Subgroups — C₁₉×#62876 #18068835

Order 4864.

7414 conjugacy classes of subgroups.

The subgroup lattice has 1004 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×#3558	C₂	1	8	yes	maximal, complemented
3	C₁₉×#3546	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3543	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3534	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3532	C₂	1	8	yes	maximal, complemented
7	C₁₉×#3510	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3508	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3500	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3498	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#3485	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#3484	C₂	1	2	yes	maximal, complemented
14	C₁₉×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	2	yes	complemented
18	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#562	C₂²	1	16	yes	complemented
22	C₁₉×H(3,𝔽₄)	C₂²	1	8	yes	complemented
23	C₁₉×#560	C₂²	1	16	yes	complemented
24	C₁₉×#560	C₂²	1	8	yes	complemented
25	C₁₉×#560	C₂²	1	16	yes	complemented
26	C₁₉×#559	C₂²	1	8	yes	complemented
27	C₁₉×#559	C₂²	1	8	yes	complemented
28	C₁₉×#556	C₂²	1	8	yes	complemented
29	C₁₉×#553	C₂²	1	16	yes	complemented
30	C₁₉×#551	C₂²	1	16	yes	complemented
31	C₁₉×#551	C₂²	1	8	yes	complemented
32	C₁₉×#550	C₂²	1	8	yes	complemented
33	C₁₉×#550	C₂²	1	8	yes	complemented
34	C₁₉×#550	C₂²	1	8	yes	complemented
35	C₁₉×#548	C₂²	1	8	yes	complemented
36	C₁₉×#548	C₂²	1	8	yes	complemented
37	C₁₉×#547	C₂²	1	8	yes	complemented
38	C₁₉×#546	C₂²	1	8	yes	complemented
39	C₁₉×#546	C₂²	1	8	yes	complemented
40	C₁₉×#546	C₂²	1	16	yes	complemented
41	C₁₉×#546	C₂²	1	16	yes	complemented
42	C₁₉×#546	C₂²	1	16	yes	complemented
43	C₁₉×#546	C₂²	1	8	yes	complemented
44	C₁₉×#546	C₂²	1	16	yes	complemented
45	C₁₉×#546	C₂²	1	8	yes	complemented
46	D₄²×C₁₉	C₂²	1	8	yes	complemented
47	D₄²×C₁₉	C₂²	1	8	yes	complemented
48	D₄²×C₁₉	C₂²	1	16	yes	complemented
49	D₄²×C₁₉	C₂²	1	8	yes	complemented
50	D₄²×C₁₉	C₂²	1	8	yes	complemented
51	C₁₉×#542	C₂²	1	4	yes	complemented
52	C₁₉×#542	C₂²	1	4	yes	complemented
53	C₁₉×#542	C₂²	1	8	yes	complemented
54	C₁₉×#541	C₂²	1	4	yes	complemented
55	C₁₉×#540	C₂²	1	4	yes	complemented
56	C₁₉×#540	C₂²	1	8	yes	complemented
57	C₁₉×#540	C₂²	1	16	yes	complemented
58	C₁₉×#539	C₂²	1	8	yes	complemented
59	C₁₉×#539	C₂²	1	8	yes	complemented
60	C₁₉×#538	C₂²	1	8	yes	complemented
61	C₁₉×#538	C₂²	1	16	yes	complemented
62	C₁₉×#538	C₂²	1	16	yes	complemented
63	C₁₉×#538	C₂²	1	16	yes	complemented
64	C₁₉×#538	C₂²	1	8	yes	complemented
65	C₁₉×#537	C₂²	1	8	yes	complemented
66	C₁₉×#536	C₂²	1	2	yes	complemented
67	C₁₉×#536	C₂²	1	4	yes	complemented
68	C₁₉×#535	C₂²	1	2	yes	—
69	C₁₉×#535	C₂²	1	8	yes	complemented
70	C₁₉×#535	C₂²	1	8	yes	complemented
71	C₁₉×#535	C₂²	1	2	yes	complemented
72	C₁₉×#535	C₂²	1	4	yes	complemented
73	C₁₉×#535	C₂²	1	2	yes	complemented
74	C₁₉×#535	C₂²	1	16	yes	complemented
75	C₁₉×#535	C₂²	1	4	yes	complemented
76	C₁₉×#535	C₂²	1	4	yes	complemented
77	C₁₉×#535	C₂²	1	4	yes	complemented
78	C₁₉×#534	C₂²	1	8	yes	complemented
79	C₁₉×#534	C₂²	1	4	yes	complemented
80	C₁₉×#534	C₂²	1	16	yes	complemented
81	C₁₉×#534	C₂²	1	8	yes	complemented
82	C₁₉×#533	C₂²	1	2	yes	complemented
83	C₁₉×#532	C₂²	1	2	yes	complemented
84	C₁₉×#532	C₂²	1	8	yes	complemented
85	C₁₉×#532	C₂²	1	4	yes	complemented
86	C₁₉×#532	C₂²	1	4	yes	complemented
87	C₂×C₁₉×#127	C₂²	1	2	yes	complemented
88	C₂×C₁₉×#127	C₂²	1	4	yes	complemented
89	C₁₉×#529	C₂²	1	8	yes	complemented
90	C₁₉×#529	C₂²	1	8	yes	complemented
91	C₁₉×#529	C₂²	1	8	yes	complemented
92	C₂×C₁₉×#124	C₂²	1	2	yes	complemented
93	C₂×C₁₉×#124	C₂²	1	4	yes	complemented
94	C₁₉×#525	C₂²	1	2	yes	complemented
95	C₁₉×#525	C₂²	1	2	yes	complemented
96	C₁₉×#525	C₂²	1	4	yes	complemented
97	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
98	C₂×C₁₉×#121	C₂²	1	4	yes	complemented
99	C₂×C₁₉×#120	C₂²	1	4	yes	complemented
100	C₂×C₁₉×#120	C₂²	1	8	yes	complemented
101	C₁₉×#519	C₂²	1	1	yes	characteristic, complemented
102	C₁₉×#518	C₂²	1	2	yes	complemented
103	C₁₉×#518	C₂²	1	1	yes	characteristic, complemented
104	C₄×#41×C₁₉	C₂²	1	2	yes	complemented
105	C₄×#41×C₁₉	C₂²	1	2	yes	complemented
106	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₁₉	C₂³	1	2	yes	—
108	C₁₉×2₋¹⁺⁴	—	4	4	no	—
109	C₁₉×H(5,𝔽₂)	—	4	8	no	—
110	C₁₉×H(5,𝔽₂)	—	4	4	no	—
111	C₂×#41×C₁₉	—	4	4	no	—
112	C₂×#41×C₁₉	C₂³	1	2	yes	—
113	C₂×#41×C₁₉	C₂³	1	2	yes	—
114	C₂×#41×C₁₉	C₂³	1	4	yes	—
115	C₂×#41×C₁₉	C₂³	1	4	yes	—
116	C₂×#41×C₁₉	C₂³	1	4	yes	—
117	C₂×#41×C₁₉	C₂³	1	8	yes	—
118	C₂×#41×C₁₉	C₂³	1	4	yes	complemented
119	C₂×#41×C₁₉	C₂³	1	4	yes	complemented
120	C₂×#41×C₁₉	C₂³	1	16	yes	complemented
121	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₁₉	C₂³	1	4	yes	complemented
123	C₂²×D₄×C₁₉	—	4	4	no	—
124	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
128	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
130	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
131	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
132	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
133	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
134	C₂²×D₄×C₁₉	C₂³	1	16	yes	—
135	C₂²×D₄×C₁₉	C₂³	1	4	yes	complemented
136	C₂²×D₄×C₁₉	C₂³	1	16	yes	complemented
137	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
139	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	complemented
140	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	complemented
141	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	complemented
142	C₁₉×#127	C₂³	1	4	yes	—
143	C₁₉×#127	C₂³	1	4	yes	—
144	C₁₉×#127	C₂³	1	4	yes	—
145	C₁₉×#127	C₂³	1	8	yes	—
146	C₁₉×#127	C₂³	1	4	yes	—
147	C₁₉×#127	C₂³	1	8	yes	—
148	C₁₉×#127	C₂³	1	2	yes	complemented
149	C₁₉×#127	C₂³	1	4	yes	complemented
150	C₁₉×#127	C₂³	1	16	yes	complemented
151	C₁₉×#126	C₂³	1	8	yes	—
152	C₁₉×#126	C₂³	1	8	yes	—
153	C₁₉×#126	C₂³	1	8	yes	complemented
154	C₁₉×#126	C₂³	1	16	yes	complemented
155	C₁₉×#126	C₂³	1	8	yes	complemented
156	C₁₉×#126	C₂³	1	16	yes	complemented
157	C₁₉×#125	C₂³	1	4	yes	complemented
