Subgroups — C₁₉×#62888 #18068847

Order 4864.

6906 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3562	C₂	1	8	yes	maximal, complemented
2	C₁₉×#3560	C₂	1	8	yes	maximal, complemented
3	C₁₉×#3559	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3552	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3541	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3539	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3538	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3512	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3507	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3499	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3497	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3489	C₂	1	4	yes	maximal, complemented
13	C₁₉×#3455	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	complemented
17	C₂²×#41×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#563	C₂²	1	16	yes	complemented
19	C₁₉×#563	C₂²	1	16	yes	complemented
20	C₁₉×#562	C₂²	1	16	yes	complemented
21	C₁₉×#560	C₂²	1	16	yes	complemented
22	C₁₉×#559	C₂²	1	4	yes	complemented
23	C₁₉×#557	C₂²	1	4	yes	complemented
24	C₁₉×#556	C₂²	1	4	yes	complemented
25	C₁₉×#556	C₂²	1	8	yes	complemented
26	C₁₉×#554	C₂²	1	4	yes	complemented
27	C₁₉×#554	C₂²	1	16	yes	complemented
28	C₁₉×#553	C₂²	1	8	yes	complemented
29	C₁₉×#553	C₂²	1	16	yes	complemented
30	C₁₉×#553	C₂²	1	16	yes	complemented
31	C₁₉×#553	C₂²	1	16	yes	complemented
32	C₁₉×#552	C₂²	1	8	yes	complemented
33	C₁₉×#552	C₂²	1	8	yes	complemented
34	C₁₉×#551	C₂²	1	16	yes	complemented
35	C₁₉×#550	C₂²	1	4	yes	complemented
36	C₁₉×#550	C₂²	1	4	yes	complemented
37	D₄×Q₈×C₁₉	C₂²	1	8	yes	complemented
38	D₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
39	D₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
40	D₄×Q₈×C₁₉	C₂²	1	8	yes	complemented
41	C₁₉×#548	C₂²	1	8	yes	—
42	C₁₉×#548	C₂²	1	8	yes	complemented
43	C₁₉×#548	C₂²	1	8	yes	complemented
44	C₁₉×#547	C₂²	1	8	yes	—
45	C₁₉×#547	C₂²	1	16	yes	complemented
46	C₁₉×#547	C₂²	1	8	yes	complemented
47	C₁₉×#547	C₂²	1	16	yes	complemented
48	C₁₉×#546	C₂²	1	16	yes	—
49	C₁₉×#546	C₂²	1	8	yes	complemented
50	C₁₉×#544	C₂²	1	16	yes	complemented
51	C₁₉×#542	C₂²	1	4	yes	complemented
52	C₁₉×#542	C₂²	1	16	yes	complemented
53	C₁₉×#541	C₂²	1	4	yes	complemented
54	C₁₉×#541	C₂²	1	4	yes	complemented
55	C₁₉×#541	C₂²	1	8	yes	complemented
56	C₁₉×#541	C₂²	1	2	yes	complemented
57	C₁₉×#541	C₂²	1	4	yes	complemented
58	C₁₉×#540	C₂²	1	2	yes	complemented
59	C₁₉×#540	C₂²	1	4	yes	complemented
60	C₁₉×#540	C₂²	1	16	yes	complemented
61	C₁₉×#539	C₂²	1	4	yes	complemented
62	C₁₉×#539	C₂²	1	8	yes	complemented
63	C₁₉×#539	C₂²	1	16	yes	complemented
64	C₁₉×#539	C₂²	1	16	yes	complemented
65	C₁₉×#539	C₂²	1	16	yes	complemented
66	C₁₉×#538	C₂²	1	4	yes	—
67	C₁₉×#538	C₂²	1	16	yes	complemented
68	C₁₉×#538	C₂²	1	16	yes	complemented
69	C₁₉×#537	C₂²	1	4	yes	—
70	C₁₉×#537	C₂²	1	8	yes	—
71	C₁₉×#537	C₂²	1	4	yes	complemented
72	C₁₉×#537	C₂²	1	8	yes	complemented
73	C₁₉×#536	C₂²	1	4	yes	—
74	C₁₉×#536	C₂²	1	8	yes	—
75	C₁₉×#536	C₂²	1	4	yes	complemented
76	C₁₉×#536	C₂²	1	8	yes	complemented
77	C₁₉×#535	C₂²	1	4	yes	—
78	C₁₉×#534	C₂²	1	4	yes	—
79	C₁₉×#533	C₂²	1	1	yes	characteristic, complemented
80	C₁₉×#532	C₂²	1	2	yes	—
81	C₁₉×#532	C₂²	1	2	yes	—
82	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
83	C₁₉×#532	C₂²	1	8	yes	complemented
84	C₁₉×#532	C₂²	1	4	yes	complemented
85	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₁₉×C₄⋊Q₈	C₂²	1	4	yes	complemented
87	C₁₉×#529	C₂²	1	8	yes	complemented
88	C₁₉×#529	C₂²	1	8	yes	complemented
89	C₁₉×#529	C₂²	1	8	yes	complemented
90	C₂×C₁₉×#126	C₂²	1	4	yes	—
91	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₁₉×#125	C₂²	1	4	yes	complemented
93	C₁₉×#525	C₂²	1	4	yes	—
94	C₁₉×#525	C₂²	1	4	yes	—
95	C₁₉×#525	C₂²	1	2	yes	—
96	C₁₉×#525	C₂²	1	8	yes	complemented
97	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
98	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
99	C₁₉×#520	C₂²	1	4	yes	complemented
100	C₄×#41×C₁₉	C₂²	1	2	yes	complemented
101	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
102	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
103	C₁₉×2₋¹⁺⁴	—	4	16	no	—
104	C₂×#41×C₁₉	—	4	8	no	—
105	C₂×#41×C₁₉	C₂³	1	2	yes	—
106	C₂×#41×C₁₉	C₂³	1	4	yes	—
107	C₂×#41×C₁₉	C₂³	1	4	yes	—
108	C₂×#41×C₁₉	C₂³	1	8	yes	—
109	C₂×#41×C₁₉	C₂³	1	8	yes	—
110	C₂×#41×C₁₉	C₂³	1	16	yes	—
111	C₂×#41×C₁₉	C₂³	1	4	yes	—
112	C₂×#41×C₁₉	C₂³	1	4	yes	—
113	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
114	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
115	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
116	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
118	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
121	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
123	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
124	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	—
