C₂×C₄	—	2	8	no	—
745	C₂×C₄	—	2	8	no	—
746	C₂×C₄	—	4	8	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	4	16	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	16	no	—
758	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
759	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
760	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
761	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
762	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
763	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	8	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	8	no	—
770	C₂²	—	2	8	no	—
771	C₂²	—	2	16	no	—
772	C₂²	—	2	8	no	—
773	C₂²	—	2	8	no	—
774	C₂²	—	4	4	no	—
775	C₂²	—	4	8	no	—
776	C₂²	—	8	8	no	—
777	C₂²	—	8	8	no	—
778	C₂²	—	8	8	no	—
779	C₂²	—	8	16	no	—
780	C₂²	—	16	8	no	—
781	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
782	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	4	yes	—
783	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
784	C₄	—	2	8	no	—
785	C₄	—	2	8	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	8	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	8	no	—
790	C₂	—	2	2	no	—
791	C₂	—	2	4	no	—
792	C₂	—	4	4	no	—
793	C₂	—	4	8	no	—
794	C₂	—	4	8	no	—
795	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
796	C₂	C₁₉×H(7,𝔽₂)	1	2	yes	—

	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×#3560	C₂	semidirect
2. C₁₉×#3558	C₂	semidirect
3. C₁₉×#3537	C₂	semidirect
4. C₁₉×#3534	C₂	semidirect
5. C₁₉×#3533	C₂	semidirect
6. C₁₉×#3532	C₂	semidirect
7. C₁₉×#3505	C₂	semidirect
8. C₁₉×#3496	C₂	semidirect
9. C₁₉×#3484	C₂	semidirect
10. C₂×C₁₉×#538	C₂	semidirect
11. C₂×C₁₉×#534	C₂	semidirect
12. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
13. C₂³×D₄×C₁₉	C₂²	semidirect
14. C₁₉×#563	C₂²	semidirect
15. C₁₉×#562	C₂²	semidirect
16. C₁₉×H(3,𝔽₄)	C₂²	semidirect
17. C₁₉×#560	C₂²	semidirect
18. C₁₉×#560	C₂²	semidirect
19. C₁₉×#560	C₂²	semidirect
20. C₁₉×#559	C₂²	semidirect
21. C₁₉×#553	C₂²	semidirect
22. C₁₉×#553	C₂²	semidirect
23. C₁₉×#553	C₂²	semidirect
24. C₁₉×#552	C₂²	semidirect
25. C₁₉×#551	C₂²	semidirect
26. C₁₉×#551	C₂²	semidirect
27. C₁₉×#551	C₂²	semidirect
28. C₁₉×#548	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×#546	C₂²	semidirect
37. D₄²×C₁₉	C₂²	semidirect
38. D₄²×C₁₉	C₂²	semidirect
39. D₄²×C₁₉	C₂²	semidirect
40. D₄²×C₁₉	C₂²	semidirect
41. D₄²×C₁₉	C₂²	semidirect
42. C₁₉×#542	C₂²	semidirect
43. C₁₉×#540	C₂²	semidirect
44. C₁₉×#539	C₂²	semidirect
45. C₁₉×#539	C₂²	semidirect
46. C₁₉×#538	C₂²	semidirect
47. C₁₉×#538	C₂²	semidirect
48. C₁₉×#538	C₂²	semidirect
49. C₁₉×#538	C₂²	semidirect
50. C₁₉×#538	C₂²	semidirect
51. C₁₉×#538	C₂²	semidirect
52. C₁₉×#538	C₂²	semidirect
53. C₁₉×#537	C₂²	semidirect
54. C₁₉×#535	C₂²	semidirect
55. C₁₉×#535	C₂²	semidirect
56. C₁₉×#534	C₂²	semidirect
57. C₁₉×#534	C₂²	semidirect
58. C₁₉×#534	C₂²	semidirect
