Subgroups — C₁₉×#61876 #18067835

Order 4864.

1712 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3389	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3388	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3368	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3366	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3241	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3234	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3119	C₂	1	4	yes	maximal, complemented
10	C₁₉×#3115	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2987	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#562	—	2	1	no	—
13	C₁₉×#562	—	2	1	no	—
14	C₁₉×#557	C₂²	1	4	yes	—
15	C₁₉×#554	—	2	4	no	—
16	C₁₉×#554	C₂²	1	4	yes	—
17	C₁₉×#554	C₂²	1	4	yes	—
18	C₁₉×#550	C₂²	1	4	yes	—
19	C₁₉×#547	—	2	2	no	—
20	C₁₉×#544	—	2	2	no	—
21	C₁₉×#544	C₂²	1	2	yes	—
22	C₁₉×#540	C₂²	1	4	yes	—
23	C₁₉×#537	—	2	4	no	—
24	C₁₉×#533	—	2	1	no	—
25	C₁₉×#533	C₂²	1	1	yes	characteristic
26	C₁₉×#532	C₂²	1	2	yes	—
27	C₂×C₁₉×#125	—	2	1	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×#501	C₂²	1	4	yes	—
33	C₁₉×#499	C₂²	1	4	yes	—
34	C₁₉×#490	C₂²	1	4	yes	—
35	C₁₉×#490	C₂²	1	4	yes	—
36	C₁₉×#486	C₂²	1	4	yes	—
37	C₁₉×#482	C₂²	1	4	yes	—
38	C₁₉×#481	C₂²	1	4	yes	—
39	C₁₉×#480	C₂²	1	4	yes	—
40	C₁₉×#479	C₂²	1	4	yes	—
41	C₁₉×#478	C₂²	1	4	yes	—
42	C₁₉×#478	C₂²	1	4	yes	—
43	C₁₉×#478	C₂²	1	4	yes	—
44	C₁₉×#478	C₂²	1	4	yes	—
45	C₁₉×#478	C₂²	1	4	yes	—
46	C₁₉×#476	C₂²	1	4	yes	—
47	C₁₉×#475	C₂²	1	2	yes	—
48	C₁₉×#474	C₂²	1	4	yes	—
49	C₁₉×#474	C₂²	1	2	yes	—
50	C₁₉×#460	C₂²	1	2	yes	—
51	C₁₉×#460	C₂²	1	4	yes	—
52	C₁₉×#459	C₂²	1	2	yes	—
53	C₁₉×#459	C₂²	1	4	yes	—
54	C₁₉×#449	C₂²	1	4	yes	—
55	C₁₉×#446	C₂²	1	4	yes	—
56	C₁₉×#446	C₂²	1	4	yes	—
57	C₁₉×#442	C₂²	1	4	yes	—
58	C₁₉×#442	C₂²	1	4	yes	—
59	C₁₉×#440	C₂²	1	4	yes	—
60	C₁₉×#440	C₂²	1	4	yes	—
61	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
62	C₄×D₈×C₁₉	C₂²	1	4	yes	—
63	C₁₉×#433	C₂²	1	4	yes	—
64	C₁₉×#432	C₂²	1	2	yes	—
65	C₂×#41×C₁₉	—	2	4	no	—
66	C₂×#41×C₁₉	—	2	2	no	—
67	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
69	C₂×D₈×C₁₉	C₂³	1	4	yes	—
70	C₁₉×C₄⋊Q₈	—	2	4	no	—
71	C₁₉×C₄⋊Q₈	—	2	2	no	—
72	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
73	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
75	C₁₉×#127	C₂³	1	4	yes	—
76	C₁₉×#127	C₂³	1	2	yes	—
77	C₁₉×#125	—	2	2	no	—
78	C₁₉×#125	—	2	4	no	—
79	C₁₉×#125	—	2	4	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	D₄	1	1	yes	characteristic
83	C₁₉×#125	D₄	1	1	yes	characteristic
84	C₁₉×#125	C₂³	1	4	yes	—
85	C₁₉×#125	C₂³	1	4	yes	—
86	C₁₉×#125	C₂³	1	4	yes	—
87	C₁₉×#124	—	2	2	no	—
88	C₁₉×#123	—	2	4	no	—
89	C₁₉×#123	—	2	4	no	—
90	C₁₉×C₂²⋊Q₈	—	2	4	no	—
91	C₁₉×C₂²⋊Q₈	—	2	4	no	—
92	C₁₉×C₂²⋊Q₈	—	2	4	no	—
93	C₁₉×C₂²⋊Q₈	—	2	4	no	—
94	C₁₉×C₂²⋊Q₈	—	2	4	no	—
95	C₁₉×C₂²⋊Q₈	—	2	4	no	—
96	C₁₉×C₂²⋊Q₈	—	2	4	no	—
97	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	4	no	—
100	C₁₉×#121	—	2	4	no	—
101	C₁₉×#121	—	2	4	no	—
102	C₁₉×#121	—	2	4	no	—
