Subgroups — #18088697

Order 4864.

958 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597264	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
6	#14561865	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×#10597264	—	2	2	no	—
13	C₂×#10597264	—	2	2	no	—
14	C₂×#10597264	C₄	1	4	yes	complemented
15	C₂×C₁₉⋊#95	—	2	1	no	—
16	C₂×C₁₉⋊#95	—	2	1	no	—
17	#11926306	—	2	2	no	—
18	#11926306	—	2	2	no	—
19	#11926306	C₄	1	4	yes	complemented
20	#11926299	C₄	1	4	yes	complemented
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	—	2	1	no	—
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₁₉×#95	—	2	1	no	—
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂³×Dic₁₉	—	2	1	no	—
34	C₂³×Dic₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	4	no	—
52	C₂×C₄²×C₁₉	—	4	2	no	—
53	C₂×C₄²×C₁₉	—	4	2	no	—
54	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
56	C₂×C₄⋊Dic₁₉	—	2	1	no	—
57	C₂×C₄⋊Dic₁₉	—	2	1	no	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄⋊Dic₁₉	—	2	1	no	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	—	2	1	no	—
63	C₂×C₄⋊Dic₁₉	—	2	1	no	—
64	C₂×C₄⋊Dic₁₉	—	2	1	no	—
65	C₂×C₄⋊Dic₁₉	—	2	1	no	—
66	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
68	C₂²×C₁₉⋊C₈	—	2	1	no	—
69	C₂²×C₁₉⋊C₈	—	2	1	no	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	—	2	1	no	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
79	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
81	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
82	C₁₉×#95	—	2	4	no	—
83	C₁₉⋊#95	—	4	2	no	—
84	C₁₉⋊#95	—	4	2	no	—
85	#10597264	—	2	8	no	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	1	no	—
106	C₂²×C₄×C₁₉	—	4	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
113	C₂²×C₄×C₁₉	D₈	1	2	yes	—
114	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	C₂²×Dic₁₉	—	2	2	no	—
130	C₂²×Dic₁₉	—	2	2	no	—
131	C₂²×Dic₁₉	—	4	1	no	—
132	C₂²×Dic₁₉	—	4	1	no	—
133	C₂²×Dic₁₉	—	4	1	no	—
134	C₂²×Dic₁₉	—	4	1	no	—
135	C₂²×Dic₁₉	—	4	1	no	—
136	C₂²×Dic₁₉	—	4	1	no	—
137	C₂²×Dic₁₉	—	4	1	no	—
138	C₂²×Dic₁₉	—	4	1	no	—
139	C₂²×Dic₁₉	—	4	1	no	—
140	C₂²×Dic₁₉	—	4	1	no	—
141	C₂²×Dic₁₉	—	4	1	no	—
142	C₂²×Dic₁₉	—	4	1	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	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
150	C₄⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
151	C₄²×C₁₉	—	2	2	no	—
152	C₄²×C₁₉	—	2	2	no	—
153	C₄²×C₁₉	—	2	2	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	4	8	no	—
156	C₄⋊Dic₁₉	—	2	2	no	—
157	C₄⋊Dic₁₉	—	2	2	no	—
158	C₄⋊Dic₁₉	—	2	2	no	—
159	C₄⋊Dic₁₉	—	2	2	no	—
160	C₄⋊Dic₁₉	—	4	1	no	—
161	C₄⋊Dic₁₉	—	4	1	no	—
162	C₄⋊Dic₁₉	—	4	1	no	—
163	C₄⋊Dic₁₉	—	4	1	no	—
164	C₂×C₁₉⋊C₈	—	2	2	no	—
165	C₂×C₁₉⋊C₈	—	2	2	no	—
166	C₂×C₁₉⋊C₈	—	2	2	no	—
167	C₂×C₁₉⋊C₈	—	2	2	no	—
168	C₂×C₁₉⋊C₈	—	2	2	no	—
169	C₂×C₁₉⋊C₈	—	2	2	no	—
170	C₂×C₁₉⋊C₈	—	2	2	no	—
171	C₂×C₁₉⋊C₈	—	2	2	no	—
172	C₂×C₁₉⋊C₈	—	2	2	no	—
173	C₂×C₁₉⋊C₈	—	4	1	no	—
174	C₂×C₁₉⋊C₈	—	4	1	no	—
175	C₂×C₁₉⋊C₈	—	4	1	no	—
176	C₂×C₁₉⋊C₈	—	4	1	no	—
177	C₂×C₁₉⋊C₈	C₄²	1	4	yes	complemented
178	#10907	—	19	1	no	maximal, Sylow
179	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
181	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
182	C₂³×C₁₉	#120	1	1	yes	characteristic
183	C₂³×C₁₉	#121	1	1	yes	characteristic
