Subgroups — C₁₉×#62881 #18068840

Order 4864.

6610 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3559	C₂	1	8	yes	maximal, complemented
2	C₁₉×#3557	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3554	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3548	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3547	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3536	C₂	1	8	yes	maximal, complemented
7	C₁₉×#3535	C₂	1	8	yes	maximal, complemented
8	C₁₉×#3508	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3506	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3504	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3501	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3494	C₂	1	4	yes	maximal, complemented
13	C₁₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3455	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#563	C₂²	1	16	yes	complemented
17	C₁₉×#562	C₂²	1	16	yes	complemented
18	C₁₉×#562	C₂²	1	16	yes	complemented
19	C₁₉×#562	C₂²	1	16	yes	complemented
20	C₁₉×#559	C₂²	1	8	yes	complemented
21	C₁₉×#559	C₂²	1	8	yes	complemented
22	C₁₉×#557	C₂²	1	8	yes	complemented
23	C₁₉×#556	C₂²	1	4	yes	complemented
24	C₁₉×#555	C₂²	1	8	yes	complemented
25	C₁₉×#555	C₂²	1	4	yes	complemented
26	C₁₉×#554	C₂²	1	16	yes	—
27	C₁₉×#554	C₂²	1	8	yes	complemented
28	C₁₉×#554	C₂²	1	8	yes	complemented
29	C₁₉×#554	C₂²	1	4	yes	complemented
30	C₁₉×#554	C₂²	1	4	yes	complemented
31	C₁₉×#554	C₂²	1	8	yes	complemented
32	C₁₉×#553	C₂²	1	8	yes	complemented
33	C₁₉×#553	C₂²	1	8	yes	complemented
34	C₁₉×#553	C₂²	1	8	yes	complemented
35	C₁₉×#552	C₂²	1	16	yes	complemented
36	C₁₉×#551	C₂²	1	16	yes	—
37	C₁₉×#550	C₂²	1	4	yes	complemented
38	C₁₉×#550	C₂²	1	8	yes	complemented
39	D₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
40	D₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
41	C₁₉×#548	C₂²	1	16	yes	complemented
42	C₁₉×#547	C₂²	1	8	yes	complemented
43	C₁₉×#547	C₂²	1	4	yes	complemented
44	C₁₉×#547	C₂²	1	16	yes	complemented
45	C₁₉×#547	C₂²	1	16	yes	complemented
46	C₁₉×#546	C₂²	1	16	yes	—
47	C₁₉×#546	C₂²	1	16	yes	—
48	C₁₉×#544	C₂²	1	4	yes	—
49	C₁₉×#544	C₂²	1	4	yes	—
50	C₁₉×#544	C₂²	1	4	yes	complemented
51	C₁₉×#544	C₂²	1	4	yes	complemented
52	C₁₉×#544	C₂²	1	8	yes	complemented
53	C₁₉×#543	C₂²	1	4	yes	—
54	C₁₉×#543	C₂²	1	8	yes	—
55	C₁₉×#542	C₂²	1	4	yes	complemented
56	C₁₉×#542	C₂²	1	8	yes	complemented
57	C₁₉×#542	C₂²	1	16	yes	complemented
58	C₁₉×#542	C₂²	1	16	yes	complemented
59	C₁₉×#541	C₂²	1	2	yes	complemented
60	C₁₉×#540	C₂²	1	8	yes	—
61	C₁₉×#540	C₂²	1	4	yes	—
62	C₁₉×#540	C₂²	1	4	yes	—
63	C₁₉×#540	C₂²	1	2	yes	complemented
64	C₁₉×#540	C₂²	1	8	yes	complemented
65	C₁₉×#540	C₂²	1	4	yes	complemented
66	C₁₉×#540	C₂²	1	4	yes	complemented
67	C₁₉×#539	C₂²	1	4	yes	—
68	C₁₉×#539	C₂²	1	16	yes	complemented
69	C₁₉×#539	C₂²	1	16	yes	complemented
70	C₁₉×#539	C₂²	1	16	yes	complemented
71	C₁₉×#538	C₂²	1	4	yes	—
72	C₁₉×#538	C₂²	1	8	yes	—
73	C₁₉×#537	C₂²	1	16	yes	complemented
74	C₁₉×#537	C₂²	1	16	yes	complemented
75	C₁₉×#536	C₂²	1	16	yes	complemented
76	C₁₉×#535	C₂²	1	4	yes	—
77	C₁₉×#533	C₂²	1	1	yes	characteristic
78	C₁₉×#533	C₂²	1	2	yes	—
79	C₁₉×#533	C₂²	1	2	yes	—
80	C₁₉×#533	C₂²	1	4	yes	complemented
81	C₁₉×#533	C₂²	1	4	yes	complemented
82	C₁₉×#533	C₂²	1	4	yes	complemented
83	C₁₉×#532	C₂²	1	1	yes	characteristic
84	C₁₉×#532	C₂²	1	8	yes	complemented
85	C₁₉×#532	C₂²	1	8	yes	complemented
86	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
87	C₁₉×#529	C₂²	1	8	yes	complemented
88	C₁₉×#529	C₂²	1	8	yes	complemented
89	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
90	C₂×C₁₉×#125	C₂²	1	4	yes	complemented
91	C₁₉×#525	C₂²	1	2	yes	—
92	C₁₉×#525	C₂²	1	8	yes	—
93	C₂×C₁₉×#123	C₂²	1	4	yes	—
94	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	—
95	C₂×C₁₉×#121	C₂²	1	2	yes	—
96	C₂×C₁₉×#121	C₂²	1	4	yes	—
97	C₁₉×#520	C₂²	1	4	yes	—
98	C₁₉×#518	C₂²	1	4	yes	—
99	C₄×#41×C₁₉	C₂²	1	2	yes	—
100	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
101	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
102	C₂×C₁₉×#117	C₂²	1	2	yes	—
103	C₂×#41×C₁₉	C₂³	1	2	yes	—
104	C₂×#41×C₁₉	C₂³	1	8	yes	—
105	C₂×#41×C₁₉	C₂³	1	16	yes	—
106	C₂×#41×C₁₉	C₂³	1	16	yes	—
107	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
108	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
110	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
111	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
113	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
116	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
