Subgroups — C₁₉×#61798 #18067757

Order 4864.

1674 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3512	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3350	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3349	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3320	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3312	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3236	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3201	C₂	1	4	yes	maximal, complemented
9	C₁₉×#3116	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3097	C₂	1	4	yes	maximal, complemented
11	C₁₉×#2980	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#563	—	2	2	no	—
13	C₁₉×#559	—	2	1	no	—
14	Q₈²×C₁₉	—	2	1	no	—
15	C₁₉×#556	C₂²	1	4	yes	—
16	C₁₉×#553	—	2	4	no	—
17	C₁₉×#553	C₂²	1	4	yes	—
18	C₁₉×#552	C₂²	1	4	yes	—
19	D₄×Q₈×C₁₉	C₂²	1	4	yes	—
20	C₁₉×#542	—	2	4	no	—
21	C₁₉×#541	—	2	1	no	—
22	C₁₉×#540	—	2	1	no	—
23	C₁₉×#537	C₂²	1	2	yes	—
24	C₁₉×#536	C₂²	1	4	yes	—
25	C₁₉×#533	C₂²	1	2	yes	—
26	C₁₉×#532	C₂²	1	1	yes	characteristic
27	C₁₉×#529	—	2	2	no	—
28	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
29	C₁₉×#520	C₂²	1	2	yes	—
30	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#501	C₂²	1	4	yes	—
32	C₁₉×#491	C₂²	1	4	yes	—
33	C₁₉×#485	C₂²	1	4	yes	—
34	C₁₉×#485	C₂²	1	4	yes	—
35	C₁₉×#485	C₂²	1	4	yes	—
36	C₁₉×#485	C₂²	1	4	yes	—
37	C₁₉×#484	C₂²	1	4	yes	—
38	C₁₉×#484	C₂²	1	4	yes	—
39	C₁₉×#483	C₂²	1	4	yes	—
40	C₁₉×#483	C₂²	1	4	yes	—
41	C₁₉×#482	C₂²	1	4	yes	—
42	C₁₉×#479	C₂²	1	4	yes	—
43	C₁₉×#479	C₂²	1	4	yes	—
44	C₁₉×#477	C₂²	1	2	yes	—
45	C₁₉×#476	C₂²	1	2	yes	—
46	C₁₉×#470	C₂²	1	4	yes	—
47	C₁₉×#468	C₂²	1	4	yes	—
48	C₁₉×#467	C₂²	1	4	yes	—
49	C₁₉×#465	C₂²	1	4	yes	—
50	C₁₉×#462	C₂²	1	2	yes	—
51	C₁₉×#461	C₂²	1	2	yes	—
52	C₁₉×#452	C₂²	1	4	yes	—
53	C₁₉×#451	C₂²	1	4	yes	—
54	C₁₉×#448	C₂²	1	4	yes	—
55	C₁₉×#441	C₂²	1	4	yes	—
56	C₁₉×#440	C₂²	1	4	yes	—
57	C₁₉×#435	C₂²	1	4	yes	—
58	C₁₉×#435	C₂²	1	4	yes	—
59	C₁₉×#432	C₂²	1	2	yes	—
60	C₁₉×#428	C₂²	1	4	yes	—
61	C₁₉×#427	C₂²	1	4	yes	—
62	C₁₉×#419	C₂²	1	4	yes	—
63	C₂×C₁₉×#103	C₂²	1	4	yes	—
64	C₁₉×#408	C₂²	1	4	yes	—
65	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×#41×C₁₉	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
68	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
69	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
70	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
71	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
72	C₁₉×C₄⋊Q₈	—	2	4	no	—
73	C₁₉×C₄⋊Q₈	—	2	4	no	—
74	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
75	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
77	C₁₉×#127	D₄	1	1	yes	characteristic
78	C₁₉×#126	—	2	4	no	—
79	C₁₉×#126	—	2	4	no	—
80	C₁₉×#126	—	2	4	no	—
81	C₁₉×#126	—	2	4	no	—
82	C₁₉×#125	—	2	4	no	—
83	C₁₉×#125	—	2	1	no	—
84	C₁₉×#125	—	2	1	no	—
85	C₁₉×#125	—	2	2	no	—
86	C₁₉×#125	C₂³	1	4	yes	—
87	C₁₉×#124	—	2	4	no	—
88	C₁₉×#124	—	2	4	no	—
89	C₁₉×#124	D₄	1	2	yes	—
90	C₁₉×#123	—	2	4	no	—
91	C₁₉×#123	—	2	4	no	—
92	C₁₉×#123	—	2	4	no	—