158	C₁₉×#125	C₂³	1	8	yes	complemented
159	C₁₉×#125	C₂³	1	8	yes	complemented
160	C₁₉×#124	C₂³	1	4	yes	—
161	C₁₉×#124	C₂³	1	4	yes	—
162	C₁₉×#124	C₂³	1	8	yes	—
163	C₁₉×#124	C₂³	1	4	yes	—
164	C₁₉×#124	C₂³	1	8	yes	—
165	C₁₉×#124	C₂³	1	8	yes	—
166	C₁₉×#124	C₂³	1	4	yes	—
167	C₁₉×#124	C₂³	1	8	yes	—
168	C₁₉×#124	C₂³	1	2	yes	complemented
169	C₁₉×#124	C₂³	1	4	yes	complemented
170	C₁₉×#124	C₂³	1	16	yes	complemented
171	C₁₉×#124	C₂³	1	2	yes	complemented
172	C₁₉×#124	C₂³	1	4	yes	complemented
173	C₁₉×#124	C₂³	1	16	yes	complemented
174	C₁₉×#124	C₂³	1	16	yes	complemented
175	C₁₉×#123	C₂³	1	4	yes	—
176	C₁₉×#123	C₂³	1	8	yes	—
177	C₁₉×#123	C₂³	1	4	yes	—
178	C₁₉×#123	C₂³	1	8	yes	—
179	C₁₉×#123	C₂³	1	8	yes	—
180	C₁₉×#123	C₂³	1	8	yes	—
181	C₁₉×#123	C₂³	1	16	yes	—
182	C₁₉×#123	C₂³	1	16	yes	complemented
183	C₁₉×#123	C₂³	1	8	yes	complemented
184	C₁₉×#123	C₂³	1	16	yes	complemented
185	C₁₉×#123	C₂³	1	8	yes	complemented
186	C₁₉×#123	C₂³	1	16	yes	complemented
187	C₁₉×#123	C₂³	1	16	yes	complemented
188	C₁₉×#123	C₂³	1	16	yes	complemented
189	C₁₉×#123	C₂³	1	16	yes	complemented
190	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
191	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
192	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	complemented
194	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	complemented
195	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	complemented
196	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	complemented
197	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	complemented
198	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	complemented
199	C₁₉×#121	C₂³	1	8	yes	—
200	C₁₉×#121	C₂³	1	8	yes	—
201	C₁₉×#121	C₂³	1	16	yes	—
202	C₁₉×#121	C₂³	1	4	yes	—
203	C₁₉×#121	C₂³	1	4	yes	—
204	C₁₉×#121	C₂³	1	8	yes	—
205	C₁₉×#121	C₂³	1	8	yes	—
206	C₁₉×#121	C₂³	1	8	yes	—
207	C₁₉×#121	C₂³	1	8	yes	—
208	C₁₉×#121	C₂³	1	8	yes	—
209	C₁₉×#121	C₂³	1	16	yes	—
210	C₁₉×#121	C₂³	1	16	yes	—
211	C₁₉×#121	C₂³	1	16	yes	—
212	C₁₉×#121	C₂³	1	16	yes	—
213	C₁₉×#121	C₂³	1	8	yes	complemented
214	C₁₉×#121	C₂³	1	16	yes	complemented
215	C₁₉×#121	C₂³	1	16	yes	complemented
216	C₁₉×#121	C₂³	1	8	yes	complemented
217	C₁₉×#121	C₂³	1	16	yes	complemented
218	C₁₉×#121	C₂³	1	16	yes	complemented
219	C₁₉×#121	C₂³	1	16	yes	complemented
220	C₁₉×#121	C₂³	1	16	yes	complemented
221	C₁₉×#121	C₂³	1	16	yes	complemented
222	C₁₉×#121	C₂³	1	16	yes	complemented
223	C₁₉×#120	C₂³	1	4	yes	—
224	C₁₉×#120	C₂³	1	4	yes	—
225	C₁₉×#120	C₂³	1	8	yes	—
226	C₁₉×#120	C₂³	1	16	yes	—
227	C₁₉×#120	C₂³	1	8	yes	—
228	C₁₉×#120	C₂³	1	16	yes	—
229	C₁₉×#120	C₂³	1	8	yes	—
230	C₁₉×#120	C₂³	1	8	yes	—
231	C₁₉×#120	C₂³	1	16	yes	—
232	C₁₉×#120	C₂³	1	8	yes	—
233	C₁₉×#120	C₂³	1	8	yes	—
234	C₁₉×#120	C₂³	1	16	yes	—
235	C₁₉×#120	C₂³	1	16	yes	complemented
236	C₁₉×#120	C₂³	1	16	yes	complemented
237	C₁₉×#120	C₂³	1	16	yes	complemented
238	C₄×Q₈×C₁₉	C₂³	1	4	yes	complemented
239	C₄×Q₈×C₁₉	C₂³	1	4	yes	complemented
240	C₄×Q₈×C₁₉	C₂³	1	8	yes	complemented
241	C₄×Q₈×C₁₉	C₂³	1	8	yes	complemented
242	C₄×D₄×C₁₉	C₂³	1	8	yes	—
243	C₄×D₄×C₁₉	C₂³	1	8	yes	—
244	C₄×D₄×C₁₉	C₂³	1	8	yes	—
245	C₄×D₄×C₁₉	C₂³	1	8	yes	—
246	C₄×D₄×C₁₉	C₂³	1	8	yes	—
247	C₄×D₄×C₁₉	C₂³	1	8	yes	—
248	C₄×D₄×C₁₉	C₂³	1	4	yes	complemented
249	C₄×D₄×C₁₉	C₂³	1	4	yes	complemented
250	C₄×D₄×C₁₉	C₂³	1	8	yes	complemented
251	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
252	C₄×D₄×C₁₉	C₂³	1	8	yes	complemented
253	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
254	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
255	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
256	C₄×D₄×C₁₉	C₂³	1	16	yes	complemented
257	C₁₉×#117	C₂³	1	4	yes	—
258	C₁₉×#117	C₂³	1	4	yes	—
259	C₁₉×#117	C₂³	1	2	yes	—
260	C₁₉×#117	C₂³	1	2	yes	—
261	C₁₉×#117	C₂³	1	4	yes	—
262	C₁₉×#117	C₂³	1	4	yes	complemented
263	C₁₉×#117	C₂³	1	4	yes	complemented
264	C₁₉×#117	C₂³	1	16	yes	complemented
265	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	complemented
267	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
269	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
270	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
271	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
272	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	complemented
273	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	complemented
274	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
275	C₂×C₄²×C₁₉	C₂³	1	4	yes	complemented
276	C₂×C₄²×C₁₉	C₂³	1	4	yes	complemented
277	C₂⁴×C₁₉	—	4	4	no	—
278	C₂⁴×C₁₉	—	8	4	no	—
279	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
280	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
282	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
283	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
284	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
285	#41×C₁₉	—	2	8	no	—
286	#41×C₁₉	—	2	8	no	—
287	#41×C₁₉	—	4	8	no	—
288	#41×C₁₉	—	4	16	no	—
289	#41×C₁₉	—	4	8	no	—
290	#41×C₁₉	—	4	8	no	—
291	#41×C₁₉	—	4	8	no	—
292	#41×C₁₉	—	4	8	no	—
293	#41×C₁₉	—	8	16	no	—
294	C₂×Q₈×C₁₉	—	2	4	no	—
295	C₂×Q₈×C₁₉	—	4	8	no	—
296	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
297	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
299	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
300	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
301	C₂×D₄×C₁₉	—	2	8	no	—
302	C₂×D₄×C₁₉	—	2	4	no	—
303	C₂×D₄×C₁₉	—	4	16	no	—
304	C₂×D₄×C₁₉	—	4	8	no	—
305	C₂×D₄×C₁₉	—	4	8	no	—
306	C₂×D₄×C₁₉	—	4	8	no	—
307	C₂×D₄×C₁₉	—	4	4	no	—
308	C₂×D₄×C₁₉	—	4	4	no	—
309	C₂×D₄×C₁₉	—	4	8	no	—
310	C₂×D₄×C₁₉	—	4	16	no	—
311	C₂×D₄×C₁₉	—	8	8	no	—
312	C₂×D₄×C₁₉	—	8	16	no	—
313	C₂×D₄×C₁₉	—	8	16	no	—
314	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
315	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
316	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
317	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
318	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
319	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
320	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
