Subgroups — C₁₉×#62858 #18068817

Order 4864.

7310 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3524	C₂	1	4	yes	maximal, complemented
2	C₁₉×#3519	C₂	1	12	yes	maximal, complemented
3	C₁₉×#3517	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3513	C₂	1	12	yes	maximal, complemented
5	C₁₉×#3512	C₂	1	3	yes	maximal, complemented
6	C₁₉×#3508	C₂	1	3	yes	maximal, complemented
7	C₁₉×#3504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3494	C₂	1	6	yes	maximal, complemented
10	C₁₉×#3488	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3460	C₂	1	6	yes	maximal, complemented
12	C₁₉×#3455	C₂	1	3	yes	maximal, complemented
13	C₂×C₁₉×#540	C₂	1	3	yes	maximal, complemented
14	C₄×C₁₉×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
15	C₁₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#559	C₂²	1	12	yes	complemented
19	C₁₉×#557	C₂²	1	4	yes	complemented
20	C₁₉×#555	C₂²	1	12	yes	complemented
21	C₁₉×#554	C₂²	1	12	yes	complemented
22	C₁₉×#553	C₂²	1	12	yes	complemented
23	C₁₉×#553	C₂²	1	12	yes	complemented
24	C₁₉×#553	C₂²	1	24	yes	complemented
25	C₁₉×#553	C₂²	1	12	yes	complemented
26	C₁₉×#552	C₂²	1	12	yes	complemented
27	C₁₉×#551	C₂²	1	24	yes	complemented
28	C₁₉×#550	C₂²	1	4	yes	complemented
29	C₁₉×#550	C₂²	1	4	yes	complemented
30	C₁₉×#550	C₂²	1	12	yes	complemented
31	C₁₉×#548	C₂²	1	4	yes	complemented
32	C₁₉×#547	C₂²	1	12	yes	complemented
33	C₁₉×#546	C₂²	1	12	yes	complemented
34	C₁₉×#546	C₂²	1	24	yes	complemented
35	C₁₉×#546	C₂²	1	24	yes	complemented
36	D₄²×C₁₉	C₂²	1	12	yes	complemented
37	D₄²×C₁₉	C₂²	1	12	yes	complemented
38	C₁₉×#544	C₂²	1	6	yes	complemented
39	C₁₉×#542	C₂²	1	6	yes	complemented
40	C₁₉×#542	C₂²	1	6	yes	complemented
41	C₁₉×#542	C₂²	1	12	yes	complemented
42	C₁₉×#541	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#541	C₂²	1	3	yes	complemented
44	C₁₉×#540	C₂²	1	3	yes	complemented
45	C₁₉×#540	C₂²	1	6	yes	complemented
46	C₁₉×#540	C₂²	1	6	yes	complemented
47	C₁₉×#540	C₂²	1	6	yes	complemented
48	C₁₉×#540	C₂²	1	12	yes	complemented
49	C₁₉×#540	C₂²	1	12	yes	complemented
50	C₁₉×#540	C₂²	1	3	yes	complemented
51	C₁₉×#540	C₂²	1	12	yes	complemented
52	C₁₉×#539	C₂²	1	12	yes	complemented
53	C₁₉×#538	C₂²	1	12	yes	complemented
54	C₁₉×#538	C₂²	1	24	yes	complemented
55	C₁₉×#537	C₂²	1	6	yes	complemented
56	C₁₉×#535	C₂²	1	6	yes	complemented
57	C₁₉×#535	C₂²	1	6	yes	complemented
58	C₁₉×#533	C₂²	1	3	yes	complemented
59	C₁₉×#532	C₂²	1	3	yes	complemented
60	C₁₉×#532	C₂²	1	12	yes	complemented
61	C₁₉×#532	C₂²	1	12	yes	complemented
62	C₂×C₁₉×#127	C₂²	1	3	yes	complemented
63	C₁₉×#529	C₂²	1	12	yes	complemented
64	C₁₉×#529	C₂²	1	12	yes	complemented
65	C₁₉×#529	C₂²	1	12	yes	complemented
66	C₁₉×#529	C₂²	1	12	yes	complemented
67	C₂×C₁₉×#125	C₂²	1	3	yes	complemented
68	C₁₉×#525	C₂²	1	6	yes	complemented
69	C₁₉×#525	C₂²	1	24	yes	complemented
70	C₂×C₁₉×#123	C₂²	1	12	yes	complemented
71	C₂×C₁₉×#121	C₂²	1	6	yes	complemented
72	C₂×C₁₉×#121	C₂²	1	12	yes	complemented
73	C₁₉×#520	C₂²	1	2	yes	—
74	C₁₉×#520	C₂²	1	6	yes	complemented
75	C₁₉×#520	C₂²	1	2	yes	complemented
76	C₁₉×#520	C₂²	1	6	yes	complemented
77	C₁₉×#520	C₂²	1	4	yes	complemented
78	C₁₉×#519	C₂²	1	2	yes	complemented
79	C₁₉×#518	C₂²	1	6	yes	complemented
80	C₁₉×#518	C₂²	1	6	yes	complemented
81	C₁₉×#518	C₂²	1	12	yes	complemented
82	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
83	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
84	C₄×#41×C₁₉	C₂²	1	3	yes	complemented
85	C₄×#41×C₁₉	C₂²	1	3	yes	complemented
86	C₄×#41×C₁₉	C₂²	1	6	yes	complemented
87	C₄×#41×C₁₉	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	complemented
89	C₂×C₄×D₄×C₁₉	C₂²	1	12	yes	complemented
90	C₂×C₁₉×#117	C₂²	1	3	yes	complemented
91	C₂×C₁₉×#117	C₂²	1	3	yes	complemented
92	C₁₉×H(5,𝔽₂)	—	2	16	no	—
93	C₂×#41×C₁₉	—	2	8	no	—
94	C₂×#41×C₁₉	C₂³	1	3	yes	—
95	C₂×#41×C₁₉	C₂³	1	6	yes	—
96	C₂×#41×C₁₉	C₂³	1	4	yes	—
97	C₂×#41×C₁₉	C₂³	1	3	yes	—
98	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×#41×C₁₉	C₂³	1	24	yes	—
100	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
103	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
104	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
105	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
106	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
107	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
108	C₂³×C₄×C₁₉	C₂³	1	12	yes	—
109	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