120	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
121	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
122	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	—
123	C₁₉×#127	C₂³	1	4	yes	—
124	C₁₉×#127	C₂³	1	4	yes	—
125	C₁₉×#127	C₂³	1	1	yes	characteristic
126	C₁₉×#127	C₂³	1	8	yes	—
127	C₁₉×#126	C₂³	1	8	yes	—
128	C₁₉×#126	C₂³	1	8	yes	—
129	C₁₉×#126	C₂³	1	16	yes	—
130	C₁₉×#126	C₂³	1	16	yes	—
131	C₁₉×#126	C₂³	1	16	yes	—
132	C₁₉×#125	C₂³	1	4	yes	—
133	C₁₉×#125	C₂³	1	4	yes	—
134	C₁₉×#125	C₂³	1	2	yes	—
135	C₁₉×#125	C₂³	1	16	yes	—
136	C₁₉×#125	C₂³	1	8	yes	—
137	C₁₉×#125	C₂³	1	8	yes	—
138	C₁₉×#125	C₂³	1	8	yes	—
139	C₁₉×#125	C₂³	1	2	yes	—
140	C₁₉×#125	C₂³	1	2	yes	—
141	C₁₉×#125	C₂³	1	4	yes	—
142	C₁₉×#125	C₂³	1	8	yes	—
143	C₁₉×#125	C₂³	1	8	yes	—
144	C₁₉×#125	C₂³	1	16	yes	—
145	C₁₉×#124	C₂³	1	8	yes	—
146	C₁₉×#124	C₂³	1	8	yes	—
147	C₁₉×#124	C₂³	1	2	yes	—
148	C₁₉×#124	C₂³	1	16	yes	—
149	C₁₉×#124	C₂³	1	16	yes	—
150	C₁₉×#124	C₂³	1	16	yes	—
151	C₁₉×#124	C₂³	1	16	yes	—
152	C₁₉×#123	C₂³	1	16	yes	—
153	C₁₉×#123	C₂³	1	16	yes	—
154	C₁₉×#123	C₂³	1	16	yes	—
155	C₁₉×#123	C₂³	1	4	yes	—
156	C₁₉×#123	C₂³	1	8	yes	—
157	C₁₉×#123	C₂³	1	8	yes	—
158	C₁₉×#123	C₂³	1	16	yes	—
159	C₁₉×#123	C₂³	1	16	yes	—
160	C₁₉×#123	C₂³	1	16	yes	—
161	C₁₉×#123	C₂³	1	16	yes	—
162	C₁₉×#123	C₂³	1	16	yes	—
163	C₁₉×#123	C₂³	1	16	yes	—
164	C₁₉×#123	C₂³	1	16	yes	—
165	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
166	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
167	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
168	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
169	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
170	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
171	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
172	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
173	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
174	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
175	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
177	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
178	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
180	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
181	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
182	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
183	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
184	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
185	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
186	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
187	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
188	C₁₉×#121	C₂³	1	8	yes	—
189	C₁₉×#121	C₂³	1	16	yes	—
190	C₁₉×#121	C₂³	1	16	yes	—
191	C₁₉×#121	C₂³	1	8	yes	—
192	C₁₉×#121	C₂³	1	4	yes	—
193	C₁₉×#121	C₂³	1	4	yes	—
194	C₁₉×#121	C₂³	1	8	yes	—
195	C₁₉×#121	C₂³	1	8	yes	—
196	C₁₉×#121	C₂³	1	8	yes	—
197	C₁₉×#121	C₂³	1	8	yes	—
198	C₁₉×#121	C₂³	1	16	yes	—
199	C₁₉×#121	C₂³	1	16	yes	—
200	C₁₉×#121	C₂³	1	16	yes	—
201	C₁₉×#121	C₂³	1	16	yes	—
202	C₁₉×#121	C₂³	1	16	yes	—
203	C₁₉×#121	C₂³	1	16	yes	—
204	C₁₉×#121	C₂³	1	16	yes	—
205	C₁₉×#120	C₂³	1	16	yes	—
206	C₁₉×#120	C₂³	1	4	yes	—
207	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
208	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
209	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
210	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
211	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
212	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
213	C₄×Q₈×C₁₉	C₂³	1	16	yes	—
214	C₄×D₄×C₁₉	C₂³	1	4	yes	—
215	C₄×D₄×C₁₉	C₂³	1	4	yes	—
216	C₄×D₄×C₁₉	C₂³	1	4	yes	—
217	C₄×D₄×C₁₉	C₂³	1	4	yes	—
218	C₄×D₄×C₁₉	C₂³	1	8	yes	—
219	C₄×D₄×C₁₉	C₂³	1	4	yes	—
220	C₄×D₄×C₁₉	C₂³	1	8	yes	—
221	C₄×D₄×C₁₉	C₂³	1	8	yes	—
222	C₄×D₄×C₁₉	C₂³	1	8	yes	—
223	C₄×D₄×C₁₉	C₂³	1	8	yes	—
224	C₄×D₄×C₁₉	C₂³	1	16	yes	—
225	C₄×D₄×C₁₉	C₂³	1	8	yes	—
226	C₄×D₄×C₁₉	C₂³	1	8	yes	—
227	C₄×D₄×C₁₉	C₂³	1	16	yes	—
228	C₄×D₄×C₁₉	C₂³	1	4	yes	—
229	C₄×D₄×C₁₉	C₂³	1	16	yes	—
230	C₄×D₄×C₁₉	C₂³	1	16	yes	—
231	C₄×D₄×C₁₉	C₂³	1	16	yes	—
232	C₁₉×#117	C₂³	1	4	yes	—
233	C₁₉×#117	C₂³	1	4	yes	—
234	C₁₉×#117	C₂³	1	2	yes	—
235	C₁₉×#117	C₂³	1	2	yes	—
236	C₁₉×#117	C₂³	1	4	yes	—
237	C₁₉×#117	C₂³	1	4	yes	—
238	C₁₉×#117	C₂³	1	2	yes	—
239	C₁₉×#117	C₂³	1	2	yes	—
240	C₁₉×#117	C₂³	1	2	yes	—
241	C₁₉×#117	C₂³	1	4	yes	—
242	C₁₉×#117	C₂³	1	8	yes	—
243	C₁₉×#117	C₂³	1	8	yes	—
244	C₁₉×#117	C₂³	1	16	yes	—
245	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
247	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
248	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
