Subgroups — C₁₉×#18695 #18024654

Order 4864.

866 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3552	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1638	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1637	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1636	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1635	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1494	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	2	no	—
13	C₁₉×#557	C₂²	1	1	yes	characteristic
14	C₁₉×#556	C₂²	1	1	yes	characteristic
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#553	—	2	1	no	—
17	D₄×Q₈×C₁₉	—	2	1	no	—
18	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#548	—	2	1	no	—
20	C₁₉×#547	C₂²	1	1	yes	characteristic
21	C₁₉×#544	—	2	1	no	—
22	C₁₉×#542	—	2	1	no	—
23	C₁₉×#541	—	2	1	no	—
24	C₁₉×#539	—	2	2	no	—
25	C₁₉×#536	—	2	1	no	—
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₁₉×#529	C₂²	1	1	yes	characteristic
29	C₁₉×#529	C₂²	1	1	yes	characteristic
30	C₁₉×#501	—	2	1	no	—
31	C₁₉×#501	—	2	1	no	—
32	C₁₉×#489	—	2	1	no	—
33	C₁₉×#489	—	2	1	no	—
34	C₁₉×#487	—	2	2	no	—
35	C₁₉×#487	C₂²	1	2	yes	—
36	C₁₉×#487	C₂²	1	2	yes	—
37	C₁₉×#483	—	2	1	no	—
38	C₁₉×#483	—	2	1	no	—
39	C₁₉×#480	—	2	1	no	—
40	C₁₉×#480	—	2	1	no	—
41	C₁₉×#477	C₂²	1	2	yes	—
42	C₁₉×#477	C₂²	1	2	yes	—
43	C₁₉×#476	C₂²	1	2	yes	—
44	C₁₉×#476	C₂²	1	2	yes	—
45	C₁₉×#432	C₂²	1	1	yes	characteristic
46	C₁₉×#432	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#103	—	2	2	no	—
48	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
49	C₁₉×#332	C₂²	1	2	yes	—
50	C₁₉×#332	C₂²	1	2	yes	—
51	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₉×Q₈⋊C₈	C₂²	1	2	yes	—
53	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
54	C₁₉×D₄⋊C₈	C₂²	1	2	yes	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×Q₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₁₉×C₄⋊Q₈	—	2	2	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	—	2	1	no	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	1	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₉×#126	—	2	2	no	—
73	C₁₉×#126	—	2	2	no	—
74	C₁₉×#126	—	2	2	no	—
75	C₁₉×#126	—	2	1	no	—
76	C₁₉×#126	—	2	1	no	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	—	2	2	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	D₄	1	1	yes	characteristic
82	C₁₉×#125	D₄	1	1	yes	characteristic
83	C₁₉×#124	—	2	2	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×#124	D₄	1	1	yes	characteristic
86	C₁₉×#124	D₄	1	1	yes	characteristic
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	1	no	—
90	C₁₉×#123	—	2	1	no	—
91	C₁₉×#123	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	1	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	1	no	—
100	C₁₉×C₂²⋊Q₈	—	2	1	no	—
101	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
102	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	D₄	1	1	yes	characteristic
106	C₁₉×#121	D₄	1	1	yes	characteristic
107	C₄×Q₈×C₁₉	—	2	1	no	—
108	C₄×Q₈×C₁₉	—	2	1	no	—
109	C₄×Q₈×C₁₉	—	2	1	no	—
110	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₄×D₄×C₁₉	—	2	2	no	—
113	C₄×D₄×C₁₉	—	2	2	no	—
114	C₄×D₄×C₁₉	—	2	1	no	—
115	C₄×D₄×C₁₉	—	2	1	no	—
116	C₄×D₄×C₁₉	—	2	1	no	—
117	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₁₉×#117	—	2	1	no	—
120	C₁₉×#117	—	2	1	no	—
121	C₁₉×#117	—	2	1	no	—
122	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₁₉×#107	—	2	2	no	—
129	C₁₉×#107	—	2	2	no	—
130	C₁₉×#106	—	2	2	no	—
131	C₁₉×#106	—	2	2	no	—
132	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
133	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#103	—	2	4	no	—
137	C₁₉×#103	—	2	4	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	2	no	—
140	C₁₉×C₂²⋊C₈	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×#97	—	2	1	no	—
143	C₁₉×#97	—	2	1	no	—
144	C₄×C₈×C₁₉	—	2	1	no	—
145	C₄×C₈×C₁₉	C₂³	1	2	yes	—
146	#41×C₁₉	—	8	2	no	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	—	2	1	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	4	4	no	—