111	C₁₉×C₄⋊Q₈	C₂³	1	12	yes	—
112	C₁₉×#127	C₂³	1	3	yes	—
113	C₁₉×#127	C₂³	1	6	yes	—
114	C₁₉×#127	C₂³	1	12	yes	—
115	C₁₉×#127	C₂³	1	12	yes	—
116	C₁₉×#126	C₂³	1	4	yes	—
117	C₁₉×#126	C₂³	1	12	yes	—
118	C₁₉×#126	C₂³	1	12	yes	—
119	C₁₉×#126	C₂³	1	24	yes	—
120	C₁₉×#126	C₂³	1	12	yes	—
121	C₁₉×#125	C₂³	1	3	yes	—
122	C₁₉×#125	C₂³	1	6	yes	—
123	C₁₉×#125	C₂³	1	12	yes	—
124	C₁₉×#125	C₂³	1	4	yes	—
125	C₁₉×#125	C₂³	1	12	yes	—
126	C₁₉×#125	C₂³	1	12	yes	—
127	C₁₉×#125	C₂³	1	1	yes	characteristic
128	C₁₉×#124	C₂³	1	6	yes	—
129	C₁₉×#124	C₂³	1	12	yes	—
130	C₁₉×#124	C₂³	1	12	yes	—
131	C₁₉×#124	C₂³	1	12	yes	—
132	C₁₉×#124	C₂³	1	24	yes	—
133	C₁₉×#123	C₂³	1	12	yes	—
134	C₁₉×#123	C₂³	1	24	yes	—
135	C₁₉×#123	C₂³	1	24	yes	—
136	C₁₉×#123	C₂³	1	24	yes	—
137	C₁₉×#123	C₂³	1	12	yes	—
138	C₁₉×#123	C₂³	1	12	yes	—
139	C₁₉×#123	C₂³	1	24	yes	—
140	C₁₉×#123	C₂³	1	12	yes	—
141	C₁₉×#123	C₂³	1	12	yes	—
142	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
144	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
145	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
146	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
147	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
148	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
149	C₁₉×#121	C₂³	1	6	yes	—
150	C₁₉×#121	C₂³	1	12	yes	—
151	C₁₉×#121	C₂³	1	24	yes	—
152	C₁₉×#121	C₂³	1	12	yes	—
153	C₁₉×#121	C₂³	1	12	yes	—
154	C₁₉×#121	C₂³	1	24	yes	—
155	C₁₉×#121	C₂³	1	12	yes	—
156	C₁₉×#121	C₂³	1	24	yes	—
157	C₁₉×#121	C₂³	1	6	yes	—
158	C₁₉×#121	C₂³	1	24	yes	—
159	C₁₉×#121	C₂³	1	12	yes	—
160	C₁₉×#121	C₂³	1	12	yes	—
161	C₁₉×#121	C₂³	1	12	yes	—
162	C₁₉×#121	C₂³	1	12	yes	—
163	C₁₉×#121	C₂³	1	12	yes	—
164	C₁₉×#121	C₂³	1	24	yes	—
165	C₁₉×#120	C₂³	1	24	yes	—
166	C₁₉×#120	C₂³	1	24	yes	—
167	C₁₉×#120	C₂³	1	12	yes	—
168	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
172	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
173	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
174	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
175	C₄×Q₈×C₁₉	C₂³	1	12	yes	—
176	C₄×D₄×C₁₉	C₂³	1	6	yes	—
177	C₄×D₄×C₁₉	C₂³	1	12	yes	—
178	C₄×D₄×C₁₉	C₂³	1	6	yes	—
179	C₄×D₄×C₁₉	C₂³	1	12	yes	—
180	C₄×D₄×C₁₉	C₂³	1	12	yes	—
181	C₄×D₄×C₁₉	C₂³	1	12	yes	—
182	C₄×D₄×C₁₉	C₂³	1	12	yes	—
183	C₄×D₄×C₁₉	C₂³	1	24	yes	—
184	C₄×D₄×C₁₉	C₂³	1	12	yes	—
185	C₄×D₄×C₁₉	C₂³	1	6	yes	—
186	C₄×D₄×C₁₉	C₂³	1	12	yes	—
187	C₄×D₄×C₁₉	C₂³	1	6	yes	—
188	C₄×D₄×C₁₉	C₂³	1	12	yes	—
189	C₄×D₄×C₁₉	C₂³	1	12	yes	—
190	C₄×D₄×C₁₉	C₂³	1	6	yes	—
191	C₄×D₄×C₁₉	C₂³	1	12	yes	—
192	C₄×D₄×C₁₉	C₂³	1	6	yes	—
193	C₄×D₄×C₁₉	C₂³	1	12	yes	—
194	C₄×D₄×C₁₉	C₂³	1	12	yes	—
195	C₄×D₄×C₁₉	C₂³	1	24	yes	—
196	C₄×D₄×C₁₉	C₂³	1	24	yes	—
197	C₄×D₄×C₁₉	C₂³	1	12	yes	—
198	C₁₉×#117	C₂³	1	1	yes	characteristic
199	C₁₉×#117	C₂³	1	3	yes	—
200	C₁₉×#117	C₂³	1	3	yes	—
201	C₁₉×#117	C₂³	1	3	yes	—
202	C₁₉×#117	C₂³	1	3	yes	—
203	C₁₉×#117	C₂³	1	3	yes	—
204	C₁₉×#117	C₂³	1	6	yes	—
205	C₁₉×#117	C₂³	1	6	yes	—
206	C₁₉×#117	C₂³	1	6	yes	—
207	C₁₉×#117	C₂³	1	6	yes	—
208	C₁₉×#117	C₂³	1	6	yes	—
209	C₁₉×#117	C₂³	1	12	yes	—
210	C₁₉×#117	C₂³	1	12	yes	—
211	C₁₉×#117	C₂³	1	24	yes	—
212	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
213	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
214	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
215	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
216	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
217	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
218	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
219	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
220	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	—
221	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
222	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
223	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
224	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
225	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
226	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
227	C₂⁴×C₁₉	C₂⁴	1	12	yes	—
228	#41×C₁₉	—	2	4	no	—
229	#41×C₁₉	—	2	16	no	—
230	#41×C₁₉	—	2	12	no	—
231	#41×C₁₉	—	2	12	no	—
232	#41×C₁₉	—	2	24	no	—
233	#41×C₁₉	—	8	24	no	—
234	#41×C₁₉	#41	1	8	yes	complemented
235	C₂×Q₈×C₁₉	—	2	4	no	—
236	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
237	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
239	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₁₉	—	2	12	no	—
