Subgroups — C₁₉×#24407 #18030366

Order 4864.

1476 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3485	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#458	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#410	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2413	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2406	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2044	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2022	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1899	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1890	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1867	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1790	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#547	—	2	2	no	—
15	C₁₉×#547	—	2	2	no	—
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	2	no	—
18	C₁₉×#536	—	2	1	no	—
19	C₁₉×#534	—	2	1	no	—
20	C₁₉×#534	C₂²	1	2	yes	—
21	C₁₉×#525	—	2	1	no	—
22	C₂×C₁₉×#123	—	2	1	no	—
23	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#123	C₂²	1	2	yes	—
25	C₂×C₁₉×#123	C₂²	1	2	yes	—
26	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#518	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
29	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#458	—	2	4	no	—
31	C₁₉×#410	—	2	4	no	—
32	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#99	C₂²	1	2	yes	—
34	C₂×C₁₉×#99	C₂²	1	2	yes	—
35	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#99	C₂²	1	2	yes	complemented
37	C₁₉×#398	—	2	2	no	—
38	C₁₉×#396	—	2	2	no	—
39	C₁₉×#395	—	2	1	no	—
40	C₁₉×#394	—	2	1	no	—
41	C₁₉×#389	—	2	2	no	—
42	C₁₉×#388	—	2	2	no	—
43	C₁₉×#386	C₂²	1	1	yes	characteristic
44	C₁₉×#386	C₂²	1	2	yes	—
45	C₁₉×#386	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#385	—	2	1	no	—
47	C₁₉×#385	—	2	1	no	—
48	C₁₉×#385	C₂²	1	2	yes	complemented
49	C₁₉×#381	C₂²	1	2	yes	complemented
50	C₁₉×#381	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×#342	C₂²	1	2	yes	complemented
52	C₁₉×#342	C₂²	1	2	yes	complemented
53	C₁₉×H(5,𝔽₂)	—	2	2	no	—
54	C₁₉×H(5,𝔽₂)	—	2	2	no	—
55	C₁₉×H(5,𝔽₂)	—	4	2	no	—
56	C₂×#41×C₁₉	—	2	2	no	—
57	C₂×#41×C₁₉	—	2	2	no	—
58	C₂×#41×C₁₉	—	2	1	no	—
59	C₂×#41×C₁₉	—	2	2	no	—
60	C₂×#41×C₁₉	—	2	2	no	—
61	C₂×#41×C₁₉	—	2	2	no	—
62	C₂×#41×C₁₉	—	4	2	no	—
63	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	—	2	2	no	—
66	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×C₄⋊Q₈	—	2	2	no	—
76	C₁₉×#124	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×#123	—	2	2	no	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	2	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	2	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	4	no	—
89	C₁₉×#123	—	4	2	no	—
90	C₁₉×#123	—	4	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×#121	—	2	1	no	—