126	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₉×C₄⋊Q₈	C₂³	1	8	yes	—
129	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₁₉×C₄⋊Q₈	C₂³	1	16	yes	—
131	C₁₉×#127	C₂³	1	2	yes	—
132	C₁₉×#127	C₂³	1	2	yes	—
133	C₁₉×#127	C₂³	1	1	yes	characteristic
134	C₁₉×#127	C₂³	1	8	yes	—
135	C₁₉×#126	C₂³	1	16	yes	—
136	C₁₉×#126	C₂³	1	16	yes	—
137	C₁₉×#126	C₂³	1	8	yes	—
138	C₁₉×#126	C₂³	1	16	yes	—
139	C₁₉×#126	C₂³	1	16	yes	—
140	C₁₉×#126	C₂³	1	8	yes	—
141	C₁₉×#126	C₂³	1	16	yes	—
142	C₁₉×#126	C₂³	1	16	yes	—
143	C₁₉×#125	C₂³	1	4	yes	—
144	C₁₉×#125	C₂³	1	16	yes	—
145	C₁₉×#125	C₂³	1	4	yes	—
146	C₁₉×#125	C₂³	1	16	yes	—
147	C₁₉×#125	C₂³	1	8	yes	—
148	C₁₉×#125	C₂³	1	8	yes	—
149	C₁₉×#125	C₂³	1	2	yes	—
150	C₁₉×#125	C₂³	1	16	yes	—
151	C₁₉×#125	C₂³	1	16	yes	—
152	C₁₉×#124	C₂³	1	4	yes	—
153	C₁₉×#124	C₂³	1	8	yes	—
154	C₁₉×#124	C₂³	1	8	yes	—
155	C₁₉×#124	C₂³	1	4	yes	—
156	C₁₉×#124	C₂³	1	8	yes	—
157	C₁₉×#124	C₂³	1	16	yes	—
158	C₁₉×#124	C₂³	1	2	yes	—
159	C₁₉×#124	C₂³	1	16	yes	—
160	C₁₉×#123	C₂³	1	8	yes	—
161	C₁₉×#123	C₂³	1	8	yes	—
162	C₁₉×#123	C₂³	1	4	yes	—
163	C₁₉×#123	C₂³	1	16	yes	—
164	C₁₉×#123	C₂³	1	16	yes	—
165	C₁₉×#123	C₂³	1	8	yes	—
166	C₁₉×#123	C₂³	1	8	yes	—
167	C₁₉×#123	C₂³	1	16	yes	—
168	C₁₉×#123	C₂³	1	16	yes	—
169	C₁₉×#123	C₂³	1	16	yes	—
170	C₁₉×#123	C₂³	1	16	yes	—
171	C₁₉×#123	C₂³	1	16	yes	—
172	C₁₉×#123	C₂³	1	16	yes	—
173	C₁₉×#123	C₂³	1	16	yes	—
174	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
175	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
178	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
180	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
181	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
182	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
183	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
184	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
185	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
186	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
187	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
188	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
189	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
190	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
191	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
192	C₁₉×C₂²⋊Q₈	C₂³	1	16	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	4	yes	—
198	C₁₉×#121	C₂³	1	8	yes	—
199	C₁₉×#121	C₂³	1	8	yes	—
200	C₁₉×#121	C₂³	1	4	yes	—
201	C₁₉×#121	C₂³	1	8	yes	—
202	C₁₉×#121	C₂³	1	4	yes	—
203	C₁₉×#121	C₂³	1	16	yes	—
204	C₁₉×#121	C₂³	1	16	yes	—
205	C₁₉×#121	C₂³	1	16	yes	—
206	C₁₉×#121	C₂³	1	16	yes	—
207	C₁₉×#121	C₂³	1	16	yes	—
208	C₁₉×#121	C₂³	1	16	yes	—
209	C₁₉×#121	C₂³	1	16	yes	—
210	C₁₉×#121	C₂³	1	16	yes	—
211	C₁₉×#120	C₂³	1	8	yes	—
212	C₁₉×#120	C₂³	1	8	yes	—
213	C₁₉×#120	C₂³	1	4	yes	—
214	C₁₉×#120	C₂³	1	16	yes	—
215	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
216	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
217	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
218	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
219	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
220	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
221	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
222	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
223	C₄×D₄×C₁₉	C₂³	1	8	yes	—
224	C₄×D₄×C₁₉	C₂³	1	4	yes	—
225	C₄×D₄×C₁₉	C₂³	1	16	yes	—
226	C₄×D₄×C₁₉	C₂³	1	8	yes	—
227	C₄×D₄×C₁₉	C₂³	1	8	yes	—
228	C₄×D₄×C₁₉	C₂³	1	4	yes	—
229	C₄×D₄×C₁₉	C₂³	1	4	yes	—
230	C₄×D₄×C₁₉	C₂³	1	8	yes	—
231	C₄×D₄×C₁₉	C₂³	1	16	yes	—
232	C₄×D₄×C₁₉	C₂³	1	16	yes	—
233	C₄×D₄×C₁₉	C₂³	1	4	yes	—
234	C₄×D₄×C₁₉	C₂³	1	8	yes	—
235	C₄×D₄×C₁₉	C₂³	1	16	yes	—
236	C₄×D₄×C₁₉	C₂³	1	16	yes	—
237	C₄×D₄×C₁₉	C₂³	1	16	yes	—
238	C₄×D₄×C₁₉	C₂³	1	8	yes	—
239	C₄×D₄×C₁₉	C₂³	1	8	yes	—
240	C₁₉×#117	C₂³	1	2	yes	—
241	C₁₉×#117	C₂³	1	2	yes	—
242	C₁₉×#117	C₂³	1	4	yes	—
243	C₁₉×#117	C₂³	1	2	yes	—
244	C₁₉×#117	C₂³	1	4	yes	—
245	C₁₉×#117	C₂³	1	8	yes	—
246	C₁₉×#117	C₂³	1	16	yes	—
247	C₁₉×#117	C₂³	1	16	yes	—
248	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
251	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
252	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
253	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
254	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
255	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
256	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
257	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
259	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
260	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
263	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
264	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
266	#41×C₁₉	—	2	16	no	—
267	#41×C₁₉	—	2	8	no	—
268	#41×C₁₉	—	4	8	no	—
269	#41×C₁₉	—	4	8	no	—
270	#41×C₁₉	—	4	32	no	—
271	#41×C₁₉	—	4	8	no	—