241	C₂×D₄×C₁₉	—	2	48	no	—
242	C₂×D₄×C₁₉	—	2	24	no	—
243	C₂×D₄×C₁₉	—	8	12	no	—
244	C₂×D₄×C₁₉	—	8	12	no	—
245	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
246	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
247	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
248	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
249	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
250	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
251	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
252	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
253	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
254	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
255	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
256	C₂²×C₄×C₁₉	—	2	12	no	—
257	C₂²×C₄×C₁₉	—	8	12	no	—
258	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
259	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
260	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
261	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
262	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
263	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
265	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
266	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
267	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
268	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
269	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
270	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
271	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
272	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
273	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
274	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
276	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
277	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
278	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
279	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
280	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
281	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
282	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
283	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
286	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
289	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
290	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
291	C₂²⋊C₄×C₁₉	C₂⁴	1	2	yes	—
292	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
293	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
294	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
295	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
296	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
297	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
298	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
299	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
300	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
301	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
302	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
303	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
304	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
305	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
306	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
307	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
308	C₄²×C₁₉	C₂⁴	1	3	yes	—
309	C₄²×C₁₉	C₂⁴	1	6	yes	—
310	C₄²×C₁₉	C₂⁴	1	3	yes	—
311	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
312	C₄²×C₁₉	C₂⁴	1	4	yes	—
313	C₄²×C₁₉	C₂⁴	1	12	yes	—
314	C₄²×C₁₉	C₂⁴	1	12	yes	—
315	C₄²×C₁₉	C₂⁴	1	12	yes	—
316	C₄²×C₁₉	C₂⁴	1	6	yes	—
317	#62858	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
318	C₂³×C₁₉	—	2	6	no	—
319	C₂³×C₁₉	—	2	24	no	—
320	C₂³×C₁₉	—	4	12	no	—
321	C₂³×C₁₉	—	4	6	no	—
322	C₂³×C₁₉	—	4	12	no	—
323	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
324	C₂³×C₁₉	C₂⁵	1	12	yes	—
325	C₂³×C₁₉	C₂⁵	1	3	yes	—
326	C₂³×C₁₉	C₂⁵	1	3	yes	—
327	Q₈×C₁₉	—	2	6	no	—
328	Q₈×C₁₉	—	2	4	no	—
329	Q₈×C₁₉	—	4	12	no	—
330	Q₈×C₁₉	C₂×#41	1	4	yes	—
331	D₄×C₁₉	—	2	24	no	—
332	D₄×C₁₉	—	2	12	no	—
333	D₄×C₁₉	—	2	24	no	—
334	D₄×C₁₉	—	2	12	no	—
335	D₄×C₁₉	—	2	6	no	—
336	D₄×C₁₉	—	4	12	no	—
337	D₄×C₁₉	—	4	12	no	—
338	D₄×C₁₉	—	4	24	no	—
339	D₄×C₁₉	—	4	24	no	—
340	D₄×C₁₉	—	4	12	no	—
341	D₄×C₁₉	C₂×#41	1	12	yes	—
342	C₂×C₄×C₁₉	—	2	6	no	—
343	C₂×C₄×C₁₉	—	2	2	no	—
344	C₂×C₄×C₁₉	—	2	6	no	—
