Subgroups — C₁₉×#18337 #18024296

Order 4864.

1016 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1599	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1598	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1597	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1509	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#544	C₂²	1	1	yes	characteristic
10	C₁₉×#542	—	2	2	no	—
11	C₁₉×#541	—	2	2	no	—
12	C₁₉×#539	—	2	1	no	—
13	C₁₉×#539	C₂²	1	2	yes	—
14	C₁₉×#537	C₂²	1	1	yes	characteristic
15	C₁₉×#536	—	2	1	no	—
16	C₁₉×#533	—	2	2	no	—
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
18	C₁₉×#529	—	2	2	no	—
19	C₁₉×#529	—	2	1	no	—
20	C₁₉×#529	C₂²	1	2	yes	—
21	C₂×C₁₉×#124	—	2	1	no	—
22	C₄×#41×C₁₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#496	—	2	2	no	—
25	C₁₉×#490	—	2	2	no	—
26	C₁₉×#460	—	2	2	no	—
27	C₁₉×#459	—	2	2	no	—
28	C₁₉×#450	C₂²	1	4	yes	—
29	C₁₉×#447	C₂²	1	4	yes	—
30	C₁₉×#432	C₂²	1	2	yes	—
31	C₁₉×#394	C₂²	1	2	yes	—
32	C₁₉×#394	C₂²	1	2	yes	—
33	C₁₉×#390	—	2	1	no	—
34	C₁₉×#390	—	2	1	no	—
35	C₁₉×#390	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#328	C₂²	1	4	yes	—
38	C₁₉×#327	C₂²	1	4	yes	—
39	C₁₉×#324	C₂²	1	2	yes	—
40	C₁₉×#324	C₂²	1	2	yes	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
46	C₂×SD₁₆×C₁₉	—	2	4	no	—
47	C₂×D₈×C₁₉	—	2	4	no	—
48	C₁₉×C₄⋊Q₈	—	2	2	no	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×#127	—	2	2	no	—
51	C₁₉×#127	—	2	2	no	—
52	C₁₉×#126	—	2	2	no	—
53	C₁₉×#126	—	2	2	no	—
54	C₁₉×#126	—	2	2	no	—
55	C₁₉×#126	—	2	2	no	—
56	C₁₉×#125	—	2	1	no	—
57	C₁₉×#125	—	2	2	no	—
58	C₁₉×#125	—	2	2	no	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	D₄	1	2	yes	—
61	C₁₉×#124	—	2	2	no	—
62	C₁₉×#124	—	2	1	no	—
63	C₁₉×#124	—	4	4	no	—
64	C₁₉×#124	D₄	1	2	yes	—
65	C₁₉×#123	—	2	2	no	—
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
76	C₁₉×#121	—	2	2	no	—
77	C₁₉×#121	—	2	1	no	—
78	C₁₉×#121	C₂³	1	2	yes	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×Q₈×C₁₉	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	2	2	no	—
84	C₄×Q₈×C₁₉	D₄	1	2	yes	—
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	2	no	—
89	C₄×D₄×C₁₉	—	2	2	no	—
90	C₄×D₄×C₁₉	D₄	1	2	yes	—
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	—	2	2	no	—
93	C₁₉×#117	—	2	1	no	—
94	C₁₉×#117	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₄²×C₁₉	—	2	2	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
108	C₁₉×C₄⋊C₈	—	2	2	no	—
109	C₁₉×#102	—	2	4	no	—
110	C₁₉×#102	—	2	4	no	—
111	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
112	C₁₉×#97	—	2	2	no	—
113	C₁₉×#95	C₂³	1	2	yes	—
114	C₂⁴×C₁₉	—	2	2	no	—
115	#41×C₁₉	—	4	2	no	—
116	#41×C₁₉	—	4	2	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	2	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	4	1	no	—
122	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	—	4	2	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	—	4	2	no	—
133	C₂×D₄×C₁₉	—	4	1	no	—
134	C₂×D₄×C₁₉	—	8	2	no	—
135	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
147	SD₁₆×C₁₉	—	8	4	no	—
148	D₈×C₁₉	—	8	4	no	—
149	C₂×C₈×C₁₉	—	2	4	no	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	2	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	4	2	no	—
166	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	4	4	no	—
178	C₂²⋊C₄×C₁₉	—	4	4	no	—
179	C₂²⋊C₄×C₁₉	—	8	2	no	—