272	#41×C₁₉	—	4	16	no	—
273	#41×C₁₉	—	4	16	no	—
274	C₂×Q₈×C₁₉	—	2	8	no	—
275	C₂×Q₈×C₁₉	—	4	4	no	—
276	C₂×Q₈×C₁₉	—	4	16	no	—
277	C₂×Q₈×C₁₉	—	4	16	no	—
278	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
279	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
280	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
281	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
282	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
283	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
284	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
285	C₂×D₄×C₁₉	—	4	4	no	—
286	C₂×D₄×C₁₉	—	4	8	no	—
287	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
288	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
289	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
290	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
291	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
292	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
293	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
294	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
295	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
296	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
297	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
298	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
299	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₁₉	—	2	4	no	—
301	C₂²×C₄×C₁₉	—	4	8	no	—
302	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
306	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
311	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
312	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
313	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
314	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
315	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
316	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
317	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
321	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
322	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
323	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
325	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
327	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
328	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
329	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
330	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
331	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
332	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
333	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
334	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
335	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
336	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
337	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
338	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
339	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
340	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
341	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
342	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
343	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
344	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
345	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
346	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
348	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
349	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
350	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
351	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
352	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
353	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
354	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
355	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
356	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
357	C₄²×C₁₉	C₂⁴	1	2	yes	—
358	C₄²×C₁₉	C₂⁴	1	2	yes	—
359	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
360	C₄²×C₁₉	C₂⁴	1	4	yes	—
361	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
362	C₄²×C₁₉	C₂⁴	1	8	yes	—
363	C₄²×C₁₉	C₂⁴	1	2	yes	—
364	C₄²×C₁₉	C₂⁴	1	8	yes	—
365	C₄²×C₁₉	C₂⁴	1	8	yes	—
366	C₄²×C₁₉	C₂⁴	1	16	yes	—
367	#62888	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂³×C₁₉	—	2	2	no	—
369	C₂³×C₁₉	—	4	4	no	—
370	C₂³×C₁₉	—	4	2	no	—
371	C₂³×C₁₉	—	4	8	no	—
372	C₂³×C₁₉	C₂⁵	1	2	yes	—
373	C₂³×C₁₉	C₂⁵	1	8	yes	—
374	C₂³×C₁₉	C₂⁵	1	4	yes	—
375	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
376	Q₈×C₁₉	—	2	8	no	—
377	Q₈×C₁₉	—	2	8	no	—
378	Q₈×C₁₉	—	2	4	no	—
379	Q₈×C₁₉	—	2	8	no	—
380	Q₈×C₁₉	—	4	16	no	—
381	Q₈×C₁₉	—	4	4	no	—
382	Q₈×C₁₉	—	4	4	no	—
383	D₄×C₁₉	—	2	16	no	—
384	D₄×C₁₉	—	2	8	no	—
385	D₄×C₁₉	—	2	8	no	—
386	D₄×C₁₉	—	2	4	no	—
387	D₄×C₁₉	—	4	4	no	—
388	D₄×C₁₉	—	4	8	no	—
389	D₄×C₁₉	—	4	8	no	—
390	D₄×C₁₉	—	4	16	no	—
391	D₄×C₁₉	—	4	8	no	—
392	D₄×C₁₉	—	4	4	no	—