103	C₁₉×#121	—	2	4	no	—
104	C₁₉×#121	C₂³	1	4	yes	—
105	C₄×Q₈×C₁₉	—	2	4	no	—
106	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
107	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
108	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
109	C₄×D₄×C₁₉	—	2	2	no	—
110	C₄×D₄×C₁₉	—	2	4	no	—
111	C₄×D₄×C₁₉	—	2	2	no	—
112	C₄×D₄×C₁₉	C₂³	1	4	yes	—
113	C₄×D₄×C₁₉	C₂³	1	4	yes	—
114	C₄×D₄×C₁₉	C₂³	1	4	yes	—
115	C₄×D₄×C₁₉	C₂³	1	4	yes	—
116	C₄×D₄×C₁₉	C₂³	1	2	yes	—
117	C₁₉×#117	—	2	2	no	—
118	C₁₉×#117	—	2	1	no	—
119	C₁₉×#117	C₂³	1	1	yes	characteristic
120	C₁₉×#117	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₉	—	2	1	no	—
127	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₁₉×#107	C₂³	1	4	yes	—
129	C₁₉×#107	C₂³	1	4	yes	—
130	C₁₉×#107	C₂³	1	4	yes	—
131	C₁₉×#106	C₂³	1	4	yes	—
132	C₁₉×#106	C₂³	1	4	yes	—
133	C₁₉×#106	C₂³	1	4	yes	—
134	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
135	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
136	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
137	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
138	C₁₉×#103	C₂³	1	4	yes	—
139	C₁₉×#102	C₂³	1	4	yes	—
140	C₁₉×#102	C₂³	1	4	yes	—
141	C₁₉×#102	C₂³	1	4	yes	—
142	C₁₉×#102	C₂³	1	4	yes	—
143	C₁₉×#102	C₂³	1	4	yes	—
144	C₁₉×#102	C₂³	1	4	yes	—
145	C₁₉×#102	C₂³	1	4	yes	—
146	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
147	C₁₉×#97	C₂³	1	4	yes	—
148	C₁₉×#97	C₂³	1	4	yes	—
149	C₄×C₈×C₁₉	C₂³	1	4	yes	—
150	#41×C₁₉	—	2	2	no	—
151	#41×C₁₉	—	2	2	no	—
152	#41×C₁₉	—	8	4	no	—
153	#41×C₁₉	—	8	8	no	—
154	C₂×Q₈×C₁₉	—	2	4	no	—
155	C₂×Q₈×C₁₉	—	2	2	no	—
156	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
157	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
158	C₂×D₄×C₁₉	—	2	1	no	—
159	C₂×D₄×C₁₉	—	2	4	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	4	no	—
162	C₂×D₄×C₁₉	—	2	4	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
165	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	4	no	—
171	C₂²×C₄×C₁₉	—	2	4	no	—
172	C₂²×C₄×C₁₉	—	2	4	no	—
173	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
175	SD₁₆×C₁₉	—	2	8	no	—
176	D₈×C₁₉	—	2	8	no	—
177	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
178	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	4	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	4	no	—
183	C₄⋊C₄×C₁₉	—	2	4	no	—
184	C₄⋊C₄×C₁₉	—	2	4	no	—
185	C₄⋊C₄×C₁₉	—	2	4	no	—
186	C₄⋊C₄×C₁₉	—	2	4	no	—
187	C₄⋊C₄×C₁₉	—	2	4	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	4	no	—
190	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
192	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
193	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
195	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
196	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	2	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	4	no	—
205	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	—	2	2	no	—
208	C₄²×C₁₉	—	2	4	no	—
