Subgroups — #14577239

Order 2432.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927277	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927253	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927249	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927244	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927243	C₂	1	2	yes	maximal, complemented
6	#11927242	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927223	C₂	1	2	yes	maximal, complemented
8	#11927220	C₂	1	2	yes	maximal, complemented
9	#11927189	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927188	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927184	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927091	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927076	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927074	C₂	1	2	yes	maximal, complemented
17	#11927055	C₂	1	2	yes	maximal, complemented
18	#11927053	C₂	1	2	yes	maximal, complemented
19	C₄×#64541	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#64543	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×C₂²⋊D₁₉	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
27	C₂×#64543	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
29	C₂×#64541	C₂²	1	1	yes	characteristic
30	C₂×#64541	C₂²	1	2	yes	complemented
31	C₂²×C₄×D₁₉	C₂²	1	2	yes	complemented
32	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
35	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
40	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	#10597399	C₂²	1	2	yes	—
42	#10597399	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
44	#10597386	C₂²	1	1	yes	characteristic
45	#10597385	C₂²	1	2	yes	—
46	#10597385	C₂²	1	2	yes	complemented
47	#10597384	C₂²	1	1	yes	characteristic
48	#10597384	C₂²	1	1	yes	characteristic, complemented
49	#10597383	C₂²	1	2	yes	—
50	#10597382	C₂²	1	1	yes	characteristic, complemented
51	#10597381	C₂²	1	2	yes	complemented
52	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
53	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
54	#10597376	C₂²	1	1	yes	characteristic
55	#10597376	C₂²	1	2	yes	complemented
56	#10597376	C₂²	1	2	yes	complemented
57	#10597375	C₂²	1	2	yes	complemented
58	#10597375	C₂²	1	2	yes	complemented
59	#10597375	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
66	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
70	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
74	#10597372	C₂²	1	2	yes	complemented
75	#10597372	C₂²	1	1	yes	characteristic, complemented
76	#10597370	C₂²	1	2	yes	complemented
77	#10597370	C₂²	1	2	yes	complemented
78	#10597370	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₄×Dic₁₉	C₂²	1	2	yes	complemented
81	#10597344	C₂²	1	2	yes	complemented
82	#10597343	C₂²	1	1	yes	characteristic, complemented
83	#10597342	C₂²	1	2	yes	complemented
84	#10597341	C₂²	1	1	yes	characteristic, complemented
85	#10597340	C₂²	1	2	yes	complemented
86	#10597339	C₂²	1	1	yes	characteristic, complemented
87	#10597338	C₂²	1	1	yes	characteristic, complemented
88	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