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#120	—	2	2	no	—
102	C₁₉×#120	—	2	2	no	—
103	C₁₉×#120	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	2	no	—
107	C₄×D₄×C₁₉	—	2	2	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	—	2	4	no	—
110	C₁₉×#117	—	4	2	no	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
120	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
133	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₉	—	2	2	no	—
141	C₁₉×#99	—	2	2	no	—
142	C₁₉×#99	—	2	4	no	—
143	C₁₉×#99	—	2	4	no	—
144	C₁₉×#99	—	4	2	no	—
145	C₁₉×#99	D₄	1	4	yes	complemented
146	C₁₉×#95	—	2	1	no	—
147	C₁₉×#95	—	2	2	no	—
148	C₁₉×#95	—	2	2	no	—
149	C₁₉×#95	—	2	1	no	—
150	C₁₉×#95	—	2	1	no	—
151	C₁₉×#95	—	2	1	no	—
152	C₁₉×#95	—	2	2	no	—
153	C₁₉×#95	—	2	2	no	—
154	C₂⁴×C₁₉	—	2	1	no	—
155	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
156	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
159	#41×C₁₉	—	4	4	no	—
160	#41×C₁₉	—	4	4	no	—
161	#41×C₁₉	—	4	4	no	—
162	#41×C₁₉	—	4	4	no	—
163	#41×C₁₉	—	4	4	no	—
164	#41×C₁₉	—	4	4	no	—
165	#41×C₁₉	—	4	2	no	—
166	#41×C₁₉	—	4	2	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	2	2	no	—
169	C₂×Q₈×C₁₉	—	2	2	no	—
170	C₂×Q₈×C₁₉	—	4	1	no	—
171	C₂×D₄×C₁₉	—	2	2	no	—
172	C₂×D₄×C₁₉	—	2	2	no	—
173	C₂×D₄×C₁₉	—	2	2	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	2	no	—
176	C₂×D₄×C₁₉	—	2	2	no	—
177	C₂×D₄×C₁₉	—	2	2	no	—
178	C₂×D₄×C₁₉	—	2	2	no	—
179	C₂×D₄×C₁₉	—	2	2	no	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	2	no	—
183	C₂×D₄×C₁₉	—	2	2	no	—
184	C₂×D₄×C₁₉	—	2	2	no	—
185	C₂×D₄×C₁₉	—	2	2	no	—
186	C₂×D₄×C₁₉	—	2	2	no	—
187	C₂×D₄×C₁₉	—	2	2	no	—
188	C₂×D₄×C₁₉	—	2	2	no	—
189	C₂×D₄×C₁₉	—	4	1	no	—
190	C₂×D₄×C₁₉	—	4	4	no	—
191	C₂×D₄×C₁₉	—	4	4	no	—
192	C₂×D₄×C₁₉	—	4	2	no	—
193	C₂×D₄×C₁₉	—	4	2	no	—
194	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₁₉	#41	1	2	yes	—
196	C₂²×C₄×C₁₉	—	2	1	no	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	2	no	—
199	C₂²×C₄×C₁₉	—	2	1	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	2	no	—
202	C₂²×C₄×C₁₉	—	2	2	no	—
203	C₂²×C₄×C₁₉	—	2	1	no	—
204	C₂²×C₄×C₁₉	—	2	2	no	—
205	C₂²×C₄×C₁₉	—	2	1	no	—
206	C₂²×C₄×C₁₉	—	2	1	no	—
207	C₂²×C₄×C₁₉	—	2	1	no	—
208	C₂²×C₄×C₁₉	—	2	1	no	—
209	C₂²×C₄×C₁₉	—	2	1	no	—
210	C₂²×C₄×C₁₉	—	2	1	no	—
211	C₂²×C₄×C₁₉	—	2	2	no	—
212	C₂²×C₄×C₁₉	—	2	2	no	—
213	C₂²×C₄×C₁₉	—	2	1	no	—
214	C₂²×C₄×C₁₉	—	2	1	no	—
215	C₂²×C₄×C₁₉	—	2	1	no	—
216	C₂²×C₄×C₁₉	—	2	2	no	—
217	C₂²×C₄×C₁₉	—	2	1	no	—
218	C₂²×C₄×C₁₉	—	2	1	no	—
219	C₂²×C₄×C₁₉	—	2	2	no	—
220	C₂²×C₄×C₁₉	—	4	2	no	—
221	C₂²×C₄×C₁₉	—	4	1	no	—
222	C₂²×C₄×C₁₉	—	4	1	no	—
223	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
232	C₄⋊C₄×C₁₉	—	2	2	no	—
233	C₄⋊C₄×C₁₉	—	2	2	no	—