209	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₉	C₂⁴	1	2	yes	—
212	C₄²×C₁₉	C₂⁴	1	4	yes	—
213	#61876	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	2	4	no	—
216	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₉	—	2	1	no	—
218	Q₈×C₁₉	—	4	4	no	—
219	Q₈×C₁₉	—	8	4	no	—
220	Q₈×C₁₉	—	8	2	no	—
221	Q₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
222	D₄×C₁₉	—	2	4	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	2	4	no	—
225	D₄×C₁₉	—	2	4	no	—
226	D₄×C₁₉	—	4	4	no	—
227	D₄×C₁₉	—	8	2	no	—
228	D₄×C₁₉	—	8	4	no	—
229	D₄×C₁₉	—	8	4	no	—
230	D₄×C₁₉	—	8	4	no	—
231	D₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	8	no	—
241	C₂×C₄×C₁₉	—	8	2	no	—
242	C₂×C₄×C₁₉	—	8	4	no	—
243	C₂×C₄×C₁₉	—	8	4	no	—
244	C₂×C₄×C₁₉	—	8	4	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
252	C₈×C₁₉	—	2	4	no	—
253	C₈×C₁₉	—	2	4	no	—
254	#3548	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#3504	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#3389	C₂×C₁₉	1	4	yes	complemented
257	#3388	C₂×C₁₉	1	4	yes	complemented
258	#3368	C₂×C₁₉	1	4	yes	complemented
259	#3366	C₂×C₁₉	1	4	yes	complemented
260	#3241	C₂×C₁₉	1	4	yes	complemented
261	#3234	C₂×C₁₉	1	2	yes	complemented
262	#3119	C₂×C₁₉	1	4	yes	complemented
263	#3115	C₂×C₁₉	1	2	yes	complemented
264	#2987	C₂×C₁₉	1	1	yes	characteristic, complemented
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	2	1	no	—
267	C₂²×C₁₉	—	2	2	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	2	no	—
275	C₄×C₁₉	—	2	4	no	—
276	C₄×C₁₉	—	2	4	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	2	no	—
279	C₄×C₁₉	—	4	4	no	—
280	C₄×C₁₉	—	4	4	no	—
281	C₄×C₁₉	—	4	2	no	—
282	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
283	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
284	#562	—	2	1	no	—
285	#562	—	2	1	no	—
286	#557	C₂²×C₁₉	1	4	yes	—
287	#554	—	2	4	no	—
288	#554	C₂²×C₁₉	1	4	yes	—
289	#554	C₂²×C₁₉	1	4	yes	—
290	#550	C₂²×C₁₉	1	4	yes	—
291	#547	—	2	2	no	—
292	#544	—	2	2	no	—
293	#544	C₂²×C₁₉	1	2	yes	—
294	#540	C₂²×C₁₉	1	4	yes	—
295	#537	—	2	4	no	—
296	#533	—	2	1	no	—
297	#533	C₂²×C₁₉	1	1	yes	characteristic
298	#532	C₂²×C₁₉	1	2	yes	—
299	C₂×#125	—	2	1	no	—
300	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
301	#520	C₂²×C₁₉	1	2	yes	—
302	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
303	#501	C₂²×C₁₉	1	4	yes	—
304	#501	C₂²×C₁₉	1	4	yes	—
305	#499	C₂²×C₁₉	1	4	yes	—
306	#490	C₂²×C₁₉	1	4	yes	—
307	#490	C₂²×C₁₉	1	4	yes	—
308	#486	C₂²×C₁₉	1	4	yes	—
309	#482	C₂²×C₁₉	1	4	yes	—
310	#481	C₂²×C₁₉	1	4	yes	—
311	#480	C₂²×C₁₉	1	4	yes	—
312	#479	C₂²×C₁₉	1	4	yes	—
313	#478	C₂²×C₁₉	1	4	yes	—
314	#478	C₂²×C₁₉	1	4	yes	—
315	#478	C₂²×C₁₉	1	4	yes	—
316	#478	C₂²×C₁₉	1	4	yes	—
317	#478	C₂²×C₁₉	1	4	yes	—
318	#476	C₂²×C₁₉	1	4	yes	—
319	#475	C₂²×C₁₉	1	2	yes	—
320	#474	C₂²×C₁₉	1	4	yes	—
321	#474	C₂²×C₁₉	1	2	yes	—
322	#460	C₂²×C₁₉	1	2	yes	—
323	#460	C₂²×C₁₉	1	4	yes	—
324	#459	C₂²×C₁₉	1	2	yes	—
325	#459	C₂²×C₁₉	1	4	yes	—
326	#449	C₂²×C₁₉	1	4	yes	—
327	#446	C₂²×C₁₉	1	4	yes	—
328	#446	C₂²×C₁₉	1	4	yes	—