321	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
322	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
323	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
324	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
325	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
326	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
327	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
328	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
329	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
330	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
331	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
332	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
333	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
334	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
335	C₂²×C₄×C₁₉	—	2	4	no	—
336	C₂²×C₄×C₁₉	—	4	4	no	—
337	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
338	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
339	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
344	C₂²×C₄×C₁₉	C₂⁴	1	8	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	8	yes	—
349	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
350	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
351	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
352	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
353	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
354	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
356	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
357	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
359	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
360	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
361	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
363	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
364	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
365	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
366	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
367	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
368	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
369	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
370	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
371	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
372	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
373	C₂²⋊C₄×C₁₉	C₂⁴	1	2	yes	—
374	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
375	C₂²⋊C₄×C₁₉	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
377	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
378	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
379	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
381	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
382	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
383	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
384	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
385	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
387	C₂²⋊C₄×C₁₉	C₂⁴	1	8	yes	—
388	C₄²×C₁₉	C₂⁴	1	2	yes	—
389	C₄²×C₁₉	C₂⁴	1	2	yes	—
390	C₄²×C₁₉	C₂⁴	1	4	yes	—
391	C₄²×C₁₉	C₂⁴	1	4	yes	—
392	C₄²×C₁₉	C₂⁴	1	4	yes	—
393	C₄²×C₁₉	C₂⁴	1	8	yes	—
394	C₄²×C₁₉	C₂⁴	1	8	yes	—
395	C₄²×C₁₉	C₂⁴	1	8	yes	—
396	#62876	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
397	C₂³×C₁₉	—	2	2	no	—
398	C₂³×C₁₉	—	2	4	no	—
399	C₂³×C₁₉	—	2	8	no	—
400	C₂³×C₁₉	—	4	2	no	—
401	C₂³×C₁₉	—	4	8	no	—
402	C₂³×C₁₉	—	4	4	no	—
403	C₂³×C₁₉	—	4	8	no	—
404	C₂³×C₁₉	—	4	16	no	—
405	C₂³×C₁₉	—	4	8	no	—
406	C₂³×C₁₉	—	4	4	no	—
407	C₂³×C₁₉	—	4	16	no	—
408	C₂³×C₁₉	—	4	8	no	—
409	C₂³×C₁₉	—	8	16	no	—
410	C₂³×C₁₉	C₂⁵	1	2	yes	—
411	C₂³×C₁₉	C₂⁵	1	4	yes	—
412	C₂³×C₁₉	C₂⁵	1	8	yes	—
413	C₂³×C₁₉	C₂⁵	1	4	yes	—
414	C₂³×C₁₉	C₂⁵	1	4	yes	—
415	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
416	Q₈×C₁₉	—	2	8	no	—
417	Q₈×C₁₉	—	2	4	no	—
418	Q₈×C₁₉	—	2	4	no	—
419	Q₈×C₁₉	—	4	4	no	—
420	Q₈×C₁₉	—	4	8	no	—
421	D₄×C₁₉	—	2	8	no	—
422	D₄×C₁₉	—	2	8	no	—
423	D₄×C₁₉	—	2	8	no	—
424	D₄×C₁₉	—	2	8	no	—
425	D₄×C₁₉	—	2	8	no	—
426	D₄×C₁₉	—	2	4	no	—
427	D₄×C₁₉	—	2	4	no	—
428	D₄×C₁₉	—	4	8	no	—
429	D₄×C₁₉	—	4	8	no	—
430	D₄×C₁₉	—	4	8	no	—
431	D₄×C₁₉	—	4	8	no	—
432	D₄×C₁₉	—	4	8	no	—
433	D₄×C₁₉	—	4	8	no	—
434	D₄×C₁₉	—	4	16	no	—
435	D₄×C₁₉	—	4	8	no	—
436	D₄×C₁₉	—	4	8	no	—
437	D₄×C₁₉	—	4	16	no	—
438	D₄×C₁₉	—	4	16	no	—
439	D₄×C₁₉	—	4	16	no	—
440	D₄×C₁₉	—	4	16	no	—
441	D₄×C₁₉	—	4	4	no	—
442	C₂×C₄×C₁₉	—	2	2	no	—
443	C₂×C₄×C₁₉	—	2	4	no	—
444	C₂×C₄×C₁₉	—	2	8	no	—
445	C₂×C₄×C₁₉	—	2	8	no	—
446	C₂×C₄×C₁₉	—	2	8	no	—
447	C₂×C₄×C₁₉	—	4	8	no	—
448	C₂×C₄×C₁₉	—	4	4	no	—
449	C₂×C₄×C₁₉	—	4	8	no	—
450	C₂×C₄×C₁₉	—	4	8	no	—
451	C₂×C₄×C₁₉	—	4	4	no	—
452	C₂×C₄×C₁₉	—	4	16	no	—
453	C₂×C₄×C₁₉	—	4	8	no	—
454	C₂×C₄×C₁₉	—	4	8	no	—
455	C₂×C₄×C₁₉	—	4	8	no	—
456	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
457	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
458	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
459	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
460	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
461	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
462	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
463	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
464	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
465	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
466	#3562	C₂×C₁₉	1	8	yes	complemented
467	#3558	C₂×C₁₉	1	8	yes	complemented
468	#3546	C₂×C₁₉	1	8	yes	complemented
469	#3543	C₂×C₁₉	1	8	yes	complemented
470	#3534	C₂×C₁₉	1	8	yes	complemented
471	#3532	C₂×C₁₉	1	8	yes	complemented
472	#3510	C₂×C₁₉	1	2	yes	complemented
473	#3508	C₂×C₁₉	1	2	yes	complemented
474	#3500	C₂×C₁₉	1	2	yes	complemented
475	#3498	C₂×C₁₉	1	2	yes	complemented
476	#3487	C₂×C₁₉	1	1	yes	characteristic, complemented
477	#3485	C₂×C₁₉	1	1	yes	characteristic, complemented
478	#3484	C₂×C₁₉	1	2	yes	complemented
479	#3455	C₂×C₁₉	1	2	yes	complemented
480	C₂×#535	C₂×C₁₉	1	1	yes	characteristic, complemented
481	C₂²×C₁₉	—	2	2	no	—
482	C₂²×C₁₉	—	2	2	no	—
483	C₂²×C₁₉	—	2	4	no	—
484	C₂²×C₁₉	—	2	4	no	—