249	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
250	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
251	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
252	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
253	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
254	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
255	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
256	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
257	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
258	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
260	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
261	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
262	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
264	#41×C₁₉	—	2	8	no	—
265	#41×C₁₉	—	8	8	no	—
266	#41×C₁₉	—	8	16	no	—
267	#41×C₁₉	—	8	16	no	—
268	C₂×Q₈×C₁₉	—	8	8	no	—
269	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
270	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
271	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
272	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
273	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
274	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
275	C₂×D₄×C₁₉	—	2	8	no	—
276	C₂×D₄×C₁₉	—	8	4	no	—
277	C₂×D₄×C₁₉	—	8	4	no	—
278	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
279	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
280	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
281	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
282	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
283	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
284	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
285	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
286	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
287	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
288	C₂²×C₄×C₁₉	—	2	4	no	—
289	C₂²×C₄×C₁₉	—	8	4	no	—
290	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
297	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
300	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
301	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
302	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
303	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
306	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
308	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
309	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
311	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
314	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
315	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
316	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
318	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
320	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
321	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
322	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
323	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
325	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
327	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
328	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
329	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
330	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
331	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
333	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
334	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
335	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
336	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
337	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
338	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
339	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
340	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
341	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
342	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
343	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
344	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
345	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
346	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
348	C₄²×C₁₉	C₂⁴	1	2	yes	—
349	C₄²×C₁₉	C₂⁴	1	4	yes	—
350	C₄²×C₁₉	C₂⁴	1	2	yes	—
351	C₄²×C₁₉	C₂⁴	1	4	yes	—
352	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
353	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
354	C₄²×C₁₉	C₂⁴	1	4	yes	—
355	C₄²×C₁₉	C₂⁴	1	8	yes	—
356	C₄²×C₁₉	C₂⁴	1	2	yes	—
357	C₄²×C₁₉	C₂⁴	1	8	yes	—