93	C₁₉×#123	—	2	4	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	4	no	—
97	C₁₉×C₂²⋊Q₈	—	2	4	no	—
98	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
99	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
100	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
101	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	—	2	4	no	—
104	C₁₉×#121	—	2	4	no	—
105	C₁₉×#121	D₄	1	4	yes	—
106	C₁₉×#121	C₂³	1	4	yes	—
107	C₄×Q₈×C₁₉	—	2	2	no	—
108	C₄×Q₈×C₁₉	—	2	4	no	—
109	C₄×Q₈×C₁₉	—	2	2	no	—
110	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
111	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
112	C₄×D₄×C₁₉	—	2	2	no	—
113	C₄×D₄×C₁₉	—	2	4	no	—
114	C₄×D₄×C₁₉	—	2	4	no	—
115	C₄×D₄×C₁₉	—	2	2	no	—
116	C₄×D₄×C₁₉	—	2	4	no	—
117	C₄×D₄×C₁₉	C₂³	1	2	yes	—
118	C₄×D₄×C₁₉	C₂³	1	4	yes	—
119	C₁₉×#117	—	2	2	no	—
120	C₁₉×#117	—	2	4	no	—
121	C₁₉×#117	—	2	1	no	—
122	C₁₉×#117	C₂³	1	4	yes	—
123	C₁₉×#117	C₂³	1	4	yes	—
124	C₁₉×#117	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₉	—	2	1	no	—
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₁₉×#107	C₂³	1	4	yes	—
131	C₁₉×#107	C₂³	1	4	yes	—
132	C₁₉×#107	C₂³	1	4	yes	—
133	C₁₉×#106	C₂³	1	4	yes	—
134	C₁₉×#106	C₂³	1	4	yes	—
135	C₁₉×#106	C₂³	1	4	yes	—
136	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
137	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
138	C₁₉×#103	C₂³	1	4	yes	—
139	C₁₉×#103	C₂³	1	4	yes	—
140	C₁₉×#103	C₂³	1	4	yes	—
141	C₁₉×#103	C₂³	1	4	yes	—
142	C₁₉×#103	C₂³	1	4	yes	—
143	C₁₉×#103	C₂³	1	4	yes	—
144	C₁₉×#103	C₂³	1	4	yes	—
145	C₁₉×#102	C₂³	1	4	yes	—
146	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
147	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
148	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
149	C₁₉×#97	C₂³	1	4	yes	—
150	#41×C₁₉	—	4	2	no	—
151	#41×C₁₉	—	4	2	no	—
152	#41×C₁₉	—	4	2	no	—
153	C₂×Q₈×C₁₉	—	2	2	no	—
154	C₂×Q₈×C₁₉	—	2	4	no	—
155	C₂×Q₈×C₁₉	—	4	4	no	—
156	C₂×Q₈×C₁₉	—	4	4	no	—
157	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
158	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
160	C₂×D₄×C₁₉	—	2	1	no	—
161	C₂×D₄×C₁₉	—	2	4	no	—
162	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
163	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
164	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	4	no	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
174	Q₁₆×C₁₉	—	4	4	no	—
175	SD₁₆×C₁₉	—	4	4	no	—
176	M₁₆×C₁₉	—	4	4	no	—
177	C₂×C₈×C₁₉	—	4	4	no	—
178	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
179	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
180	C₄⋊C₄×C₁₉	—	2	4	no	—
181	C₄⋊C₄×C₁₉	—	2	4	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	4	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	4	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	4	no	—
190	C₄⋊C₄×C₁₉	—	2	4	no	—
191	C₄⋊C₄×C₁₉	—	2	4	no	—
192	C₄⋊C₄×C₁₉	—	2	4	no	—
193	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
194	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
195	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