485	C₂²×C₁₉	—	2	4	no	—
486	C₂²×C₁₉	—	2	8	no	—
487	C₂²×C₁₉	—	2	8	no	—
488	C₂²×C₁₉	—	2	8	no	—
489	C₂²×C₁₉	—	2	16	no	—
490	C₂²×C₁₉	—	2	8	no	—
491	C₂²×C₁₉	—	2	4	no	—
492	C₂²×C₁₉	—	4	4	no	—
493	C₂²×C₁₉	—	8	4	no	—
494	C₂²×C₁₉	—	8	8	no	—
495	C₂²×C₁₉	—	8	16	no	—
496	C₂²×C₁₉	—	16	8	no	—
497	C₂²×C₁₉	—	16	4	no	—
498	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
499	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
500	C₄×C₁₉	—	2	2	no	—
501	C₄×C₁₉	—	2	4	no	—
502	C₄×C₁₉	—	2	4	no	—
503	C₄×C₁₉	—	2	4	no	—
504	C₄×C₁₉	—	2	8	no	—
505	C₄×C₁₉	—	2	4	no	—
506	C₄×C₁₉	—	2	8	no	—
507	C₄×C₁₉	—	2	4	no	—
508	C₄×C₁₉	C₂×H(5,𝔽₂)	1	4	yes	—
509	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic, complemented
510	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	2	yes	complemented
511	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic, complemented
512	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic, complemented
513	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
514	#562	C₂²×C₁₉	1	16	yes	complemented
515	H(3,𝔽₄)	C₂²×C₁₉	1	8	yes	complemented
516	#560	C₂²×C₁₉	1	16	yes	complemented
517	#560	C₂²×C₁₉	1	8	yes	complemented
518	#560	C₂²×C₁₉	1	16	yes	complemented
519	#559	C₂²×C₁₉	1	8	yes	complemented
520	#559	C₂²×C₁₉	1	8	yes	complemented
521	#556	C₂²×C₁₉	1	8	yes	complemented
522	#553	C₂²×C₁₉	1	16	yes	complemented
523	#551	C₂²×C₁₉	1	16	yes	complemented
524	#551	C₂²×C₁₉	1	8	yes	complemented
525	#550	C₂²×C₁₉	1	8	yes	complemented
526	#550	C₂²×C₁₉	1	8	yes	complemented
527	#550	C₂²×C₁₉	1	8	yes	complemented
528	#548	C₂²×C₁₉	1	8	yes	complemented
529	#548	C₂²×C₁₉	1	8	yes	complemented
530	#547	C₂²×C₁₉	1	8	yes	complemented
531	#546	C₂²×C₁₉	1	8	yes	complemented
532	#546	C₂²×C₁₉	1	8	yes	complemented
533	#546	C₂²×C₁₉	1	16	yes	complemented
534	#546	C₂²×C₁₉	1	16	yes	complemented
535	#546	C₂²×C₁₉	1	16	yes	complemented
536	#546	C₂²×C₁₉	1	8	yes	complemented
537	#546	C₂²×C₁₉	1	16	yes	complemented
538	#546	C₂²×C₁₉	1	8	yes	complemented
539	D₄²	C₂²×C₁₉	1	8	yes	complemented
540	D₄²	C₂²×C₁₉	1	8	yes	complemented
541	D₄²	C₂²×C₁₉	1	16	yes	complemented
542	D₄²	C₂²×C₁₉	1	8	yes	complemented
543	D₄²	C₂²×C₁₉	1	8	yes	complemented
544	#542	C₂²×C₁₉	1	4	yes	complemented
545	#542	C₂²×C₁₉	1	4	yes	complemented
546	#542	C₂²×C₁₉	1	8	yes	complemented
547	#541	C₂²×C₁₉	1	4	yes	complemented
548	#540	C₂²×C₁₉	1	4	yes	complemented
549	#540	C₂²×C₁₉	1	8	yes	complemented
550	#540	C₂²×C₁₉	1	16	yes	complemented
551	#539	C₂²×C₁₉	1	8	yes	complemented
552	#539	C₂²×C₁₉	1	8	yes	complemented
553	#538	C₂²×C₁₉	1	8	yes	complemented
554	#538	C₂²×C₁₉	1	16	yes	complemented
555	#538	C₂²×C₁₉	1	16	yes	complemented
556	#538	C₂²×C₁₉	1	16	yes	complemented
557	#538	C₂²×C₁₉	1	8	yes	complemented
558	#537	C₂²×C₁₉	1	8	yes	complemented
559	#536	C₂²×C₁₉	1	2	yes	complemented
560	#536	C₂²×C₁₉	1	4	yes	complemented
561	#535	C₂²×C₁₉	1	2	yes	—
562	#535	C₂²×C₁₉	1	8	yes	complemented
563	#535	C₂²×C₁₉	1	8	yes	complemented
564	#535	C₂²×C₁₉	1	2	yes	complemented
565	#535	C₂²×C₁₉	1	4	yes	complemented
566	#535	C₂²×C₁₉	1	2	yes	complemented
567	#535	C₂²×C₁₉	1	16	yes	complemented
568	#535	C₂²×C₁₉	1	4	yes	complemented
569	#535	C₂²×C₁₉	1	4	yes	complemented
570	#535	C₂²×C₁₉	1	4	yes	complemented
571	#534	C₂²×C₁₉	1	8	yes	complemented
572	#534	C₂²×C₁₉	1	4	yes	complemented
573	#534	C₂²×C₁₉	1	16	yes	complemented
574	#534	C₂²×C₁₉	1	8	yes	complemented
575	#533	C₂²×C₁₉	1	2	yes	complemented
576	#532	C₂²×C₁₉	1	2	yes	complemented
577	#532	C₂²×C₁₉	1	8	yes	complemented
578	#532	C₂²×C₁₉	1	4	yes	complemented
579	#532	C₂²×C₁₉	1	4	yes	complemented
580	C₂×#127	C₂²×C₁₉	1	2	yes	complemented
581	C₂×#127	C₂²×C₁₉	1	4	yes	complemented
582	#529	C₂²×C₁₉	1	8	yes	complemented
583	#529	C₂²×C₁₉	1	8	yes	complemented
584	#529	C₂²×C₁₉	1	8	yes	complemented
585	C₂×#124	C₂²×C₁₉	1	2	yes	complemented
586	C₂×#124	C₂²×C₁₉	1	4	yes	complemented
587	#525	C₂²×C₁₉	1	2	yes	complemented
588	#525	C₂²×C₁₉	1	2	yes	complemented
589	#525	C₂²×C₁₉	1	4	yes	complemented
590	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
591	C₂×#121	C₂²×C₁₉	1	4	yes	complemented
592	C₂×#120	C₂²×C₁₉	1	4	yes	complemented
593	C₂×#120	C₂²×C₁₉	1	8	yes	complemented
594	#519	C₂²×C₁₉	1	1	yes	characteristic, complemented
595	#518	C₂²×C₁₉	1	2	yes	complemented
596	#518	C₂²×C₁₉	1	1	yes	characteristic, complemented
597	C₄×#41	C₂²×C₁₉	1	2	yes	complemented
598	C₄×#41	C₂²×C₁₉	1	2	yes	complemented
599	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
600	C₂×C₁₉	—	2	2	no	—
601	C₂×C₁₉	—	4	2	no	—
602	C₂×C₁₉	—	4	8	no	—
603	C₂×C₁₉	—	4	4	no	—
604	C₂×C₁₉	—	4	4	no	—
605	C₂×C₁₉	—	4	4	no	—
606	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂×C₁₉	H(7,𝔽₂)	1	2	yes	—
608	C₂⁵	C₂³×C₁₉	1	2	yes	—
609	2₋¹⁺⁴	—	4	4	no	—
610	H(5,𝔽₂)	—	4	8	no	—
611	H(5,𝔽₂)	—	4	4	no	—
612	C₂×#41	—	4	4	no	—
613	C₂×#41	C₂³×C₁₉	1	2	yes	—
614	C₂×#41	C₂³×C₁₉	1	2	yes	—
615	C₂×#41	C₂³×C₁₉	1	4	yes	—
616	C₂×#41	C₂³×C₁₉	1	4	yes	—
617	C₂×#41	C₂³×C₁₉	1	4	yes	—
618	C₂×#41	C₂³×C₁₉	1	8	yes	—
619	C₂×#41	C₂³×C₁₉	1	4	yes	complemented
620	C₂×#41	C₂³×C₁₉	1	4	yes	complemented
621	C₂×#41	C₂³×C₁₉	1	16	yes	complemented
622	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
623	C₂²×Q₈	C₂³×C₁₉	1	4	yes	complemented
624	C₂²×D₄	—	4	4	no	—
625	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
626	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
627	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
628	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
629	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
630	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
631	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
632	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
633	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
634	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
635	C₂²×D₄	C₂³×C₁₉	1	16	yes	—
636	C₂²×D₄	C₂³×C₁₉	1	4	yes	complemented
637	C₂²×D₄	C₂³×C₁₉	1	16	yes	complemented
638	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
640	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	complemented
641	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	complemented
