Subgroups — C₁₉×#32969 #18038928

Order 4864.

1350 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3079	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1859	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1856	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1806	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1792	C₂	1	2	yes	maximal
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
12	C₁₉×#520	—	2	2	no	—
13	C₁₉×#520	C₂²	1	2	yes	—
14	C₁₉×#518	—	2	2	no	—
15	C₁₉×#518	—	2	2	no	—
16	C₁₉×#518	C₂²	1	1	yes	characteristic
17	C₄×#41×C₁₉	—	2	2	no	—
18	C₄×#41×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₉	—	2	2	no	—
20	C₂×C₄×D₄×C₁₉	—	2	2	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#477	—	2	2	no	—
23	C₁₉×#476	—	2	2	no	—
24	C₁₉×#475	—	2	2	no	—
25	C₁₉×#474	—	2	2	no	—
26	C₁₉×#428	C₂²	1	4	yes	complemented
27	C₁₉×#423	C₂²	1	2	yes	complemented
28	C₂×C₁₉×#104	C₂²	1	4	yes	—
29	C₁₉×#417	C₂²	1	4	yes	—
30	C₂×C₁₉×#100	C₂²	1	2	yes	—
31	C₁₉×#399	—	2	2	no	—
32	C₁₉×#390	C₂²	1	2	yes	—
33	C₁₉×#384	C₂²	1	2	yes	complemented
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#343	C₂²	1	2	yes	complemented
36	C₁₉×#339	C₂²	1	4	yes	complemented
37	C₁₉×H(5,𝔽₂)	—	2	4	no	—
38	C₁₉×H(5,𝔽₂)	—	2	2	no	—
39	C₁₉×H(5,𝔽₂)	Q₈	1	4	yes	complemented
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	—	2	2	no	—
47	C₂³×C₄×C₁₉	D₄	1	2	yes	—
48	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
49	C₁₉×C₄⋊Q₈	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	—	4	8	no	—
52	C₄×Q₈×C₁₉	—	2	2	no	—
53	C₄×Q₈×C₁₉	D₄	1	2	yes	—
54	C₄×Q₈×C₁₉	D₄	1	2	yes	—
55	C₄×D₄×C₁₉	—	2	4	no	—
56	C₄×D₄×C₁₉	—	2	4	no	—
57	C₄×D₄×C₁₉	—	2	4	no	—
58	C₄×D₄×C₁₉	—	2	4	no	—
59	C₄×D₄×C₁₉	—	2	2	no	—
60	C₄×D₄×C₁₉	—	2	2	no	—
61	C₄×D₄×C₁₉	—	2	4	no	—
62	C₄×D₄×C₁₉	—	2	2	no	—
63	C₄×D₄×C₁₉	—	2	2	no	—
64	C₄×D₄×C₁₉	—	2	2	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	D₄	1	2	yes	—
68	C₄×D₄×C₁₉	D₄	1	2	yes	—
69	C₁₉×#117	—	2	4	no	—
70	C₁₉×#117	—	2	2	no	—
71	C₁₉×#117	—	2	2	no	—
72	C₁₉×#117	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
85	C₂×C₄²×C₁₉	—	2	2	no	—
86	C₂×C₄²×C₁₉	—	2	2	no	—
87	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
89	C₁₉×#107	—	2	4	no	—
90	C₁₉×#106	—	2	4	no	—
91	C₁₉×C₄⋊C₈	—	2	2	no	—
92	C₁₉×C₄⋊C₈	—	2	2	no	—
93	C₁₉×#104	—	2	8	no	—
94	C₁₉×#103	—	2	4	no	—
95	C₁₉×#102	—	2	4	no	—
96	C₁₉×#100	—	2	4	no	—
97	C₁₉×#95	—	2	1	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
100	#41×C₁₉	—	2	8	no	—
101	#41×C₁₉	—	2	8	no	—
102	#41×C₁₉	—	2	2	no	—
103	#41×C₁₉	—	2	2	no	—
104	#41×C₁₉	C₂×Q₈	1	4	yes	—
105	#41×C₁₉	#41	1	4	yes	—
106	C₂×Q₈×C₁₉	—	4	4	no	—
107	C₂×Q₈×C₁₉	—	4	1	no	—
108	C₂×Q₈×C₁₉	—	4	1	no	—
109	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₉	—	2	4	no	—
111	C₂×D₄×C₁₉	—	2	8	no	—
112	C₂×D₄×C₁₉	—	2	8	no	—
113	C₂×D₄×C₁₉	—	2	8	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	8	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
120	C₂×D₄×C₁₉	#41	1	2	yes	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	4	4	no	—
133	C₂²×C₄×C₁₉	—	8	4	no	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	M₁₆×C₁₉	—	2	4	no	—
139	M₁₆×C₁₉	—	2	4	no	—
140	C₂×C₈×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	4	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	4	no	—
147	C₄⋊C₄×C₁₉	—	4	8	no	—
148	C₄⋊C₄×C₁₉	—	4	2	no	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₁₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₉	—	2	4	no	—
153	C₂²⋊C₄×C₁₉	—	2	2	no	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	4	8	no	—
158	C₄²×C₁₉	—	2	4	no	—
159	C₄²×C₁₉	—	2	2	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	2	4	no	—
163	C₄²×C₁₉	C₂×D₄	1	2	yes	—
164	C₄²×C₁₉	C₂×D₄	1	2	yes	—
165	#32969	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	2	8	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	8	2	no	—