89	#10597336	C₂²	1	1	yes	characteristic, complemented
90	#10597335	C₂²	1	2	yes	complemented
91	#10597334	C₂²	1	1	yes	characteristic, complemented
92	#10597333	C₂²	1	1	yes	characteristic, complemented
93	#10597332	C₂²	1	2	yes	complemented
94	#10597331	C₂²	1	2	yes	complemented
95	#10597331	C₂²	1	2	yes	complemented
96	#10597330	C₂²	1	2	yes	complemented
97	#10597330	C₂²	1	2	yes	complemented
98	#10597329	C₂²	1	2	yes	complemented
99	#10597329	C₂²	1	2	yes	complemented
100	#10597328	C₂²	1	2	yes	complemented
101	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
102	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
104	#10597325	C₂²	1	2	yes	complemented
105	#10597325	C₂²	1	2	yes	complemented
106	#10597324	C₂²	1	2	yes	complemented
107	#10597324	C₂²	1	2	yes	complemented
108	#10597323	C₂²	1	2	yes	complemented
109	#10597322	C₂²	1	2	yes	complemented
110	#10597321	C₂²	1	1	yes	characteristic, complemented
111	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
114	#10597318	C₂²	1	2	yes	complemented
115	#10597318	C₂²	1	1	yes	characteristic, complemented
116	#10597318	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
119	#10597316	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₉	C₂³	1	2	yes	—
124	C₂³×D₁₉	C₂³	1	2	yes	—
125	C₂×D₄×C₁₉	—	2	4	no	—
126	C₂×D₄×C₁₉	C₂³	1	2	yes	—
127	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₉	—	2	8	no	—
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₉	C₂³	1	2	yes	—
149	C₂²×Dic₁₉	C₂³	1	2	yes	—
150	C₂²×Dic₁₉	C₂³	1	2	yes	—
151	#64543	—	2	4	no	—
152	D₄×D₁₉	—	2	4	no	—
153	#64541	—	2	4	no	—
154	#64541	—	4	4	no	—
155	C₂×D₇₆	C₂³	1	1	yes	characteristic
156	C₂×D₇₆	C₂³	1	1	yes	characteristic
157	C₂×D₇₆	C₂³	1	2	yes	—
158	C₂×C₄×D₁₉	—	4	4	no	—
159	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₉	C₂³	1	2	yes	—
163	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₉	C₂³	1	2	yes	—
167	C₂×C₄×D₁₉	C₂³	1	2	yes	—
168	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
169	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
170	C₂×Dic₃₈	C₂³	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₄²×C₁₉	C₂³	1	1	yes	characteristic
179	C₄²×C₁₉	C₂³	1	1	yes	characteristic
180	C₄²×C₁₉	C₂³	1	1	yes	characteristic
181	C₄²×C₁₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
191	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
203	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	C₄⋊Dic₁₉	C₂³	1	2	yes	—
206	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₁₉⋊C₄	C₂³	1	2	yes	—
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	2	yes	—
217	Dic₁₉⋊C₄	C₂³	1	2	yes	—
218	Dic₁₉⋊C₄	C₂³	1	2	yes	—
219	Dic₁₉⋊C₄	C₂³	1	2	yes	—
220	Dic₁₉⋊C₄	C₂³	1	2	yes	—
221	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₉	C₂³	1	2	yes	—
229	C₄×Dic₁₉	C₂³	1	2	yes	—
230	C₂³×C₁₉	—	2	4	no	—
231	C₂³×C₁₉	—	2	4	no	—
232	C₂³×C₁₉	—	4	2	no	—
233	C₂³×C₁₉	C₂⁴	1	2	yes	—
234	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
235	C₂³×C₁₉	C₂⁴	1	2	yes	—
236	C₂²×D₁₉	—	2	4	no	—
237	C₂²×D₁₉	—	2	4	no	—
238	C₂²×D₁₉	—	4	2	no	—
239	C₂²×D₁₉	C₂⁴	1	2	yes	—