642	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	complemented
643	#127	C₂³×C₁₉	1	4	yes	—
644	#127	C₂³×C₁₉	1	4	yes	—
645	#127	C₂³×C₁₉	1	4	yes	—
646	#127	C₂³×C₁₉	1	8	yes	—
647	#127	C₂³×C₁₉	1	4	yes	—
648	#127	C₂³×C₁₉	1	8	yes	—
649	#127	C₂³×C₁₉	1	2	yes	complemented
650	#127	C₂³×C₁₉	1	4	yes	complemented
651	#127	C₂³×C₁₉	1	16	yes	complemented
652	#126	C₂³×C₁₉	1	8	yes	—
653	#126	C₂³×C₁₉	1	8	yes	—
654	#126	C₂³×C₁₉	1	8	yes	complemented
655	#126	C₂³×C₁₉	1	16	yes	complemented
656	#126	C₂³×C₁₉	1	8	yes	complemented
657	#126	C₂³×C₁₉	1	16	yes	complemented
658	#125	C₂³×C₁₉	1	4	yes	complemented
659	#125	C₂³×C₁₉	1	8	yes	complemented
660	#125	C₂³×C₁₉	1	8	yes	complemented
661	#124	C₂³×C₁₉	1	4	yes	—
662	#124	C₂³×C₁₉	1	4	yes	—
663	#124	C₂³×C₁₉	1	8	yes	—
664	#124	C₂³×C₁₉	1	4	yes	—
665	#124	C₂³×C₁₉	1	8	yes	—
666	#124	C₂³×C₁₉	1	8	yes	—
667	#124	C₂³×C₁₉	1	4	yes	—
668	#124	C₂³×C₁₉	1	8	yes	—
669	#124	C₂³×C₁₉	1	2	yes	complemented
670	#124	C₂³×C₁₉	1	4	yes	complemented
671	#124	C₂³×C₁₉	1	16	yes	complemented
672	#124	C₂³×C₁₉	1	2	yes	complemented
673	#124	C₂³×C₁₉	1	4	yes	complemented
674	#124	C₂³×C₁₉	1	16	yes	complemented
675	#124	C₂³×C₁₉	1	16	yes	complemented
676	#123	C₂³×C₁₉	1	4	yes	—
677	#123	C₂³×C₁₉	1	8	yes	—
678	#123	C₂³×C₁₉	1	4	yes	—
679	#123	C₂³×C₁₉	1	8	yes	—
680	#123	C₂³×C₁₉	1	8	yes	—
681	#123	C₂³×C₁₉	1	8	yes	—
682	#123	C₂³×C₁₉	1	16	yes	—
683	#123	C₂³×C₁₉	1	16	yes	complemented
684	#123	C₂³×C₁₉	1	8	yes	complemented
685	#123	C₂³×C₁₉	1	16	yes	complemented
686	#123	C₂³×C₁₉	1	8	yes	complemented
687	#123	C₂³×C₁₉	1	16	yes	complemented
688	#123	C₂³×C₁₉	1	16	yes	complemented
689	#123	C₂³×C₁₉	1	16	yes	complemented
690	#123	C₂³×C₁₉	1	16	yes	complemented
691	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
692	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
693	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
694	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	complemented
695	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	complemented
696	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	complemented
697	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	complemented
698	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
699	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	complemented
700	#121	C₂³×C₁₉	1	8	yes	—
701	#121	C₂³×C₁₉	1	8	yes	—
702	#121	C₂³×C₁₉	1	16	yes	—
703	#121	C₂³×C₁₉	1	4	yes	—
704	#121	C₂³×C₁₉	1	4	yes	—
705	#121	C₂³×C₁₉	1	8	yes	—
706	#121	C₂³×C₁₉	1	8	yes	—
707	#121	C₂³×C₁₉	1	8	yes	—
708	#121	C₂³×C₁₉	1	8	yes	—
709	#121	C₂³×C₁₉	1	8	yes	—
710	#121	C₂³×C₁₉	1	16	yes	—
711	#121	C₂³×C₁₉	1	16	yes	—
712	#121	C₂³×C₁₉	1	16	yes	—
713	#121	C₂³×C₁₉	1	16	yes	—
714	#121	C₂³×C₁₉	1	8	yes	complemented
715	#121	C₂³×C₁₉	1	16	yes	complemented
716	#121	C₂³×C₁₉	1	16	yes	complemented
717	#121	C₂³×C₁₉	1	8	yes	complemented
718	#121	C₂³×C₁₉	1	16	yes	complemented
719	#121	C₂³×C₁₉	1	16	yes	complemented
720	#121	C₂³×C₁₉	1	16	yes	complemented
721	#121	C₂³×C₁₉	1	16	yes	complemented
722	#121	C₂³×C₁₉	1	16	yes	complemented
723	#121	C₂³×C₁₉	1	16	yes	complemented
724	#120	C₂³×C₁₉	1	4	yes	—
725	#120	C₂³×C₁₉	1	4	yes	—
726	#120	C₂³×C₁₉	1	8	yes	—
727	#120	C₂³×C₁₉	1	16	yes	—
728	#120	C₂³×C₁₉	1	8	yes	—
729	#120	C₂³×C₁₉	1	16	yes	—
730	#120	C₂³×C₁₉	1	8	yes	—
731	#120	C₂³×C₁₉	1	8	yes	—
732	#120	C₂³×C₁₉	1	16	yes	—
733	#120	C₂³×C₁₉	1	8	yes	—
734	#120	C₂³×C₁₉	1	8	yes	—
735	#120	C₂³×C₁₉	1	16	yes	—
736	#120	C₂³×C₁₉	1	16	yes	complemented
737	#120	C₂³×C₁₉	1	16	yes	complemented
738	#120	C₂³×C₁₉	1	16	yes	complemented
739	C₄×Q₈	C₂³×C₁₉	1	4	yes	complemented
740	C₄×Q₈	C₂³×C₁₉	1	4	yes	complemented
741	C₄×Q₈	C₂³×C₁₉	1	8	yes	complemented
742	C₄×Q₈	C₂³×C₁₉	1	8	yes	complemented
743	C₄×D₄	C₂³×C₁₉	1	8	yes	—
744	C₄×D₄	C₂³×C₁₉	1	8	yes	—
745	C₄×D₄	C₂³×C₁₉	1	8	yes	—
746	C₄×D₄	C₂³×C₁₉	1	8	yes	—
747	C₄×D₄	C₂³×C₁₉	1	8	yes	—
748	C₄×D₄	C₂³×C₁₉	1	8	yes	—
749	C₄×D₄	C₂³×C₁₉	1	4	yes	complemented
750	C₄×D₄	C₂³×C₁₉	1	4	yes	complemented
751	C₄×D₄	C₂³×C₁₉	1	8	yes	complemented
752	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
753	C₄×D₄	C₂³×C₁₉	1	8	yes	complemented
754	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
755	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
756	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
757	C₄×D₄	C₂³×C₁₉	1	16	yes	complemented
758	#117	C₂³×C₁₉	1	4	yes	—
759	#117	C₂³×C₁₉	1	4	yes	—
760	#117	C₂³×C₁₉	1	2	yes	—
761	#117	C₂³×C₁₉	1	2	yes	—
762	#117	C₂³×C₁₉	1	4	yes	—
763	#117	C₂³×C₁₉	1	4	yes	complemented
764	#117	C₂³×C₁₉	1	4	yes	complemented
765	#117	C₂³×C₁₉	1	16	yes	complemented
766	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
767	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	complemented
768	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	complemented
774	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	complemented
775	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
776	C₂×C₄²	C₂³×C₁₉	1	4	yes	complemented
777	C₂×C₄²	C₂³×C₁₉	1	4	yes	complemented
778	C₁₉	#62876	1	1	yes	characteristic, direct product factor, Sylow
779	C₂⁴	—	4	4	no	—
780	C₂⁴	—	8	4	no	—
781	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
782	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
783	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
784	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
785	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
786	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
787	#41	—	2	8	no	—
788	#41	—	2	8	no	—
789	#41	—	4	8	no	—
790	#41	—	4	16	no	—
791	#41	—	4	8	no	—
792	#41	—	4	8	no	—
793	#41	—	4	8	no	—
794	#41	—	4	8	no	—
795	#41	—	8	16	no	—
796	C₂×Q₈	—	2	4	no	—
797	C₂×Q₈	—	4	8	no	—
798	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
799	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
800	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
801	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
802	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
803	C₂×D₄	—	2	8	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	4	16	no	—
806	C₂×D₄	—	4	8	no	—
807	C₂×D₄	—	4	8	no	—