184	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂³×C₁₉	#123	1	1	yes	characteristic
186	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
187	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
188	C₂³×C₁₉	#135	1	1	yes	characteristic
189	C₂³×C₁₉	#135	1	1	yes	characteristic
190	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₂³×C₁₉	#137	1	1	yes	characteristic
193	C₂³×C₁₉	#137	1	1	yes	characteristic
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	#107	1	4	yes	complemented
222	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
250	C₂×Dic₁₉	—	4	2	no	—
251	C₂×Dic₁₉	—	4	2	no	—
252	C₂×Dic₁₉	—	4	2	no	—
253	C₂×Dic₁₉	—	4	2	no	—
254	C₂×Dic₁₉	—	4	2	no	—
255	C₂×Dic₁₉	—	4	2	no	—
256	C₂×Dic₁₉	—	8	1	no	—
257	C₂×Dic₁₉	—	8	1	no	—
258	C₂×Dic₁₉	—	8	1	no	—
259	C₂×Dic₁₉	—	8	1	no	—
260	C₂×Dic₁₉	—	8	1	no	—
261	C₂×Dic₁₉	—	8	1	no	—
262	C₂×Dic₁₉	—	8	1	no	—
263	C₂×Dic₁₉	—	8	1	no	—
264	C₁₉⋊C₈	—	2	4	no	—
265	C₁₉⋊C₈	—	4	2	no	—
266	C₂²×#107	—	19	1	no	—
267	C₂×C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
268	C₂×#340	—	19	1	no	—
269	C₂×#340	—	19	1	no	—
270	C₂×#340	—	19	1	no	—
271	C₂×#336	—	19	1	no	—
272	C₄⋊#95	—	19	1	no	—
273	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₁₉	#385	1	1	yes	characteristic
275	C₂²×C₁₉	#385	1	1	yes	characteristic
276	C₂²×C₁₉	#386	1	1	yes	characteristic
277	C₂²×C₁₉	#387	1	1	yes	characteristic
278	C₂²×C₁₉	#388	1	1	yes	characteristic
279	C₂²×C₁₉	#389	1	1	yes	characteristic
280	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
281	C₂²×C₁₉	#427	1	1	yes	characteristic
282	C₂²×C₁₉	#428	1	1	yes	characteristic
283	C₂²×C₁₉	#428	1	1	yes	characteristic
284	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
285	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
286	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
287	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
288	C₂²×C₁₉	#440	1	1	yes	characteristic
289	C₂²×C₁₉	#440	1	1	yes	characteristic
290	C₂²×C₁₉	#441	1	1	yes	characteristic
291	C₂²×C₁₉	#442	1	1	yes	characteristic
292	C₂²×C₁₉	#447	1	1	yes	characteristic
293	C₂²×C₁₉	#449	1	1	yes	characteristic
294	C₂²×C₁₉	#451	1	1	yes	characteristic
295	C₂²×C₁₉	#452	1	1	yes	characteristic
296	C₂²×C₁₉	#459	1	1	yes	characteristic
297	C₂²×C₁₉	#462	1	1	yes	characteristic
298	C₂²×C₁₉	#463	1	1	yes	characteristic
299	C₂²×C₁₉	#464	1	1	yes	characteristic
300	C₂²×C₁₉	#474	1	1	yes	characteristic
301	C₂²×C₁₉	#477	1	1	yes	characteristic
302	C₂²×C₁₉	#478	1	1	yes	characteristic
303	C₂²×C₁₉	#479	1	1	yes	characteristic
304	C₂²×C₁₉	#480	1	1	yes	characteristic
305	C₂²×C₁₉	#482	1	1	yes	characteristic
306	C₂²×C₁₉	#484	1	1	yes	characteristic
307	C₂²×C₁₉	#485	1	1	yes	characteristic
308	C₄×C₁₉	—	2	4	no	—
309	C₄×C₁₉	—	4	2	no	—
310	C₄×C₁₉	—	4	4	no	—
311	C₄×C₁₉	—	4	4	no	—
312	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
313	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
314	C₄×C₁₉	#387	1	1	yes	characteristic
315	C₄×C₁₉	#387	1	1	yes	characteristic
316	C₄×C₁₉	#387	1	1	yes	characteristic
317	C₄×C₁₉	#388	1	1	yes	characteristic
318	C₄×C₁₉	#389	1	1	yes	characteristic
319	C₄×C₁₉	#391	1	1	yes	characteristic
320	Dic₁₉	—	8	2	no	—
321	Dic₁₉	—	8	2	no	—
322	C₂³×C₈	—	19	1	no	—
323	C₂³×C₈	—	19	1	no	—
324	C₂²×C₄⋊C₄	—	19	1	no	—
325	C₂²×C₄⋊C₄	—	19	1	no	—