240	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
242	D₄×C₁₉	—	2	4	no	—
243	D₄×C₁₉	—	2	2	no	—
244	D₄×C₁₉	#41	1	4	yes	complemented
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	4	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₁₉	—	2	2	no	—
262	C₂²⋊D₁₉	—	2	4	no	—
263	C₂²⋊D₁₉	—	2	4	no	—
264	C₂²⋊D₁₉	—	2	4	no	—
265	C₂²⋊D₁₉	—	2	4	no	—
266	C₂²⋊D₁₉	—	2	4	no	—
267	C₂²⋊D₁₉	—	4	2	no	—
268	C₂²⋊D₁₉	—	4	2	no	—
269	C₂²⋊D₁₉	#41	1	4	yes	complemented
270	C₂×Dic₁₉	—	2	4	no	—
271	C₂×Dic₁₉	—	2	4	no	—
272	C₂×Dic₁₉	—	4	2	no	—
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₉	C₂⁴	1	2	yes	—
275	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₉	C₂⁴	1	2	yes	—
277	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₉	C₂⁴	1	2	yes	—
281	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
282	D₇₆	—	2	2	no	—
283	D₇₆	—	2	2	no	—
284	D₇₆	—	4	2	no	—
285	C₄×D₁₉	—	2	2	no	—
286	C₄×D₁₉	—	2	2	no	—
287	C₄×D₁₉	—	2	2	no	—
288	C₄×D₁₉	—	2	2	no	—
289	C₄×D₁₉	—	2	4	no	—
290	C₄×D₁₉	—	2	2	no	—
291	C₄×D₁₉	—	2	2	no	—
292	C₄×D₁₉	—	4	2	no	—
293	C₄×D₁₉	—	4	2	no	—
294	Dic₃₈	—	2	2	no	—
295	Dic₃₈	—	2	2	no	—
296	Dic₃₈	—	4	2	no	—
297	#3481	—	19	1	no	maximal, Sylow
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	2	no	—
303	C₂²×C₁₉	—	2	2	no	—
304	C₂²×C₁₉	—	2	2	no	—
305	C₂²×C₁₉	—	4	8	no	—
306	C₂²×C₁₉	C₂×#41	1	4	yes	—
307	C₂²×C₁₉	C₂×#41	1	2	yes	—
308	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
309	C₂×D₁₉	—	2	1	no	—
310	C₂×D₁₉	—	2	1	no	—
311	C₂×D₁₉	—	2	1	no	—
312	C₂×D₁₉	—	2	1	no	—
313	C₂×D₁₉	—	2	2	no	—
314	C₂×D₁₉	—	2	2	no	—
315	C₂×D₁₉	—	2	2	no	—
316	C₂×D₁₉	—	2	1	no	—
317	C₂×D₁₉	—	4	8	no	—
318	C₂×D₁₉	C₂×#41	1	2	yes	—
319	C₄×C₁₉	—	2	1	no	—
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	2	1	no	—
322	C₄×C₁₉	—	2	2	no	—
323	C₄×C₁₉	—	2	2	no	—
324	C₄×C₁₉	—	2	1	no	—
325	C₄×C₁₉	C₂×#41	1	2	yes	—
326	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
327	Dic₁₉	—	2	1	no	—
328	Dic₁₉	—	2	2	no	—
329	Dic₁₉	—	2	1	no	—
330	Dic₁₉	—	2	1	no	—
331	Dic₁₉	—	2	2	no	—
332	Dic₁₉	—	2	1	no	—
333	Dic₁₉	—	2	2	no	—
334	Dic₁₉	—	2	1	no	—
335	Dic₁₉	C₂×#41	1	2	yes	—
336	#559	—	19	1	no	—
337	#554	—	19	1	no	—
338	#554	—	19	1	no	—
339	#553	—	19	2	no	—
340	#553	—	19	1	no	—
341	#553	—	19	1	no	—
342	#551	—	19	2	no	—
343	#551	—	19	2	no	—
344	#546	—	19	1	no	—
345	#546	—	19	1	no	—
346	#546	—	19	2	no	—
347	D₄²	—	19	1	no	—
348	#532	—	19	1	no	—
349	#529	—	19	2	no	—
350	#529	—	19	1	no	—
351	#529	—	19	1	no	—
352	#525	—	19	2	no	—
353	#525	—	19	2	no	—
354	C₄×#41	—	19	1	no	—
355	C₄×#41	—	19	1	no	—
356	C₂×C₄×D₄	—	19	2	no	—
357	C₂×C₄×D₄	—	19	1	no	—
358	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic, complemented
359	C₂×C₁₉	—	2	4	no	—
360	C₂×C₁₉	—	2	2	no	—
361	C₂×C₁₉	—	4	2	no	—
362	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
363	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
364	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	D₁₉	—	2	2	no	—
366	D₁₉	—	4	1	no	—
367	D₁₉	—	4	2	no	—
368	C₂×#41	—	19	1	no	—
369	C₂×#41	—	19	1	no	—
370	C₂×#41	—	19	2	no	—
371	C₂²×D₄	—	19	2	no	—
372	C₂²×D₄	—	19	1	no	—
373	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