59. C₁₉×#534	C₂²	semidirect
60. C₁₉×#534	C₂²	semidirect
61. C₁₉×#534	C₂²	semidirect
62. C₁₉×#532	C₂²	semidirect
63. C₁₉×#529	C₂²	semidirect
64. C₂×C₁₉×#126	C₂²	semidirect
65. C₂×C₁₉×#124	C₂²	semidirect
66. C₁₉×#525	C₂²	semidirect
67. C₁₉×#525	C₂²	semidirect
68. C₂×C₁₉×#123	C₂²	semidirect
69. C₂×C₁₉×#123	C₂²	semidirect
70. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
71. C₂×C₁₉×#121	C₂²	semidirect
72. C₂×C₁₉×#121	C₂²	semidirect
73. C₂×C₁₉×#121	C₂²	semidirect
74. C₂×C₁₉×#121	C₂²	semidirect
75. C₂×C₁₉×#120	C₂²	semidirect
76. C₂×C₁₉×#120	C₂²	semidirect
77. C₂×C₁₉×#120	C₂²	semidirect
78. C₁₉×#518	C₂²	semidirect
79. C₂×C₄×D₄×C₁₉	C₂²	semidirect
80. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
85. C₂×#41×C₁₉	C₂³	semidirect
86. C₂×#41×C₁₉	C₂³	semidirect
87. C₂²×Q₈×C₁₉	C₂³	semidirect
97. C₂²×D₄×C₁₉	C₂³	semidirect
98. C₂²×D₄×C₁₉	C₂³	semidirect
99. C₂²×D₄×C₁₉	C₂³	semidirect
100. C₂²×D₄×C₁₉	C₂³	semidirect
103. C₂³×C₄×C₁₉	C₂³	semidirect
104. C₁₉×C₄⋊Q₈	C₂³	semidirect
107. C₁₉×#127	C₂³	semidirect
108. C₁₉×#126	C₂³	semidirect
109. C₁₉×#126	C₂³	semidirect
110. C₁₉×#126	C₂³	semidirect
111. C₁₉×#126	C₂³	semidirect
112. C₁₉×#126	C₂³	semidirect
113. C₁₉×#125	C₂³	semidirect
114. C₁₉×#125	C₂³	semidirect
117. C₁₉×#124	C₂³	semidirect
118. C₁₉×#124	C₂³	semidirect
119. C₁₉×#124	C₂³	semidirect
120. C₁₉×#124	C₂³	semidirect
121. C₁₉×#124	C₂³	semidirect
128. C₁₉×#123	C₂³	semidirect
129. C₁₉×#123	C₂³	semidirect
130. C₁₉×#123	C₂³	semidirect
131. C₁₉×#123	C₂³	semidirect
132. C₁₉×#123	C₂³	semidirect
133. C₁₉×#123	C₂³	semidirect
134. C₁₉×#123	C₂³	semidirect
135. C₁₉×#123	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
142. C₁₉×C₂²⋊Q₈	C₂³	semidirect
152. C₁₉×#121	C₂³	semidirect
153. C₁₉×#121	C₂³	semidirect
154. C₁₉×#121	C₂³	semidirect
155. C₁₉×#121	C₂³	semidirect
156. C₁₉×#121	C₂³	semidirect
157. C₁₉×#121	C₂³	semidirect
158. C₁₉×#121	C₂³	semidirect
159. C₁₉×#121	C₂³	semidirect
160. C₁₉×#121	C₂³	semidirect
161. C₁₉×#121	C₂³	semidirect
162. C₁₉×#121	C₂³	semidirect
163. C₁₉×#121	C₂³	semidirect
164. C₁₉×#121	C₂³	semidirect
173. C₁₉×#120	C₂³	semidirect
174. C₁₉×#120	C₂³	semidirect
175. C₁₉×#120	C₂³	semidirect
176. C₁₉×#120	C₂³	semidirect
177. C₁₉×#120	C₂³	semidirect
178. C₄×Q₈×C₁₉	C₂³	semidirect
181. C₄×D₄×C₁₉	C₂³	semidirect
182. C₄×D₄×C₁₉	C₂³	semidirect
183. C₄×D₄×C₁₉	C₂³	semidirect
184. C₄×D₄×C₁₉	C₂³	semidirect
185. C₄×D₄×C₁₉	C₂³	semidirect
186. C₄×D₄×C₁₉	C₂³	semidirect
187. C₄×D₄×C₁₉	C₂³	semidirect
188. C₄×D₄×C₁₉	C₂³	semidirect
189. C₄×D₄×C₁₉	C₂³	semidirect
190. C₄×D₄×C₁₉	C₂³	semidirect
191. C₄×D₄×C₁₉	C₂³	semidirect
193. C₁₉×#117	C₂³	semidirect
194. C₁₉×#117	C₂³	semidirect
196. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
197. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
198. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
199. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
200. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
209. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
210. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
211. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
212. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
213. C₂×C₄²×C₁₉	C₂³	semidirect
306. #62863	C₁₉	direct (N × H)
366. #3560	C₂×C₁₉	semidirect
367. #3558	C₂×C₁₉	semidirect
368. #3537	C₂×C₁₉	semidirect
369. #3534	C₂×C₁₉	semidirect
370. #3533	C₂×C₁₉	semidirect
371. #3532	C₂×C₁₉	semidirect
372. #3505	C₂×C₁₉	semidirect
373. #3496	C₂×C₁₉	semidirect
374. #3484	C₂×C₁₉	semidirect
375. C₂×#538	C₂×C₁₉	semidirect
376. C₂×#534	C₂×C₁₉	semidirect
403. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
404. C₂³×D₄	C₂²×C₁₉	semidirect
405. #563	C₂²×C₁₉	semidirect
406. #562	C₂²×C₁₉	semidirect
407. H(3,𝔽₄)	C₂²×C₁₉	semidirect
408. #560	C₂²×C₁₉	semidirect
409. #560	C₂²×C₁₉	semidirect
410. #560	C₂²×C₁₉	semidirect
411. #559	C₂²×C₁₉	semidirect
412. #553	C₂²×C₁₉	semidirect
413. #553	C₂²×C₁₉	semidirect
414. #553	C₂²×C₁₉	semidirect
415. #552	C₂²×C₁₉	semidirect
416. #551	C₂²×C₁₉	semidirect
417. #551	C₂²×C₁₉	semidirect
418. #551	C₂²×C₁₉	semidirect
419. #548	C₂²×C₁₉	semidirect
420. #547	C₂²×C₁₉	semidirect
421. #547	C₂²×C₁₉	semidirect
422. #546	C₂²×C₁₉	semidirect
423. #546	C₂²×C₁₉	semidirect
424. #546	C₂²×C₁₉	semidirect
425. #546	C₂²×C₁₉	semidirect
426. #546	C₂²×C₁₉	semidirect
427. #546	C₂²×C₁₉	semidirect
428. D₄²	C₂²×C₁₉	semidirect
429. D₄²	C₂²×C₁₉	semidirect
430. D₄²	C₂²×C₁₉	semidirect
431. D₄²	C₂²×C₁₉	semidirect
432. D₄²	C₂²×C₁₉	semidirect
433. #542	C₂²×C₁₉	semidirect
434. #540	C₂²×C₁₉	semidirect
435. #539	C₂²×C₁₉	semidirect
436. #539	C₂²×C₁₉	semidirect
437. #538	C₂²×C₁₉	semidirect
438. #538	C₂²×C₁₉	semidirect
439. #538	C₂²×C₁₉	semidirect
440. #538	C₂²×C₁₉	semidirect
441. #538	C₂²×C₁₉	semidirect
442. #538	C₂²×C₁₉	semidirect
443. #538	C₂²×C₁₉	semidirect
444. #537	C₂²×C₁₉	semidirect
445. #535	C₂²×C₁₉	semidirect
446. #535	C₂²×C₁₉	semidirect
447. #534	C₂²×C₁₉	semidirect
448. #534	C₂²×C₁₉	semidirect
449. #534	C₂²×C₁₉	semidirect
450. #534	C₂²×C₁₉	semidirect
451. #534	C₂²×C₁₉	semidirect
452. #534	C₂²×C₁₉	semidirect
453. #532	C₂²×C₁₉	semidirect
454. #529	C₂²×C₁₉	semidirect
455. C₂×#126	C₂²×C₁₉	semidirect
456. C₂×#124	C₂²×C₁₉	semidirect
457. #525	C₂²×C₁₉	semidirect
458. #525	C₂²×C₁₉	semidirect
459. C₂×#123	C₂²×C₁₉	semidirect
460. C₂×#123	C₂²×C₁₉	semidirect
461. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
462. C₂×#121	C₂²×C₁₉	semidirect
463. C₂×#121	C₂²×C₁₉	semidirect
464. C₂×#121	C₂²×C₁₉	semidirect
465. C₂×#121	C₂²×C₁₉	semidirect
466. C₂×#120	C₂²×C₁₉	semidirect
467. C₂×#120	C₂²×C₁₉	semidirect
468. C₂×#120	C₂²×C₁₉	semidirect
469. #518	C₂²×C₁₉	semidirect
470. C₂×C₄×D₄	C₂²×C₁₉	semidirect
471. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
483. C₂×#41	C₂³×C₁₉	semidirect