234	C₄⋊C₄×C₁₉	—	2	1	no	—
235	C₄⋊C₄×C₁₉	—	2	1	no	—
236	C₄⋊C₄×C₁₉	—	2	2	no	—
237	C₄⋊C₄×C₁₉	—	2	2	no	—
238	C₄⋊C₄×C₁₉	—	2	2	no	—
239	C₄⋊C₄×C₁₉	—	2	2	no	—
240	C₄⋊C₄×C₁₉	—	4	4	no	—
241	C₄⋊C₄×C₁₉	—	4	4	no	—
242	C₄⋊C₄×C₁₉	—	4	4	no	—
243	C₄⋊C₄×C₁₉	—	4	2	no	—
244	C₄⋊C₄×C₁₉	—	4	1	no	—
245	C₄⋊C₄×C₁₉	—	4	1	no	—
246	C₄⋊C₄×C₁₉	—	4	2	no	—
247	C₄⋊C₄×C₁₉	—	4	2	no	—
248	C₂²⋊C₄×C₁₉	—	2	2	no	—
249	C₂²⋊C₄×C₁₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₉	—	2	2	no	—
251	C₂²⋊C₄×C₁₉	—	2	2	no	—
252	C₂²⋊C₄×C₁₉	—	2	2	no	—
253	C₂²⋊C₄×C₁₉	—	2	2	no	—
254	C₂²⋊C₄×C₁₉	—	2	2	no	—
255	C₂²⋊C₄×C₁₉	—	2	2	no	—
256	C₂²⋊C₄×C₁₉	—	2	2	no	—
257	C₂²⋊C₄×C₁₉	—	2	2	no	—
258	C₂²⋊C₄×C₁₉	—	2	2	no	—
259	C₂²⋊C₄×C₁₉	—	2	2	no	—
260	C₂²⋊C₄×C₁₉	—	2	2	no	—
261	C₂²⋊C₄×C₁₉	—	2	1	no	—
262	C₂²⋊C₄×C₁₉	—	2	1	no	—
263	C₂²⋊C₄×C₁₉	—	2	2	no	—
264	C₂²⋊C₄×C₁₉	—	2	2	no	—
265	C₂²⋊C₄×C₁₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₉	—	4	2	no	—
267	C₂²⋊C₄×C₁₉	—	4	2	no	—
268	C₂²⋊C₄×C₁₉	—	4	4	no	—
269	C₂²⋊C₄×C₁₉	—	4	2	no	—
270	C₂²⋊C₄×C₁₉	—	4	2	no	—
271	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
272	C₄²×C₁₉	—	2	2	no	—
273	C₄²×C₁₉	—	4	4	no	—
274	#24407	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂³×C₁₉	—	2	1	no	—
276	C₂³×C₁₉	—	2	1	no	—
277	C₂³×C₁₉	—	2	2	no	—
278	C₂³×C₁₉	—	2	1	no	—
279	C₂³×C₁₉	—	2	1	no	—
280	C₂³×C₁₉	—	2	1	no	—
281	C₂³×C₁₉	—	2	2	no	—
282	C₂³×C₁₉	—	2	2	no	—
283	C₂³×C₁₉	—	4	1	no	—
284	C₂³×C₁₉	—	4	1	no	—
285	C₂³×C₁₉	—	4	1	no	—
286	C₂³×C₁₉	—	4	1	no	—
287	C₂³×C₁₉	—	4	1	no	—
288	C₂³×C₁₉	—	4	1	no	—
289	C₂³×C₁₉	—	4	2	no	—
290	C₂³×C₁₉	—	4	2	no	—
291	C₂³×C₁₉	—	4	2	no	—
292	C₂³×C₁₉	—	8	1	no	—
293	C₂³×C₁₉	—	8	1	no	—
294	C₂³×C₁₉	#121	1	2	yes	—
295	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
296	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
297	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
299	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
300	Q₈×C₁₉	—	4	4	no	—
301	Q₈×C₁₉	—	4	2	no	—
302	D₄×C₁₉	—	2	4	no	—
303	D₄×C₁₉	—	2	4	no	—
304	D₄×C₁₉	—	4	4	no	—
305	D₄×C₁₉	—	4	2	no	—
306	D₄×C₁₉	—	4	4	no	—
307	D₄×C₁₉	—	4	2	no	—
308	D₄×C₁₉	—	4	2	no	—
309	D₄×C₁₉	—	4	2	no	—
310	D₄×C₁₉	—	4	2	no	—
311	D₄×C₁₉	—	4	2	no	—
312	D₄×C₁₉	—	4	2	no	—
313	D₄×C₁₉	—	8	2	no	—
314	D₄×C₁₉	—	8	2	no	—
315	C₂×C₄×C₁₉	—	2	1	no	—
316	C₂×C₄×C₁₉	—	2	1	no	—
317	C₂×C₄×C₁₉	—	2	1	no	—
318	C₂×C₄×C₁₉	—	2	1	no	—
319	C₂×C₄×C₁₉	—	2	1	no	—
320	C₂×C₄×C₁₉	—	2	1	no	—
321	C₂×C₄×C₁₉	—	2	2	no	—
322	C₂×C₄×C₁₉	—	2	2	no	—
323	C₂×C₄×C₁₉	—	2	2	no	—
324	C₂×C₄×C₁₉	—	2	2	no	—
325	C₂×C₄×C₁₉	—	2	2	no	—
326	C₂×C₄×C₁₉	—	2	4	no	—
327	C₂×C₄×C₁₉	—	2	2	no	—
328	C₂×C₄×C₁₉	—	2	2	no	—
329	C₂×C₄×C₁₉	—	2	1	no	—
330	C₂×C₄×C₁₉	—	2	2	no	—
331	C₂×C₄×C₁₉	—	2	1	no	—
332	C₂×C₄×C₁₉	—	2	1	no	—
333	C₂×C₄×C₁₉	—	2	4	no	—
334	C₂×C₄×C₁₉	—	2	2	no	—