374	C₂³×C₄	—	19	2	no	—
375	C₂³×C₄	C₂×D₁₉	1	2	yes	complemented
376	C₄⋊Q₈	—	19	1	no	—
377	#127	—	19	1	no	—
378	#126	—	19	2	no	—
379	#126	—	19	2	no	—
380	#126	—	19	2	no	—
381	#126	—	19	2	no	—
382	#125	—	19	2	no	—
383	#125	—	19	1	no	—
384	#125	—	19	1	no	—
385	#124	—	19	1	no	—
386	#124	—	19	2	no	—
387	#124	—	19	2	no	—
388	#124	—	19	1	no	—
389	#123	—	19	2	no	—
390	#123	—	19	2	no	—
391	#123	—	19	2	no	—
392	#123	—	19	2	no	—
393	#123	—	19	2	no	—
394	#123	—	19	2	no	—
395	#123	—	19	2	no	—
396	#123	—	19	2	no	—
397	C₂²⋊Q₈	—	19	2	no	—
398	C₂²⋊Q₈	—	19	2	no	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	2	no	—
401	C₂²⋊Q₈	—	19	1	no	—
402	C₂²⋊Q₈	—	19	2	no	—
403	C₂²⋊Q₈	—	19	2	no	—
404	#121	—	19	1	no	—
405	#121	—	19	1	no	—
406	#121	—	19	2	no	—
407	#121	—	19	2	no	—
408	#121	—	19	1	no	—
409	#121	—	19	2	no	—
410	#121	—	19	2	no	—
411	#121	—	19	1	no	—
412	#121	—	19	2	no	—
413	#121	—	19	2	no	—
414	#120	—	19	2	no	—
415	#120	—	19	2	no	—
416	#120	—	19	2	no	—
417	#120	—	19	2	no	—
418	C₄×Q₈	—	19	1	no	—
419	C₄×Q₈	—	19	1	no	—
420	C₄×Q₈	—	19	1	no	—
421	C₄×Q₈	—	19	1	no	—
422	C₄×D₄	—	19	1	no	—
423	C₄×D₄	—	19	1	no	—
424	C₄×D₄	—	19	1	no	—
425	C₄×D₄	—	19	2	no	—
426	C₄×D₄	—	19	2	no	—
427	C₄×D₄	—	19	2	no	—
428	C₄×D₄	—	19	2	no	—
429	C₄×D₄	—	19	2	no	—
430	C₄×D₄	—	19	2	no	—
431	C₄×D₄	—	19	2	no	—
432	C₄×D₄	—	19	2	no	—
433	C₄×D₄	—	19	2	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	—	19	1	no	—
436	C₄×D₄	—	19	1	no	—
437	C₄×D₄	—	19	1	no	—
438	C₄×D₄	—	19	2	no	—
439	C₄×D₄	—	19	2	no	—
440	C₄×D₄	—	19	1	no	—
441	C₄×D₄	—	19	1	no	—
442	C₄×D₄	—	19	1	no	—
443	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
444	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
445	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
446	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
447	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
448	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
449	#117	—	19	1	no	—
450	#117	—	19	2	no	—
451	#117	—	19	1	no	—
452	#117	—	19	2	no	—
453	#117	—	19	1	no	—
454	#117	—	19	1	no	—
455	#117	—	19	2	no	—
456	C₂×C₄⋊C₄	—	19	2	no	—
457	C₂×C₄⋊C₄	—	19	1	no	—
458	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
459	C₂×C₂²⋊C₄	—	19	2	no	—
460	C₂×C₂²⋊C₄	—	19	2	no	—
461	C₂×C₂²⋊C₄	—	19	2	no	—
462	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	complemented
463	C₂×C₄²	—	19	2	no	—
464	C₂×C₄²	—	19	1	no	—
465	C₂×C₄²	—	19	1	no	—
466	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
467	C₁₉	#3481	1	1	yes	characteristic, complemented, Sylow
468	C₂⁴	—	19	2	no	—
469	C₂⁴	C₂²×D₁₉	1	2	yes	—
470	#41	—	38	4	no	—
471	#41	—	38	4	no	—
472	#41	—	76	4	no	—
473	C₂×Q₈	—	19	1	no	—
474	C₂×Q₈	—	19	1	no	—
475	C₂×Q₈	—	19	2	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	19	1	no	—
478	C₂×D₄	—	19	2	no	—
479	C₂×D₄	—	19	1	no	—
480	C₂×D₄	—	19	2	no	—
481	C₂×D₄	—	19	2	no	—
482	C₂×D₄	—	19	2	no	—
483	C₂×D₄	—	19	2	no	—
484	C₂×D₄	—	19	2	no	—
485	C₂×D₄	—	19	2	no	—
486	C₂×D₄	—	19	1	no	—
487	C₂×D₄	—	19	1	no	—
488	C₂×D₄	—	19	2	no	—
489	C₂×D₄	—	38	8	no	—
490	C₂×D₄	—	38	4	no	—