345	C₂×C₄×C₁₉	—	2	6	no	—
346	C₂×C₄×C₁₉	—	2	6	no	—
347	C₂×C₄×C₁₉	—	2	24	no	—
348	C₂×C₄×C₁₉	—	4	6	no	—
349	C₂×C₄×C₁₉	—	4	12	no	—
350	C₂×C₄×C₁₉	—	4	12	no	—
351	C₂×C₄×C₁₉	—	4	24	no	—
352	C₂×C₄×C₁₉	—	4	6	no	—
353	C₂×C₄×C₁₉	—	4	12	no	—
354	C₂×C₄×C₁₉	—	4	12	no	—
355	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
356	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
357	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
358	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
359	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
360	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
361	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
362	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
363	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
364	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
365	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
366	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
367	#3524	C₂×C₁₉	1	4	yes	complemented
368	#3519	C₂×C₁₉	1	12	yes	complemented
369	#3517	C₂×C₁₉	1	4	yes	complemented
370	#3513	C₂×C₁₉	1	12	yes	complemented
371	#3512	C₂×C₁₉	1	3	yes	complemented
372	#3508	C₂×C₁₉	1	3	yes	complemented
373	#3504	C₂×C₁₉	1	1	yes	characteristic, complemented
374	#3498	C₂×C₁₉	1	1	yes	characteristic, complemented
375	#3494	C₂×C₁₉	1	6	yes	complemented
376	#3488	C₂×C₁₉	1	2	yes	complemented
377	#3460	C₂×C₁₉	1	6	yes	complemented
378	#3455	C₂×C₁₉	1	3	yes	complemented
379	C₂×#540	C₂×C₁₉	1	3	yes	complemented
380	C₄×H(5,𝔽₂)	C₂×C₁₉	1	2	yes	complemented
381	#3428	C₂×C₁₉	1	1	yes	characteristic, complemented
382	C₂²×C₁₉	—	2	6	no	—
383	C₂²×C₁₉	—	2	1	no	—
384	C₂²×C₁₉	—	2	3	no	—
385	C₂²×C₁₉	—	2	12	no	—
386	C₂²×C₁₉	—	2	12	no	—
387	C₂²×C₁₉	—	2	6	no	—
388	C₂²×C₁₉	—	2	12	no	—
389	C₂²×C₁₉	—	2	2	no	—
390	C₂²×C₁₉	—	8	6	no	—
391	C₂²×C₁₉	—	8	24	no	—
392	C₂²×C₁₉	C₂²×#41	1	6	yes	—
393	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
394	C₄×C₁₉	—	2	1	no	—
395	C₄×C₁₉	—	2	4	no	—
396	C₄×C₁₉	—	2	3	no	—
397	C₄×C₁₉	—	2	2	no	—
398	C₄×C₁₉	—	2	6	no	—
399	C₄×C₁₉	—	2	12	no	—
400	C₄×C₁₉	—	2	2	no	—
401	C₄×C₁₉	—	2	6	no	—
402	C₄×C₁₉	—	2	4	no	—
403	C₄×C₁₉	C₂²×#41	1	6	yes	—
404	C₄×C₁₉	C₂²×#41	1	2	yes	—
405	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	2	yes	—
406	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
407	#559	C₂²×C₁₉	1	12	yes	complemented
408	#557	C₂²×C₁₉	1	4	yes	complemented
409	#555	C₂²×C₁₉	1	12	yes	complemented
410	#554	C₂²×C₁₉	1	12	yes	complemented
411	#553	C₂²×C₁₉	1	12	yes	complemented
412	#553	C₂²×C₁₉	1	12	yes	complemented
413	#553	C₂²×C₁₉	1	24	yes	complemented
414	#553	C₂²×C₁₉	1	12	yes	complemented
415	#552	C₂²×C₁₉	1	12	yes	complemented
416	#551	C₂²×C₁₉	1	24	yes	complemented
417	#550	C₂²×C₁₉	1	4	yes	complemented
418	#550	C₂²×C₁₉	1	4	yes	complemented
419	#550	C₂²×C₁₉	1	12	yes	complemented
420	#548	C₂²×C₁₉	1	4	yes	complemented
421	#547	C₂²×C₁₉	1	12	yes	complemented
422	#546	C₂²×C₁₉	1	12	yes	complemented
423	#546	C₂²×C₁₉	1	24	yes	complemented
424	#546	C₂²×C₁₉	1	24	yes	complemented
425	D₄²	C₂²×C₁₉	1	12	yes	complemented
426	D₄²	C₂²×C₁₉	1	12	yes	complemented
427	#544	C₂²×C₁₉	1	6	yes	complemented
428	#542	C₂²×C₁₉	1	6	yes	complemented
429	#542	C₂²×C₁₉	1	6	yes	complemented
430	#542	C₂²×C₁₉	1	12	yes	complemented
431	#541	C₂²×C₁₉	1	1	yes	characteristic, complemented
432	#541	C₂²×C₁₉	1	3	yes	complemented
433	#540	C₂²×C₁₉	1	3	yes	complemented
434	#540	C₂²×C₁₉	1	6	yes	complemented
435	#540	C₂²×C₁₉	1	6	yes	complemented
436	#540	C₂²×C₁₉	1	6	yes	complemented
437	#540	C₂²×C₁₉	1	12	yes	complemented
438	#540	C₂²×C₁₉	1	12	yes	complemented
439	#540	C₂²×C₁₉	1	3	yes	complemented
440	#540	C₂²×C₁₉	1	12	yes	complemented
441	#539	C₂²×C₁₉	1	12	yes	complemented
442	#538	C₂²×C₁₉	1	12	yes	complemented
443	#538	C₂²×C₁₉	1	24	yes	complemented
444	#537	C₂²×C₁₉	1	6	yes	complemented
445	#535	C₂²×C₁₉	1	6	yes	complemented
446	#535	C₂²×C₁₉	1	6	yes	complemented
447	#533	C₂²×C₁₉	1	3	yes	complemented
448	#532	C₂²×C₁₉	1	3	yes	complemented
449	#532	C₂²×C₁₉	1	12	yes	complemented
450	#532	C₂²×C₁₉	1	12	yes	complemented
451	C₂×#127	C₂²×C₁₉	1	3	yes	complemented
452	#529	C₂²×C₁₉	1	12	yes	complemented
453	#529	C₂²×C₁₉	1	12	yes	complemented
454	#529	C₂²×C₁₉	1	12	yes	complemented
455	#529	C₂²×C₁₉	1	12	yes	complemented
456	C₂×#125	C₂²×C₁₉	1	3	yes	complemented
457	#525	C₂²×C₁₉	1	6	yes	complemented
458	#525	C₂²×C₁₉	1	24	yes	complemented