329	#442	C₂²×C₁₉	1	4	yes	—
330	#442	C₂²×C₁₉	1	4	yes	—
331	#440	C₂²×C₁₉	1	4	yes	—
332	#440	C₂²×C₁₉	1	4	yes	—
333	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
334	C₄×D₈	C₂²×C₁₉	1	4	yes	—
335	#433	C₂²×C₁₉	1	4	yes	—
336	#432	C₂²×C₁₉	1	2	yes	—
337	C₂×C₁₉	—	4	1	no	—
338	C₂×C₁₉	—	4	2	no	—
339	C₂×C₁₉	—	8	4	no	—
340	C₂×C₁₉	#3486	1	1	yes	characteristic
341	C₂×C₁₉	#3585	1	2	yes	—
342	C₂×#41	—	2	4	no	—
343	C₂×#41	—	2	2	no	—
344	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
346	C₂×D₈	C₂³×C₁₉	1	4	yes	—
347	C₄⋊Q₈	—	2	4	no	—
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
350	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
351	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
352	#127	C₂³×C₁₉	1	2	yes	—
353	#127	C₂³×C₁₉	1	4	yes	—
354	#125	—	2	2	no	—
355	#125	—	2	4	no	—
356	#125	—	2	4	no	—
357	#125	—	2	1	no	—
358	#125	—	2	1	no	—
359	#125	D₄×C₁₉	1	1	yes	characteristic
360	#125	D₄×C₁₉	1	1	yes	characteristic
361	#125	C₂³×C₁₉	1	4	yes	—
362	#125	C₂³×C₁₉	1	4	yes	—
363	#125	C₂³×C₁₉	1	4	yes	—
364	#124	—	2	2	no	—
365	#123	—	2	4	no	—
366	#123	—	2	4	no	—
367	C₂²⋊Q₈	—	2	4	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	C₂²⋊Q₈	—	2	4	no	—
371	C₂²⋊Q₈	—	2	4	no	—
372	C₂²⋊Q₈	—	2	4	no	—
373	C₂²⋊Q₈	—	2	4	no	—
374	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
375	#121	—	2	2	no	—
376	#121	—	2	4	no	—
377	#121	—	2	4	no	—
378	#121	—	2	4	no	—
379	#121	—	2	4	no	—
380	#121	—	2	4	no	—
381	#121	C₂³×C₁₉	1	4	yes	—
382	C₄×Q₈	—	2	4	no	—
383	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
384	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
385	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	C₂³×C₁₉	1	2	yes	—
390	C₄×D₄	C₂³×C₁₉	1	4	yes	—
391	C₄×D₄	C₂³×C₁₉	1	4	yes	—
392	C₄×D₄	C₂³×C₁₉	1	4	yes	—
393	C₄×D₄	C₂³×C₁₉	1	4	yes	—
394	#117	—	2	2	no	—
395	#117	—	2	1	no	—
396	#117	C₂³×C₁₉	1	1	yes	characteristic
397	#117	C₂³×C₁₉	1	2	yes	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	4	no	—
401	C₂×C₄⋊C₄	—	2	4	no	—
402	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	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	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
414	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
415	#103	C₂³×C₁₉	1	4	yes	—
416	#102	C₂³×C₁₉	1	4	yes	—
417	#102	C₂³×C₁₉	1	4	yes	—
418	#102	C₂³×C₁₉	1	4	yes	—
419	#102	C₂³×C₁₉	1	4	yes	—
420	#102	C₂³×C₁₉	1	4	yes	—
421	#102	C₂³×C₁₉	1	4	yes	—
422	#102	C₂³×C₁₉	1	4	yes	—
423	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
424	#97	C₂³×C₁₉	1	4	yes	—
425	#97	C₂³×C₁₉	1	4	yes	—
426	C₄×C₈	C₂³×C₁₉	1	4	yes	—
427	C₁₉	#61876	1	1	yes	characteristic, direct product factor, Sylow
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	8	4	no	—
431	#41	—	8	8	no	—
432	C₂×Q₈	—	2	4	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	C₂×D₄×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	—	2	2	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
443	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