196	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
197	C₂²⋊C₄×C₁₉	—	2	4	no	—
198	C₂²⋊C₄×C₁₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	2	4	no	—
203	C₂²⋊C₄×C₁₉	—	2	4	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	4	no	—
206	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
207	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
208	C₄²×C₁₉	—	2	2	no	—
209	C₄²×C₁₉	—	2	1	no	—
210	C₄²×C₁₉	—	2	4	no	—
211	C₄²×C₁₉	—	2	4	no	—
212	C₄²×C₁₉	—	2	4	no	—
213	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₉	C₂⁴	1	2	yes	—
216	#61798	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
219	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₉	—	2	4	no	—
221	Q₈×C₁₉	—	2	2	no	—
222	Q₈×C₁₉	—	2	4	no	—
223	Q₈×C₁₉	—	4	2	no	—
224	Q₈×C₁₉	—	4	4	no	—
225	Q₈×C₁₉	—	8	4	no	—
226	D₄×C₁₉	—	2	2	no	—
227	D₄×C₁₉	—	4	4	no	—
228	D₄×C₁₉	—	4	2	no	—
229	D₄×C₁₉	—	4	4	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	8	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	8	2	no	—
243	C₂×C₄×C₁₉	—	8	4	no	—
244	C₂×C₄×C₁₉	—	8	2	no	—
245	C₂×C₄×C₁₉	—	8	4	no	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
251	C₈×C₁₉	—	2	4	no	—
252	C₈×C₁₉	—	2	4	no	—
253	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
254	#3512	C₂×C₁₉	1	1	yes	characteristic
255	#3350	C₂×C₁₉	1	4	yes	complemented
256	#3349	C₂×C₁₉	1	4	yes	complemented
257	#3320	C₂×C₁₉	1	4	yes	complemented
258	#3312	C₂×C₁₉	1	4	yes	complemented
259	#3236	C₂×C₁₉	1	2	yes	complemented
260	#3201	C₂×C₁₉	1	4	yes	complemented
261	#3116	C₂×C₁₉	1	2	yes	complemented
262	#3097	C₂×C₁₉	1	4	yes	complemented
263	#2980	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂²×C₁₉	—	2	2	no	—
265	C₂²×C₁₉	—	2	4	no	—
266	C₂²×C₁₉	—	2	4	no	—
267	C₂²×C₁₉	—	2	4	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
272	C₄×C₁₉	—	2	2	no	—
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	4	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	4	4	no	—
278	C₄×C₁₉	—	4	4	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	4	no	—
281	C₄×C₁₉	#585	1	2	yes	—
282	#563	—	2	2	no	—
283	#559	—	2	1	no	—
284	Q₈²	—	2	1	no	—
285	#556	C₂²×C₁₉	1	4	yes	—
286	#553	—	2	4	no	—
287	#553	C₂²×C₁₉	1	4	yes	—
288	#552	C₂²×C₁₉	1	4	yes	—
289	D₄×Q₈	C₂²×C₁₉	1	4	yes	—
290	#542	—	2	4	no	—
291	#541	—	2	1	no	—
292	#540	—	2	1	no	—
293	#537	C₂²×C₁₉	1	2	yes	—
294	#536	C₂²×C₁₉	1	4	yes	—
295	#533	C₂²×C₁₉	1	2	yes	—
296	#532	C₂²×C₁₉	1	1	yes	characteristic
297	#529	—	2	2	no	—
298	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
299	#520	C₂²×C₁₉	1	2	yes	—
300	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
301	#501	C₂²×C₁₉	1	4	yes	—
302	#491	C₂²×C₁₉	1	4	yes	—
303	#485	C₂²×C₁₉	1	4	yes	—
304	#485	C₂²×C₁₉	1	4	yes	—
305	#485	C₂²×C₁₉	1	4	yes	—
306	#485	C₂²×C₁₉	1	4	yes	—
307	#484	C₂²×C₁₉	1	4	yes	—
308	#484	C₂²×C₁₉	1	4	yes	—
309	#483	C₂²×C₁₉	1	4	yes	—
310	#483	C₂²×C₁₉	1	4	yes	—
311	#482	C₂²×C₁₉	1	4	yes	—
312	#479	C₂²×C₁₉	1	4	yes	—
313	#479	C₂²×C₁₉	1	4	yes	—
314	#477	C₂²×C₁₉	1	2	yes	—
315	#476	C₂²×C₁₉	1	2	yes	—
