Subgroups — C₁₉×#62853 #18068812

Order 4864.

11222 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#585	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3497	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3496	C₂	1	12	yes	maximal, complemented
4	C₁₉×#3489	C₂	1	16	yes	maximal, complemented
5	C₁₉×#3488	C₂	1	16	yes	maximal, complemented
6	C₁₉×#3449	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₉×#537	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#585	—	2	32	no	—
10	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	8	yes	complemented
11	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	8	yes	complemented
13	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	12	yes	complemented
14	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₁₉	C₂²	1	12	yes	complemented
16	C₂²×#41×C₁₉	C₂²	1	16	yes	complemented
17	C₁₉×#550	C₂²	1	16	yes	complemented
18	D₄×Q₈×C₁₉	C₂²	1	16	yes	complemented
19	C₁₉×#548	C₂²	1	32	yes	complemented
20	C₁₉×#547	C₂²	1	48	yes	complemented
21	C₁₉×#546	C₂²	1	96	yes	complemented
22	D₄²×C₁₉	C₂²	1	48	yes	complemented
23	C₁₉×#537	C₂²	1	12	yes	complemented
24	C₁₉×#537	C₂²	1	48	yes	complemented
25	C₁₉×#537	C₂²	1	24	yes	complemented
26	C₁₉×#537	C₂²	1	4	yes	complemented
27	C₁₉×#536	C₂²	1	24	yes	complemented
28	C₁₉×#535	C₂²	1	24	yes	complemented
29	C₁₉×#534	C₂²	1	24	yes	complemented
30	C₁₉×#532	C₂²	1	24	yes	complemented
31	C₁₉×#525	C₂²	1	48	yes	complemented
32	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	24	yes	complemented
33	C₂×C₁₉×#121	C₂²	1	24	yes	complemented
34	C₂×C₁₉×#121	C₂²	1	24	yes	complemented
35	C₁₉×#520	C₂²	1	16	yes	complemented
36	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
37	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	complemented
38	C₂×C₁₉×#117	C₂²	1	3	yes	complemented
39	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	complemented
40	C₁₉×2₋¹⁺⁴	—	2	64	no	—
41	C₁₉×2₋¹⁺⁴	—	2	32	no	—
42	C₁₉×H(5,𝔽₂)	—	2	64	no	—
43	C₁₉×H(5,𝔽₂)	—	2	96	no	—
44	C₂×#41×C₁₉	—	2	128	no	—
45	C₂×#41×C₁₉	—	2	96	no	—
46	C₂×#41×C₁₉	D₄	1	16	yes	complemented
47	C₂×#41×C₁₉	C₂³	1	24	yes	—
48	C₂×#41×C₁₉	C₂³	1	24	yes	—
49	C₂×#41×C₁₉	C₂³	1	24	yes	—
50	C₂×#41×C₁₉	C₂³	1	8	yes	—
51	C₂×#41×C₁₉	C₂³	1	48	yes	—
52	C₂×#41×C₁₉	C₂³	1	16	yes	—
53	C₂×#41×C₁₉	C₂³	1	8	yes	—
54	C₂²×Q₈×C₁₉	C₂³	1	12	yes	—
55	C₂²×Q₈×C₁₉	C₂³	1	16	yes	—
56	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	24	yes	—
58	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
59	C₂²×D₄×C₁₉	C₂³	1	48	yes	—
60	C₂²×D₄×C₁₉	C₂³	1	24	yes	—
61	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	24	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
65	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
66	C₁₉×#127	C₂³	1	24	yes	—
67	C₁₉×#124	C₂³	1	48	yes	—
68	C₁₉×#123	C₂³	1	96	yes	—
69	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
70	C₁₉×C₂²⋊Q₈	C₂³	1	96	yes	—
71	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
72	C₁₉×#121	C₂³	1	48	yes	—
73	C₁₉×#121	C₂³	1	48	yes	—
74	C₁₉×#121	C₂³	1	96	yes	—
75	C₁₉×#121	C₂³	1	96	yes	—
76	C₁₉×#121	C₂³	1	16	yes	—
77	C₁₉×#121	C₂³	1	16	yes	—
78	C₁₉×#120	C₂³	1	96	yes	—
79	C₄×Q₈×C₁₉	C₂³	1	16	yes	—
80	C₄×D₄×C₁₉	C₂³	1	48	yes	—
81	C₄×D₄×C₁₉	C₂³	1	48	yes	—
82	C₄×D₄×C₁₉	C₂³	1	48	yes	—
83	C₁₉×#117	C₂³	1	24	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
90	C₂×C₂²⋊C₄×C₁₉	C₂³	1	48	yes	—
91	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
92	C₂⁴×C₁₉	C₂⁴	1	24	yes	—
93	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
94	#41×C₁₉	—	2	64	no	—