393	D₄×C₁₉	—	4	4	no	—
394	D₄×C₁₉	—	4	4	no	—
395	D₄×C₁₉	—	4	16	no	—
396	C₂×C₄×C₁₉	—	2	2	no	—
397	C₂×C₄×C₁₉	—	2	8	no	—
398	C₂×C₄×C₁₉	—	2	4	no	—
399	C₂×C₄×C₁₉	—	2	4	no	—
400	C₂×C₄×C₁₉	—	2	16	no	—
401	C₂×C₄×C₁₉	—	2	8	no	—
402	C₂×C₄×C₁₉	—	4	4	no	—
403	C₂×C₄×C₁₉	—	4	8	no	—
404	C₂×C₄×C₁₉	—	4	2	no	—
405	C₂×C₄×C₁₉	—	4	4	no	—
406	C₂×C₄×C₁₉	—	4	16	no	—
407	C₂×C₄×C₁₉	—	4	8	no	—
408	C₂×C₄×C₁₉	—	4	2	no	—
409	C₂×C₄×C₁₉	—	4	16	no	—
410	C₂×C₄×C₁₉	—	4	16	no	—
411	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
412	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
413	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
414	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
415	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
416	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
417	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
418	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
419	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
420	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
421	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
422	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
423	#3562	C₂×C₁₉	1	8	yes	complemented
424	#3560	C₂×C₁₉	1	8	yes	complemented
425	#3559	C₂×C₁₉	1	8	yes	complemented
426	#3552	C₂×C₁₉	1	8	yes	complemented
427	#3541	C₂×C₁₉	1	8	yes	complemented
428	#3539	C₂×C₁₉	1	4	yes	complemented
429	#3538	C₂×C₁₉	1	4	yes	complemented
430	#3512	C₂×C₁₉	1	2	yes	complemented
431	#3507	C₂×C₁₉	1	2	yes	complemented
432	#3499	C₂×C₁₉	1	2	yes	complemented
433	#3497	C₂×C₁₉	1	2	yes	complemented
434	#3489	C₂×C₁₉	1	4	yes	complemented
435	#3455	C₂×C₁₉	1	1	yes	characteristic, complemented
436	C₂×#541	C₂×C₁₉	1	1	yes	characteristic, complemented
437	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
438	C₂²×C₁₉	—	2	2	no	—
439	C₂²×C₁₉	—	2	2	no	—
440	C₂²×C₁₉	—	2	4	no	—
441	C₂²×C₁₉	—	2	8	no	—
442	C₂²×C₁₉	—	2	8	no	—
443	C₂²×C₁₉	—	2	8	no	—
444	C₂²×C₁₉	—	2	8	no	—
445	C₂²×C₁₉	—	2	4	no	—
446	C₂²×C₁₉	—	8	2	no	—
447	C₂²×C₁₉	—	8	8	no	—
448	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
450	C₄×C₁₉	—	2	2	no	—
451	C₄×C₁₉	—	2	8	no	—
452	C₄×C₁₉	—	2	4	no	—
453	C₄×C₁₉	—	2	8	no	—
454	C₄×C₁₉	—	2	8	no	—
455	C₄×C₁₉	—	2	4	no	—
456	C₄×C₁₉	—	2	8	no	—
457	C₄×C₁₉	—	2	2	no	—
458	C₄×C₁₉	—	2	2	no	—
459	C₄×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
460	C₄×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
461	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	complemented
462	C₂²×#41	C₂²×C₁₉	1	2	yes	—
463	#563	C₂²×C₁₉	1	16	yes	complemented
464	#563	C₂²×C₁₉	1	16	yes	complemented
465	#562	C₂²×C₁₉	1	16	yes	complemented
466	#560	C₂²×C₁₉	1	16	yes	complemented
467	#559	C₂²×C₁₉	1	4	yes	complemented
468	#557	C₂²×C₁₉	1	4	yes	complemented
469	#556	C₂²×C₁₉	1	4	yes	complemented
470	#556	C₂²×C₁₉	1	8	yes	complemented
471	#554	C₂²×C₁₉	1	4	yes	complemented
472	#554	C₂²×C₁₉	1	16	yes	complemented
473	#553	C₂²×C₁₉	1	8	yes	complemented
474	#553	C₂²×C₁₉	1	16	yes	complemented
475	#553	C₂²×C₁₉	1	16	yes	complemented
476	#553	C₂²×C₁₉	1	16	yes	complemented
477	#552	C₂²×C₁₉	1	8	yes	complemented
478	#552	C₂²×C₁₉	1	8	yes	complemented
479	#551	C₂²×C₁₉	1	16	yes	complemented
480	#550	C₂²×C₁₉	1	4	yes	complemented
481	#550	C₂²×C₁₉	1	4	yes	complemented
482	D₄×Q₈	C₂²×C₁₉	1	8	yes	complemented
483	D₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
484	D₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
485	D₄×Q₈	C₂²×C₁₉	1	8	yes	complemented
486	#548	C₂²×C₁₉	1	8	yes	—
487	#548	C₂²×C₁₉	1	8	yes	complemented
488	#548	C₂²×C₁₉	1	8	yes	complemented
489	#547	C₂²×C₁₉	1	8	yes	—
490	#547	C₂²×C₁₉	1	16	yes	complemented
491	#547	C₂²×C₁₉	1	8	yes	complemented
492	#547	C₂²×C₁₉	1	16	yes	complemented
493	#546	C₂²×C₁₉	1	16	yes	—
494	#546	C₂²×C₁₉	1	8	yes	complemented
495	#544	C₂²×C₁₉	1	16	yes	complemented
496	#542	C₂²×C₁₉	1	4	yes	complemented
497	#542	C₂²×C₁₉	1	16	yes	complemented
498	#541	C₂²×C₁₉	1	4	yes	complemented
499	#541	C₂²×C₁₉	1	4	yes	complemented
500	#541	C₂²×C₁₉	1	8	yes	complemented
501	#541	C₂²×C₁₉	1	2	yes	complemented
502	#541	C₂²×C₁₉	1	4	yes	complemented
503	#540	C₂²×C₁₉	1	2	yes	complemented
504	#540	C₂²×C₁₉	1	4	yes	complemented
505	#540	C₂²×C₁₉	1	16	yes	complemented
506	#539	C₂²×C₁₉	1	4	yes	complemented
507	#539	C₂²×C₁₉	1	8	yes	complemented
508	#539	C₂²×C₁₉	1	16	yes	complemented
509	#539	C₂²×C₁₉	1	16	yes	complemented
510	#539	C₂²×C₁₉	1	16	yes	complemented
511	#538	C₂²×C₁₉	1	4	yes	—
512	#538	C₂²×C₁₉	1	16	yes	complemented
513	#538	C₂²×C₁₉	1	16	yes	complemented
514	#537	C₂²×C₁₉	1	4	yes	—
515	#537	C₂²×C₁₉	1	8	yes	—
516	#537	C₂²×C₁₉	1	4	yes	complemented
517	#537	C₂²×C₁₉	1	8	yes	complemented
518	#536	C₂²×C₁₉	1	4	yes	—
519	#536	C₂²×C₁₉	1	8	yes	—
520	#536	C₂²×C₁₉	1	4	yes	complemented
521	#536	C₂²×C₁₉	1	8	yes	complemented
522	#535	C₂²×C₁₉	1	4	yes	—
523	#534	C₂²×C₁₉	1	4	yes	—
524	#533	C₂²×C₁₉	1	1	yes	characteristic, complemented