153	C₂×Q₈×C₁₉	—	4	1	no	—
154	C₂×Q₈×C₁₉	—	8	2	no	—
155	C₂×Q₈×C₁₉	—	8	2	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	—	2	2	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	2	2	no	—
175	C₂×C₈×C₁₉	—	4	2	no	—
176	C₄⋊C₄×C₁₉	—	2	2	no	—
177	C₄⋊C₄×C₁₉	—	2	2	no	—
178	C₄⋊C₄×C₁₉	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	1	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	1	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	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	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	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	1	no	—
217	C₂²⋊C₄×C₁₉	—	2	1	no	—
218	C₄²×C₁₉	—	2	2	no	—
219	C₄²×C₁₉	—	2	2	no	—
220	C₄²×C₁₉	—	2	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
226	#18695	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂³×C₁₉	—	2	1	no	—
228	C₂³×C₁₉	—	2	1	no	—
229	C₂³×C₁₉	#120	1	1	yes	characteristic
230	Q₈×C₁₉	—	2	2	no	—
231	Q₈×C₁₉	—	2	2	no	—
232	Q₈×C₁₉	—	4	4	no	—
233	Q₈×C₁₉	—	4	2	no	—
234	Q₈×C₁₉	—	4	2	no	—
235	Q₈×C₁₉	—	8	2	no	—
236	Q₈×C₁₉	—	8	2	no	—
237	Q₈×C₁₉	—	8	2	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	2	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	1	no	—
249	C₂×C₄×C₁₉	—	2	1	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	8	2	no	—
258	C₂×C₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	—	8	2	no	—
260	C₂×C₄×C₁₉	—	8	2	no	—
261	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
267	C₈×C₁₉	—	4	2	no	—
268	C₈×C₁₉	—	4	2	no	—
269	C₈×C₁₉	—	4	2	no	—
270	#3552	C₂×C₁₉	1	1	yes	characteristic
271	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#3238	C₂×C₁₉	1	1	yes	characteristic, complemented
273	C₂×#487	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1638	C₂×C₁₉	1	2	yes	complemented
275	#1637	C₂×C₁₉	1	2	yes	complemented
276	#1636	C₂×C₁₉	1	2	yes	complemented
277	#1635	C₂×C₁₉	1	2	yes	complemented
278	#1556	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1494	C₂×C₁₉	1	1	yes	characteristic, complemented
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	—	4	1	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	#454	1	2	yes	—
290	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	2	no	—
297	C₄×C₁₉	—	4	1	no	—
298	C₄×C₁₉	—	4	2	no	—
299	C₄×C₁₉	—	4	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	8	2	no	—
304	C₄×C₁₉	#577	1	2	yes	—
305	C₄×C₁₉	#578	1	2	yes	—
306	#563	—	2	2	no	—
307	#557	C₂²×C₁₉	1	1	yes	characteristic
308	#556	C₂²×C₁₉	1	1	yes	characteristic
309	#554	—	2	1	no	—
310	#553	—	2	1	no	—
311	D₄×Q₈	—	2	1	no	—
312	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
313	#548	—	2	1	no	—
314	#547	C₂²×C₁₉	1	1	yes	characteristic
315	#544	—	2	1	no	—
316	#542	—	2	1	no	—
317	#541	—	2	1	no	—
318	#539	—	2	2	no	—
319	#536	—	2	1	no	—
320	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
322	#529	C₂²×C₁₉	1	1	yes	characteristic
323	#529	C₂²×C₁₉	1	1	yes	characteristic
324	#501	—	2	1	no	—
325	#501	—	2	1	no	—
326	#489	—	2	1	no	—
327	#489	—	2	1	no	—
328	#487	—	2	2	no	—
329	#487	C₂²×C₁₉	1	2	yes	—
330	#487	C₂²×C₁₉	1	2	yes	—
331	#483	—	2	1	no	—
332	#483	—	2	1	no	—
333	#480	—	2	1	no	—
334	#480	—	2	1	no	—
335	#477	C₂²×C₁₉	1	2	yes	—
336	#477	C₂²×C₁₉	1	2	yes	—
337	#476	C₂²×C₁₉	1	2	yes	—
338	#476	C₂²×C₁₉	1	2	yes	—
339	#432	C₂²×C₁₉	1	1	yes	characteristic
340	#432	C₂²×C₁₉	1	1	yes	characteristic
341	C₂×#103	—	2	2	no	—
342	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
343	#332	C₂²×C₁₉	1	2	yes	—
344	#332	C₂²×C₁₉	1	2	yes	—
345	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
346	Q₈⋊C₈	C₂²×C₁₉	1	2	yes	—
347	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
348	D₄⋊C₈	C₂²×C₁₉	1	2	yes	—
349	C₂×C₁₉	—	2	2	no	—
350	C₂×C₁₉	—	8	1	no	—
351	C₂×C₁₉	—	8	1	no	—
352	C₂×C₁₉	#3009	1	1	yes	characteristic
353	C₂×C₁₉	#3011	1	1	yes	characteristic
354	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
355	C₂×#41	—	2	1	no	—