358	C₄²×C₁₉	C₂⁴	1	16	yes	—
359	#62881	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂³×C₁₉	—	2	2	no	—
361	C₂³×C₁₉	—	2	8	no	—
362	C₂³×C₁₉	—	4	4	no	—
363	C₂³×C₁₉	—	4	2	no	—
364	C₂³×C₁₉	—	4	4	no	—
365	C₂³×C₁₉	C₂⁵	1	2	yes	—
366	C₂³×C₁₉	C₂⁵	1	8	yes	—
367	C₂³×C₁₉	C₂⁵	1	4	yes	—
368	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
369	Q₈×C₁₉	—	2	4	no	—
370	Q₈×C₁₉	—	4	4	no	—
371	Q₈×C₁₉	—	4	4	no	—
372	Q₈×C₁₉	—	4	16	no	—
373	Q₈×C₁₉	—	4	4	no	—
374	Q₈×C₁₉	—	4	8	no	—
375	D₄×C₁₉	—	2	8	no	—
376	D₄×C₁₉	—	2	8	no	—
377	D₄×C₁₉	—	2	8	no	—
378	D₄×C₁₉	—	2	4	no	—
379	D₄×C₁₉	—	4	16	no	—
380	D₄×C₁₉	—	4	16	no	—
381	D₄×C₁₉	—	4	16	no	—
382	D₄×C₁₉	—	4	4	no	—
383	D₄×C₁₉	—	4	8	no	—
384	D₄×C₁₉	—	4	16	no	—
385	C₂×C₄×C₁₉	—	2	2	no	—
386	C₂×C₄×C₁₉	—	2	4	no	—
387	C₂×C₄×C₁₉	—	2	4	no	—
388	C₂×C₄×C₁₉	—	2	8	no	—
389	C₂×C₄×C₁₉	—	4	2	no	—
390	C₂×C₄×C₁₉	—	4	4	no	—
391	C₂×C₄×C₁₉	—	4	8	no	—
392	C₂×C₄×C₁₉	—	4	8	no	—
393	C₂×C₄×C₁₉	—	4	2	no	—
394	C₂×C₄×C₁₉	—	4	16	no	—
395	C₂×C₄×C₁₉	—	4	16	no	—
396	C₂×C₄×C₁₉	—	4	16	no	—
397	C₂×C₄×C₁₉	—	4	8	no	—
398	C₂×C₄×C₁₉	—	4	8	no	—
399	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
400	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
401	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
402	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
403	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
404	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
405	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
406	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
407	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
408	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
409	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
410	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
411	#3559	C₂×C₁₉	1	8	yes	complemented
412	#3557	C₂×C₁₉	1	4	yes	complemented
413	#3554	C₂×C₁₉	1	8	yes	complemented
414	#3548	C₂×C₁₉	1	4	yes	complemented
415	#3547	C₂×C₁₉	1	8	yes	complemented
416	#3536	C₂×C₁₉	1	8	yes	complemented
417	#3535	C₂×C₁₉	1	8	yes	complemented
418	#3508	C₂×C₁₉	1	2	yes	complemented
419	#3506	C₂×C₁₉	1	2	yes	complemented
420	#3504	C₂×C₁₉	1	2	yes	complemented
421	#3501	C₂×C₁₉	1	2	yes	complemented
422	#3494	C₂×C₁₉	1	4	yes	complemented
423	#3458	C₂×C₁₉	1	1	yes	characteristic, complemented
424	#3455	C₂×C₁₉	1	1	yes	characteristic, complemented
425	C₂×#540	C₂×C₁₉	1	1	yes	characteristic, complemented
426	C₂²×C₁₉	—	2	2	no	—
427	C₂²×C₁₉	—	2	2	no	—
428	C₂²×C₁₉	—	2	4	no	—
429	C₂²×C₁₉	—	2	8	no	—
430	C₂²×C₁₉	—	2	8	no	—
431	C₂²×C₁₉	—	2	8	no	—
432	C₂²×C₁₉	—	2	4	no	—
433	C₂²×C₁₉	—	2	8	no	—
434	C₂²×C₁₉	—	8	2	no	—
435	C₂²×C₁₉	—	8	8	no	—
436	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
437	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
438	C₄×C₁₉	—	2	2	no	—
439	C₄×C₁₉	—	2	4	no	—
440	C₄×C₁₉	—	2	2	no	—
441	C₄×C₁₉	—	2	8	no	—
442	C₄×C₁₉	—	2	8	no	—
443	C₄×C₁₉	—	2	8	no	—
444	C₄×C₁₉	—	2	2	no	—
445	C₄×C₁₉	—	2	4	no	—
446	C₄×C₁₉	—	2	8	no	—
447	C₄×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
448	C₄×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
449	#563	C₂²×C₁₉	1	16	yes	complemented
450	#562	C₂²×C₁₉	1	16	yes	complemented
451	#562	C₂²×C₁₉	1	16	yes	complemented
452	#562	C₂²×C₁₉	1	16	yes	complemented
453	#559	C₂²×C₁₉	1	8	yes	complemented
454	#559	C₂²×C₁₉	1	8	yes	complemented
455	#557	C₂²×C₁₉	1	8	yes	complemented
456	#556	C₂²×C₁₉	1	4	yes	complemented
457	#555	C₂²×C₁₉	1	8	yes	complemented
458	#555	C₂²×C₁₉	1	4	yes	complemented
459	#554	C₂²×C₁₉	1	16	yes	—
460	#554	C₂²×C₁₉	1	8	yes	complemented
461	#554	C₂²×C₁₉	1	8	yes	complemented
462	#554	C₂²×C₁₉	1	4	yes	complemented
463	#554	C₂²×C₁₉	1	4	yes	complemented
464	#554	C₂²×C₁₉	1	8	yes	complemented
465	#553	C₂²×C₁₉	1	8	yes	complemented
466	#553	C₂²×C₁₉	1	8	yes	complemented
467	#553	C₂²×C₁₉	1	8	yes	complemented
468	#552	C₂²×C₁₉	1	16	yes	complemented
469	#551	C₂²×C₁₉	1	16	yes	—
470	#550	C₂²×C₁₉	1	4	yes	complemented
471	#550	C₂²×C₁₉	1	8	yes	complemented
472	D₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
473	D₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
474	#548	C₂²×C₁₉	1	16	yes	complemented
475	#547	C₂²×C₁₉	1	8	yes	complemented
476	#547	C₂²×C₁₉	1	4	yes	complemented
477	#547	C₂²×C₁₉	1	16	yes	complemented
478	#547	C₂²×C₁₉	1	16	yes	complemented
479	#546	C₂²×C₁₉	1	16	yes	—
480	#546	C₂²×C₁₉	1	16	yes	—
481	#544	C₂²×C₁₉	1	4	yes	—
482	#544	C₂²×C₁₉	1	4	yes	—
483	#544	C₂²×C₁₉	1	4	yes	complemented
484	#544	C₂²×C₁₉	1	4	yes	complemented
485	#544	C₂²×C₁₉	1	8	yes	complemented
486	#543	C₂²×C₁₉	1	4	yes	—