173	C₂³×C₁₉	—	8	2	no	—
174	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
175	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₉	—	2	2	no	—
177	Q₈×C₁₉	—	8	2	no	—
178	Q₈×C₁₉	—	8	2	no	—
179	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	complemented
180	D₄×C₁₉	—	2	16	no	—
181	D₄×C₁₉	—	2	4	no	—
182	D₄×C₁₉	—	2	4	no	—
183	D₄×C₁₉	—	2	4	no	—
184	D₄×C₁₉	—	2	2	no	—
185	D₄×C₁₉	—	2	4	no	—
186	D₄×C₁₉	C₂²⋊Q₈	1	4	yes	complemented
187	C₂×C₄×C₁₉	—	2	8	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	8	2	no	—
205	C₂×C₄×C₁₉	—	8	2	no	—
206	C₂×C₄×C₁₉	—	8	2	no	—
207	C₂×C₄×C₁₉	—	8	4	no	—
208	C₂×C₄×C₁₉	—	8	2	no	—
209	C₂×C₄×C₁₉	#120	1	2	yes	—
210	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
215	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
216	C₈×C₁₉	—	4	4	no	—
217	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
218	#3079	C₂×C₁₉	1	2	yes	complemented
219	#2542	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1859	C₂×C₁₉	1	4	yes	complemented
221	#1856	C₂×C₁₉	1	2	yes	complemented
222	#1806	C₂×C₁₉	1	2	yes	complemented
223	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#1792	C₂×C₁₉	1	2	yes	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	4	no	—
228	C₂²×C₁₉	—	2	4	no	—
229	C₂²×C₁₉	—	4	4	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	8	2	no	—
235	C₂²×C₁₉	—	8	8	no	—
236	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
237	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
238	C₂²×C₁₉	#525	1	1	yes	characteristic
239	C₄×C₁₉	—	2	4	no	—
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	2	no	—
242	C₄×C₁₉	—	4	4	no	—
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	4	2	no	—
246	C₄×C₁₉	—	8	2	no	—
247	C₄×C₁₉	#453	1	2	yes	—
248	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
249	C₄×C₁₉	#525	1	2	yes	—
250	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
252	C₂×C₂²⋊Q₈	—	2	2	no	—
253	#520	—	2	2	no	—
254	#520	C₂²×C₁₉	1	2	yes	—
255	#518	—	2	2	no	—
256	#518	—	2	2	no	—
257	#518	C₂²×C₁₉	1	1	yes	characteristic
258	C₄×#41	—	2	2	no	—
259	C₄×#41	C₂²×C₁₉	1	2	yes	—
260	C₂×C₄×D₄	—	2	2	no	—
261	C₂×C₄×D₄	—	2	2	no	—
262	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
263	#477	—	2	2	no	—
264	#476	—	2	2	no	—
265	#475	—	2	2	no	—
266	#474	—	2	2	no	—
267	#428	C₂²×C₁₉	1	4	yes	complemented
268	#423	C₂²×C₁₉	1	2	yes	complemented
269	C₂×#104	C₂²×C₁₉	1	4	yes	—
270	#417	C₂²×C₁₉	1	4	yes	—
271	C₂×#100	C₂²×C₁₉	1	2	yes	—
272	#399	—	2	2	no	—
273	#390	C₂²×C₁₉	1	2	yes	—
274	#384	C₂²×C₁₉	1	2	yes	complemented
275	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
276	#343	C₂²×C₁₉	1	2	yes	complemented
277	#339	C₂²×C₁₉	1	4	yes	complemented
278	C₂×C₁₉	—	2	1	no	—
279	C₂×C₁₉	—	2	1	no	—
280	C₂×C₁₉	—	4	4	no	—
281	C₂×C₁₉	—	4	4	no	—
282	C₂×C₁₉	#2848	1	1	yes	characteristic
283	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
284	C₂×C₁₉	#3022	1	1	yes	characteristic
285	H(5,𝔽₂)	—	2	4	no	—
286	H(5,𝔽₂)	—	2	2	no	—
287	H(5,𝔽₂)	Q₈×C₁₉	1	4	yes	complemented
288	C₂×#41	—	2	2	no	—
289	C₂×#41	C₂³×C₁₉	1	2	yes	—
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	D₄×C₁₉	1	2	yes	—
296	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	—	4	8	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	D₄×C₁₉	1	2	yes	—
302	C₄×Q₈	D₄×C₁₉	1	2	yes	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	D₄×C₁₉	1	2	yes	—
316	C₄×D₄	D₄×C₁₉	1	2	yes	—
317	#117	—	2	4	no	—
318	#117	—	2	2	no	—
319	#117	—	2	2	no	—
320	#117	C₂³×C₁₉	1	2	yes	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	4	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
333	C₂×C₄²	—	2	2	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
337	#107	—	2	4	no	—
338	#106	—	2	4	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	—	2	2	no	—
341	#104	—	2	8	no	—
342	#103	—	2	4	no	—