459	C₂×#123	C₂²×C₁₉	1	12	yes	complemented
460	C₂×#121	C₂²×C₁₉	1	6	yes	complemented
461	C₂×#121	C₂²×C₁₉	1	12	yes	complemented
462	#520	C₂²×C₁₉	1	2	yes	—
463	#520	C₂²×C₁₉	1	6	yes	complemented
464	#520	C₂²×C₁₉	1	2	yes	complemented
465	#520	C₂²×C₁₉	1	6	yes	complemented
466	#520	C₂²×C₁₉	1	4	yes	complemented
467	#519	C₂²×C₁₉	1	2	yes	complemented
468	#518	C₂²×C₁₉	1	6	yes	complemented
469	#518	C₂²×C₁₉	1	6	yes	complemented
470	#518	C₂²×C₁₉	1	12	yes	complemented
471	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
472	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
473	C₄×#41	C₂²×C₁₉	1	3	yes	complemented
474	C₄×#41	C₂²×C₁₉	1	3	yes	complemented
475	C₄×#41	C₂²×C₁₉	1	6	yes	complemented
476	C₄×#41	C₂²×C₁₉	1	4	yes	complemented
477	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	complemented
478	C₂×C₄×D₄	C₂²×C₁₉	1	12	yes	complemented
479	C₂×#117	C₂²×C₁₉	1	3	yes	complemented
480	C₂×#117	C₂²×C₁₉	1	3	yes	complemented
481	C₂×C₁₉	—	2	6	no	—
482	C₂×C₁₉	—	4	3	no	—
483	C₂×C₁₉	—	4	12	no	—
484	C₂×C₁₉	—	4	1	no	—
485	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
486	C₂×C₁₉	H(7,𝔽₂)	1	2	yes	—
487	H(5,𝔽₂)	—	2	16	no	—
488	C₂×#41	—	2	8	no	—
489	C₂×#41	C₂³×C₁₉	1	3	yes	—
490	C₂×#41	C₂³×C₁₉	1	6	yes	—
491	C₂×#41	C₂³×C₁₉	1	4	yes	—
492	C₂×#41	C₂³×C₁₉	1	3	yes	—
493	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
494	C₂×#41	C₂³×C₁₉	1	24	yes	—
495	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
496	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
498	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
499	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
500	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
501	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
502	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
503	C₂³×C₄	C₂³×C₁₉	1	12	yes	—
504	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
506	C₄⋊Q₈	C₂³×C₁₉	1	12	yes	—
507	#127	C₂³×C₁₉	1	3	yes	—
508	#127	C₂³×C₁₉	1	6	yes	—
509	#127	C₂³×C₁₉	1	12	yes	—
510	#127	C₂³×C₁₉	1	12	yes	—
511	#126	C₂³×C₁₉	1	4	yes	—
512	#126	C₂³×C₁₉	1	12	yes	—
513	#126	C₂³×C₁₉	1	12	yes	—
514	#126	C₂³×C₁₉	1	24	yes	—
515	#126	C₂³×C₁₉	1	12	yes	—
516	#125	C₂³×C₁₉	1	3	yes	—
517	#125	C₂³×C₁₉	1	6	yes	—
518	#125	C₂³×C₁₉	1	12	yes	—
519	#125	C₂³×C₁₉	1	4	yes	—
520	#125	C₂³×C₁₉	1	12	yes	—
521	#125	C₂³×C₁₉	1	12	yes	—
522	#125	C₂³×C₁₉	1	1	yes	characteristic
523	#124	C₂³×C₁₉	1	6	yes	—
524	#124	C₂³×C₁₉	1	12	yes	—
525	#124	C₂³×C₁₉	1	12	yes	—
526	#124	C₂³×C₁₉	1	12	yes	—
527	#124	C₂³×C₁₉	1	24	yes	—
528	#123	C₂³×C₁₉	1	12	yes	—
529	#123	C₂³×C₁₉	1	24	yes	—
530	#123	C₂³×C₁₉	1	24	yes	—
531	#123	C₂³×C₁₉	1	24	yes	—
532	#123	C₂³×C₁₉	1	12	yes	—
533	#123	C₂³×C₁₉	1	12	yes	—
534	#123	C₂³×C₁₉	1	24	yes	—
535	#123	C₂³×C₁₉	1	12	yes	—
536	#123	C₂³×C₁₉	1	12	yes	—
537	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
538	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
539	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
540	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
541	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
542	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
543	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
544	#121	C₂³×C₁₉	1	6	yes	—
545	#121	C₂³×C₁₉	1	12	yes	—
546	#121	C₂³×C₁₉	1	24	yes	—
547	#121	C₂³×C₁₉	1	12	yes	—
548	#121	C₂³×C₁₉	1	12	yes	—
549	#121	C₂³×C₁₉	1	24	yes	—
550	#121	C₂³×C₁₉	1	12	yes	—
551	#121	C₂³×C₁₉	1	24	yes	—
552	#121	C₂³×C₁₉	1	6	yes	—
553	#121	C₂³×C₁₉	1	24	yes	—
554	#121	C₂³×C₁₉	1	12	yes	—
555	#121	C₂³×C₁₉	1	12	yes	—
556	#121	C₂³×C₁₉	1	12	yes	—
557	#121	C₂³×C₁₉	1	12	yes	—
558	#121	C₂³×C₁₉	1	12	yes	—
559	#121	C₂³×C₁₉	1	24	yes	—
560	#120	C₂³×C₁₉	1	24	yes	—
561	#120	C₂³×C₁₉	1	24	yes	—
562	#120	C₂³×C₁₉	1	12	yes	—
563	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
564	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
565	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
566	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
567	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
568	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
569	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
570	C₄×Q₈	C₂³×C₁₉	1	12	yes	—
571	C₄×D₄	C₂³×C₁₉	1	6	yes	—
572	C₄×D₄	C₂³×C₁₉	1	12	yes	—
573	C₄×D₄	C₂³×C₁₉	1	6	yes	—
574	C₄×D₄	C₂³×C₁₉	1	12	yes	—
575	C₄×D₄	C₂³×C₁₉	1	12	yes	—
576	C₄×D₄	C₂³×C₁₉	1	12	yes	—
577	C₄×D₄	C₂³×C₁₉	1	12	yes	—
578	C₄×D₄	C₂³×C₁₉	1	24	yes	—
579	C₄×D₄	C₂³×C₁₉	1	12	yes	—