487	#543	C₂²×C₁₉	1	8	yes	—
488	#542	C₂²×C₁₉	1	4	yes	complemented
489	#542	C₂²×C₁₉	1	8	yes	complemented
490	#542	C₂²×C₁₉	1	16	yes	complemented
491	#542	C₂²×C₁₉	1	16	yes	complemented
492	#541	C₂²×C₁₉	1	2	yes	complemented
493	#540	C₂²×C₁₉	1	8	yes	—
494	#540	C₂²×C₁₉	1	4	yes	—
495	#540	C₂²×C₁₉	1	4	yes	—
496	#540	C₂²×C₁₉	1	2	yes	complemented
497	#540	C₂²×C₁₉	1	8	yes	complemented
498	#540	C₂²×C₁₉	1	4	yes	complemented
499	#540	C₂²×C₁₉	1	4	yes	complemented
500	#539	C₂²×C₁₉	1	4	yes	—
501	#539	C₂²×C₁₉	1	16	yes	complemented
502	#539	C₂²×C₁₉	1	16	yes	complemented
503	#539	C₂²×C₁₉	1	16	yes	complemented
504	#538	C₂²×C₁₉	1	4	yes	—
505	#538	C₂²×C₁₉	1	8	yes	—
506	#537	C₂²×C₁₉	1	16	yes	complemented
507	#537	C₂²×C₁₉	1	16	yes	complemented
508	#536	C₂²×C₁₉	1	16	yes	complemented
509	#535	C₂²×C₁₉	1	4	yes	—
510	#533	C₂²×C₁₉	1	1	yes	characteristic
511	#533	C₂²×C₁₉	1	2	yes	—
512	#533	C₂²×C₁₉	1	2	yes	—
513	#533	C₂²×C₁₉	1	4	yes	complemented
514	#533	C₂²×C₁₉	1	4	yes	complemented
515	#533	C₂²×C₁₉	1	4	yes	complemented
516	#532	C₂²×C₁₉	1	1	yes	characteristic
517	#532	C₂²×C₁₉	1	8	yes	complemented
518	#532	C₂²×C₁₉	1	8	yes	complemented
519	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
520	#529	C₂²×C₁₉	1	8	yes	complemented
521	#529	C₂²×C₁₉	1	8	yes	complemented
522	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
523	C₂×#125	C₂²×C₁₉	1	4	yes	complemented
524	#525	C₂²×C₁₉	1	2	yes	—
525	#525	C₂²×C₁₉	1	8	yes	—
526	C₂×#123	C₂²×C₁₉	1	4	yes	—
527	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	—
528	C₂×#121	C₂²×C₁₉	1	2	yes	—
529	C₂×#121	C₂²×C₁₉	1	4	yes	—
530	#520	C₂²×C₁₉	1	4	yes	—
531	#518	C₂²×C₁₉	1	4	yes	—
532	C₄×#41	C₂²×C₁₉	1	2	yes	—
533	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
534	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
535	C₂×#117	C₂²×C₁₉	1	2	yes	—
536	C₂×C₁₉	—	2	2	no	—
537	C₂×C₁₉	—	4	4	no	—
538	C₂×C₁₉	—	4	2	no	—
539	C₂×C₁₉	—	4	8	no	—
540	C₂×C₁₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
541	C₂×C₁₉	H(7,𝔽₂)	1	2	yes	—
542	C₂×#41	C₂³×C₁₉	1	2	yes	—
543	C₂×#41	C₂³×C₁₉	1	8	yes	—
544	C₂×#41	C₂³×C₁₉	1	16	yes	—
545	C₂×#41	C₂³×C₁₉	1	16	yes	—
546	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
547	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
548	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
549	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
550	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
552	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
553	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
554	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
555	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
559	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
560	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
561	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	—
562	#127	C₂³×C₁₉	1	4	yes	—
563	#127	C₂³×C₁₉	1	4	yes	—
564	#127	C₂³×C₁₉	1	1	yes	characteristic
565	#127	C₂³×C₁₉	1	8	yes	—
566	#126	C₂³×C₁₉	1	8	yes	—
567	#126	C₂³×C₁₉	1	8	yes	—
568	#126	C₂³×C₁₉	1	16	yes	—
569	#126	C₂³×C₁₉	1	16	yes	—
570	#126	C₂³×C₁₉	1	16	yes	—
571	#125	C₂³×C₁₉	1	4	yes	—
572	#125	C₂³×C₁₉	1	4	yes	—
573	#125	C₂³×C₁₉	1	2	yes	—
574	#125	C₂³×C₁₉	1	16	yes	—
575	#125	C₂³×C₁₉	1	8	yes	—
576	#125	C₂³×C₁₉	1	8	yes	—
577	#125	C₂³×C₁₉	1	8	yes	—
578	#125	C₂³×C₁₉	1	2	yes	—
579	#125	C₂³×C₁₉	1	2	yes	—
580	#125	C₂³×C₁₉	1	4	yes	—
581	#125	C₂³×C₁₉	1	8	yes	—
582	#125	C₂³×C₁₉	1	8	yes	—
583	#125	C₂³×C₁₉	1	16	yes	—
584	#124	C₂³×C₁₉	1	8	yes	—
585	#124	C₂³×C₁₉	1	8	yes	—
586	#124	C₂³×C₁₉	1	2	yes	—
587	#124	C₂³×C₁₉	1	16	yes	—
588	#124	C₂³×C₁₉	1	16	yes	—
589	#124	C₂³×C₁₉	1	16	yes	—
590	#124	C₂³×C₁₉	1	16	yes	—
591	#123	C₂³×C₁₉	1	16	yes	—
592	#123	C₂³×C₁₉	1	16	yes	—
593	#123	C₂³×C₁₉	1	16	yes	—
594	#123	C₂³×C₁₉	1	4	yes	—
595	#123	C₂³×C₁₉	1	8	yes	—
596	#123	C₂³×C₁₉	1	8	yes	—
597	#123	C₂³×C₁₉	1	16	yes	—
598	#123	C₂³×C₁₉	1	16	yes	—
599	#123	C₂³×C₁₉	1	16	yes	—
600	#123	C₂³×C₁₉	1	16	yes	—
601	#123	C₂³×C₁₉	1	16	yes	—
602	#123	C₂³×C₁₉	1	16	yes	—
603	#123	C₂³×C₁₉	1	16	yes	—
604	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
606	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
607	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
608	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
609	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
610	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
611	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
612	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
613	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