356	C₂²×Q₈	—	2	1	no	—
357	C₂²×Q₈	—	2	1	no	—
358	C₂²×Q₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
369	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
370	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
372	#126	—	2	2	no	—
373	#126	—	2	2	no	—
374	#126	—	2	2	no	—
375	#126	—	2	1	no	—
376	#126	—	2	1	no	—
377	#125	—	2	2	no	—
378	#125	—	2	2	no	—
379	#125	—	2	2	no	—
380	#125	—	2	1	no	—
381	#125	D₄×C₁₉	1	1	yes	characteristic
382	#125	D₄×C₁₉	1	1	yes	characteristic
383	#124	—	2	2	no	—
384	#124	—	2	1	no	—
385	#124	D₄×C₁₉	1	1	yes	characteristic
386	#124	D₄×C₁₉	1	1	yes	characteristic
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	#123	—	2	1	no	—
390	#123	—	2	1	no	—
391	#123	—	2	2	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	1	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
402	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
403	#121	—	2	2	no	—
404	#121	—	2	1	no	—
405	#121	D₄×C₁₉	1	1	yes	characteristic
406	#121	D₄×C₁₉	1	1	yes	characteristic
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
411	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
418	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
428	#107	—	2	2	no	—
429	#107	—	2	2	no	—
430	#106	—	2	2	no	—
431	#106	—	2	2	no	—
432	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
433	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#103	—	2	4	no	—
437	#103	—	2	4	no	—
438	#102	—	2	2	no	—
439	#102	—	2	2	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	C₂²⋊C₈	—	2	1	no	—
442	#97	—	2	1	no	—
443	#97	—	2	1	no	—
444	C₄×C₈	—	2	1	no	—
445	C₄×C₈	C₂³×C₁₉	1	2	yes	—
446	C₁₉	#18695	1	1	yes	characteristic, direct product factor, Sylow
447	#41	—	8	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	4	4	no	—
454	C₂×Q₈	—	4	1	no	—
455	C₂×Q₈	—	8	2	no	—
456	C₂×Q₈	—	8	2	no	—
457	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	4	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
500	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
501	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	C₁₉×#120	1	1	yes	characteristic
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	4	4	no	—
533	Q₈	—	4	2	no	—
534	Q₈	—	4	2	no	—
535	Q₈	—	8	2	no	—
536	Q₈	—	8	2	no	—
537	Q₈	—	8	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	2	2	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	8	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
562	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
563	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
567	C₈	—	4	2	no	—
568	C₈	—	4	2	no	—
569	C₈	—	4	2	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	C₁₉×#454	1	2	yes	—
579	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	8	2	no	—
593	C₄	C₁₉×#577	1	2	yes	—
594	C₄	C₁₉×#578	1	2	yes	—
595	C₂	—	2	2	no	—
596	C₂	—	8	1	no	—
597	C₂	—	8	1	no	—
598	C₂	C₁₉×#3009	1	1	yes	characteristic
599	C₂	C₁₉×#3011	1	1	yes	characteristic
600	C₂	C₂×C₁₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3552	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3238	C₂	semidirect
3. C₁₉×#3238	C₂	semidirect
4. C₂×C₁₉×#487	C₂	semidirect
5. C₁₉×#1638	C₂	semidirect
6. C₁₉×#1637	C₂	semidirect
7. C₁₉×#1636	C₂	semidirect
8. C₁₉×#1635	C₂	semidirect
9. C₁₉×#1556	C₂	semidirect
10. C₁₉×#1494	C₂	semidirect
11. C₁₉×#1494	C₂	semidirect
226. #18695	C₁₉	direct (N × H)
271. #3238	C₂×C₁₉	semidirect
272. #3238	C₂×C₁₉	semidirect
273. C₂×#487	C₂×C₁₉	semidirect
274. #1638	C₂×C₁₉	semidirect
275. #1637	C₂×C₁₉	semidirect
276. #1636	C₂×C₁₉	semidirect
277. #1635	C₂×C₁₉	semidirect
278. #1556	C₂×C₁₉	semidirect
279. #1494	C₂×C₁₉	semidirect
280. #1494	C₂×C₁₉	semidirect
446. C₁₉	#18695	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×#3552	2
C₁₉×#3238	2
C₂×C₁₉×#487	2
C₁₉×#1638	2
C₁₉×#1637	2
C₁₉×#1636	2
C₁₉×#1635	2
C₁₉×#1556	2
C₁₉×#1494	2
#18695	19

Subgroups — C19×#18695 #18024654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18695 #18024654