343	#102	—	2	4	no	—
344	#100	—	2	4	no	—
345	#95	—	2	1	no	—
346	C₁₉	#32969	1	1	yes	characteristic, direct product factor, Sylow
347	C₂⁴	—	2	2	no	—
348	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
349	#41	—	2	8	no	—
350	#41	—	2	8	no	—
351	#41	—	2	2	no	—
352	#41	—	2	2	no	—
353	#41	C₂×Q₈×C₁₉	1	4	yes	—
354	#41	#41×C₁₉	1	4	yes	—
355	C₂×Q₈	—	4	4	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
369	C₂×D₄	#41×C₁₉	1	2	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	8	4	no	—
383	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
387	M₁₆	—	2	4	no	—
388	M₁₆	—	2	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	4	8	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	4	8	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	4	no	—
412	C₄²	C₂×D₄×C₁₉	1	2	yes	—
413	C₄²	C₂×D₄×C₁₉	1	2	yes	—
414	C₂³	—	2	8	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	8	2	no	—
421	C₂³	—	8	2	no	—
422	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
423	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
424	Q₈	—	2	2	no	—
425	Q₈	—	8	2	no	—
426	Q₈	—	8	2	no	—
427	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	complemented
428	D₄	—	2	16	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	2	4	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	4	no	—
434	D₄	C₁₉×C₂²⋊Q₈	1	4	yes	complemented
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	8	2	no	—
453	C₂×C₄	—	8	2	no	—
454	C₂×C₄	—	8	4	no	—
455	C₂×C₄	—	8	2	no	—
456	C₂×C₄	—	8	2	no	—
457	C₂×C₄	C₁₉×#120	1	2	yes	—
458	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
459	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
461	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
463	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
464	C₈	—	4	4	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	8	no	—
476	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
477	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
478	C₂²	C₁₉×#525	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	4	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	2	no	—
487	C₄	C₁₉×#453	1	2	yes	—
488	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
489	C₄	C₁₉×#525	1	2	yes	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	4	4	no	—
493	C₂	—	4	4	no	—
494	C₂	C₁₉×#2848	1	1	yes	characteristic
495	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
496	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3079	C₂	semidirect
3. C₁₉×#2542	C₂	semidirect
4. C₁₉×#1859	C₂	semidirect
5. C₁₉×#1856	C₂	semidirect
6. C₁₉×#1806	C₂	semidirect
7. C₁₉×#1800	C₂	semidirect
10. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
26. C₁₉×#428	C₂²	semidirect
27. C₁₉×#423	C₂²	semidirect
33. C₁₉×#384	C₂²	semidirect
34. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
35. C₁₉×#343	C₂²	semidirect
36. C₁₉×#339	C₂²	semidirect
39. C₁₉×H(5,𝔽₂)	Q₈	semidirect
165. #32969	C₁₉	direct (N × H)
179. Q₈×C₁₉	C₂²⋊Q₈	semidirect
186. D₄×C₁₉	C₂²⋊Q₈	semidirect
218. #3079	C₂×C₁₉	semidirect
219. #2542	C₂×C₁₉	semidirect
220. #1859	C₂×C₁₉	semidirect
221. #1856	C₂×C₁₉	semidirect
222. #1806	C₂×C₁₉	semidirect
223. #1800	C₂×C₁₉	semidirect
251. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
267. #428	C₂²×C₁₉	semidirect
268. #423	C₂²×C₁₉	semidirect
274. #384	C₂²×C₁₉	semidirect
275. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
276. #343	C₂²×C₁₉	semidirect
277. #339	C₂²×C₁₉	semidirect
287. H(5,𝔽₂)	Q₈×C₁₉	semidirect
346. C₁₉	#32969	direct (N × H)
427. Q₈	C₁₉×C₂²⋊Q₈	semidirect
434. D₄	C₁₉×C₂²⋊Q₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₉×H(5,𝔽₂)	2
C₁₉×#3079	2
C₁₉×#2542	2
C₁₉×#1859	2
C₁₉×#1856	2
C₁₉×#1806	2
C₁₉×#1800	2
C₁₉×#1792	2
#32969	19

Subgroups — C19×#32969 #18038928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32969 #18038928