335	C₂×C₄×C₁₉	—	2	2	no	—
336	C₂×C₄×C₁₉	—	4	2	no	—
337	C₂×C₄×C₁₉	—	4	2	no	—
338	C₂×C₄×C₁₉	—	4	2	no	—
339	C₂×C₄×C₁₉	—	4	2	no	—
340	C₂×C₄×C₁₉	—	4	4	no	—
341	C₂×C₄×C₁₉	—	4	2	no	—
342	C₂×C₄×C₁₉	—	4	2	no	—
343	C₂×C₄×C₁₉	—	4	2	no	—
344	C₂×C₄×C₁₉	—	4	1	no	—
345	C₂×C₄×C₁₉	—	4	2	no	—
346	C₂×C₄×C₁₉	—	4	1	no	—
347	C₂×C₄×C₁₉	—	4	2	no	—
348	C₂×C₄×C₁₉	—	4	2	no	—
349	C₂×C₄×C₁₉	—	4	2	no	—
350	C₂×C₄×C₁₉	—	4	1	no	—
351	C₂×C₄×C₁₉	—	4	1	no	—
352	C₂×C₄×C₁₉	—	4	2	no	—
353	C₂×C₄×C₁₉	—	4	1	no	—
354	C₂×C₄×C₁₉	—	4	1	no	—
355	C₂×C₄×C₁₉	—	4	1	no	—
356	C₂×C₄×C₁₉	—	4	1	no	—
357	C₂×C₄×C₁₉	—	4	1	no	—
358	C₂×C₄×C₁₉	—	4	1	no	—
359	C₂×C₄×C₁₉	—	4	1	no	—
360	C₂×C₄×C₁₉	—	4	2	no	—
361	C₂×C₄×C₁₉	—	4	2	no	—
362	C₂×C₄×C₁₉	—	4	2	no	—
363	C₂×C₄×C₁₉	—	8	1	no	—
364	C₂×C₄×C₁₉	—	8	1	no	—
365	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
366	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
367	C₂×C₄×C₁₉	#120	1	2	yes	—
368	C₂×C₄×C₁₉	#121	1	2	yes	—
369	#3485	C₂×C₁₉	1	1	yes	characteristic
370	C₂×#458	C₂×C₁₉	1	1	yes	characteristic, complemented
371	C₂×#410	C₂×C₁₉	1	1	yes	characteristic, complemented
372	#2413	C₂×C₁₉	1	2	yes	complemented
373	#2406	C₂×C₁₉	1	1	yes	characteristic, complemented
374	#2044	C₂×C₁₉	1	2	yes	complemented
375	#2022	C₂×C₁₉	1	2	yes	complemented
376	#1899	C₂×C₁₉	1	2	yes	complemented
377	#1890	C₂×C₁₉	1	1	yes	characteristic, complemented
378	#1867	C₂×C₁₉	1	1	yes	characteristic, complemented
379	#1790	C₂×C₁₉	1	1	yes	characteristic, complemented
380	C₂²×C₁₉	—	2	2	no	—
381	C₂²×C₁₉	—	2	1	no	—
382	C₂²×C₁₉	—	2	2	no	—
383	C₂²×C₁₉	—	2	1	no	—
384	C₂²×C₁₉	—	2	2	no	—
385	C₂²×C₁₉	—	4	1	no	—
386	C₂²×C₁₉	—	4	1	no	—
387	C₂²×C₁₉	—	4	2	no	—
388	C₂²×C₁₉	—	4	2	no	—
389	C₂²×C₁₉	—	4	2	no	—
390	C₂²×C₁₉	—	4	1	no	—
391	C₂²×C₁₉	—	4	1	no	—
392	C₂²×C₁₉	—	4	1	no	—
393	C₂²×C₁₉	—	4	2	no	—
394	C₂²×C₁₉	—	4	1	no	—
395	C₂²×C₁₉	—	4	2	no	—
396	C₂²×C₁₉	—	4	1	no	—
397	C₂²×C₁₉	—	4	2	no	—
398	C₂²×C₁₉	—	8	1	no	—
399	C₂²×C₁₉	—	8	2	no	—
400	C₂²×C₁₉	—	8	1	no	—
401	C₂²×C₁₉	—	8	2	no	—
402	C₂²×C₁₉	—	16	2	no	—
403	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
404	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
405	C₂²×C₁₉	#534	1	1	yes	characteristic
406	C₂²×C₁₉	D₄²	1	2	yes	—
407	C₂²×C₁₉	#546	1	2	yes	—
408	C₄×C₁₉	—	2	1	no	—
409	C₄×C₁₉	—	2	1	no	—
410	C₄×C₁₉	—	2	2	no	—
411	C₄×C₁₉	—	2	2	no	—
412	C₄×C₁₉	—	4	4	no	—
413	C₄×C₁₉	—	4	2	no	—
414	C₄×C₁₉	—	4	1	no	—
415	C₄×C₁₉	—	4	2	no	—
416	C₄×C₁₉	—	4	2	no	—
417	C₄×C₁₉	—	4	2	no	—
418	C₄×C₁₉	—	8	2	no	—
419	C₄×C₁₉	—	8	1	no	—
420	C₄×C₁₉	—	8	1	no	—
421	C₄×C₁₉	—	8	1	no	—
422	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
423	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
424	#547	—	2	2	no	—
425	#547	—	2	2	no	—
426	#546	—	2	2	no	—
427	#546	—	2	2	no	—
428	#536	—	2	1	no	—
