Subgroups — C₂×C₁₉×#1790 #18026566

Order 4864.

4402 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#99	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₉×#386	C₂	1	3	yes	maximal, complemented
4	C₁₉×#1790	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×H(5,𝔽₂)	—	2	12	no	—
6	C₂×C₁₉×H(5,𝔽₂)	—	2	6	no	—
7	C₂×C₁₉×H(5,𝔽₂)	C₄	1	8	yes	complemented
8	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	—
9	C₂²×#41×C₁₉	—	2	3	no	—
10	C₂³×D₄×C₁₉	—	2	3	no	—
11	C₂³×D₄×C₁₉	C₂²	1	3	yes	—
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₂²⋊C₄×C₁₉	—	2	3	no	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	complemented
15	C₂×C₁₉×#99	—	2	12	no	—
16	C₂×C₁₉×#99	C₂²	1	12	yes	complemented
17	C₁₉×#386	—	2	6	no	—
18	C₁₉×#386	C₂²	1	12	yes	complemented
19	C₂×C₁₉×#95	—	2	3	no	—
20	C₂⁵×C₁₉	—	2	1	no	—
21	C₂⁵×C₁₉	D₄	1	3	yes	—
22	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
23	C₁₉×H(5,𝔽₂)	—	2	48	no	—
24	C₁₉×H(5,𝔽₂)	—	2	48	no	—
25	C₁₉×H(5,𝔽₂)	—	2	24	no	—
26	C₁₉×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
27	C₂×#41×C₁₉	—	2	12	no	—
28	C₂×#41×C₁₉	—	2	24	no	—
29	C₂×#41×C₁₉	—	2	24	no	—
30	C₂×#41×C₁₉	—	2	12	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	3	no	—
33	C₂²×D₄×C₁₉	—	2	12	no	—
34	C₂²×D₄×C₁₉	—	2	24	no	—
35	C₂²×D₄×C₁₉	—	2	24	no	—
36	C₂²×D₄×C₁₉	—	2	6	no	—
37	C₂²×D₄×C₁₉	—	2	12	no	—
38	C₂²×D₄×C₁₉	—	2	12	no	—
39	C₂²×D₄×C₁₉	—	2	6	no	—
40	C₂²×D₄×C₁₉	C₂×C₄	1	12	yes	—
41	C₂²×D₄×C₁₉	D₄	1	12	yes	—
42	C₂²×D₄×C₁₉	D₄	1	6	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
44	C₂³×C₄×C₁₉	—	2	3	no	—
45	C₂³×C₄×C₁₉	—	2	3	no	—
46	C₂³×C₄×C₁₉	—	2	3	no	—
47	C₂³×C₄×C₁₉	—	2	3	no	—
48	C₂³×C₄×C₁₉	—	4	4	no	—
49	C₂³×C₄×C₁₉	D₄	1	3	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	complemented
51	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	4	12	no	—
55	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	complemented
56	C₁₉×#99	—	2	24	no	—
57	C₁₉×#95	—	2	12	no	—
58	C₂⁴×C₁₉	—	2	4	no	—
59	C₂⁴×C₁₉	—	2	8	no	—
60	C₂⁴×C₁₉	—	2	3	no	—
61	C₂⁴×C₁₉	—	2	3	no	—
62	C₂⁴×C₁₉	—	2	6	no	—
63	C₂⁴×C₁₉	—	4	2	no	—
64	C₂⁴×C₁₉	—	4	2	no	—
65	C₂⁴×C₁₉	—	4	6	no	—
66	C₂⁴×C₁₉	—	4	6	no	—
67	C₂⁴×C₁₉	—	8	2	no	—
68	C₂⁴×C₁₉	—	8	2	no	—
69	C₂⁴×C₁₉	C₂²⋊C₄	1	12	yes	complemented
70	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
71	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
72	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
73	C₂⁴×C₁₉	C₂×D₄	1	6	yes	—
74	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
75	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
76	#41×C₁₉	—	2	48	no	—
77	#41×C₁₉	—	2	96	no	—
78	#41×C₁₉	—	2	48	no	—
79	C₂×Q₈×C₁₉	—	2	4	no	—
80	C₂×Q₈×C₁₉	—	2	8	no	—
81	C₂×D₄×C₁₉	—	2	12	no	—
82	C₂×D₄×C₁₉	—	2	24	no	—
83	C₂×D₄×C₁₉	—	2	48	no	—
84	C₂×D₄×C₁₉	—	2	96	no	—
85	C₂×D₄×C₁₉	—	2	24	no	—
86	C₂×D₄×C₁₉	—	2	24	no	—