326	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
327	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
328	C₂²×C₄²	—	2	1	no	—
329	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
330	C₂×#107	—	19	4	no	—
331	C₂×#107	—	38	2	no	—
332	C₂×#107	—	38	2	no	—
333	C₄×C₄⋊C₄	—	2	2	no	—
334	C₄×C₄⋊C₄	—	2	2	no	—
335	C₂×#95	—	2	1	no	—
336	C₂×#95	—	38	1	no	—
337	C₂×#95	—	38	1	no	—
338	#340	—	19	4	no	—
339	#340	—	38	2	no	—
340	#340	—	38	2	no	—
341	#336	—	19	4	no	—
342	C₂×C₁₉	#1436	1	1	yes	characteristic
343	C₂×C₁₉	C₄×#107	1	1	yes	characteristic
344	C₂×C₁₉	#1776	1	1	yes	characteristic
345	C₂×C₁₉	#1852	1	1	yes	characteristic
346	C₂×C₁₉	#1854	1	1	yes	characteristic
347	C₂×C₁₉	#1862	1	1	yes	characteristic
348	C₂×C₁₉	#1863	1	1	yes	characteristic
349	C₂×C₁₉	#1878	1	1	yes	characteristic
350	C₂×C₁₉	#1879	1	1	yes	characteristic
351	C₂×C₁₉	#1918	1	1	yes	characteristic
352	C₂×C₁₉	#1921	1	1	yes	characteristic
353	C₂×C₁₉	#1925	1	1	yes	characteristic
354	C₂×C₁₉	#1928	1	1	yes	characteristic
355	C₂×C₁₉	#1947	1	1	yes	characteristic
356	C₂×C₁₉	#1949	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	—	2	1	no	—
359	C₂³×C₄	—	38	1	no	—
360	C₂³×C₄	—	38	1	no	—
361	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
362	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
363	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
364	C₂²×C₈	—	19	2	no	—
365	C₂²×C₈	—	19	2	no	—
366	C₂²×C₈	—	19	2	no	—
367	C₂²×C₈	—	19	2	no	—
368	C₂²×C₈	—	38	1	no	—
369	C₂²×C₈	—	38	1	no	—
370	C₂²×C₈	—	38	1	no	—
371	C₂²×C₈	—	38	1	no	—
372	C₂²×C₈	—	38	1	no	—
373	C₂²×C₈	—	38	1	no	—
374	C₂²×C₈	—	38	1	no	—
375	C₂²×C₈	—	38	1	no	—
376	C₂²×C₈	—	38	1	no	—
377	C₂²×C₈	—	38	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	19	2	no	—
385	C₂×C₄⋊C₄	—	19	2	no	—
386	C₂×C₄⋊C₄	—	38	1	no	—
387	C₂×C₄⋊C₄	—	38	1	no	—
388	C₂×C₄⋊C₄	—	38	1	no	—
389	C₂×C₄⋊C₄	—	38	1	no	—
390	C₂×C₄⋊C₄	—	38	1	no	—
391	C₂×C₄⋊C₄	—	38	1	no	—
392	C₂×C₄⋊C₄	—	38	1	no	—
393	C₂×C₄⋊C₄	—	38	1	no	—
394	C₂×C₄⋊C₄	—	38	1	no	—
395	C₂×C₄⋊C₄	—	38	1	no	—
396	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
397	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
398	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
399	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
400	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	2	4	no	—
407	C₂×C₄²	—	4	2	no	—
408	C₂×C₄²	—	4	2	no	—
409	C₂×C₄²	Dic₃₈	1	2	yes	—
410	C₂×C₄²	C₄×D₁₉	1	2	yes	—
411	#107	—	38	8	no	—
412	#95	—	2	4	no	—
413	#95	—	76	2	no	—
414	#95	—	76	2	no	—
415	C₁₉	#10907	1	1	yes	characteristic, complemented, Sylow
416	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	4	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	38	2	no	—
442	C₂²×C₄	—	38	2	no	—
443	C₂²×C₄	—	76	1	no	—
444	C₂²×C₄	—	76	1	no	—
445	C₂²×C₄	—	76	1	no	—
446	C₂²×C₄	—	76	1	no	—
447	C₂²×C₄	—	76	1	no	—
448	C₂²×C₄	—	76	1	no	—
449	C₂²×C₄	—	76	1	no	—
450	C₂²×C₄	—	76	1	no	—
451	C₂²×C₄	—	76	1	no	—
452	C₂²×C₄	—	76	1	no	—
453	C₂²×C₄	—	76	1	no	—
454	C₂²×C₄	—	76	1	no	—
455	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
456	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
457	C₂²×C₄	#64525	1	2	yes	—
458	C₂²×C₄	#64528	1	2	yes	—
459	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
460	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