614	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
615	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
616	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
617	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
618	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
619	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
620	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
621	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
622	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
623	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
624	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
625	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
626	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
627	#121	C₂³×C₁₉	1	8	yes	—
628	#121	C₂³×C₁₉	1	16	yes	—
629	#121	C₂³×C₁₉	1	16	yes	—
630	#121	C₂³×C₁₉	1	8	yes	—
631	#121	C₂³×C₁₉	1	4	yes	—
632	#121	C₂³×C₁₉	1	4	yes	—
633	#121	C₂³×C₁₉	1	8	yes	—
634	#121	C₂³×C₁₉	1	8	yes	—
635	#121	C₂³×C₁₉	1	8	yes	—
636	#121	C₂³×C₁₉	1	8	yes	—
637	#121	C₂³×C₁₉	1	16	yes	—
638	#121	C₂³×C₁₉	1	16	yes	—
639	#121	C₂³×C₁₉	1	16	yes	—
640	#121	C₂³×C₁₉	1	16	yes	—
641	#121	C₂³×C₁₉	1	16	yes	—
642	#121	C₂³×C₁₉	1	16	yes	—
643	#121	C₂³×C₁₉	1	16	yes	—
644	#120	C₂³×C₁₉	1	16	yes	—
645	#120	C₂³×C₁₉	1	4	yes	—
646	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
647	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
648	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
649	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
650	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
651	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
652	C₄×Q₈	C₂³×C₁₉	1	16	yes	—
653	C₄×D₄	C₂³×C₁₉	1	4	yes	—
654	C₄×D₄	C₂³×C₁₉	1	4	yes	—
655	C₄×D₄	C₂³×C₁₉	1	4	yes	—
656	C₄×D₄	C₂³×C₁₉	1	4	yes	—
657	C₄×D₄	C₂³×C₁₉	1	8	yes	—
658	C₄×D₄	C₂³×C₁₉	1	4	yes	—
659	C₄×D₄	C₂³×C₁₉	1	8	yes	—
660	C₄×D₄	C₂³×C₁₉	1	8	yes	—
661	C₄×D₄	C₂³×C₁₉	1	8	yes	—
662	C₄×D₄	C₂³×C₁₉	1	8	yes	—
663	C₄×D₄	C₂³×C₁₉	1	16	yes	—
664	C₄×D₄	C₂³×C₁₉	1	8	yes	—
665	C₄×D₄	C₂³×C₁₉	1	8	yes	—
666	C₄×D₄	C₂³×C₁₉	1	16	yes	—
667	C₄×D₄	C₂³×C₁₉	1	4	yes	—
668	C₄×D₄	C₂³×C₁₉	1	16	yes	—
669	C₄×D₄	C₂³×C₁₉	1	16	yes	—
670	C₄×D₄	C₂³×C₁₉	1	16	yes	—
671	#117	C₂³×C₁₉	1	4	yes	—
672	#117	C₂³×C₁₉	1	4	yes	—
673	#117	C₂³×C₁₉	1	2	yes	—
674	#117	C₂³×C₁₉	1	2	yes	—
675	#117	C₂³×C₁₉	1	4	yes	—
676	#117	C₂³×C₁₉	1	4	yes	—
677	#117	C₂³×C₁₉	1	2	yes	—
678	#117	C₂³×C₁₉	1	2	yes	—
679	#117	C₂³×C₁₉	1	2	yes	—
680	#117	C₂³×C₁₉	1	4	yes	—
681	#117	C₂³×C₁₉	1	8	yes	—
682	#117	C₂³×C₁₉	1	8	yes	—
683	#117	C₂³×C₁₉	1	16	yes	—
684	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
686	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
688	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
689	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
690	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
697	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
700	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
701	C₁₉	#62881	1	1	yes	characteristic, direct product factor, Sylow
702	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
703	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
704	#41	—	2	8	no	—
705	#41	—	8	8	no	—
706	#41	—	8	16	no	—
707	#41	—	8	16	no	—
708	C₂×Q₈	—	8	8	no	—
709	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
710	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
711	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
712	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
713	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
714	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	8	4	no	—
717	C₂×D₄	—	8	4	no	—
718	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
719	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
720	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
721	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
722	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
723	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
724	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
725	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
726	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
727	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	8	4	no	—
730	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
737	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
738	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
739	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
740	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