87	C₂×D₄×C₁₉	—	2	48	no	—
88	C₂×D₄×C₁₉	—	2	12	no	—
89	C₂×D₄×C₁₉	—	2	24	no	—
90	C₂×D₄×C₁₉	—	2	12	no	—
91	C₂×D₄×C₁₉	—	2	24	no	—
92	C₂×D₄×C₁₉	—	2	12	no	—
93	C₂×D₄×C₁₉	—	2	12	no	—
94	C₂×D₄×C₁₉	C₂²⋊C₄	1	24	yes	complemented
95	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
96	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	—
97	C₂²×C₄×C₁₉	—	2	12	no	—
98	C₂²×C₄×C₁₉	—	2	24	no	—
99	C₂²×C₄×C₁₉	—	2	3	no	—
100	C₂²×C₄×C₁₉	—	2	6	no	—
101	C₂²×C₄×C₁₉	—	2	3	no	—
102	C₂²×C₄×C₁₉	—	2	12	no	—
103	C₂²×C₄×C₁₉	—	2	6	no	—
104	C₂²×C₄×C₁₉	—	2	6	no	—
105	C₂²×C₄×C₁₉	—	4	4	no	—
106	C₂²×C₄×C₁₉	—	4	12	no	—
107	C₂²×C₄×C₁₉	—	4	6	no	—
108	C₂²×C₄×C₁₉	—	4	3	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	6	no	—
111	C₂²×C₄×C₁₉	—	4	6	no	—
112	C₂²×C₄×C₁₉	—	4	6	no	—
113	C₂²×C₄×C₁₉	C₂²⋊C₄	1	12	yes	complemented
114	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
115	C₂²⋊C₄×C₁₉	—	2	12	no	—
116	C₂²⋊C₄×C₁₉	—	4	24	no	—
117	C₂²⋊C₄×C₁₉	—	4	6	no	—
118	C₂×#1790	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₁₉	—	2	6	no	—
120	C₂³×C₁₉	—	2	6	no	—
121	C₂³×C₁₉	—	2	16	no	—
122	C₂³×C₁₉	—	2	6	no	—
123	C₂³×C₁₉	—	2	12	no	—
124	C₂³×C₁₉	—	2	6	no	—
125	C₂³×C₁₉	—	2	12	no	—
126	C₂³×C₁₉	—	4	3	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	4	no	—
129	C₂³×C₁₉	—	4	3	no	—
130	C₂³×C₁₉	—	4	12	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	6	no	—
133	C₂³×C₁₉	—	4	24	no	—
134	C₂³×C₁₉	—	4	6	no	—
135	C₂³×C₁₉	—	4	6	no	—
136	C₂³×C₁₉	—	4	6	no	—
137	C₂³×C₁₉	—	8	3	no	—
138	C₂³×C₁₉	—	8	3	no	—
139	C₂³×C₁₉	—	8	12	no	—
140	C₂³×C₁₉	—	8	4	no	—
141	C₂³×C₁₉	—	8	4	no	—
142	C₂³×C₁₉	—	8	16	no	—
143	C₂³×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
144	C₂³×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
145	C₂³×C₁₉	C₂×C₂²⋊C₄	1	12	yes	complemented
146	C₂³×C₁₉	#120	1	3	yes	—
147	C₂³×C₁₉	#120	1	6	yes	—
148	C₂³×C₁₉	#120	1	6	yes	—
149	C₂³×C₁₉	#120	1	1	yes	characteristic
150	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
151	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
152	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
153	Q₈×C₁₉	—	2	16	no	—
154	D₄×C₁₉	—	2	48	no	—
155	D₄×C₁₉	—	2	24	no	—
156	D₄×C₁₉	—	2	24	no	—
157	D₄×C₁₉	—	2	48	no	—
158	C₂×C₄×C₁₉	—	2	48	no	—
159	C₂×C₄×C₁₉	—	2	6	no	—
160	C₂×C₄×C₁₉	—	2	6	no	—
161	C₂×C₄×C₁₉	—	2	12	no	—
162	C₂×C₄×C₁₉	—	2	12	no	—
163	C₂×C₄×C₁₉	—	2	12	no	—
164	C₂×C₄×C₁₉	—	4	6	no	—
165	C₂×C₄×C₁₉	—	4	12	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	6	no	—
169	C₂×C₄×C₁₉	—	4	6	no	—
170	C₂×C₄×C₁₉	—	4	6	no	—
171	C₂×C₄×C₁₉	—	8	12	no	—
172	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	12	yes	complemented
173	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
174	C₂²×#99	C₂×C₁₉	1	3	yes	complemented
175	C₂×#386	C₂×C₁₉	1	3	yes	complemented
176	#1790	C₂×C₁₉	1	8	yes	direct product factor
177	C₂²×C₁₉	—	2	3	no	—