95	#41×C₁₉	—	2	192	no	—
96	#41×C₁₉	—	2	96	no	—
97	#41×C₁₉	—	2	32	no	—
98	#41×C₁₉	—	2	96	no	—
99	#41×C₁₉	—	2	96	no	—
100	#41×C₁₉	C₂×D₄	1	64	yes	complemented
101	C₂×Q₈×C₁₉	—	2	64	no	—
102	C₂×Q₈×C₁₉	—	2	48	no	—
103	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	complemented
104	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
105	C₂×Q₈×C₁₉	C₂⁴	1	24	yes	—
106	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
107	C₂×D₄×C₁₉	—	2	96	no	—
108	C₂×D₄×C₁₉	—	2	192	no	—
109	C₂×D₄×C₁₉	—	2	48	no	—
110	C₂×D₄×C₁₉	—	8	24	no	—
111	C₂×D₄×C₁₉	C₂×D₄	1	24	yes	complemented
112	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
113	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
114	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
115	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
116	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
117	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
118	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
119	C₂²×C₄×C₁₉	—	2	96	no	—
120	C₂²×C₄×C₁₉	—	8	6	no	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	24	yes	complemented
122	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
123	C₂²×C₄×C₁₉	C₂⁴	1	48	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
131	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
132	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
133	C₄⋊C₄×C₁₉	C₂⁴	1	48	yes	—
134	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
135	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
136	C₂²⋊C₄×C₁₉	C₂⁴	1	96	yes	—
137	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
138	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
139	C₄²×C₁₉	C₂⁴	1	24	yes	—
140	#62853	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₉	—	2	48	no	—
142	C₂³×C₁₉	—	4	3	no	—
143	C₂³×C₁₉	—	4	3	no	—
144	C₂³×C₁₉	—	4	24	no	—
145	C₂³×C₁₉	—	4	24	no	—
146	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
147	C₂³×C₁₉	C₂⁵	1	16	yes	—
148	C₂³×C₁₉	C₂⁵	1	6	yes	—
149	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
150	Q₈×C₁₉	—	2	16	no	—
151	Q₈×C₁₉	—	2	48	no	—
152	Q₈×C₁₉	C₂²×D₄	1	16	yes	—
153	D₄×C₁₉	—	2	96	no	—
154	D₄×C₁₉	—	2	32	no	—
155	D₄×C₁₉	—	2	16	no	—
156	D₄×C₁₉	—	2	48	no	—
157	D₄×C₁₉	—	4	48	no	—
158	D₄×C₁₉	—	4	16	no	—
159	D₄×C₁₉	C₂²×D₄	1	48	yes	—
160	C₂×C₄×C₁₉	—	2	48	no	—
161	C₂×C₄×C₁₉	—	2	32	no	—
162	C₂×C₄×C₁₉	—	2	96	no	—
163	C₂×C₄×C₁₉	—	4	6	no	—
164	C₂×C₄×C₁₉	—	4	24	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	C₂²×D₄	1	48	yes	—
167	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
168	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
169	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
170	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
171	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
172	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
173	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
174	C₂×#585	C₂×C₁₉	1	2	yes	complemented
175	#3497	C₂×C₁₉	1	4	yes	complemented
176	#3496	C₂×C₁₉	1	12	yes	complemented
177	#3489	C₂×C₁₉	1	16	yes	complemented
178	#3488	C₂×C₁₉	1	16	yes	complemented
179	#3449	C₂×C₁₉	1	6	yes	complemented
180	C₂×#537	C₂×C₁₉	1	6	yes	complemented
181	C₂×#520	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	6	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	6	no	—
186	C₂²×C₁₉	—	2	16	no	—
187	C₂²×C₁₉	—	2	16	no	—
188	C₂²×C₁₉	—	2	16	no	—
189	C₂²×C₁₉	—	4	12	no	—
190	C₂²×C₁₉	—	8	48	no	—
191	C₂²×C₁₉	C₂³×D₄	1	12	yes	—
192	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