465	C₂²×C₄	#64541	1	1	yes	characteristic
466	C₂²×C₄	#64541	1	1	yes	characteristic
467	C₂²×C₄	#64541	1	1	yes	characteristic
468	C₂²×C₄	#64541	1	1	yes	characteristic
469	C₂²×C₄	#64541	1	1	yes	characteristic
470	C₂²×C₄	#64541	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
473	C₂×C₈	—	19	4	no	—
474	C₂×C₈	—	38	2	no	—
475	C₂×C₈	—	38	2	no	—
476	C₂×C₈	—	38	2	no	—
477	C₂×C₈	—	38	2	no	—
478	C₂×C₈	—	38	2	no	—
479	C₂×C₈	—	38	2	no	—
480	C₂×C₈	—	38	2	no	—
481	C₂×C₈	—	38	2	no	—
482	C₂×C₈	—	38	2	no	—
483	C₂×C₈	—	76	1	no	—
484	C₂×C₈	—	76	1	no	—
485	C₂×C₈	—	76	1	no	—
486	C₂×C₈	—	76	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	38	2	no	—
494	C₄⋊C₄	—	38	2	no	—
495	C₄⋊C₄	—	38	2	no	—
496	C₄⋊C₄	—	38	2	no	—
497	C₄⋊C₄	—	76	1	no	—
498	C₄⋊C₄	—	76	1	no	—
499	C₄⋊C₄	—	76	1	no	—
500	C₄⋊C₄	—	76	1	no	—
501	C₄⋊C₄	Dic₁₉⋊C₄	1	4	yes	—
502	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	4	8	no	—
508	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
509	C₂³	#10597370	1	1	yes	characteristic
510	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
511	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
512	C₂³	#10597375	1	1	yes	characteristic
513	C₂³	#10597376	1	1	yes	characteristic
514	C₂³	C₂×#64525	1	1	yes	characteristic
515	C₂³	#10597378	1	1	yes	characteristic
516	C₂³	#10597388	1	1	yes	characteristic
517	C₂³	C₂×#64528	1	1	yes	characteristic
518	C₂³	#10597395	1	1	yes	characteristic
519	C₂³	#10597396	1	1	yes	characteristic
520	C₂³	#10597396	1	1	yes	characteristic
521	C₂³	#10597397	1	1	yes	characteristic
522	C₂³	#10597399	1	1	yes	characteristic
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	76	2	no	—
551	C₂×C₄	—	76	2	no	—
552	C₂×C₄	—	76	2	no	—
553	C₂×C₄	—	76	2	no	—
554	C₂×C₄	—	76	2	no	—
555	C₂×C₄	—	76	2	no	—
556	C₂×C₄	—	152	1	no	—
557	C₂×C₄	—	152	1	no	—
558	C₂×C₄	—	152	1	no	—
559	C₂×C₄	—	152	1	no	—
560	C₂×C₄	—	152	1	no	—
561	C₂×C₄	—	152	1	no	—
562	C₂×C₄	—	152	1	no	—
563	C₂×C₄	—	152	1	no	—
564	C₂×C₄	#10597264	1	4	yes	complemented
565	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
566	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
567	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
568	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
569	C₂×C₄	#10597315	1	1	yes	characteristic
570	C₂×C₄	#10597316	1	1	yes	characteristic
571	C₂×C₄	#10597316	1	1	yes	characteristic
572	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
573	C₂×C₄	#10597318	1	1	yes	characteristic
574	C₂×C₄	#10597318	1	1	yes	characteristic
575	C₂×C₄	#10597318	1	1	yes	characteristic
576	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
577	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
578	C₂×C₄	#10597321	1	1	yes	characteristic
579	C₂×C₄	#10597322	1	1	yes	characteristic
580	C₂×C₄	#10597322	1	1	yes	characteristic
581	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
582	C₂×C₄	#10597370	1	1	yes	characteristic
583	C₂×C₄	#10597370	1	1	yes	characteristic
584	C₂×C₄	#10597370	1	1	yes	characteristic
585	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
586	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
587	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
588	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
589	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