178	C₂²×C₁₉	—	2	3	no	—
179	C₂²×C₁₉	—	2	3	no	—
180	C₂²×C₁₉	—	2	3	no	—
181	C₂²×C₁₉	—	2	12	no	—
182	C₂²×C₁₉	—	2	12	no	—
183	C₂²×C₁₉	—	2	12	no	—
184	C₂²×C₁₉	—	4	6	no	—
185	C₂²×C₁₉	—	4	6	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	3	no	—
188	C₂²×C₁₉	—	4	12	no	—
189	C₂²×C₁₉	—	4	6	no	—
190	C₂²×C₁₉	—	4	6	no	—
191	C₂²×C₁₉	—	4	24	no	—
192	C₂²×C₁₉	—	8	6	no	—
193	C₂²×C₁₉	—	8	12	no	—
194	C₂²×C₁₉	—	8	16	no	—
195	C₂²×C₁₉	#379	1	6	yes	—
196	C₂²×C₁₉	#379	1	2	yes	—
197	C₂²×C₁₉	B(4,𝔽₂)	1	2	yes	—
198	C₂²×C₁₉	#458	1	2	yes	—
199	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	3	yes	—
200	C₂²×C₁₉	C₂×#120	1	3	yes	—
201	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
202	C₄×C₁₉	—	2	12	no	—
203	C₄×C₁₉	—	4	4	no	—
204	C₄×C₁₉	—	8	6	no	—
205	C₂×H(5,𝔽₂)	—	2	12	no	—
206	C₂×H(5,𝔽₂)	—	2	6	no	—
207	C₂×H(5,𝔽₂)	C₄×C₁₉	1	8	yes	complemented
208	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	—
209	C₂²×#41	—	2	3	no	—
210	C₂³×D₄	—	2	3	no	—
211	C₂³×D₄	C₂²×C₁₉	1	3	yes	—
212	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₂²⋊C₄	—	2	3	no	—
214	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	complemented
215	C₂×#99	—	2	12	no	—
216	C₂×#99	C₂²×C₁₉	1	12	yes	complemented
217	#386	—	2	6	no	—
218	#386	C₂²×C₁₉	1	12	yes	complemented
219	C₂×#95	—	2	3	no	—
220	C₂×C₁₉	—	2	3	no	—
221	C₂×C₁₉	—	2	3	no	—
222	C₂×C₁₉	—	2	6	no	—
223	C₂×C₁₉	—	4	12	no	—
224	C₂×C₁₉	#1790	1	4	yes	direct product factor
225	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
226	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
227	C₂×C₁₉	C₂×#458	1	1	yes	characteristic
228	C₂⁵	—	2	1	no	—
229	C₂⁵	D₄×C₁₉	1	3	yes	—
230	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
231	H(5,𝔽₂)	—	2	48	no	—
232	H(5,𝔽₂)	—	2	48	no	—
233	H(5,𝔽₂)	—	2	24	no	—
234	H(5,𝔽₂)	C₂×C₄×C₁₉	1	16	yes	complemented
235	C₂×#41	—	2	24	no	—
236	C₂×#41	—	2	12	no	—
237	C₂×#41	—	2	24	no	—
238	C₂×#41	—	2	12	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	—	2	3	no	—
241	C₂²×D₄	—	2	24	no	—
242	C₂²×D₄	—	2	12	no	—
243	C₂²×D₄	—	2	24	no	—
244	C₂²×D₄	—	2	6	no	—
245	C₂²×D₄	—	2	12	no	—
246	C₂²×D₄	—	2	12	no	—
247	C₂²×D₄	—	2	6	no	—
248	C₂²×D₄	C₂×C₄×C₁₉	1	12	yes	—
249	C₂²×D₄	D₄×C₁₉	1	12	yes	—
250	C₂²×D₄	D₄×C₁₉	1	6	yes	—
251	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
252	C₂³×C₄	—	2	3	no	—
253	C₂³×C₄	—	2	3	no	—
254	C₂³×C₄	—	2	3	no	—
255	C₂³×C₄	—	2	3	no	—
256	C₂³×C₄	—	4	4	no	—
257	C₂³×C₄	D₄×C₁₉	1	3	yes	—
258	C₂³×C₄	C₂³×C₁₉	1	2	yes	complemented
259	C₂×C₂²⋊C₄	—	2	12	no	—
260	C₂×C₂²⋊C₄	—	2	12	no	—
261	C₂×C₂²⋊C₄	—	2	3	no	—
262	C₂×C₂²⋊C₄	—	4	12	no	—
263	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	complemented
264	#99	—	2	24	no	—
265	#95	—	2	12	no	—
266	C₁₉	C₂×#1790	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁴	—	2	8	no	—
268	C₂⁴	—	2	4	no	—
269	C₂⁴	—	2	3	no	—
270	C₂⁴	—	2	6	no	—