316	#470	C₂²×C₁₉	1	4	yes	—
317	#468	C₂²×C₁₉	1	4	yes	—
318	#467	C₂²×C₁₉	1	4	yes	—
319	#465	C₂²×C₁₉	1	4	yes	—
320	#462	C₂²×C₁₉	1	2	yes	—
321	#461	C₂²×C₁₉	1	2	yes	—
322	#452	C₂²×C₁₉	1	4	yes	—
323	#451	C₂²×C₁₉	1	4	yes	—
324	#448	C₂²×C₁₉	1	4	yes	—
325	#441	C₂²×C₁₉	1	4	yes	—
326	#440	C₂²×C₁₉	1	4	yes	—
327	#435	C₂²×C₁₉	1	4	yes	—
328	#435	C₂²×C₁₉	1	4	yes	—
329	#432	C₂²×C₁₉	1	2	yes	—
330	#428	C₂²×C₁₉	1	4	yes	—
331	#427	C₂²×C₁₉	1	4	yes	—
332	#419	C₂²×C₁₉	1	4	yes	—
333	C₂×#103	C₂²×C₁₉	1	4	yes	—
334	#408	C₂²×C₁₉	1	4	yes	—
335	C₂×C₁₉	—	4	1	no	—
336	C₂×C₁₉	—	4	4	no	—
337	C₂×C₁₉	—	8	1	no	—
338	C₂×C₁₉	#3485	1	1	yes	characteristic
339	C₂×C₁₉	#3586	1	2	yes	—
340	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×#41	C₂³×C₁₉	1	2	yes	—
342	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
343	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
344	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
345	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
346	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
347	C₄⋊Q₈	—	2	4	no	—
348	C₄⋊Q₈	—	2	4	no	—
349	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
351	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
352	#127	D₄×C₁₉	1	1	yes	characteristic
353	#126	—	2	4	no	—
354	#126	—	2	4	no	—
355	#126	—	2	4	no	—
356	#126	—	2	4	no	—
357	#125	—	2	4	no	—
358	#125	—	2	1	no	—
359	#125	—	2	1	no	—
360	#125	—	2	2	no	—
361	#125	C₂³×C₁₉	1	4	yes	—
362	#124	—	2	4	no	—
363	#124	—	2	4	no	—
364	#124	D₄×C₁₉	1	2	yes	—
365	#123	—	2	4	no	—
366	#123	—	2	4	no	—
367	#123	—	2	4	no	—
368	#123	—	2	4	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	4	no	—
372	C₂²⋊Q₈	—	2	4	no	—
373	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
374	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
375	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
376	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
377	#121	—	2	2	no	—
378	#121	—	2	4	no	—
379	#121	—	2	4	no	—
380	#121	D₄×C₁₉	1	4	yes	—
381	#121	C₂³×C₁₉	1	4	yes	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	4	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
386	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	C₂³×C₁₉	1	2	yes	—
393	C₄×D₄	C₂³×C₁₉	1	4	yes	—
394	#117	—	2	2	no	—
395	#117	—	2	4	no	—
396	#117	—	2	1	no	—
397	#117	C₂³×C₁₉	1	1	yes	characteristic
398	#117	C₂³×C₁₉	1	4	yes	—
399	#117	C₂³×C₁₉	1	4	yes	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
405	#107	C₂³×C₁₉	1	4	yes	—
406	#107	C₂³×C₁₉	1	4	yes	—
407	#107	C₂³×C₁₉	1	4	yes	—
408	#106	C₂³×C₁₉	1	4	yes	—
409	#106	C₂³×C₁₉	1	4	yes	—
410	#106	C₂³×C₁₉	1	4	yes	—
411	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
412	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
413	#103	C₂³×C₁₉	1	4	yes	—
414	#103	C₂³×C₁₉	1	4	yes	—
415	#103	C₂³×C₁₉	1	4	yes	—
416	#103	C₂³×C₁₉	1	4	yes	—
417	#103	C₂³×C₁₉	1	4	yes	—
418	#103	C₂³×C₁₉	1	4	yes	—
419	#103	C₂³×C₁₉	1	4	yes	—
420	#102	C₂³×C₁₉	1	4	yes	—
421	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