741	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
742	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
743	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
744	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
746	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
747	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
748	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
749	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
750	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
751	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
752	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
753	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
756	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
757	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
759	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
761	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
762	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
763	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
764	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
765	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
767	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
770	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
771	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
772	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
773	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
774	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
775	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
776	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
777	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
778	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
779	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
780	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
781	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
782	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
784	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
785	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
786	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
787	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
788	C₄²	C₂⁴×C₁₉	1	2	yes	—
789	C₄²	C₂⁴×C₁₉	1	4	yes	—
790	C₄²	C₂⁴×C₁₉	1	2	yes	—
791	C₄²	C₂⁴×C₁₉	1	4	yes	—
792	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
793	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
794	C₄²	C₂⁴×C₁₉	1	4	yes	—
795	C₄²	C₂⁴×C₁₉	1	8	yes	—
796	C₄²	C₂⁴×C₁₉	1	2	yes	—
797	C₄²	C₂⁴×C₁₉	1	8	yes	—
798	C₄²	C₂⁴×C₁₉	1	16	yes	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	4	2	no	—
803	C₂³	—	4	4	no	—
804	C₂³	C₂⁵×C₁₉	1	2	yes	—
805	C₂³	C₂⁵×C₁₉	1	8	yes	—
806	C₂³	C₂⁵×C₁₉	1	4	yes	—
807	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
808	Q₈	—	2	4	no	—
809	Q₈	—	4	4	no	—
810	Q₈	—	4	4	no	—
811	Q₈	—	4	16	no	—
812	Q₈	—	4	4	no	—
813	Q₈	—	4	8	no	—
814	D₄	—	2	8	no	—
815	D₄	—	2	8	no	—
816	D₄	—	2	8	no	—
817	D₄	—	2	4	no	—
818	D₄	—	4	16	no	—
819	D₄	—	4	16	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	16	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	16	no	—
834	C₂×C₄	—	4	16	no	—
835	C₂×C₄	—	4	16	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
839	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
840	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
841	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
842	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
843	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
844	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
845	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
846	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
847	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
848	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
849	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	8	no	—
854	C₂²	—	2	8	no	—
855	C₂²	—	2	8	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	2	8	no	—
858	C₂²	—	8	2	no	—
859	C₂²	—	8	8	no	—
860	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
861	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
862	C₄	—	2	2	no	—
863	C₄	—	2	4	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	8	no	—
867	C₄	—	2	8	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	8	no	—
871	C₄	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
872	C₄	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
873	C₂	—	2	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	4	8	no	—