193	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
194	C₄×C₁₉	—	2	16	no	—
195	C₄×C₁₉	—	2	12	no	—
196	C₄×C₁₉	—	2	4	no	—
197	C₄×C₁₉	C₂³×D₄	1	4	yes	—
198	C₄×C₁₉	C₂³×D₄	1	12	yes	—
199	#585	—	2	32	no	—
200	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	8	yes	complemented
201	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	complemented
202	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	8	yes	complemented
203	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	12	yes	complemented
204	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
205	C₂²×#41	C₂²×C₁₉	1	12	yes	complemented
206	C₂²×#41	C₂²×C₁₉	1	16	yes	complemented
207	#550	C₂²×C₁₉	1	16	yes	complemented
208	D₄×Q₈	C₂²×C₁₉	1	16	yes	complemented
209	#548	C₂²×C₁₉	1	32	yes	complemented
210	#547	C₂²×C₁₉	1	48	yes	complemented
211	#546	C₂²×C₁₉	1	96	yes	complemented
212	D₄²	C₂²×C₁₉	1	48	yes	complemented
213	#537	C₂²×C₁₉	1	12	yes	complemented
214	#537	C₂²×C₁₉	1	48	yes	complemented
215	#537	C₂²×C₁₉	1	24	yes	complemented
216	#537	C₂²×C₁₉	1	4	yes	complemented
217	#536	C₂²×C₁₉	1	24	yes	complemented
218	#535	C₂²×C₁₉	1	24	yes	complemented
219	#534	C₂²×C₁₉	1	24	yes	complemented
220	#532	C₂²×C₁₉	1	24	yes	complemented
221	#525	C₂²×C₁₉	1	48	yes	complemented
222	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	24	yes	complemented
223	C₂×#121	C₂²×C₁₉	1	24	yes	complemented
224	C₂×#121	C₂²×C₁₉	1	24	yes	complemented
225	#520	C₂²×C₁₉	1	16	yes	complemented
226	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
227	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	complemented
228	C₂×#117	C₂²×C₁₉	1	3	yes	complemented
229	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	complemented
230	C₂×C₁₉	—	2	2	no	—
231	C₂×C₁₉	—	2	12	no	—
232	C₂×C₁₉	—	4	16	no	—
233	C₂×C₁₉	C₂⁴×D₄	1	1	yes	characteristic
234	C₂×C₁₉	H(7,𝔽₂)	1	1	yes	characteristic
235	C₂×C₁₉	2₋¹⁺⁶	1	1	yes	characteristic
236	2₋¹⁺⁴	—	2	64	no	—
237	2₋¹⁺⁴	—	2	32	no	—
238	H(5,𝔽₂)	—	2	64	no	—
239	H(5,𝔽₂)	—	2	96	no	—
240	C₂×#41	—	2	128	no	—
241	C₂×#41	—	2	96	no	—
242	C₂×#41	D₄×C₁₉	1	16	yes	complemented
243	C₂×#41	C₂³×C₁₉	1	24	yes	—
244	C₂×#41	C₂³×C₁₉	1	24	yes	—
245	C₂×#41	C₂³×C₁₉	1	24	yes	—
246	C₂×#41	C₂³×C₁₉	1	8	yes	—
247	C₂×#41	C₂³×C₁₉	1	48	yes	—
248	C₂×#41	C₂³×C₁₉	1	16	yes	—
249	C₂×#41	C₂³×C₁₉	1	8	yes	—
250	C₂²×Q₈	C₂³×C₁₉	1	12	yes	—
251	C₂²×Q₈	C₂³×C₁₉	1	16	yes	—
252	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
253	C₂²×D₄	C₂³×C₁₉	1	24	yes	—
254	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
255	C₂²×D₄	C₂³×C₁₉	1	48	yes	—
256	C₂²×D₄	C₂³×C₁₉	1	24	yes	—
257	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
258	C₂³×C₄	C₂³×C₁₉	1	24	yes	—
259	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
260	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
261	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
262	#127	C₂³×C₁₉	1	24	yes	—
263	#124	C₂³×C₁₉	1	48	yes	—
264	#123	C₂³×C₁₉	1	96	yes	—
265	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
266	C₂²⋊Q₈	C₂³×C₁₉	1	96	yes	—
267	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
268	#121	C₂³×C₁₉	1	48	yes	—
269	#121	C₂³×C₁₉	1	48	yes	—
270	#121	C₂³×C₁₉	1	96	yes	—
271	#121	C₂³×C₁₉	1	96	yes	—
272	#121	C₂³×C₁₉	1	16	yes	—
273	#121	C₂³×C₁₉	1	16	yes	—
274	#120	C₂³×C₁₉	1	96	yes	—
275	C₄×Q₈	C₂³×C₁₉	1	16	yes	—
276	C₄×D₄	C₂³×C₁₉	1	48	yes	—
277	C₄×D₄	C₂³×C₁₉	1	48	yes	—
278	C₄×D₄	C₂³×C₁₉	1	48	yes	—
279	#117	C₂³×C₁₉	1	24	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₉	1	48	yes	—