429	#534	—	2	1	no	—
430	#534	C₂²×C₁₉	1	2	yes	—
431	#525	—	2	1	no	—
432	C₂×#123	—	2	1	no	—
433	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
434	C₂×#123	C₂²×C₁₉	1	2	yes	—
435	C₂×#123	C₂²×C₁₉	1	2	yes	—
436	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic, complemented
437	#518	C₂²×C₁₉	1	1	yes	characteristic
438	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
439	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
440	#458	—	2	4	no	—
441	#410	—	2	4	no	—
442	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
443	C₂×#99	C₂²×C₁₉	1	2	yes	—
444	C₂×#99	C₂²×C₁₉	1	2	yes	—
445	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
446	C₂×#99	C₂²×C₁₉	1	2	yes	complemented
447	#398	—	2	2	no	—
448	#396	—	2	2	no	—
449	#395	—	2	1	no	—
450	#394	—	2	1	no	—
451	#389	—	2	2	no	—
452	#388	—	2	2	no	—
453	#386	C₂²×C₁₉	1	1	yes	characteristic
454	#386	C₂²×C₁₉	1	2	yes	—
455	#386	C₂²×C₁₉	1	1	yes	characteristic, complemented
456	#385	—	2	1	no	—
457	#385	—	2	1	no	—
458	#385	C₂²×C₁₉	1	2	yes	complemented
459	#381	C₂²×C₁₉	1	2	yes	complemented
460	#381	C₂²×C₁₉	1	1	yes	characteristic, complemented
461	#342	C₂²×C₁₉	1	2	yes	complemented
462	#342	C₂²×C₁₉	1	2	yes	complemented
463	C₂×C₁₉	—	2	2	no	—
464	C₂×C₁₉	—	2	1	no	—
465	C₂×C₁₉	—	2	1	no	—
466	C₂×C₁₉	—	2	2	no	—
467	C₂×C₁₉	—	4	2	no	—
468	C₂×C₁₉	—	8	1	no	—
469	C₂×C₁₉	—	8	2	no	—
470	C₂×C₁₉	#2410	1	1	yes	characteristic
471	C₂×C₁₉	#3025	1	1	yes	characteristic
472	C₂×C₁₉	#3028	1	1	yes	characteristic
473	H(5,𝔽₂)	—	2	2	no	—
474	H(5,𝔽₂)	—	2	2	no	—
475	H(5,𝔽₂)	—	4	2	no	—
476	C₂×#41	—	2	2	no	—
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	—	2	2	no	—
482	C₂×#41	—	4	2	no	—
483	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	—	2	2	no	—
486	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
487	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
488	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
490	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
491	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
495	C₄⋊Q₈	—	2	2	no	—
496	#124	—	2	2	no	—
497	#123	—	2	2	no	—
498	#123	—	2	2	no	—
499	#123	—	2	2	no	—
500	#123	—	2	2	no	—
501	#123	—	2	2	no	—
502	#123	—	2	2	no	—
503	#123	—	2	2	no	—
504	#123	—	2	2	no	—
505	#123	—	2	2	no	—
506	#123	—	2	2	no	—
507	#123	—	2	2	no	—
508	#123	—	2	4	no	—
509	#123	—	4	2	no	—
510	#123	—	4	2	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	#121	—	2	1	no	—
516	#121	—	2	1	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#120	—	2	2	no	—
522	#120	—	2	2	no	—
523	#120	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	#117	—	2	1	no	—
529	#117	—	2	4	no	—
530	#117	—	4	2	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	2	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