525	#532	C₂²×C₁₉	1	2	yes	—
526	#532	C₂²×C₁₉	1	2	yes	—
527	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
528	#532	C₂²×C₁₉	1	8	yes	complemented
529	#532	C₂²×C₁₉	1	4	yes	complemented
530	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
531	C₂×C₄⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
532	#529	C₂²×C₁₉	1	8	yes	complemented
533	#529	C₂²×C₁₉	1	8	yes	complemented
534	#529	C₂²×C₁₉	1	8	yes	complemented
535	C₂×#126	C₂²×C₁₉	1	4	yes	—
536	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic, complemented
537	C₂×#125	C₂²×C₁₉	1	4	yes	complemented
538	#525	C₂²×C₁₉	1	4	yes	—
539	#525	C₂²×C₁₉	1	4	yes	—
540	#525	C₂²×C₁₉	1	2	yes	—
541	#525	C₂²×C₁₉	1	8	yes	complemented
542	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
543	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
544	#520	C₂²×C₁₉	1	4	yes	complemented
545	C₄×#41	C₂²×C₁₉	1	2	yes	complemented
546	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
547	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
548	C₂×C₁₉	—	2	2	no	—
549	C₂×C₁₉	—	4	4	no	—
550	C₂×C₁₉	—	4	8	no	—
551	C₂×C₁₉	—	4	2	no	—
552	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂×C₁₉	2₋¹⁺⁶	1	2	yes	—
554	2₋¹⁺⁴	—	4	16	no	—
555	C₂×#41	—	4	8	no	—
556	C₂×#41	C₂³×C₁₉	1	2	yes	—
557	C₂×#41	C₂³×C₁₉	1	4	yes	—
558	C₂×#41	C₂³×C₁₉	1	4	yes	—
559	C₂×#41	C₂³×C₁₉	1	8	yes	—
560	C₂×#41	C₂³×C₁₉	1	8	yes	—
561	C₂×#41	C₂³×C₁₉	1	16	yes	—
562	C₂×#41	C₂³×C₁₉	1	4	yes	—
563	C₂×#41	C₂³×C₁₉	1	4	yes	—
564	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
565	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
566	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
567	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
568	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
569	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
570	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
572	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
573	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
574	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
575	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
576	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	—
577	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
578	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
579	C₄⋊Q₈	C₂³×C₁₉	1	8	yes	—
580	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
581	C₄⋊Q₈	C₂³×C₁₉	1	16	yes	—
582	#127	C₂³×C₁₉	1	2	yes	—
583	#127	C₂³×C₁₉	1	2	yes	—
584	#127	C₂³×C₁₉	1	1	yes	characteristic
585	#127	C₂³×C₁₉	1	8	yes	—
586	#126	C₂³×C₁₉	1	16	yes	—
587	#126	C₂³×C₁₉	1	16	yes	—
588	#126	C₂³×C₁₉	1	8	yes	—
589	#126	C₂³×C₁₉	1	16	yes	—
590	#126	C₂³×C₁₉	1	16	yes	—
591	#126	C₂³×C₁₉	1	8	yes	—
592	#126	C₂³×C₁₉	1	16	yes	—
593	#126	C₂³×C₁₉	1	16	yes	—
594	#125	C₂³×C₁₉	1	4	yes	—
595	#125	C₂³×C₁₉	1	16	yes	—
596	#125	C₂³×C₁₉	1	4	yes	—
597	#125	C₂³×C₁₉	1	16	yes	—
598	#125	C₂³×C₁₉	1	8	yes	—
599	#125	C₂³×C₁₉	1	8	yes	—
600	#125	C₂³×C₁₉	1	2	yes	—
601	#125	C₂³×C₁₉	1	16	yes	—
602	#125	C₂³×C₁₉	1	16	yes	—
603	#124	C₂³×C₁₉	1	4	yes	—
604	#124	C₂³×C₁₉	1	8	yes	—
605	#124	C₂³×C₁₉	1	8	yes	—
606	#124	C₂³×C₁₉	1	4	yes	—
607	#124	C₂³×C₁₉	1	8	yes	—
608	#124	C₂³×C₁₉	1	16	yes	—
609	#124	C₂³×C₁₉	1	2	yes	—
610	#124	C₂³×C₁₉	1	16	yes	—
611	#123	C₂³×C₁₉	1	8	yes	—
612	#123	C₂³×C₁₉	1	8	yes	—
613	#123	C₂³×C₁₉	1	4	yes	—
614	#123	C₂³×C₁₉	1	16	yes	—
615	#123	C₂³×C₁₉	1	16	yes	—
616	#123	C₂³×C₁₉	1	8	yes	—
617	#123	C₂³×C₁₉	1	8	yes	—
618	#123	C₂³×C₁₉	1	16	yes	—
619	#123	C₂³×C₁₉	1	16	yes	—
620	#123	C₂³×C₁₉	1	16	yes	—
621	#123	C₂³×C₁₉	1	16	yes	—
622	#123	C₂³×C₁₉	1	16	yes	—
623	#123	C₂³×C₁₉	1	16	yes	—
624	#123	C₂³×C₁₉	1	16	yes	—
625	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
626	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
627	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
628	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
629	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
630	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
631	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
632	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
633	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
634	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
635	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
636	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
637	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
638	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
639	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
640	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
641	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
642	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
643	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
644	#121	C₂³×C₁₉	1	4	yes	—
645	#121	C₂³×C₁₉	1	8	yes	—
646	#121	C₂³×C₁₉	1	8	yes	—
647	#121	C₂³×C₁₉	1	8	yes	—
648	#121	C₂³×C₁₉	1	4	yes	—