590	C₂×C₄	#10597375	1	1	yes	characteristic
591	C₂×C₄	#10597375	1	1	yes	characteristic
592	C₂×C₄	#10597376	1	1	yes	characteristic
593	C₈	—	38	4	no	—
594	C₈	—	76	2	no	—
595	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
596	C₂²	#11926417	1	1	yes	characteristic
597	C₂²	#11926417	1	1	yes	characteristic
598	C₂²	#11926423	1	1	yes	characteristic
599	C₂²	#11926428	1	1	yes	characteristic
600	C₂²	#11926435	1	1	yes	characteristic
601	C₂²	#11926442	1	1	yes	characteristic
602	C₂²	C₂×#10597264	1	1	yes	characteristic
603	C₂²	#11926580	1	1	yes	characteristic
604	C₂²	#11926584	1	1	yes	characteristic
605	C₂²	#11926587	1	1	yes	characteristic
606	C₂²	C₄×#64525	1	1	yes	characteristic
607	C₂²	C₄×#64525	1	1	yes	characteristic
608	C₂²	C₄×#64528	1	1	yes	characteristic
609	C₂²	C₄×#64528	1	1	yes	characteristic
610	C₂²	#11926642	1	1	yes	characteristic
611	C₂²	#11926644	1	1	yes	characteristic
612	C₂²	#11926649	1	1	yes	characteristic
613	C₂²	#11926654	1	1	yes	characteristic
614	C₂²	#11926678	1	1	yes	characteristic
615	C₂²	#11926689	1	1	yes	characteristic
616	C₂²	#11926700	1	1	yes	characteristic
617	C₂²	#11926706	1	1	yes	characteristic
618	C₂²	#11926739	1	1	yes	characteristic
619	C₂²	#11926754	1	1	yes	characteristic
620	C₂²	#11926759	1	1	yes	characteristic
621	C₂²	#11926766	1	1	yes	characteristic
622	C₂²	#11926824	1	1	yes	characteristic
623	C₂²	#11926839	1	1	yes	characteristic
624	C₂²	#11926844	1	1	yes	characteristic
625	C₂²	#11926851	1	1	yes	characteristic
626	C₂²	#11926857	1	1	yes	characteristic
627	C₂²	#11926868	1	1	yes	characteristic
628	C₂²	#11926879	1	1	yes	characteristic
629	C₂²	#11926885	1	1	yes	characteristic
630	C₄	—	2	4	no	—
631	C₄	—	4	4	no	—
632	C₄	—	4	4	no	—
633	C₄	—	4	2	no	—
634	C₄	—	152	2	no	—
635	C₄	—	152	2	no	—
636	C₄	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
637	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
638	C₄	#11926428	1	1	yes	characteristic
639	C₄	#11926428	1	1	yes	characteristic
640	C₄	#11926428	1	1	yes	characteristic
641	C₄	#11926435	1	1	yes	characteristic
642	C₄	#11926442	1	1	yes	characteristic
643	C₄	#11926450	1	1	yes	characteristic
644	C₂	#14561868	1	1	yes	characteristic
645	C₂	C₄×#10597264	1	1	yes	characteristic
646	C₂	#14563533	1	1	yes	characteristic
647	C₂	#14563823	1	1	yes	characteristic
648	C₂	#14563834	1	1	yes	characteristic
649	C₂	#14563882	1	1	yes	characteristic
650	C₂	#14563889	1	1	yes	characteristic
651	C₂	#14563976	1	1	yes	characteristic
652	C₂	#14563983	1	1	yes	characteristic
653	C₂	#14564206	1	1	yes	characteristic
654	C₂	#14564227	1	1	yes	characteristic
655	C₂	#14564255	1	1	yes	characteristic
656	C₂	#14564276	1	1	yes	characteristic
657	C₂	#14564393	1	1	yes	characteristic
658	C₂	#14564403	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₄×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#10907
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
14. C₂×#10597264	C₄	semidirect
19. #11926306	C₄	semidirect
20. #11926299	C₄	semidirect
177. C₂×C₁₉⋊C₈	C₄²	semidirect
221. C₂×C₄×C₁₉	#107	semidirect
415. C₁₉	#10907	semidirect
564. C₂×C₄	#10597264	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597264	2
C₂×#11926306	2
C₂×#11926299	2
#14561865	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#10907	19