543	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	2	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	2	no	—
553	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
554	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
560	C₂×C₄²	—	2	2	no	—
561	#99	—	2	2	no	—
562	#99	—	2	4	no	—
563	#99	—	2	4	no	—
564	#99	—	4	2	no	—
565	#99	D₄×C₁₉	1	4	yes	complemented
566	#95	—	2	1	no	—
567	#95	—	2	2	no	—
568	#95	—	2	2	no	—
569	#95	—	2	1	no	—
570	#95	—	2	1	no	—
571	#95	—	2	1	no	—
572	#95	—	2	2	no	—
573	#95	—	2	2	no	—
574	C₁₉	#24407	1	1	yes	characteristic, direct product factor, Sylow
575	C₂⁴	—	2	1	no	—
576	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
577	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
578	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
579	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
580	#41	—	4	4	no	—
581	#41	—	4	4	no	—
582	#41	—	4	4	no	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	—	4	4	no	—
586	#41	—	4	2	no	—
587	#41	—	4	2	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	2	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	4	1	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	4	1	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
616	C₂×D₄	#41×C₁₉	1	2	yes	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	1	no	—
643	C₂²×C₄	—	4	1	no	—
644	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
645	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
649	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
650	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
652	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	4	4	no	—
662	C₄⋊C₄	—	4	4	no	—
663	C₄⋊C₄	—	4	4	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	1	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	—	2	1	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	2	no	—
688	C₂²⋊C₄	—	4	2	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	4	2	no	—
692	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
693	C₄²	—	2	2	no	—
694	C₄²	—	4	4	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	8	1	no	—
713	C₂³	—	8	1	no	—
714	C₂³	C₁₉×#121	1	2	yes	—
715	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
716	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
717	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
718	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
719	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
720	Q₈	—	4	4	no	—
721	Q₈	—	4	2	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	4	no	—
724	D₄	—	4	4	no	—
725	D₄	—	4	2	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	2	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	2	no	—
734	D₄	—	8	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	8	1	no	—