453	SD₁₆	—	2	8	no	—
454	D₈	—	2	8	no	—
455	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
456	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
469	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
470	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
471	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
472	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
473	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
474	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
475	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	4	no	—
487	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
488	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
489	C₄²	C₂⁴×C₁₉	1	4	yes	—
490	C₄²	C₂⁴×C₁₉	1	2	yes	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	4	no	—
493	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
494	Q₈	—	2	1	no	—
495	Q₈	—	4	4	no	—
496	Q₈	—	8	2	no	—
497	Q₈	—	8	4	no	—
498	Q₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
499	D₄	—	2	4	no	—
500	D₄	—	2	1	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	4	4	no	—
504	D₄	—	8	2	no	—
505	D₄	—	8	4	no	—
506	D₄	—	8	4	no	—
507	D₄	—	8	4	no	—
508	D₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	8	4	no	—
519	C₂×C₄	—	8	4	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	4	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
525	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
528	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
529	C₈	—	2	4	no	—
530	C₈	—	2	4	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	4	no	—
538	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	4	no	—
544	C₄	—	2	4	no	—
545	C₄	—	4	4	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	2	no	—
548	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
549	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
550	C₂	—	4	1	no	—
551	C₂	—	4	2	no	—
552	C₂	—	8	4	no	—
553	C₂	C₁₉×#3486	1	1	yes	characteristic
554	C₂	C₁₉×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3548	C₂	semidirect
2. C₁₉×#3504	C₂	semidirect
3. C₁₉×#3389	C₂	semidirect
4. C₁₉×#3388	C₂	semidirect
5. C₁₉×#3368	C₂	semidirect
6. C₁₉×#3366	C₂	semidirect
7. C₁₉×#3241	C₂	semidirect
8. C₁₉×#3234	C₂	semidirect
9. C₁₉×#3119	C₂	semidirect
10. C₁₉×#3115	C₂	semidirect
11. C₁₉×#2987	C₂	semidirect
213. #61876	C₁₉	direct (N × H)
254. #3548	C₂×C₁₉	semidirect
255. #3504	C₂×C₁₉	semidirect
256. #3389	C₂×C₁₉	semidirect
257. #3388	C₂×C₁₉	semidirect
258. #3368	C₂×C₁₉	semidirect
259. #3366	C₂×C₁₉	semidirect
260. #3241	C₂×C₁₉	semidirect
261. #3234	C₂×C₁₉	semidirect
262. #3119	C₂×C₁₉	semidirect
263. #3115	C₂×C₁₉	semidirect
264. #2987	C₂×C₁₉	semidirect
427. C₁₉	#61876	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×#3548	2
C₁₉×#3504	2
C₁₉×#3389	2
C₁₉×#3388	2
C₁₉×#3368	2
C₁₉×#3366	2
C₁₉×#3241	2
C₁₉×#3234	2
C₁₉×#3119	2
C₁₉×#3115	2
C₁₉×#2987	2
#61876	19

Subgroups — C19×#61876 #18067835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61876 #18067835