649	#121	C₂³×C₁₉	1	8	yes	—
650	#121	C₂³×C₁₉	1	8	yes	—
651	#121	C₂³×C₁₉	1	4	yes	—
652	#121	C₂³×C₁₉	1	8	yes	—
653	#121	C₂³×C₁₉	1	4	yes	—
654	#121	C₂³×C₁₉	1	16	yes	—
655	#121	C₂³×C₁₉	1	16	yes	—
656	#121	C₂³×C₁₉	1	16	yes	—
657	#121	C₂³×C₁₉	1	16	yes	—
658	#121	C₂³×C₁₉	1	16	yes	—
659	#121	C₂³×C₁₉	1	16	yes	—
660	#121	C₂³×C₁₉	1	16	yes	—
661	#121	C₂³×C₁₉	1	16	yes	—
662	#120	C₂³×C₁₉	1	8	yes	—
663	#120	C₂³×C₁₉	1	8	yes	—
664	#120	C₂³×C₁₉	1	4	yes	—
665	#120	C₂³×C₁₉	1	16	yes	—
666	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
667	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
668	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
669	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
670	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
671	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
672	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
673	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
674	C₄×D₄	C₂³×C₁₉	1	8	yes	—
675	C₄×D₄	C₂³×C₁₉	1	4	yes	—
676	C₄×D₄	C₂³×C₁₉	1	16	yes	—
677	C₄×D₄	C₂³×C₁₉	1	8	yes	—
678	C₄×D₄	C₂³×C₁₉	1	8	yes	—
679	C₄×D₄	C₂³×C₁₉	1	4	yes	—
680	C₄×D₄	C₂³×C₁₉	1	4	yes	—
681	C₄×D₄	C₂³×C₁₉	1	8	yes	—
682	C₄×D₄	C₂³×C₁₉	1	16	yes	—
683	C₄×D₄	C₂³×C₁₉	1	16	yes	—
684	C₄×D₄	C₂³×C₁₉	1	4	yes	—
685	C₄×D₄	C₂³×C₁₉	1	8	yes	—
686	C₄×D₄	C₂³×C₁₉	1	16	yes	—
687	C₄×D₄	C₂³×C₁₉	1	16	yes	—
688	C₄×D₄	C₂³×C₁₉	1	16	yes	—
689	C₄×D₄	C₂³×C₁₉	1	8	yes	—
690	C₄×D₄	C₂³×C₁₉	1	8	yes	—
691	#117	C₂³×C₁₉	1	2	yes	—
692	#117	C₂³×C₁₉	1	2	yes	—
693	#117	C₂³×C₁₉	1	4	yes	—
694	#117	C₂³×C₁₉	1	2	yes	—
695	#117	C₂³×C₁₉	1	4	yes	—
696	#117	C₂³×C₁₉	1	8	yes	—
697	#117	C₂³×C₁₉	1	16	yes	—
698	#117	C₂³×C₁₉	1	16	yes	—
699	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
702	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
703	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
704	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
705	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
706	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
707	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
711	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
714	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
715	C₁₉	#62888	1	1	yes	characteristic, direct product factor, Sylow
716	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
717	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
718	#41	—	2	16	no	—
719	#41	—	2	8	no	—
720	#41	—	4	8	no	—
721	#41	—	4	8	no	—
722	#41	—	4	32	no	—
723	#41	—	4	8	no	—
724	#41	—	4	16	no	—
725	#41	—	4	16	no	—
726	C₂×Q₈	—	2	8	no	—
727	C₂×Q₈	—	4	4	no	—
728	C₂×Q₈	—	4	16	no	—
729	C₂×Q₈	—	4	16	no	—
730	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
731	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
732	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
733	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
734	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
735	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
736	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	4	8	no	—
739	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
740	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
741	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
742	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
743	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
744	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
745	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
746	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
747	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
748	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
749	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
750	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
751	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	4	8	no	—
754	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
755	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
758	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
763	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
764	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
765	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
766	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
767	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
768	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
769	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
770	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
771	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
772	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
773	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
774	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
775	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
777	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
778	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