580	C₄×D₄	C₂³×C₁₉	1	6	yes	—
581	C₄×D₄	C₂³×C₁₉	1	12	yes	—
582	C₄×D₄	C₂³×C₁₉	1	6	yes	—
583	C₄×D₄	C₂³×C₁₉	1	12	yes	—
584	C₄×D₄	C₂³×C₁₉	1	12	yes	—
585	C₄×D₄	C₂³×C₁₉	1	6	yes	—
586	C₄×D₄	C₂³×C₁₉	1	12	yes	—
587	C₄×D₄	C₂³×C₁₉	1	6	yes	—
588	C₄×D₄	C₂³×C₁₉	1	12	yes	—
589	C₄×D₄	C₂³×C₁₉	1	12	yes	—
590	C₄×D₄	C₂³×C₁₉	1	24	yes	—
591	C₄×D₄	C₂³×C₁₉	1	24	yes	—
592	C₄×D₄	C₂³×C₁₉	1	12	yes	—
593	#117	C₂³×C₁₉	1	1	yes	characteristic
594	#117	C₂³×C₁₉	1	3	yes	—
595	#117	C₂³×C₁₉	1	3	yes	—
596	#117	C₂³×C₁₉	1	3	yes	—
597	#117	C₂³×C₁₉	1	3	yes	—
598	#117	C₂³×C₁₉	1	3	yes	—
599	#117	C₂³×C₁₉	1	6	yes	—
600	#117	C₂³×C₁₉	1	6	yes	—
601	#117	C₂³×C₁₉	1	6	yes	—
602	#117	C₂³×C₁₉	1	6	yes	—
603	#117	C₂³×C₁₉	1	6	yes	—
604	#117	C₂³×C₁₉	1	12	yes	—
605	#117	C₂³×C₁₉	1	12	yes	—
606	#117	C₂³×C₁₉	1	24	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
617	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
618	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
619	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
620	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
621	C₁₉	#62858	1	1	yes	characteristic, direct product factor, Sylow
622	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
623	C₂⁴	C₂⁴×C₁₉	1	12	yes	—
624	#41	—	2	4	no	—
625	#41	—	2	16	no	—
626	#41	—	2	12	no	—
627	#41	—	2	12	no	—
628	#41	—	2	24	no	—
629	#41	—	8	24	no	—
630	#41	#41×C₁₉	1	8	yes	complemented
631	C₂×Q₈	—	2	4	no	—
632	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
633	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
635	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
636	C₂×D₄	—	2	12	no	—
637	C₂×D₄	—	2	48	no	—
638	C₂×D₄	—	2	24	no	—
639	C₂×D₄	—	8	12	no	—
640	C₂×D₄	—	8	12	no	—
641	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
642	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
643	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
644	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
645	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
646	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
647	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
648	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
649	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
650	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
651	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
652	C₂²×C₄	—	2	12	no	—
653	C₂²×C₄	—	8	12	no	—
654	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
655	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
656	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
657	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
658	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
659	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
661	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
662	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
663	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
664	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
665	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
666	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
667	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
668	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
669	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
670	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
672	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
673	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
674	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
675	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
676	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
677	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
678	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
679	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
682	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
683	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
684	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
685	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
686	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
687	C₂²⋊C₄	C₂⁴×C₁₉	1	2	yes	—
688	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
689	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
690	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
691	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
692	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