180	C₂²⋊C₄×C₁₉	—	8	2	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	2	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	4	2	no	—
189	C₄²×C₁₉	C₂×D₄	1	2	yes	—
190	C₄²×C₁₉	C₂×D₄	1	2	yes	—
191	#18337	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	—	4	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₁₉	—	4	4	no	—
202	Q₈×C₁₉	—	4	2	no	—
203	Q₈×C₁₉	—	4	2	no	—
204	Q₈×C₁₉	—	8	1	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	4	2	no	—
207	D₄×C₁₉	—	4	4	no	—
208	D₄×C₁₉	—	4	4	no	—
209	D₄×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	2	no	—
211	D₄×C₁₉	—	8	4	no	—
212	D₄×C₁₉	—	8	2	no	—
213	D₄×C₁₉	—	8	1	no	—
214	D₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	2	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	4	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#120	1	2	yes	—
239	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
241	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
242	C₈×C₁₉	—	4	4	no	—
243	#3461	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#3217	C₂×C₁₉	1	2	yes	complemented
245	#2548	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#1599	C₂×C₁₉	1	2	yes	complemented
247	#1598	C₂×C₁₉	1	2	yes	complemented
248	#1597	C₂×C₁₉	1	4	yes	complemented
249	#1509	C₂×C₁₉	1	2	yes	complemented
250	#1467	C₂×C₁₉	1	1	yes	characteristic, complemented
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	8	2	no	—
257	C₂²×C₁₉	—	8	2	no	—
258	C₂²×C₁₉	—	8	2	no	—
259	C₂²×C₁₉	—	8	2	no	—
260	C₂²×C₁₉	—	8	2	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
264	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₂²×C₁₉	#575	1	1	yes	characteristic
266	C₄×C₁₉	—	2	2	no	—
267	C₄×C₁₉	—	2	2	no	—
268	C₄×C₁₉	—	2	1	no	—
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	—	4	1	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	2	no	—
276	C₄×C₁₉	—	8	2	no	—
277	C₄×C₁₉	#454	1	2	yes	—
278	#544	C₂²×C₁₉	1	1	yes	characteristic
279	#542	—	2	2	no	—
280	#541	—	2	2	no	—
281	#539	—	2	1	no	—
282	#539	C₂²×C₁₉	1	2	yes	—
283	#537	C₂²×C₁₉	1	1	yes	characteristic
284	#536	—	2	1	no	—
285	#533	—	2	2	no	—
286	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
287	#529	—	2	2	no	—
288	#529	—	2	1	no	—
289	#529	C₂²×C₁₉	1	2	yes	—
290	C₂×#124	—	2	1	no	—
291	C₄×#41	—	2	1	no	—
292	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
293	#496	—	2	2	no	—
294	#490	—	2	2	no	—
295	#460	—	2	2	no	—
296	#459	—	2	2	no	—
297	#450	C₂²×C₁₉	1	4	yes	—
298	#447	C₂²×C₁₉	1	4	yes	—
299	#432	C₂²×C₁₉	1	2	yes	—
300	#394	C₂²×C₁₉	1	2	yes	—
301	#394	C₂²×C₁₉	1	2	yes	—
302	#390	—	2	1	no	—
303	#390	—	2	1	no	—
304	#390	—	2	1	no	—
305	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
306	#328	C₂²×C₁₉	1	4	yes	—
307	#327	C₂²×C₁₉	1	4	yes	—
308	#324	C₂²×C₁₉	1	2	yes	—
309	#324	C₂²×C₁₉	1	2	yes	—
310	C₂×C₁₉	—	2	1	no	—
311	C₂×C₁₉	—	2	1	no	—
312	C₂×C₁₉	—	8	2	no	—
313	C₂×C₁₉	—	16	2	no	—
314	C₂×C₁₉	#3006	1	1	yes	characteristic
315	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
316	C₂×C₁₉	#3027	1	1	yes	characteristic
317	C₂×#41	—	2	1	no	—
318	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×D₈	—	2	4	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	—	2	2	no	—
326	#127	—	2	2	no	—
327	#127	—	2	2	no	—
328	#126	—	2	2	no	—
329	#126	—	2	2	no	—
330	#126	—	2	2	no	—
331	#126	—	2	2	no	—
332	#125	—	2	1	no	—