779	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
780	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
781	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
782	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
783	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
784	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
785	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
786	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
787	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
788	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
789	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
790	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
791	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
792	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
793	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
794	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
795	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
796	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
797	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
798	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
799	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
800	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
801	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
802	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
803	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
804	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
805	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
806	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
807	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
808	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
809	C₄²	C₂⁴×C₁₉	1	2	yes	—
810	C₄²	C₂⁴×C₁₉	1	2	yes	—
811	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
812	C₄²	C₂⁴×C₁₉	1	4	yes	—
813	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
814	C₄²	C₂⁴×C₁₉	1	8	yes	—
815	C₄²	C₂⁴×C₁₉	1	2	yes	—
816	C₄²	C₂⁴×C₁₉	1	8	yes	—
817	C₄²	C₂⁴×C₁₉	1	8	yes	—
818	C₄²	C₂⁴×C₁₉	1	16	yes	—
819	C₂³	—	2	2	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	4	8	no	—
823	C₂³	C₂⁵×C₁₉	1	2	yes	—
824	C₂³	C₂⁵×C₁₉	1	8	yes	—
825	C₂³	C₂⁵×C₁₉	1	4	yes	—
826	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
827	Q₈	—	2	8	no	—
828	Q₈	—	2	8	no	—
829	Q₈	—	2	4	no	—
830	Q₈	—	2	8	no	—
831	Q₈	—	4	16	no	—
832	Q₈	—	4	4	no	—
833	Q₈	—	4	4	no	—
834	D₄	—	2	16	no	—
835	D₄	—	2	8	no	—
836	D₄	—	2	8	no	—
837	D₄	—	2	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	16	no	—
841	D₄	—	4	8	no	—
842	D₄	—	4	16	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	16	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	16	no	—
856	C₂×C₄	—	4	16	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	16	no	—
860	C₂×C₄	—	4	8	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
863	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
864	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
865	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
866	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
867	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
868	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
869	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
870	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
871	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
872	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
873	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	2	8	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	8	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	8	2	no	—
883	C₂²	—	8	8	no	—
884	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
885	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
886	C₄	—	2	2	no	—
887	C₄	—	2	8	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	8	no	—
890	C₄	—	2	8	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	8	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
896	C₄	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
897	C₂	—	2	2	no	—
898	C₂	—	4	2	no	—
899	C₂	—	4	8	no	—
900	C₂	—	4	4	no	—
901	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂	C₁₉×2₋¹⁺⁶	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×#3562	C₂	semidirect
2. C₁₉×#3560	C₂	semidirect
3. C₁₉×#3559	C₂	semidirect
4. C₁₉×#3552	C₂	semidirect
5. C₁₉×#3541	C₂	semidirect
6. C₁₉×#3539	C₂	semidirect
7. C₁₉×#3538	C₂	semidirect
8. C₁₉×#3512	C₂	semidirect
9. C₁₉×#3507	C₂	semidirect
10. C₁₉×#3499	C₂	semidirect
11. C₁₉×#3497	C₂	semidirect
12. C₁₉×#3489	C₂	semidirect
13. C₁₉×#3455	C₂	semidirect
14. C₂×C₁₉×#541	C₂	semidirect
15. C₁₉×#3449	C₂	semidirect
16. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
18. C₁₉×#563	C₂²	semidirect
19. C₁₉×#563	C₂²	semidirect
20. C₁₉×#562	C₂²	semidirect
21. C₁₉×#560	C₂²	semidirect
22. C₁₉×#559	C₂²	semidirect