484. C₂×#41	C₂³×C₁₉	semidirect
485. C₂²×Q₈	C₂³×C₁₉	semidirect
495. C₂²×D₄	C₂³×C₁₉	semidirect
496. C₂²×D₄	C₂³×C₁₉	semidirect
497. C₂²×D₄	C₂³×C₁₉	semidirect
498. C₂²×D₄	C₂³×C₁₉	semidirect
501. C₂³×C₄	C₂³×C₁₉	semidirect
502. C₄⋊Q₈	C₂³×C₁₉	semidirect
505. #127	C₂³×C₁₉	semidirect
506. #126	C₂³×C₁₉	semidirect
507. #126	C₂³×C₁₉	semidirect
508. #126	C₂³×C₁₉	semidirect
509. #126	C₂³×C₁₉	semidirect
510. #126	C₂³×C₁₉	semidirect
511. #125	C₂³×C₁₉	semidirect
512. #125	C₂³×C₁₉	semidirect
515. #124	C₂³×C₁₉	semidirect
516. #124	C₂³×C₁₉	semidirect
517. #124	C₂³×C₁₉	semidirect
518. #124	C₂³×C₁₉	semidirect
519. #124	C₂³×C₁₉	semidirect
526. #123	C₂³×C₁₉	semidirect
527. #123	C₂³×C₁₉	semidirect
528. #123	C₂³×C₁₉	semidirect
529. #123	C₂³×C₁₉	semidirect
530. #123	C₂³×C₁₉	semidirect
531. #123	C₂³×C₁₉	semidirect
532. #123	C₂³×C₁₉	semidirect
533. #123	C₂³×C₁₉	semidirect
535. C₂²⋊Q₈	C₂³×C₁₉	semidirect
536. C₂²⋊Q₈	C₂³×C₁₉	semidirect
537. C₂²⋊Q₈	C₂³×C₁₉	semidirect
538. C₂²⋊Q₈	C₂³×C₁₉	semidirect
539. C₂²⋊Q₈	C₂³×C₁₉	semidirect
540. C₂²⋊Q₈	C₂³×C₁₉	semidirect
550. #121	C₂³×C₁₉	semidirect
551. #121	C₂³×C₁₉	semidirect
552. #121	C₂³×C₁₉	semidirect
553. #121	C₂³×C₁₉	semidirect
554. #121	C₂³×C₁₉	semidirect
555. #121	C₂³×C₁₉	semidirect
556. #121	C₂³×C₁₉	semidirect
557. #121	C₂³×C₁₉	semidirect
558. #121	C₂³×C₁₉	semidirect
559. #121	C₂³×C₁₉	semidirect
560. #121	C₂³×C₁₉	semidirect
561. #121	C₂³×C₁₉	semidirect
562. #121	C₂³×C₁₉	semidirect
571. #120	C₂³×C₁₉	semidirect
572. #120	C₂³×C₁₉	semidirect
573. #120	C₂³×C₁₉	semidirect
574. #120	C₂³×C₁₉	semidirect
575. #120	C₂³×C₁₉	semidirect
576. C₄×Q₈	C₂³×C₁₉	semidirect
579. C₄×D₄	C₂³×C₁₉	semidirect
580. C₄×D₄	C₂³×C₁₉	semidirect
581. C₄×D₄	C₂³×C₁₉	semidirect
582. C₄×D₄	C₂³×C₁₉	semidirect
583. C₄×D₄	C₂³×C₁₉	semidirect
584. C₄×D₄	C₂³×C₁₉	semidirect
585. C₄×D₄	C₂³×C₁₉	semidirect
586. C₄×D₄	C₂³×C₁₉	semidirect
587. C₄×D₄	C₂³×C₁₉	semidirect
588. C₄×D₄	C₂³×C₁₉	semidirect
589. C₄×D₄	C₂³×C₁₉	semidirect
591. #117	C₂³×C₁₉	semidirect
592. #117	C₂³×C₁₉	semidirect
594. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
595. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
596. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
597. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
598. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
607. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
608. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
609. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
610. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
611. C₂×C₄²	C₂³×C₁₉	semidirect
612. C₁₉	#62863	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×#3560	2
C₁₉×#3558	2
C₁₉×#3537	2
C₁₉×#3534	2
C₁₉×#3533	2
C₁₉×#3532	2
C₁₉×#3505	2
C₁₉×#3496	2
C₁₉×#3484	2
C₂×C₁₉×#538	2
C₂×C₁₉×#534	2
#62863	19

Subgroups — C19×#62863 #18068822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62863 #18068822