422	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
423	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
424	#97	C₂³×C₁₉	1	4	yes	—
425	C₁₉	#61798	1	1	yes	characteristic, direct product factor, Sylow
426	#41	—	4	2	no	—
427	#41	—	4	2	no	—
428	#41	—	4	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
434	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
435	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
439	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
440	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
441	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
450	Q₁₆	—	4	4	no	—
451	SD₁₆	—	4	4	no	—
452	M₁₆	—	4	4	no	—
453	C₂×C₈	—	4	4	no	—
454	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
455	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
471	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
472	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
483	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	4	no	—
489	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
491	C₄²	C₂⁴×C₁₉	1	2	yes	—
492	C₂³	—	2	1	no	—
493	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
494	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
495	Q₈	—	2	4	no	—
496	Q₈	—	2	2	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	4	no	—
500	Q₈	—	8	4	no	—
501	D₄	—	2	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	4	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	4	no	—
519	C₂×C₄	—	8	4	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
523	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
525	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
526	C₈	—	2	4	no	—
527	C₈	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	2	no	—
535	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
536	C₄	—	2	1	no	—
537	C₄	—	2	4	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	4	no	—
545	C₄	C₁₉×#585	1	2	yes	—
546	C₂	—	4	4	no	—
547	C₂	—	4	1	no	—
548	C₂	—	8	1	no	—
549	C₂	C₁₉×#3485	1	1	yes	characteristic
550	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3512	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3550	C₂	semidirect
3. C₁₉×#3350	C₂	semidirect
4. C₁₉×#3349	C₂	semidirect
5. C₁₉×#3320	C₂	semidirect
6. C₁₉×#3312	C₂	semidirect
7. C₁₉×#3236	C₂	semidirect
8. C₁₉×#3201	C₂	semidirect
9. C₁₉×#3116	C₂	semidirect
10. C₁₉×#3097	C₂	semidirect
11. C₁₉×#2980	C₂	semidirect
216. #61798	C₁₉	direct (N × H)
253. #3550	C₂×C₁₉	semidirect
255. #3350	C₂×C₁₉	semidirect
256. #3349	C₂×C₁₉	semidirect
257. #3320	C₂×C₁₉	semidirect
258. #3312	C₂×C₁₉	semidirect
259. #3236	C₂×C₁₉	semidirect
260. #3201	C₂×C₁₉	semidirect
261. #3116	C₂×C₁₉	semidirect
262. #3097	C₂×C₁₉	semidirect
263. #2980	C₂×C₁₉	semidirect
425. C₁₉	#61798	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×#3550	2
C₁₉×#3512	2
C₁₉×#3350	2
C₁₉×#3349	2
C₁₉×#3320	2
C₁₉×#3312	2
C₁₉×#3236	2
C₁₉×#3201	2
C₁₉×#3116	2
C₁₉×#3097	2
C₁₉×#2980	2
#61798	19

Subgroups — C19×#61798 #18067757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61798 #18067757