333	#125	—	2	2	no	—
334	#125	—	2	2	no	—
335	#125	—	2	2	no	—
336	#125	D₄×C₁₉	1	2	yes	—
337	#124	—	2	2	no	—
338	#124	—	2	1	no	—
339	#124	—	4	4	no	—
340	#124	D₄×C₁₉	1	2	yes	—
341	#123	—	2	2	no	—
342	#123	—	2	2	no	—
343	#123	—	2	2	no	—
344	#123	—	2	2	no	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
352	#121	—	2	2	no	—
353	#121	—	2	1	no	—
354	#121	C₂³×C₁₉	1	2	yes	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	D₄×C₁₉	1	2	yes	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	D₄×C₁₉	1	2	yes	—
367	#117	—	2	2	no	—
368	#117	—	2	2	no	—
369	#117	—	2	1	no	—
370	#117	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₄²	—	2	2	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
384	C₄⋊C₈	—	2	2	no	—
385	#102	—	2	4	no	—
386	#102	—	2	4	no	—
387	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
388	#97	—	2	2	no	—
389	#95	C₂³×C₁₉	1	2	yes	—
390	C₁₉	#18337	1	1	yes	characteristic, direct product factor, Sylow
391	C₂⁴	—	2	2	no	—
392	#41	—	4	2	no	—
393	#41	—	4	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	8	2	no	—
412	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
424	SD₁₆	—	8	4	no	—
425	D₈	—	8	4	no	—
426	C₂×C₈	—	2	4	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
444	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	4	4	no	—
456	C₂²⋊C₄	—	8	2	no	—
457	C₂²⋊C₄	—	8	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	4	2	no	—
466	C₄²	C₂×D₄×C₁₉	1	2	yes	—
467	C₄²	C₂×D₄×C₁₉	1	2	yes	—
468	C₂³	—	2	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	Q₈	—	4	4	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	8	1	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	8	4	no	—
488	D₄	—	8	2	no	—
489	D₄	—	8	1	no	—
490	D₄	—	8	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
514	C₂×C₄	C₁₉×#120	1	2	yes	—
515	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
516	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
518	C₈	—	4	4	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
532	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
533	C₂²	C₁₉×#575	1	1	yes	characteristic
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	2	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	2	no	—
544	C₄	—	8	2	no	—
545	C₄	C₁₉×#454	1	2	yes	—
546	C₂	—	2	1	no	—
547	C₂	—	2	1	no	—
548	C₂	—	8	2	no	—
549	C₂	—	16	2	no	—
550	C₂	C₁₉×#3006	1	1	yes	characteristic
551	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
552	C₂	C₁₉×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ 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
1. C₁₉×#3461	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₁₉×#2548	C₂	semidirect
4. C₁₉×#1599	C₂	semidirect
5. C₁₉×#1598	C₂	semidirect
6. C₁₉×#1597	C₂	semidirect
7. C₁₉×#1509	C₂	semidirect
8. C₁₉×#1467	C₂	semidirect
191. #18337	C₁₉	direct (N × H)
243. #3461	C₂×C₁₉	semidirect
244. #3217	C₂×C₁₉	semidirect
245. #2548	C₂×C₁₉	semidirect
246. #1599	C₂×C₁₉	semidirect
247. #1598	C₂×C₁₉	semidirect
248. #1597	C₂×C₁₉	semidirect
249. #1509	C₂×C₁₉	semidirect
250. #1467	C₂×C₁₉	semidirect
390. C₁₉	#18337	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×#3461	2
C₁₉×#3217	2
C₁₉×#2548	2
C₁₉×#1599	2
C₁₉×#1598	2
C₁₉×#1597	2
C₁₉×#1509	2
C₁₉×#1467	2
#18337	19

Subgroups — C19×#18337 #18024296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18337 #18024296