808	C₂×D₄	—	4	8	no	—
809	C₂×D₄	—	4	4	no	—
810	C₂×D₄	—	4	4	no	—
811	C₂×D₄	—	4	8	no	—
812	C₂×D₄	—	4	16	no	—
813	C₂×D₄	—	8	8	no	—
814	C₂×D₄	—	8	16	no	—
815	C₂×D₄	—	8	16	no	—
816	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
817	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
818	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
819	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
820	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
821	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
822	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
823	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
824	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
825	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
826	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
827	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
828	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
829	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
830	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
831	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
832	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
833	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
834	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
835	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
836	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	4	4	no	—
839	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
841	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
844	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
845	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
846	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
847	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
848	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
849	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
850	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
851	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
852	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
853	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
854	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
856	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
859	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
860	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
861	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
862	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
863	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
864	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
865	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
866	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
867	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
868	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
869	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
870	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
871	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
872	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
873	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
874	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
875	C₂²⋊C₄	C₂⁴×C₁₉	1	2	yes	—
876	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
877	C₂²⋊C₄	C₂⁴×C₁₉	1	2	yes	—
878	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
879	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
880	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
881	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
882	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
883	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
884	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
885	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
886	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
887	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
888	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
889	C₂²⋊C₄	C₂⁴×C₁₉	1	8	yes	—
890	C₄²	C₂⁴×C₁₉	1	2	yes	—
891	C₄²	C₂⁴×C₁₉	1	2	yes	—
892	C₄²	C₂⁴×C₁₉	1	4	yes	—
893	C₄²	C₂⁴×C₁₉	1	4	yes	—
894	C₄²	C₂⁴×C₁₉	1	4	yes	—
895	C₄²	C₂⁴×C₁₉	1	8	yes	—
896	C₄²	C₂⁴×C₁₉	1	8	yes	—
897	C₄²	C₂⁴×C₁₉	1	8	yes	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	4	no	—
900	C₂³	—	2	8	no	—
901	C₂³	—	4	2	no	—
902	C₂³	—	4	8	no	—
903	C₂³	—	4	4	no	—
904	C₂³	—	4	8	no	—
905	C₂³	—	4	16	no	—
906	C₂³	—	4	8	no	—
907	C₂³	—	4	4	no	—
908	C₂³	—	4	16	no	—
909	C₂³	—	4	8	no	—
910	C₂³	—	8	16	no	—
911	C₂³	C₂⁵×C₁₉	1	2	yes	—
912	C₂³	C₂⁵×C₁₉	1	4	yes	—
913	C₂³	C₂⁵×C₁₉	1	8	yes	—
914	C₂³	C₂⁵×C₁₉	1	4	yes	—
915	C₂³	C₂⁵×C₁₉	1	4	yes	—
916	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
917	Q₈	—	2	8	no	—
918	Q₈	—	2	4	no	—
919	Q₈	—	2	4	no	—
920	Q₈	—	4	4	no	—
921	Q₈	—	4	8	no	—
922	D₄	—	2	8	no	—
923	D₄	—	2	8	no	—
924	D₄	—	2	8	no	—
925	D₄	—	2	8	no	—
926	D₄	—	2	8	no	—
927	D₄	—	2	4	no	—
928	D₄	—	2	4	no	—
929	D₄	—	4	8	no	—
930	D₄	—	4	8	no	—
931	D₄	—	4	8	no	—
932	D₄	—	4	8	no	—
933	D₄	—	4	8	no	—
934	D₄	—	4	8	no	—
935	D₄	—	4	16	no	—
936	D₄	—	4	8	no	—
937	D₄	—	4	8	no	—
938	D₄	—	4	16	no	—
939	D₄	—	4	16	no	—
940	D₄	—	4	16	no	—
941	D₄	—	4	16	no	—
942	D₄	—	4	4	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	4	no	—
945	C₂×C₄	—	2	8	no	—
946	C₂×C₄	—	2	8	no	—
947	C₂×C₄	—	2	8	no	—
948	C₂×C₄	—	4	8	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	—	4	8	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	16	no	—
954	C₂×C₄	—	4	8	no	—
955	C₂×C₄	—	4	8	no	—
956	C₂×C₄	—	4	8	no	—
957	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
958	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
959	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
960	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
961	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
962	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
963	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
964	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
965	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
966	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	4	no	—