693	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
694	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
695	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
696	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
697	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
698	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
699	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
700	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
701	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
702	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
703	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
704	C₄²	C₂⁴×C₁₉	1	3	yes	—
705	C₄²	C₂⁴×C₁₉	1	6	yes	—
706	C₄²	C₂⁴×C₁₉	1	3	yes	—
707	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
708	C₄²	C₂⁴×C₁₉	1	4	yes	—
709	C₄²	C₂⁴×C₁₉	1	12	yes	—
710	C₄²	C₂⁴×C₁₉	1	12	yes	—
711	C₄²	C₂⁴×C₁₉	1	12	yes	—
712	C₄²	C₂⁴×C₁₉	1	6	yes	—
713	C₂³	—	2	6	no	—
714	C₂³	—	2	24	no	—
715	C₂³	—	4	12	no	—
716	C₂³	—	4	6	no	—
717	C₂³	—	4	12	no	—
718	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
719	C₂³	C₂⁵×C₁₉	1	12	yes	—
720	C₂³	C₂⁵×C₁₉	1	3	yes	—
721	C₂³	C₂⁵×C₁₉	1	3	yes	—
722	Q₈	—	2	6	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	4	12	no	—
725	Q₈	C₂×#41×C₁₉	1	4	yes	—
726	D₄	—	2	24	no	—
727	D₄	—	2	12	no	—
728	D₄	—	2	24	no	—
729	D₄	—	2	12	no	—
730	D₄	—	2	6	no	—
731	D₄	—	4	12	no	—
732	D₄	—	4	12	no	—
733	D₄	—	4	24	no	—
734	D₄	—	4	24	no	—
735	D₄	—	4	12	no	—
736	D₄	C₂×#41×C₁₉	1	12	yes	—
737	C₂×C₄	—	2	6	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	6	no	—
740	C₂×C₄	—	2	6	no	—
741	C₂×C₄	—	2	6	no	—
742	C₂×C₄	—	2	24	no	—
743	C₂×C₄	—	4	6	no	—
744	C₂×C₄	—	4	12	no	—
745	C₂×C₄	—	4	12	no	—
746	C₂×C₄	—	4	24	no	—
747	C₂×C₄	—	4	6	no	—
748	C₂×C₄	—	4	12	no	—
749	C₂×C₄	—	4	12	no	—
750	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
751	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
752	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
753	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
754	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
755	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
756	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
757	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
758	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
759	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
760	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
761	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
762	C₂²	—	2	6	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	3	no	—
765	C₂²	—	2	12	no	—
766	C₂²	—	2	12	no	—
767	C₂²	—	2	6	no	—
768	C₂²	—	2	12	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	8	6	no	—
771	C₂²	—	8	24	no	—
772	C₂²	C₂²×#41×C₁₉	1	6	yes	—
773	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
774	C₄	—	2	1	no	—
775	C₄	—	2	4	no	—
776	C₄	—	2	3	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	6	no	—
779	C₄	—	2	12	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	6	no	—
782	C₄	—	2	4	no	—
783	C₄	C₂²×#41×C₁₉	1	6	yes	—
784	C₄	C₂²×#41×C₁₉	1	2	yes	—
785	C₂	—	2	6	no	—
786	C₂	—	4	1	no	—
787	C₂	—	4	12	no	—
788	C₂	—	4	3	no	—
789	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
790	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×#3524	C₂	semidirect
2. C₁₉×#3519	C₂	semidirect
3. C₁₉×#3517	C₂	semidirect
4. C₁₉×#3513	C₂	semidirect
5. C₁₉×#3512	C₂	semidirect
6. C₁₉×#3508	C₂	semidirect
7. C₁₉×#3504	C₂	semidirect
8. C₁₉×#3498	C₂	semidirect
9. C₁₉×#3494	C₂	semidirect
10. C₁₉×#3488	C₂	semidirect
11. C₁₉×#3460	C₂	semidirect
12. C₁₉×#3455	C₂	semidirect
13. C₂×C₁₉×#540	C₂	semidirect
14. C₄×C₁₉×H(5,𝔽₂)	C₂	semidirect
15. C₁₉×#3428	C₂	semidirect
18. C₁₉×#559	C₂²	semidirect
19. C₁₉×#557	C₂²	semidirect
20. C₁₉×#555	C₂²	semidirect
21. C₁₉×#554	C₂²	semidirect
22. C₁₉×#553	C₂²	semidirect
23. C₁₉×#553	C₂²	semidirect
24. C₁₉×#553	C₂²	semidirect
25. C₁₉×#553	C₂²	semidirect
26. C₁₉×#552	C₂²	semidirect
27. C₁₉×#551	C₂²	semidirect
28. C₁₉×#550	C₂²	semidirect
29. C₁₉×#550	C₂²	semidirect
30. C₁₉×#550	C₂²	semidirect
31. C₁₉×#548	C₂²	semidirect
32. C₁₉×#547	C₂²	semidirect
33. C₁₉×#546	C₂²	semidirect
34. C₁₉×#546	C₂²	semidirect
35. C₁₉×#546	C₂²	semidirect
36. D₄²×C₁₉	C₂²	semidirect
37. D₄²×C₁₉	C₂²	semidirect
38. C₁₉×#544	C₂²	semidirect
39. C₁₉×#542	C₂²	semidirect
40. C₁₉×#542	C₂²	semidirect
41. C₁₉×#542	C₂²	semidirect