287	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
288	C₁₉	#62853	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁴	C₂⁴×C₁₉	1	24	yes	—
290	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
291	#41	—	2	64	no	—
292	#41	—	2	192	no	—
293	#41	—	2	96	no	—
294	#41	—	2	32	no	—
295	#41	—	2	96	no	—
296	#41	—	2	96	no	—
297	#41	C₂×D₄×C₁₉	1	64	yes	complemented
298	C₂×Q₈	—	2	64	no	—
299	C₂×Q₈	—	2	48	no	—
300	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	complemented
301	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
302	C₂×Q₈	C₂⁴×C₁₉	1	24	yes	—
303	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
304	C₂×D₄	—	2	96	no	—
305	C₂×D₄	—	2	192	no	—
306	C₂×D₄	—	2	48	no	—
307	C₂×D₄	—	8	24	no	—
308	C₂×D₄	C₂×D₄×C₁₉	1	24	yes	complemented
309	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
310	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
311	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
312	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
313	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
314	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
315	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
316	C₂²×C₄	—	2	96	no	—
317	C₂²×C₄	—	8	6	no	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	24	yes	complemented
319	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
320	C₂²×C₄	C₂⁴×C₁₉	1	48	yes	—
321	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
322	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
324	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
325	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
326	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
328	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
329	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
330	C₄⋊C₄	C₂⁴×C₁₉	1	48	yes	—
331	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
332	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
333	C₂²⋊C₄	C₂⁴×C₁₉	1	96	yes	—
334	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
335	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
336	C₄²	C₂⁴×C₁₉	1	24	yes	—
337	C₂³	—	2	48	no	—
338	C₂³	—	4	3	no	—
339	C₂³	—	4	3	no	—
340	C₂³	—	4	24	no	—
341	C₂³	—	4	24	no	—
342	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
343	C₂³	C₂⁵×C₁₉	1	16	yes	—
344	C₂³	C₂⁵×C₁₉	1	6	yes	—
345	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
346	Q₈	—	2	16	no	—
347	Q₈	—	2	48	no	—
348	Q₈	C₂²×D₄×C₁₉	1	16	yes	—
349	D₄	—	2	96	no	—
350	D₄	—	2	32	no	—
351	D₄	—	2	16	no	—
352	D₄	—	2	48	no	—
353	D₄	—	4	48	no	—
354	D₄	—	4	16	no	—
355	D₄	C₂²×D₄×C₁₉	1	48	yes	—
356	C₂×C₄	—	2	48	no	—
357	C₂×C₄	—	2	32	no	—
358	C₂×C₄	—	2	96	no	—
359	C₂×C₄	—	4	6	no	—
360	C₂×C₄	—	4	24	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	C₂²×D₄×C₁₉	1	48	yes	—
363	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
364	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
365	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
366	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
367	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
368	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
369	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	6	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	6	no	—
374	C₂²	—	2	16	no	—
375	C₂²	—	2	16	no	—
376	C₂²	—	2	16	no	—
377	C₂²	—	4	12	no	—
378	C₂²	—	8	48	no	—
379	C₂²	C₂³×D₄×C₁₉	1	12	yes	—
380	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
381	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