970	C₂²	—	2	4	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	8	no	—
973	C₂²	—	2	8	no	—
974	C₂²	—	2	8	no	—
975	C₂²	—	2	16	no	—
976	C₂²	—	2	8	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	4	4	no	—
979	C₂²	—	8	8	no	—
980	C₂²	—	8	4	no	—
981	C₂²	—	8	16	no	—
982	C₂²	—	16	8	no	—
983	C₂²	—	16	4	no	—
984	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
985	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
986	C₄	—	2	2	no	—
987	C₄	—	2	4	no	—
988	C₄	—	2	4	no	—
989	C₄	—	2	4	no	—
990	C₄	—	2	8	no	—
991	C₄	—	2	4	no	—
992	C₄	—	2	8	no	—
993	C₄	—	2	4	no	—
994	C₄	C₂×C₁₉×H(5,𝔽₂)	1	4	yes	—
995	C₂	—	2	2	no	—
996	C₂	—	4	2	no	—
997	C₂	—	4	8	no	—
998	C₂	—	4	4	no	—
999	C₂	—	4	4	no	—
1000	C₂	—	4	4	no	—
1001	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
1002	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×#3562	C₂	semidirect
2. C₁₉×#3558	C₂	semidirect
3. C₁₉×#3546	C₂	semidirect
4. C₁₉×#3543	C₂	semidirect
5. C₁₉×#3534	C₂	semidirect
6. C₁₉×#3532	C₂	semidirect
7. C₁₉×#3510	C₂	semidirect
8. C₁₉×#3508	C₂	semidirect
9. C₁₉×#3500	C₂	semidirect
10. C₁₉×#3498	C₂	semidirect
11. C₁₉×#3487	C₂	semidirect
12. C₁₉×#3485	C₂	semidirect
13. C₁₉×#3484	C₂	semidirect
14. C₁₉×#3455	C₂	semidirect
15. C₂×C₁₉×#535	C₂	semidirect
16. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
17. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
19. C₂²×#41×C₁₉	C₂²	semidirect
20. C₂³×D₄×C₁₉	C₂²	semidirect
21. C₁₉×#562	C₂²	semidirect
22. C₁₉×H(3,𝔽₄)	C₂²	semidirect
23. C₁₉×#560	C₂²	semidirect
24. C₁₉×#560	C₂²	semidirect
25. C₁₉×#560	C₂²	semidirect
26. C₁₉×#559	C₂²	semidirect
27. C₁₉×#559	C₂²	semidirect
28. C₁₉×#556	C₂²	semidirect
29. C₁₉×#553	C₂²	semidirect
30. C₁₉×#551	C₂²	semidirect
31. C₁₉×#551	C₂²	semidirect
32. C₁₉×#550	C₂²	semidirect
33. C₁₉×#550	C₂²	semidirect
34. C₁₉×#550	C₂²	semidirect
35. C₁₉×#548	C₂²	semidirect
36. C₁₉×#548	C₂²	semidirect
37. C₁₉×#547	C₂²	semidirect
38. C₁₉×#546	C₂²	semidirect
39. C₁₉×#546	C₂²	semidirect
40. C₁₉×#546	C₂²	semidirect
41. C₁₉×#546	C₂²	semidirect
42. C₁₉×#546	C₂²	semidirect
43. C₁₉×#546	C₂²	semidirect
44. C₁₉×#546	C₂²	semidirect
45. C₁₉×#546	C₂²	semidirect
46. D₄²×C₁₉	C₂²	semidirect
47. D₄²×C₁₉	C₂²	semidirect
48. D₄²×C₁₉	C₂²	semidirect
49. D₄²×C₁₉	C₂²	semidirect
50. D₄²×C₁₉	C₂²	semidirect
51. C₁₉×#542	C₂²	semidirect
52. C₁₉×#542	C₂²	semidirect
53. C₁₉×#542	C₂²	semidirect
54. C₁₉×#541	C₂²	semidirect
55. C₁₉×#540	C₂²	semidirect
56. C₁₉×#540	C₂²	semidirect
57. C₁₉×#540	C₂²	semidirect
58. C₁₉×#539	C₂²	semidirect
59. C₁₉×#539	C₂²	semidirect
60. C₁₉×#538	C₂²	semidirect
61. C₁₉×#538	C₂²	semidirect
62. C₁₉×#538	C₂²	semidirect
63. C₁₉×#538	C₂²	semidirect
64. C₁₉×#538	C₂²	semidirect
65. C₁₉×#537	C₂²	semidirect
66. C₁₉×#536	C₂²	semidirect
67. C₁₉×#536	C₂²	semidirect
69. C₁₉×#535	C₂²	semidirect
70. C₁₉×#535	C₂²	semidirect
71. C₁₉×#535	C₂²	semidirect
72. C₁₉×#535	C₂²	semidirect
73. C₁₉×#535	C₂²	semidirect
74. C₁₉×#535	C₂²	semidirect
75. C₁₉×#535	C₂²	semidirect
76. C₁₉×#535	C₂²	semidirect
77. C₁₉×#535	C₂²	semidirect
78. C₁₉×#534	C₂²	semidirect
79. C₁₉×#534	C₂²	semidirect
80. C₁₉×#534	C₂²	semidirect
81. C₁₉×#534	C₂²	semidirect
82. C₁₉×#533	C₂²	semidirect
83. C₁₉×#532	C₂²	semidirect
84. C₁₉×#532	C₂²	semidirect
85. C₁₉×#532	C₂²	semidirect
86. C₁₉×#532	C₂²	semidirect
87. C₂×C₁₉×#127	C₂²	semidirect
88. C₂×C₁₉×#127	C₂²	semidirect
89. C₁₉×#529	C₂²	semidirect
90. C₁₉×#529	C₂²	semidirect
91. C₁₉×#529	C₂²	semidirect
92. C₂×C₁₉×#124	C₂²	semidirect
93. C₂×C₁₉×#124	C₂²	semidirect
94. C₁₉×#525	C₂²	semidirect
95. C₁₉×#525	C₂²	semidirect
96. C₁₉×#525	C₂²	semidirect
97. C₂×C₁₉×#123	C₂²	semidirect
98. C₂×C₁₉×#121	C₂²	semidirect
99. C₂×C₁₉×#120	C₂²	semidirect
100. C₂×C₁₉×#120	C₂²	semidirect
101. C₁₉×#519	C₂²	semidirect
102. C₁₉×#518	C₂²	semidirect
103. C₁₉×#518	C₂²	semidirect
104. C₄×#41×C₁₉	C₂²	semidirect
105. C₄×#41×C₁₉	C₂²	semidirect
106. C₂×C₁₉×#117	C₂²	semidirect
118. C₂×#41×C₁₉	C₂³	semidirect
119. C₂×#41×C₁₉	C₂³	semidirect
120. C₂×#41×C₁₉	C₂³	semidirect
122. C₂²×Q₈×C₁₉	C₂³	semidirect
135. C₂²×D₄×C₁₉	C₂³	semidirect
136. C₂²×D₄×C₁₉	C₂³	semidirect
139. C₁₉×C₄⋊Q₈	C₂³	semidirect
140. C₁₉×C₄⋊Q₈	C₂³	semidirect
141. C₁₉×C₄⋊Q₈	C₂³	semidirect
148. C₁₉×#127	C₂³	semidirect
149. C₁₉×#127	C₂³	semidirect
150. C₁₉×#127	C₂³	semidirect
153. C₁₉×#126	C₂³	semidirect
154. C₁₉×#126	C₂³	semidirect
155. C₁₉×#126	C₂³	semidirect
156. C₁₉×#126	C₂³	semidirect
157. C₁₉×#125	C₂³	semidirect
158. C₁₉×#125	C₂³	semidirect
159. C₁₉×#125	C₂³	semidirect
168. C₁₉×#124	C₂³	semidirect
169. C₁₉×#124	C₂³	semidirect
170. C₁₉×#124	C₂³	semidirect
171. C₁₉×#124	C₂³	semidirect
172. C₁₉×#124	C₂³	semidirect
173. C₁₉×#124	C₂³	semidirect
174. C₁₉×#124	C₂³	semidirect
182. C₁₉×#123	C₂³	semidirect
183. C₁₉×#123	C₂³	semidirect
184. C₁₉×#123	C₂³	semidirect
185. C₁₉×#123	C₂³	semidirect
186. C₁₉×#123	C₂³	semidirect
187. C₁₉×#123	C₂³	semidirect
188. C₁₉×#123	C₂³	semidirect
189. C₁₉×#123	C₂³	semidirect
193. C₁₉×C₂²⋊Q₈	C₂³	semidirect
194. C₁₉×C₂²⋊Q₈	C₂³	semidirect
195. C₁₉×C₂²⋊Q₈	C₂³	semidirect
196. C₁₉×C₂²⋊Q₈	C₂³	semidirect
197. C₁₉×C₂²⋊Q₈	C₂³	semidirect
198. C₁₉×C₂²⋊Q₈	C₂³	semidirect
213. C₁₉×#121	C₂³	semidirect
214. C₁₉×#121	C₂³	semidirect
215. C₁₉×#121	C₂³	semidirect
216. C₁₉×#121	C₂³	semidirect
217. C₁₉×#121	C₂³	semidirect
218. C₁₉×#121	C₂³	semidirect
219. C₁₉×#121	C₂³	semidirect
220. C₁₉×#121	C₂³	semidirect
221. C₁₉×#121	C₂³	semidirect
222. C₁₉×#121	C₂³	semidirect
235. C₁₉×#120	C₂³	semidirect
236. C₁₉×#120	C₂³	semidirect
237. C₁₉×#120	C₂³	semidirect
238. C₄×Q₈×C₁₉	C₂³	semidirect
239. C₄×Q₈×C₁₉	C₂³	semidirect
240. C₄×Q₈×C₁₉	C₂³	semidirect
241. C₄×Q₈×C₁₉	C₂³	semidirect
248. C₄×D₄×C₁₉	C₂³	semidirect
249. C₄×D₄×C₁₉	C₂³	semidirect
250. C₄×D₄×C₁₉	C₂³	semidirect
251. C₄×D₄×C₁₉	C₂³	semidirect
252. C₄×D₄×C₁₉	C₂³	semidirect
253. C₄×D₄×C₁₉	C₂³	semidirect
254. C₄×D₄×C₁₉	C₂³	semidirect
255. C₄×D₄×C₁₉	C₂³	semidirect
256. C₄×D₄×C₁₉	C₂³	semidirect
262. C₁₉×#117	C₂³	semidirect
263. C₁₉×#117	C₂³	semidirect
264. C₁₉×#117	C₂³	semidirect
266. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
272. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
273. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
275. C₂×C₄²×C₁₉	C₂³	semidirect
276. C₂×C₄²×C₁₉	C₂³	semidirect
396. #62876	C₁₉	direct (N × H)
466. #3562	C₂×C₁₉	semidirect
467. #3558	C₂×C₁₉	semidirect
468. #3546	C₂×C₁₉	semidirect
469. #3543	C₂×C₁₉	semidirect
470. #3534	C₂×C₁₉	semidirect
471. #3532	C₂×C₁₉	semidirect
472. #3510	C₂×C₁₉	semidirect
473. #3508	C₂×C₁₉	semidirect
474. #3500	C₂×C₁₉	semidirect
475. #3498	C₂×C₁₉	semidirect
476. #3487	C₂×C₁₉	semidirect
477. #3485	C₂×C₁₉	semidirect
478. #3484	C₂×C₁₉	semidirect
479. #3455	C₂×C₁₉	semidirect
480. C₂×#535	C₂×C₁₉	semidirect
509. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
510. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
511. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
512. C₂²×#41	C₂²×C₁₉	semidirect
513. C₂³×D₄	C₂²×C₁₉	semidirect
514. #562	C₂²×C₁₉	semidirect
515. H(3,𝔽₄)	C₂²×C₁₉	semidirect
516. #560	C₂²×C₁₉	semidirect
517. #560	C₂²×C₁₉	semidirect
518. #560	C₂²×C₁₉	semidirect
519. #559	C₂²×C₁₉	semidirect
520. #559	C₂²×C₁₉	semidirect
521. #556	C₂²×C₁₉	semidirect
522. #553	C₂²×C₁₉	semidirect
523. #551	C₂²×C₁₉	semidirect
524. #551	C₂²×C₁₉	semidirect
525. #550	C₂²×C₁₉	semidirect
526. #550	C₂²×C₁₉	semidirect
527. #550	C₂²×C₁₉	semidirect
528. #548	C₂²×C₁₉	semidirect
529. #548	C₂²×C₁₉	semidirect
530. #547	C₂²×C₁₉	semidirect
531. #546	C₂²×C₁₉	semidirect
532. #546	C₂²×C₁₉	semidirect
533. #546	C₂²×C₁₉	semidirect
534. #546	C₂²×C₁₉	semidirect
535. #546	C₂²×C₁₉	semidirect
536. #546	C₂²×C₁₉	semidirect
537. #546	C₂²×C₁₉	semidirect
538. #546	C₂²×C₁₉	semidirect
539. D₄²	C₂²×C₁₉	semidirect
540. D₄²	C₂²×C₁₉	semidirect
541. D₄²	C₂²×C₁₉	semidirect
542. D₄²	C₂²×C₁₉	semidirect
543. D₄²	C₂²×C₁₉	semidirect
544. #542	C₂²×C₁₉	semidirect
545. #542	C₂²×C₁₉	semidirect
546. #542	C₂²×C₁₉	semidirect
547. #541	C₂²×C₁₉	semidirect
548. #540	C₂²×C₁₉	semidirect
549. #540	C₂²×C₁₉	semidirect
550. #540	C₂²×C₁₉	semidirect
551. #539	C₂²×C₁₉	semidirect
552. #539	C₂²×C₁₉	semidirect
553. #538	C₂²×C₁₉	semidirect
554. #538	C₂²×C₁₉	semidirect
555. #538	C₂²×C₁₉	semidirect
556. #538	C₂²×C₁₉	semidirect
557. #538	C₂²×C₁₉	semidirect
558. #537	C₂²×C₁₉	semidirect
559. #536	C₂²×C₁₉	semidirect
560. #536	C₂²×C₁₉	semidirect
562. #535	C₂²×C₁₉	semidirect
563. #535	C₂²×C₁₉	semidirect
564. #535	C₂²×C₁₉	semidirect
565. #535	C₂²×C₁₉	semidirect
566. #535	C₂²×C₁₉	semidirect
567. #535	C₂²×C₁₉	semidirect
568. #535	C₂²×C₁₉	semidirect
569. #535	C₂²×C₁₉	semidirect
570. #535	C₂²×C₁₉	semidirect
571. #534	C₂²×C₁₉	semidirect
572. #534	C₂²×C₁₉	semidirect
573. #534	C₂²×C₁₉	semidirect
574. #534	C₂²×C₁₉	semidirect
575. #533	C₂²×C₁₉	semidirect
576. #532	C₂²×C₁₉	semidirect
577. #532	C₂²×C₁₉	semidirect
578. #532	C₂²×C₁₉	semidirect
579. #532	C₂²×C₁₉	semidirect
580. C₂×#127	C₂²×C₁₉	semidirect
581. C₂×#127	C₂²×C₁₉	semidirect
582. #529	C₂²×C₁₉	semidirect
583. #529	C₂²×C₁₉	semidirect
584. #529	C₂²×C₁₉	semidirect
585. C₂×#124	C₂²×C₁₉	semidirect
586. C₂×#124	C₂²×C₁₉	semidirect
587. #525	C₂²×C₁₉	semidirect
588. #525	C₂²×C₁₉	semidirect
589. #525	C₂²×C₁₉	semidirect
590. C₂×#123	C₂²×C₁₉	semidirect
591. C₂×#121	C₂²×C₁₉	semidirect
592. C₂×#120	C₂²×C₁₉	semidirect
593. C₂×#120	C₂²×C₁₉	semidirect
594. #519	C₂²×C₁₉	semidirect
595. #518	C₂²×C₁₉	semidirect
596. #518	C₂²×C₁₉	semidirect
597. C₄×#41	C₂²×C₁₉	semidirect
598. C₄×#41	C₂²×C₁₉	semidirect
599. C₂×#117	C₂²×C₁₉	semidirect
619. C₂×#41	C₂³×C₁₉	semidirect
620. C₂×#41	C₂³×C₁₉	semidirect
621. C₂×#41	C₂³×C₁₉	semidirect
623. C₂²×Q₈	C₂³×C₁₉	semidirect
636. C₂²×D₄	C₂³×C₁₉	semidirect
637. C₂²×D₄	C₂³×C₁₉	semidirect
640. C₄⋊Q₈	C₂³×C₁₉	semidirect
641. C₄⋊Q₈	C₂³×C₁₉	semidirect
642. C₄⋊Q₈	C₂³×C₁₉	semidirect
649. #127	C₂³×C₁₉	semidirect
650. #127	C₂³×C₁₉	semidirect
651. #127	C₂³×C₁₉	semidirect
654. #126	C₂³×C₁₉	semidirect
655. #126	C₂³×C₁₉	semidirect
656. #126	C₂³×C₁₉	semidirect
657. #126	C₂³×C₁₉	semidirect
658. #125	C₂³×C₁₉	semidirect
659. #125	C₂³×C₁₉	semidirect
660. #125	C₂³×C₁₉	semidirect
669. #124	C₂³×C₁₉	semidirect
670. #124	C₂³×C₁₉	semidirect
671. #124	C₂³×C₁₉	semidirect
672. #124	C₂³×C₁₉	semidirect
673. #124	C₂³×C₁₉	semidirect
674. #124	C₂³×C₁₉	semidirect
675. #124	C₂³×C₁₉	semidirect
683. #123	C₂³×C₁₉	semidirect
684. #123	C₂³×C₁₉	semidirect
685. #123	C₂³×C₁₉	semidirect
686. #123	C₂³×C₁₉	semidirect
687. #123	C₂³×C₁₉	semidirect
688. #123	C₂³×C₁₉	semidirect
689. #123	C₂³×C₁₉	semidirect
690. #123	C₂³×C₁₉	semidirect
694. C₂²⋊Q₈	C₂³×C₁₉	semidirect
695. C₂²⋊Q₈	C₂³×C₁₉	semidirect
696. C₂²⋊Q₈	C₂³×C₁₉	semidirect
697. C₂²⋊Q₈	C₂³×C₁₉	semidirect
698. C₂²⋊Q₈	C₂³×C₁₉	semidirect
699. C₂²⋊Q₈	C₂³×C₁₉	semidirect
714. #121	C₂³×C₁₉	semidirect
715. #121	C₂³×C₁₉	semidirect
716. #121	C₂³×C₁₉	semidirect
717. #121	C₂³×C₁₉	semidirect
718. #121	C₂³×C₁₉	semidirect
719. #121	C₂³×C₁₉	semidirect
720. #121	C₂³×C₁₉	semidirect
721. #121	C₂³×C₁₉	semidirect
722. #121	C₂³×C₁₉	semidirect
723. #121	C₂³×C₁₉	semidirect
736. #120	C₂³×C₁₉	semidirect
737. #120	C₂³×C₁₉	semidirect
738. #120	C₂³×C₁₉	semidirect
739. C₄×Q₈	C₂³×C₁₉	semidirect
740. C₄×Q₈	C₂³×C₁₉	semidirect
741. C₄×Q₈	C₂³×C₁₉	semidirect
742. C₄×Q₈	C₂³×C₁₉	semidirect
749. C₄×D₄	C₂³×C₁₉	semidirect
750. C₄×D₄	C₂³×C₁₉	semidirect
751. C₄×D₄	C₂³×C₁₉	semidirect
752. C₄×D₄	C₂³×C₁₉	semidirect
753. C₄×D₄	C₂³×C₁₉	semidirect
754. C₄×D₄	C₂³×C₁₉	semidirect
755. C₄×D₄	C₂³×C₁₉	semidirect
756. C₄×D₄	C₂³×C₁₉	semidirect
757. C₄×D₄	C₂³×C₁₉	semidirect
763. #117	C₂³×C₁₉	semidirect
764. #117	C₂³×C₁₉	semidirect
765. #117	C₂³×C₁₉	semidirect
767. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
773. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
774. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
776. C₂×C₄²	C₂³×C₁₉	semidirect
777. C₂×C₄²	C₂³×C₁₉	semidirect
778. C₁₉	#62876	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×#3558	2
C₁₉×#3546	2
C₁₉×#3543	2
C₁₉×#3534	2
C₁₉×#3532	2
C₁₉×#3510	2
C₁₉×#3508	2
C₁₉×#3500	2
C₁₉×#3498	2
C₁₉×#3487	2
C₁₉×#3485	2
C₁₉×#3484	2
C₁₉×#3455	2
C₂×C₁₉×#535	2
#62876	19

Subgroups — C19×#62876 #18068835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62876 #18068835