876	C₂	—	4	4	no	—
877	C₂	C₂²×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
878	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×#3559	C₂	semidirect
2. C₁₉×#3557	C₂	semidirect
3. C₁₉×#3554	C₂	semidirect
4. C₁₉×#3548	C₂	semidirect
5. C₁₉×#3547	C₂	semidirect
6. C₁₉×#3536	C₂	semidirect
7. C₁₉×#3535	C₂	semidirect
8. C₁₉×#3508	C₂	semidirect
9. C₁₉×#3506	C₂	semidirect
10. C₁₉×#3504	C₂	semidirect
11. C₁₉×#3501	C₂	semidirect
12. C₁₉×#3494	C₂	semidirect
13. C₁₉×#3458	C₂	semidirect
14. C₁₉×#3455	C₂	semidirect
15. C₂×C₁₉×#540	C₂	semidirect
16. C₁₉×#563	C₂²	semidirect
17. C₁₉×#562	C₂²	semidirect
18. C₁₉×#562	C₂²	semidirect
19. C₁₉×#562	C₂²	semidirect
20. C₁₉×#559	C₂²	semidirect
21. C₁₉×#559	C₂²	semidirect
22. C₁₉×#557	C₂²	semidirect
23. C₁₉×#556	C₂²	semidirect
24. C₁₉×#555	C₂²	semidirect
25. C₁₉×#555	C₂²	semidirect
27. C₁₉×#554	C₂²	semidirect
28. C₁₉×#554	C₂²	semidirect
29. C₁₉×#554	C₂²	semidirect
30. C₁₉×#554	C₂²	semidirect
31. C₁₉×#554	C₂²	semidirect
32. C₁₉×#553	C₂²	semidirect
33. C₁₉×#553	C₂²	semidirect
34. C₁₉×#553	C₂²	semidirect
35. C₁₉×#552	C₂²	semidirect
37. C₁₉×#550	C₂²	semidirect
38. C₁₉×#550	C₂²	semidirect
39. D₄×Q₈×C₁₉	C₂²	semidirect
40. D₄×Q₈×C₁₉	C₂²	semidirect
41. C₁₉×#548	C₂²	semidirect
42. C₁₉×#547	C₂²	semidirect
43. C₁₉×#547	C₂²	semidirect
44. C₁₉×#547	C₂²	semidirect
45. C₁₉×#547	C₂²	semidirect
50. C₁₉×#544	C₂²	semidirect
51. C₁₉×#544	C₂²	semidirect
52. C₁₉×#544	C₂²	semidirect
55. C₁₉×#542	C₂²	semidirect
56. C₁₉×#542	C₂²	semidirect
57. C₁₉×#542	C₂²	semidirect
58. C₁₉×#542	C₂²	semidirect
59. C₁₉×#541	C₂²	semidirect
63. C₁₉×#540	C₂²	semidirect
64. C₁₉×#540	C₂²	semidirect
65. C₁₉×#540	C₂²	semidirect
66. C₁₉×#540	C₂²	semidirect
68. C₁₉×#539	C₂²	semidirect
69. C₁₉×#539	C₂²	semidirect
70. C₁₉×#539	C₂²	semidirect
73. C₁₉×#537	C₂²	semidirect
74. C₁₉×#537	C₂²	semidirect
75. C₁₉×#536	C₂²	semidirect
80. C₁₉×#533	C₂²	semidirect
81. C₁₉×#533	C₂²	semidirect
82. C₁₉×#533	C₂²	semidirect
84. C₁₉×#532	C₂²	semidirect
85. C₁₉×#532	C₂²	semidirect
87. C₁₉×#529	C₂²	semidirect
88. C₁₉×#529	C₂²	semidirect
90. C₂×C₁₉×#125	C₂²	semidirect
359. #62881	C₁₉	direct (N × H)
411. #3559	C₂×C₁₉	semidirect
412. #3557	C₂×C₁₉	semidirect
413. #3554	C₂×C₁₉	semidirect
414. #3548	C₂×C₁₉	semidirect
415. #3547	C₂×C₁₉	semidirect
416. #3536	C₂×C₁₉	semidirect
417. #3535	C₂×C₁₉	semidirect
418. #3508	C₂×C₁₉	semidirect
419. #3506	C₂×C₁₉	semidirect
420. #3504	C₂×C₁₉	semidirect
421. #3501	C₂×C₁₉	semidirect
422. #3494	C₂×C₁₉	semidirect
423. #3458	C₂×C₁₉	semidirect
424. #3455	C₂×C₁₉	semidirect
425. C₂×#540	C₂×C₁₉	semidirect
449. #563	C₂²×C₁₉	semidirect
450. #562	C₂²×C₁₉	semidirect
451. #562	C₂²×C₁₉	semidirect
452. #562	C₂²×C₁₉	semidirect
453. #559	C₂²×C₁₉	semidirect
454. #559	C₂²×C₁₉	semidirect
455. #557	C₂²×C₁₉	semidirect
456. #556	C₂²×C₁₉	semidirect
457. #555	C₂²×C₁₉	semidirect
458. #555	C₂²×C₁₉	semidirect
460. #554	C₂²×C₁₉	semidirect
461. #554	C₂²×C₁₉	semidirect
462. #554	C₂²×C₁₉	semidirect
463. #554	C₂²×C₁₉	semidirect
464. #554	C₂²×C₁₉	semidirect
465. #553	C₂²×C₁₉	semidirect
466. #553	C₂²×C₁₉	semidirect
467. #553	C₂²×C₁₉	semidirect
468. #552	C₂²×C₁₉	semidirect
470. #550	C₂²×C₁₉	semidirect
471. #550	C₂²×C₁₉	semidirect
472. D₄×Q₈	C₂²×C₁₉	semidirect
473. D₄×Q₈	C₂²×C₁₉	semidirect
474. #548	C₂²×C₁₉	semidirect
475. #547	C₂²×C₁₉	semidirect
476. #547	C₂²×C₁₉	semidirect
477. #547	C₂²×C₁₉	semidirect
478. #547	C₂²×C₁₉	semidirect
483. #544	C₂²×C₁₉	semidirect
484. #544	C₂²×C₁₉	semidirect
485. #544	C₂²×C₁₉	semidirect
488. #542	C₂²×C₁₉	semidirect
489. #542	C₂²×C₁₉	semidirect
490. #542	C₂²×C₁₉	semidirect
491. #542	C₂²×C₁₉	semidirect
492. #541	C₂²×C₁₉	semidirect
496. #540	C₂²×C₁₉	semidirect
497. #540	C₂²×C₁₉	semidirect
498. #540	C₂²×C₁₉	semidirect
499. #540	C₂²×C₁₉	semidirect
501. #539	C₂²×C₁₉	semidirect
502. #539	C₂²×C₁₉	semidirect
503. #539	C₂²×C₁₉	semidirect
506. #537	C₂²×C₁₉	semidirect
507. #537	C₂²×C₁₉	semidirect
508. #536	C₂²×C₁₉	semidirect
513. #533	C₂²×C₁₉	semidirect
514. #533	C₂²×C₁₉	semidirect
515. #533	C₂²×C₁₉	semidirect
517. #532	C₂²×C₁₉	semidirect
518. #532	C₂²×C₁₉	semidirect
520. #529	C₂²×C₁₉	semidirect
521. #529	C₂²×C₁₉	semidirect
523. C₂×#125	C₂²×C₁₉	semidirect
701. C₁₉	#62881	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×#3559	2
C₁₉×#3557	2
C₁₉×#3554	2
C₁₉×#3548	2
C₁₉×#3547	2
C₁₉×#3536	2
C₁₉×#3535	2
C₁₉×#3508	2
C₁₉×#3506	2
C₁₉×#3504	2
C₁₉×#3501	2
C₁₉×#3494	2
C₁₉×#3458	2
C₁₉×#3455	2
C₂×C₁₉×#540	2
#62881	19

Subgroups — C19×#62881 #18068840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62881 #18068840