42. C₁₉×#541	C₂²	semidirect
43. C₁₉×#541	C₂²	semidirect
44. C₁₉×#540	C₂²	semidirect
45. C₁₉×#540	C₂²	semidirect
46. C₁₉×#540	C₂²	semidirect
47. C₁₉×#540	C₂²	semidirect
48. C₁₉×#540	C₂²	semidirect
49. C₁₉×#540	C₂²	semidirect
50. C₁₉×#540	C₂²	semidirect
51. C₁₉×#540	C₂²	semidirect
52. C₁₉×#539	C₂²	semidirect
53. C₁₉×#538	C₂²	semidirect
54. C₁₉×#538	C₂²	semidirect
55. C₁₉×#537	C₂²	semidirect
56. C₁₉×#535	C₂²	semidirect
57. C₁₉×#535	C₂²	semidirect
58. C₁₉×#533	C₂²	semidirect
59. C₁₉×#532	C₂²	semidirect
60. C₁₉×#532	C₂²	semidirect
61. C₁₉×#532	C₂²	semidirect
62. C₂×C₁₉×#127	C₂²	semidirect
63. C₁₉×#529	C₂²	semidirect
64. C₁₉×#529	C₂²	semidirect
65. C₁₉×#529	C₂²	semidirect
66. C₁₉×#529	C₂²	semidirect
67. C₂×C₁₉×#125	C₂²	semidirect
68. C₁₉×#525	C₂²	semidirect
69. C₁₉×#525	C₂²	semidirect
70. C₂×C₁₉×#123	C₂²	semidirect
71. C₂×C₁₉×#121	C₂²	semidirect
72. C₂×C₁₉×#121	C₂²	semidirect
74. C₁₉×#520	C₂²	semidirect
75. C₁₉×#520	C₂²	semidirect
76. C₁₉×#520	C₂²	semidirect
77. C₁₉×#520	C₂²	semidirect
78. C₁₉×#519	C₂²	semidirect
79. C₁₉×#518	C₂²	semidirect
80. C₁₉×#518	C₂²	semidirect
81. C₁₉×#518	C₂²	semidirect
84. C₄×#41×C₁₉	C₂²	semidirect
85. C₄×#41×C₁₉	C₂²	semidirect
86. C₄×#41×C₁₉	C₂²	semidirect
87. C₄×#41×C₁₉	C₂²	semidirect
88. C₂×C₄×D₄×C₁₉	C₂²	semidirect
89. C₂×C₄×D₄×C₁₉	C₂²	semidirect
90. C₂×C₁₉×#117	C₂²	semidirect
91. C₂×C₁₉×#117	C₂²	semidirect
234. #41×C₁₉	#41	semidirect
317. #62858	C₁₉	direct (N × H)
367. #3524	C₂×C₁₉	semidirect
368. #3519	C₂×C₁₉	semidirect
369. #3517	C₂×C₁₉	semidirect
370. #3513	C₂×C₁₉	semidirect
371. #3512	C₂×C₁₉	semidirect
372. #3508	C₂×C₁₉	semidirect
373. #3504	C₂×C₁₉	semidirect
374. #3498	C₂×C₁₉	semidirect
375. #3494	C₂×C₁₉	semidirect
376. #3488	C₂×C₁₉	semidirect
377. #3460	C₂×C₁₉	semidirect
378. #3455	C₂×C₁₉	semidirect
379. C₂×#540	C₂×C₁₉	semidirect
380. C₄×H(5,𝔽₂)	C₂×C₁₉	semidirect
381. #3428	C₂×C₁₉	semidirect
407. #559	C₂²×C₁₉	semidirect
408. #557	C₂²×C₁₉	semidirect
409. #555	C₂²×C₁₉	semidirect
410. #554	C₂²×C₁₉	semidirect
411. #553	C₂²×C₁₉	semidirect
412. #553	C₂²×C₁₉	semidirect
413. #553	C₂²×C₁₉	semidirect
414. #553	C₂²×C₁₉	semidirect
415. #552	C₂²×C₁₉	semidirect
416. #551	C₂²×C₁₉	semidirect
417. #550	C₂²×C₁₉	semidirect
418. #550	C₂²×C₁₉	semidirect
419. #550	C₂²×C₁₉	semidirect
420. #548	C₂²×C₁₉	semidirect
421. #547	C₂²×C₁₉	semidirect
422. #546	C₂²×C₁₉	semidirect
423. #546	C₂²×C₁₉	semidirect
424. #546	C₂²×C₁₉	semidirect
425. D₄²	C₂²×C₁₉	semidirect
426. D₄²	C₂²×C₁₉	semidirect
427. #544	C₂²×C₁₉	semidirect
428. #542	C₂²×C₁₉	semidirect
429. #542	C₂²×C₁₉	semidirect
430. #542	C₂²×C₁₉	semidirect
431. #541	C₂²×C₁₉	semidirect
432. #541	C₂²×C₁₉	semidirect
433. #540	C₂²×C₁₉	semidirect
434. #540	C₂²×C₁₉	semidirect
435. #540	C₂²×C₁₉	semidirect
436. #540	C₂²×C₁₉	semidirect
437. #540	C₂²×C₁₉	semidirect
438. #540	C₂²×C₁₉	semidirect
439. #540	C₂²×C₁₉	semidirect
440. #540	C₂²×C₁₉	semidirect
441. #539	C₂²×C₁₉	semidirect
442. #538	C₂²×C₁₉	semidirect
443. #538	C₂²×C₁₉	semidirect
444. #537	C₂²×C₁₉	semidirect
445. #535	C₂²×C₁₉	semidirect
446. #535	C₂²×C₁₉	semidirect
447. #533	C₂²×C₁₉	semidirect
448. #532	C₂²×C₁₉	semidirect
449. #532	C₂²×C₁₉	semidirect
450. #532	C₂²×C₁₉	semidirect
451. C₂×#127	C₂²×C₁₉	semidirect
452. #529	C₂²×C₁₉	semidirect
453. #529	C₂²×C₁₉	semidirect
454. #529	C₂²×C₁₉	semidirect
455. #529	C₂²×C₁₉	semidirect
456. C₂×#125	C₂²×C₁₉	semidirect
457. #525	C₂²×C₁₉	semidirect
458. #525	C₂²×C₁₉	semidirect
459. C₂×#123	C₂²×C₁₉	semidirect
460. C₂×#121	C₂²×C₁₉	semidirect
461. C₂×#121	C₂²×C₁₉	semidirect
463. #520	C₂²×C₁₉	semidirect
464. #520	C₂²×C₁₉	semidirect
465. #520	C₂²×C₁₉	semidirect
466. #520	C₂²×C₁₉	semidirect
467. #519	C₂²×C₁₉	semidirect
468. #518	C₂²×C₁₉	semidirect
469. #518	C₂²×C₁₉	semidirect
470. #518	C₂²×C₁₉	semidirect
473. C₄×#41	C₂²×C₁₉	semidirect
474. C₄×#41	C₂²×C₁₉	semidirect
475. C₄×#41	C₂²×C₁₉	semidirect
476. C₄×#41	C₂²×C₁₉	semidirect
477. C₂×C₄×D₄	C₂²×C₁₉	semidirect
478. C₂×C₄×D₄	C₂²×C₁₉	semidirect
479. C₂×#117	C₂²×C₁₉	semidirect
480. C₂×#117	C₂²×C₁₉	semidirect
621. C₁₉	#62858	direct (N × H)
630. #41	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3524	2
C₁₉×#3519	2
C₁₉×#3517	2
C₁₉×#3513	2
C₁₉×#3512	2
C₁₉×#3508	2
C₁₉×#3504	2
C₁₉×#3498	2
C₁₉×#3494	2
C₁₉×#3488	2
C₁₉×#3460	2
C₁₉×#3455	2
C₂×C₁₉×#540	2
C₄×C₁₉×H(5,𝔽₂)	2
C₁₉×#3428	2
#62858	19

Subgroups — C19×#62858 #18068817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62858 #18068817