382	C₄	—	2	16	no	—
383	C₄	—	2	12	no	—
384	C₄	—	2	4	no	—
385	C₄	C₂³×D₄×C₁₉	1	4	yes	—
386	C₄	C₂³×D₄×C₁₉	1	12	yes	—
387	C₂	—	2	2	no	—
388	C₂	—	2	12	no	—
389	C₂	—	4	16	no	—
390	C₂	C₂⁴×D₄×C₁₉	1	1	yes	characteristic
391	C₂	C₁₉×H(7,𝔽₂)	1	1	yes	characteristic
392	C₂	C₁₉×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#585	C₂	semidirect
2. C₁₉×#3497	C₂	semidirect
3. C₁₉×#3496	C₂	semidirect
4. C₁₉×#3489	C₂	semidirect
5. C₁₉×#3488	C₂	semidirect
6. C₁₉×#3449	C₂	semidirect
7. C₂×C₁₉×#537	C₂	semidirect
8. C₂×C₁₉×#520	C₂	semidirect
10. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
11. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
12. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
13. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
15. C₂²×#41×C₁₉	C₂²	semidirect
16. C₂²×#41×C₁₉	C₂²	semidirect
17. C₁₉×#550	C₂²	semidirect
18. D₄×Q₈×C₁₉	C₂²	semidirect
19. C₁₉×#548	C₂²	semidirect
20. C₁₉×#547	C₂²	semidirect
21. C₁₉×#546	C₂²	semidirect
22. D₄²×C₁₉	C₂²	semidirect
23. C₁₉×#537	C₂²	semidirect
24. C₁₉×#537	C₂²	semidirect
25. C₁₉×#537	C₂²	semidirect
26. C₁₉×#537	C₂²	semidirect
27. C₁₉×#536	C₂²	semidirect
28. C₁₉×#535	C₂²	semidirect
29. C₁₉×#534	C₂²	semidirect
30. C₁₉×#532	C₂²	semidirect
31. C₁₉×#525	C₂²	semidirect
32. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₁₉×#121	C₂²	semidirect
34. C₂×C₁₉×#121	C₂²	semidirect
35. C₁₉×#520	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
37. C₂×C₄×D₄×C₁₉	C₂²	semidirect
38. C₂×C₁₉×#117	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
46. C₂×#41×C₁₉	D₄	semidirect
100. #41×C₁₉	C₂×D₄	semidirect
103. C₂×Q₈×C₁₉	C₂×D₄	semidirect
111. C₂×D₄×C₁₉	C₂×D₄	semidirect
121. C₂²×C₄×C₁₉	C₂×D₄	semidirect
140. #62853	C₁₉	direct (N × H)
174. C₂×#585	C₂×C₁₉	semidirect
175. #3497	C₂×C₁₉	semidirect
176. #3496	C₂×C₁₉	semidirect
177. #3489	C₂×C₁₉	semidirect
178. #3488	C₂×C₁₉	semidirect
179. #3449	C₂×C₁₉	semidirect
180. C₂×#537	C₂×C₁₉	semidirect
181. C₂×#520	C₂×C₁₉	semidirect
200. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
201. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
202. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
203. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
205. C₂²×#41	C₂²×C₁₉	semidirect
206. C₂²×#41	C₂²×C₁₉	semidirect
207. #550	C₂²×C₁₉	semidirect
208. D₄×Q₈	C₂²×C₁₉	semidirect
209. #548	C₂²×C₁₉	semidirect
210. #547	C₂²×C₁₉	semidirect
211. #546	C₂²×C₁₉	semidirect
212. D₄²	C₂²×C₁₉	semidirect
213. #537	C₂²×C₁₉	semidirect
214. #537	C₂²×C₁₉	semidirect
215. #537	C₂²×C₁₉	semidirect
216. #537	C₂²×C₁₉	semidirect
217. #536	C₂²×C₁₉	semidirect
218. #535	C₂²×C₁₉	semidirect
219. #534	C₂²×C₁₉	semidirect
220. #532	C₂²×C₁₉	semidirect
221. #525	C₂²×C₁₉	semidirect
222. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
223. C₂×#121	C₂²×C₁₉	semidirect
224. C₂×#121	C₂²×C₁₉	semidirect
225. #520	C₂²×C₁₉	semidirect
226. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
227. C₂×C₄×D₄	C₂²×C₁₉	semidirect
228. C₂×#117	C₂²×C₁₉	semidirect
229. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
242. C₂×#41	D₄×C₁₉	semidirect
288. C₁₉	#62853	direct (N × H)
297. #41	C₂×D₄×C₁₉	semidirect
300. C₂×Q₈	C₂×D₄×C₁₉	semidirect
308. C₂×D₄	C₂×D₄×C₁₉	semidirect
318. C₂²×C₄	C₂×D₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#585	2
C₁₉×#3497	2
C₁₉×#3496	2
C₁₉×#3489	2
C₁₉×#3488	2
C₁₉×#3449	2
C₂×C₁₉×#537	2
C₂×C₁₉×#520	2
#62853	19

Subgroups — C19×#62853 #18068812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62853 #18068812