271	C₂⁴	—	2	3	no	—
272	C₂⁴	—	4	2	no	—
273	C₂⁴	—	4	2	no	—
274	C₂⁴	—	4	6	no	—
275	C₂⁴	—	4	6	no	—
276	C₂⁴	—	8	2	no	—
277	C₂⁴	—	8	2	no	—
278	C₂⁴	C₂²⋊C₄×C₁₉	1	12	yes	complemented
279	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
280	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
281	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
282	C₂⁴	C₂×D₄×C₁₉	1	6	yes	—
283	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
284	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
285	#41	—	2	96	no	—
286	#41	—	2	48	no	—
287	#41	—	2	48	no	—
288	C₂×Q₈	—	2	8	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×D₄	—	2	24	no	—
291	C₂×D₄	—	2	12	no	—
292	C₂×D₄	—	2	96	no	—
293	C₂×D₄	—	2	48	no	—
294	C₂×D₄	—	2	24	no	—
295	C₂×D₄	—	2	24	no	—
296	C₂×D₄	—	2	48	no	—
297	C₂×D₄	—	2	24	no	—
298	C₂×D₄	—	2	12	no	—
299	C₂×D₄	—	2	24	no	—
300	C₂×D₄	—	2	12	no	—
301	C₂×D₄	—	2	12	no	—
302	C₂×D₄	—	2	12	no	—
303	C₂×D₄	C₂²⋊C₄×C₁₉	1	24	yes	complemented
304	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
305	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	—
306	C₂²×C₄	—	2	24	no	—
307	C₂²×C₄	—	2	12	no	—
308	C₂²×C₄	—	2	3	no	—
309	C₂²×C₄	—	2	6	no	—
310	C₂²×C₄	—	2	3	no	—
311	C₂²×C₄	—	2	12	no	—
312	C₂²×C₄	—	2	6	no	—
313	C₂²×C₄	—	2	6	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	—	4	12	no	—
316	C₂²×C₄	—	4	6	no	—
317	C₂²×C₄	—	4	3	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	6	no	—
320	C₂²×C₄	—	4	6	no	—
321	C₂²×C₄	—	4	6	no	—
322	C₂²×C₄	C₂²⋊C₄×C₁₉	1	12	yes	complemented
323	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
324	C₂²⋊C₄	—	2	12	no	—
325	C₂²⋊C₄	—	4	24	no	—
326	C₂²⋊C₄	—	4	6	no	—
327	C₂³	—	2	6	no	—
328	C₂³	—	2	6	no	—
329	C₂³	—	2	16	no	—
330	C₂³	—	2	12	no	—
331	C₂³	—	2	6	no	—
332	C₂³	—	2	12	no	—
333	C₂³	—	2	6	no	—
334	C₂³	—	4	3	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	3	no	—
338	C₂³	—	4	12	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	6	no	—
341	C₂³	—	4	24	no	—
342	C₂³	—	4	6	no	—
343	C₂³	—	4	6	no	—
344	C₂³	—	4	6	no	—
345	C₂³	—	8	3	no	—
346	C₂³	—	8	3	no	—
347	C₂³	—	8	12	no	—
348	C₂³	—	8	4	no	—
349	C₂³	—	8	4	no	—
350	C₂³	—	8	16	no	—
351	C₂³	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
352	C₂³	C₂×C₂²⋊C₄×C₁₉	1	6	yes	—
353	C₂³	C₂×C₂²⋊C₄×C₁₉	1	12	yes	complemented
354	C₂³	C₁₉×#120	1	3	yes	—
355	C₂³	C₁₉×#120	1	6	yes	—
356	C₂³	C₁₉×#120	1	6	yes	—
357	C₂³	C₁₉×#120	1	1	yes	characteristic
358	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
359	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
360	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
361	Q₈	—	2	16	no	—
362	D₄	—	2	48	no	—
363	D₄	—	2	48	no	—
364	D₄	—	2	24	no	—
365	D₄	—	2	24	no	—
366	C₂×C₄	—	2	48	no	—
367	C₂×C₄	—	2	12	no	—
368	C₂×C₄	—	2	12	no	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	12	no	—