23. C₁₉×#557	C₂²	semidirect
24. C₁₉×#556	C₂²	semidirect
25. C₁₉×#556	C₂²	semidirect
26. C₁₉×#554	C₂²	semidirect
27. C₁₉×#554	C₂²	semidirect
28. C₁₉×#553	C₂²	semidirect
29. C₁₉×#553	C₂²	semidirect
30. C₁₉×#553	C₂²	semidirect
31. C₁₉×#553	C₂²	semidirect
32. C₁₉×#552	C₂²	semidirect
33. C₁₉×#552	C₂²	semidirect
34. C₁₉×#551	C₂²	semidirect
35. C₁₉×#550	C₂²	semidirect
36. C₁₉×#550	C₂²	semidirect
37. D₄×Q₈×C₁₉	C₂²	semidirect
38. D₄×Q₈×C₁₉	C₂²	semidirect
39. D₄×Q₈×C₁₉	C₂²	semidirect
40. D₄×Q₈×C₁₉	C₂²	semidirect
42. C₁₉×#548	C₂²	semidirect
43. C₁₉×#548	C₂²	semidirect
45. C₁₉×#547	C₂²	semidirect
46. C₁₉×#547	C₂²	semidirect
47. C₁₉×#547	C₂²	semidirect
49. C₁₉×#546	C₂²	semidirect
50. C₁₉×#544	C₂²	semidirect
51. C₁₉×#542	C₂²	semidirect
52. C₁₉×#542	C₂²	semidirect
53. C₁₉×#541	C₂²	semidirect
54. C₁₉×#541	C₂²	semidirect
55. C₁₉×#541	C₂²	semidirect
56. C₁₉×#541	C₂²	semidirect
57. C₁₉×#541	C₂²	semidirect
58. C₁₉×#540	C₂²	semidirect
59. C₁₉×#540	C₂²	semidirect
60. C₁₉×#540	C₂²	semidirect
61. C₁₉×#539	C₂²	semidirect
62. C₁₉×#539	C₂²	semidirect
63. C₁₉×#539	C₂²	semidirect
64. C₁₉×#539	C₂²	semidirect
65. C₁₉×#539	C₂²	semidirect
67. C₁₉×#538	C₂²	semidirect
68. C₁₉×#538	C₂²	semidirect
71. C₁₉×#537	C₂²	semidirect
72. C₁₉×#537	C₂²	semidirect
75. C₁₉×#536	C₂²	semidirect
76. C₁₉×#536	C₂²	semidirect
79. C₁₉×#533	C₂²	semidirect
82. C₁₉×#532	C₂²	semidirect
83. C₁₉×#532	C₂²	semidirect
84. C₁₉×#532	C₂²	semidirect
85. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
86. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
87. C₁₉×#529	C₂²	semidirect
88. C₁₉×#529	C₂²	semidirect
89. C₁₉×#529	C₂²	semidirect
91. C₂×C₁₉×#125	C₂²	semidirect
92. C₂×C₁₉×#125	C₂²	semidirect
96. C₁₉×#525	C₂²	semidirect
98. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
99. C₁₉×#520	C₂²	semidirect
100. C₄×#41×C₁₉	C₂²	semidirect
101. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
367. #62888	C₁₉	direct (N × H)
423. #3562	C₂×C₁₉	semidirect
424. #3560	C₂×C₁₉	semidirect
425. #3559	C₂×C₁₉	semidirect
426. #3552	C₂×C₁₉	semidirect
427. #3541	C₂×C₁₉	semidirect
428. #3539	C₂×C₁₉	semidirect
429. #3538	C₂×C₁₉	semidirect
430. #3512	C₂×C₁₉	semidirect
431. #3507	C₂×C₁₉	semidirect
432. #3499	C₂×C₁₉	semidirect
433. #3497	C₂×C₁₉	semidirect
434. #3489	C₂×C₁₉	semidirect
435. #3455	C₂×C₁₉	semidirect
436. C₂×#541	C₂×C₁₉	semidirect
437. #3449	C₂×C₁₉	semidirect
461. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
463. #563	C₂²×C₁₉	semidirect
464. #563	C₂²×C₁₉	semidirect
465. #562	C₂²×C₁₉	semidirect
466. #560	C₂²×C₁₉	semidirect
467. #559	C₂²×C₁₉	semidirect
468. #557	C₂²×C₁₉	semidirect
469. #556	C₂²×C₁₉	semidirect
470. #556	C₂²×C₁₉	semidirect
471. #554	C₂²×C₁₉	semidirect
472. #554	C₂²×C₁₉	semidirect
473. #553	C₂²×C₁₉	semidirect
474. #553	C₂²×C₁₉	semidirect
475. #553	C₂²×C₁₉	semidirect
476. #553	C₂²×C₁₉	semidirect
477. #552	C₂²×C₁₉	semidirect
478. #552	C₂²×C₁₉	semidirect
479. #551	C₂²×C₁₉	semidirect
480. #550	C₂²×C₁₉	semidirect
481. #550	C₂²×C₁₉	semidirect
482. D₄×Q₈	C₂²×C₁₉	semidirect
483. D₄×Q₈	C₂²×C₁₉	semidirect
484. D₄×Q₈	C₂²×C₁₉	semidirect
485. D₄×Q₈	C₂²×C₁₉	semidirect
487. #548	C₂²×C₁₉	semidirect
488. #548	C₂²×C₁₉	semidirect
490. #547	C₂²×C₁₉	semidirect
491. #547	C₂²×C₁₉	semidirect
492. #547	C₂²×C₁₉	semidirect
494. #546	C₂²×C₁₉	semidirect
495. #544	C₂²×C₁₉	semidirect
496. #542	C₂²×C₁₉	semidirect
497. #542	C₂²×C₁₉	semidirect
498. #541	C₂²×C₁₉	semidirect
499. #541	C₂²×C₁₉	semidirect
500. #541	C₂²×C₁₉	semidirect
501. #541	C₂²×C₁₉	semidirect
502. #541	C₂²×C₁₉	semidirect
503. #540	C₂²×C₁₉	semidirect
504. #540	C₂²×C₁₉	semidirect
505. #540	C₂²×C₁₉	semidirect
506. #539	C₂²×C₁₉	semidirect
507. #539	C₂²×C₁₉	semidirect
508. #539	C₂²×C₁₉	semidirect
509. #539	C₂²×C₁₉	semidirect
510. #539	C₂²×C₁₉	semidirect
512. #538	C₂²×C₁₉	semidirect
513. #538	C₂²×C₁₉	semidirect
516. #537	C₂²×C₁₉	semidirect
517. #537	C₂²×C₁₉	semidirect
520. #536	C₂²×C₁₉	semidirect
521. #536	C₂²×C₁₉	semidirect
524. #533	C₂²×C₁₉	semidirect
527. #532	C₂²×C₁₉	semidirect
528. #532	C₂²×C₁₉	semidirect
529. #532	C₂²×C₁₉	semidirect
530. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
531. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
532. #529	C₂²×C₁₉	semidirect
533. #529	C₂²×C₁₉	semidirect
534. #529	C₂²×C₁₉	semidirect
536. C₂×#125	C₂²×C₁₉	semidirect
537. C₂×#125	C₂²×C₁₉	semidirect
541. #525	C₂²×C₁₉	semidirect
543. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
544. #520	C₂²×C₁₉	semidirect
545. C₄×#41	C₂²×C₁₉	semidirect
546. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
715. C₁₉	#62888	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×#3562	2
C₁₉×#3560	2
C₁₉×#3559	2
C₁₉×#3552	2
C₁₉×#3541	2
C₁₉×#3539	2
C₁₉×#3538	2
C₁₉×#3512	2
C₁₉×#3507	2
C₁₉×#3499	2
C₁₉×#3497	2
C₁₉×#3489	2
C₁₉×#3455	2
C₂×C₁₉×#541	2
C₁₉×#3449	2
#62888	19

Subgroups — C19×#62888 #18068847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62888 #18068847