784	C₂×C₄	—	8	1	no	—
785	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
786	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
787	C₂×C₄	C₁₉×#120	1	2	yes	—
788	C₂×C₄	C₁₉×#121	1	2	yes	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	8	1	no	—
808	C₂²	—	8	2	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	2	no	—
811	C₂²	—	16	2	no	—
812	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
813	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
814	C₂²	C₁₉×#534	1	1	yes	characteristic
815	C₂²	D₄²×C₁₉	1	2	yes	—
816	C₂²	C₁₉×#546	1	2	yes	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	4	4	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	8	2	no	—
828	C₄	—	8	1	no	—
829	C₄	—	8	1	no	—
830	C₄	—	8	1	no	—
831	C₂	—	2	2	no	—
832	C₂	—	2	1	no	—
833	C₂	—	2	1	no	—
834	C₂	—	2	2	no	—
835	C₂	—	4	2	no	—
836	C₂	—	8	1	no	—
837	C₂	—	8	2	no	—
838	C₂	C₁₉×#2410	1	1	yes	characteristic
839	C₂	C₁₉×#3025	1	1	yes	characteristic
840	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₁₉×#3485	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₉×#458	C₂	semidirect
3. C₂×C₁₉×#410	C₂	semidirect
4. C₁₉×#2413	C₂	semidirect
5. C₁₉×#2406	C₂	semidirect
6. C₁₉×#2044	C₂	semidirect
7. C₁₉×#2022	C₂	semidirect
8. C₁₉×#1899	C₂	semidirect
9. C₁₉×#1890	C₂	semidirect
10. C₁₉×#1867	C₂	semidirect
11. C₁₉×#1790	C₂	semidirect
26. C₂×C₁₉×#123	C₂²	semidirect
28. C₂×C₁₉×#117	C₂²	semidirect
29. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
36. C₂×C₁₉×#99	C₂²	semidirect
45. C₁₉×#386	C₂²	semidirect
48. C₁₉×#385	C₂²	semidirect
49. C₁₉×#381	C₂²	semidirect
50. C₁₉×#381	C₂²	semidirect
51. C₁₉×#342	C₂²	semidirect
52. C₁₉×#342	C₂²	semidirect
145. C₁₉×#99	D₄	semidirect
274. #24407	C₁₉	direct (N × H)
370. C₂×#458	C₂×C₁₉	semidirect
371. C₂×#410	C₂×C₁₉	semidirect
372. #2413	C₂×C₁₉	semidirect
373. #2406	C₂×C₁₉	semidirect
374. #2044	C₂×C₁₉	semidirect
375. #2022	C₂×C₁₉	semidirect
376. #1899	C₂×C₁₉	semidirect
377. #1890	C₂×C₁₉	semidirect
378. #1867	C₂×C₁₉	semidirect
379. #1790	C₂×C₁₉	semidirect
436. C₂×#123	C₂²×C₁₉	semidirect
438. C₂×#117	C₂²×C₁₉	semidirect
439. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
446. C₂×#99	C₂²×C₁₉	semidirect
455. #386	C₂²×C₁₉	semidirect
458. #385	C₂²×C₁₉	semidirect
459. #381	C₂²×C₁₉	semidirect
460. #381	C₂²×C₁₉	semidirect
461. #342	C₂²×C₁₉	semidirect
462. #342	C₂²×C₁₉	semidirect
565. #99	D₄×C₁₉	semidirect
574. C₁₉	#24407	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×#3485	2
C₂×C₁₉×#458	2
C₂×C₁₉×#410	2
C₁₉×#2413	2
C₁₉×#2406	2
C₁₉×#2044	2
C₁₉×#2022	2
C₁₉×#1899	2
C₁₉×#1890	2
C₁₉×#1867	2
C₁₉×#1790	2
#24407	19

Subgroups — C19×#24407 #18030366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24407 #18030366