372	C₂×C₄	—	4	6	no	—
373	C₂×C₄	—	4	12	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	6	no	—
377	C₂×C₄	—	4	6	no	—
378	C₂×C₄	—	4	6	no	—
379	C₂×C₄	—	8	12	no	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	12	yes	complemented
381	C₂²	—	2	3	no	—
382	C₂²	—	2	3	no	—
383	C₂²	—	2	3	no	—
384	C₂²	—	2	3	no	—
385	C₂²	—	2	12	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	4	6	no	—
389	C₂²	—	4	6	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	3	no	—
392	C₂²	—	4	12	no	—
393	C₂²	—	4	6	no	—
394	C₂²	—	4	6	no	—
395	C₂²	—	4	24	no	—
396	C₂²	—	8	6	no	—
397	C₂²	—	8	12	no	—
398	C₂²	—	8	16	no	—
399	C₂²	C₁₉×#379	1	6	yes	—
400	C₂²	C₁₉×#379	1	2	yes	—
401	C₂²	C₁₉×B(4,𝔽₂)	1	2	yes	—
402	C₂²	C₁₉×#458	1	2	yes	—
403	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	3	yes	—
404	C₂²	C₂×C₁₉×#120	1	3	yes	—
405	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
406	C₄	—	2	12	no	—
407	C₄	—	4	4	no	—
408	C₄	—	8	6	no	—
409	C₂	—	2	3	no	—
410	C₂	—	2	3	no	—
411	C₂	—	2	6	no	—
412	C₂	—	4	12	no	—
413	C₂	C₁₉×#1790	1	4	yes	direct product factor
414	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
415	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
416	C₂	C₂×C₁₉×#458	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#99	C₂	semidirect
3. C₂×C₁₉×#386	C₂	semidirect
4. C₁₉×#1790	C₂	direct (N × H)
7. C₂×C₁₉×H(5,𝔽₂)	C₄	semidirect
12. C₂⁴×C₄×C₁₉	C₂²	semidirect
14. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
16. C₂×C₁₉×#99	C₂²	semidirect
18. C₁₉×#386	C₂²	semidirect
26. C₁₉×H(5,𝔽₂)	C₂×C₄	semidirect
50. C₂³×C₄×C₁₉	C₂³	semidirect
55. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
69. C₂⁴×C₁₉	C₂²⋊C₄	semidirect
94. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
113. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
118. C₂×#1790	C₁₉	direct (N × H)
145. C₂³×C₁₉	C₂×C₂²⋊C₄	semidirect
172. C₂×C₄×C₁₉	C₂×C₂²⋊C₄	semidirect
174. C₂²×#99	C₂×C₁₉	semidirect
175. C₂×#386	C₂×C₁₉	semidirect
176. #1790	C₂×C₁₉	direct (N × H)
207. C₂×H(5,𝔽₂)	C₄×C₁₉	semidirect
212. C₂⁴×C₄	C₂²×C₁₉	semidirect
214. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
216. C₂×#99	C₂²×C₁₉	semidirect
218. #386	C₂²×C₁₉	semidirect
224. C₂×C₁₉	#1790	direct (N × H)
234. H(5,𝔽₂)	C₂×C₄×C₁₉	semidirect
258. C₂³×C₄	C₂³×C₁₉	semidirect
263. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
266. C₁₉	C₂×#1790	direct (N × H)
278. C₂⁴	C₂²⋊C₄×C₁₉	semidirect
303. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
322. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect
353. C₂³	C₂×C₂²⋊C₄×C₁₉	semidirect
380. C₂×C₄	C₂×C₂²⋊C₄×C₁₉	semidirect
413. C₂	C₁₉×#1790	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×H(5,𝔽₂)	2
C₂²×C₁₉×#99	2
C₂×C₁₉×#386	2
C₁₉×#1790	2
C₂×#1790	19

Subgroups — C2×C19×#1790 #18026566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1790 #18026566