491	C₂×D₄	C₂²×D₁₉	1	2	yes	—
492	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
494	C₂²×C₄	—	4	4	no	—
495	C₂²×C₄	—	19	2	no	—
496	C₂²×C₄	—	19	2	no	—
497	C₂²×C₄	—	19	2	no	—
498	C₂²×C₄	—	19	1	no	—
499	C₂²×C₄	—	19	1	no	—
500	C₂²×C₄	—	19	1	no	—
501	C₂²×C₄	—	19	1	no	—
502	C₂²×C₄	—	19	1	no	—
503	C₂²×C₄	—	19	1	no	—
504	C₂²×C₄	—	19	2	no	—
505	C₂²×C₄	—	19	2	no	—
506	C₂²×C₄	—	19	2	no	—
507	C₂²×C₄	—	76	4	no	—
508	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
511	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
513	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
514	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
515	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
516	C₄⋊C₄	—	19	1	no	—
517	C₄⋊C₄	—	19	2	no	—
518	C₄⋊C₄	—	19	2	no	—
519	C₄⋊C₄	—	19	2	no	—
520	C₄⋊C₄	—	19	2	no	—
521	C₄⋊C₄	—	19	1	no	—
522	C₄⋊C₄	—	19	2	no	—
523	C₄⋊C₄	—	19	1	no	—
524	C₄⋊C₄	—	19	1	no	—
525	C₄⋊C₄	—	19	2	no	—
526	C₄⋊C₄	—	19	2	no	—
527	C₄⋊C₄	—	19	2	no	—
528	C₄⋊C₄	—	19	1	no	—
529	C₄⋊C₄	—	19	1	no	—
530	C₄⋊C₄	—	19	1	no	—
531	C₄⋊C₄	—	19	1	no	—
532	C₄⋊C₄	—	19	2	no	—
533	C₄⋊C₄	—	19	2	no	—
534	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
537	C₂²⋊C₄	—	19	1	no	—
538	C₂²⋊C₄	—	19	2	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	2	no	—
541	C₂²⋊C₄	—	19	2	no	—
542	C₂²⋊C₄	—	19	2	no	—
543	C₂²⋊C₄	—	19	1	no	—
544	C₂²⋊C₄	—	19	2	no	—
545	C₂²⋊C₄	—	19	2	no	—
546	C₂²⋊C₄	—	19	1	no	—
547	C₂²⋊C₄	—	19	2	no	—
548	C₂²⋊C₄	—	19	2	no	—
549	C₂²⋊C₄	—	19	2	no	—
550	C₂²⋊C₄	—	19	2	no	—
551	C₂²⋊C₄	—	19	2	no	—
552	C₂²⋊C₄	—	19	1	no	—
553	C₂²⋊C₄	—	19	2	no	—
554	C₂²⋊C₄	—	19	1	no	—
555	C₂²⋊C₄	—	19	1	no	—
556	C₂²⋊C₄	—	19	2	no	—
557	C₂²⋊C₄	—	19	2	no	—
558	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
562	C₄²	—	19	1	no	—
563	C₄²	—	19	2	no	—
564	C₄²	—	19	1	no	—
565	C₄²	—	19	2	no	—
566	C₄²	—	19	1	no	—
567	C₄²	—	19	1	no	—
568	C₄²	—	19	1	no	—
569	C₄²	—	19	1	no	—
570	C₄²	—	19	2	no	—
571	C₄²	C₂²×D₁₉	1	1	yes	characteristic
572	C₄²	C₂²×D₁₉	1	1	yes	characteristic
573	C₄²	C₂²×D₁₉	1	1	yes	characteristic
574	C₄²	C₂²×D₁₉	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	19	1	no	—
579	C₂³	—	19	2	no	—
580	C₂³	—	19	1	no	—
581	C₂³	—	38	4	no	—
582	C₂³	—	38	4	no	—
583	C₂³	—	76	2	no	—
584	C₂³	C₂³×D₁₉	1	2	yes	—
585	C₂³	C₂³×D₁₉	1	2	yes	—
586	C₂³	C₂³×D₁₉	1	1	yes	characteristic
587	Q₈	—	38	2	no	—
588	Q₈	—	38	2	no	—
589	Q₈	—	76	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	19	4	no	—
593	D₄	—	38	2	no	—
594	D₄	—	38	4	no	—
595	D₄	—	38	4	no	—
596	D₄	—	38	4	no	—
597	D₄	—	38	4	no	—
598	D₄	—	38	4	no	—
599	D₄	—	38	2	no	—
600	D₄	—	38	2	no	—
601	D₄	—	76	2	no	—
602	D₄	—	76	2	no	—
603	D₄	—	76	2	no	—
604	D₄	#64541	1	4	yes	complemented
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	19	1	no	—
614	C₂×C₄	—	19	1	no	—
615	C₂×C₄	—	19	1	no	—
616	C₂×C₄	—	19	2	no	—
617	C₂×C₄	—	19	2	no	—
618	C₂×C₄	—	19	1	no	—
619	C₂×C₄	—	19	1	no	—
620	C₂×C₄	—	19	1	no	—
621	C₂×C₄	—	19	2	no	—
622	C₂×C₄	—	38	2	no	—
623	C₂×C₄	—	38	2	no	—
624	C₂×C₄	—	38	4	no	—
625	C₂×C₄	—	38	4	no	—
626	C₂×C₄	—	38	2	no	—
627	C₂×C₄	—	38	2	no	—
628	C₂×C₄	—	38	2	no	—
629	C₂×C₄	—	38	4	no	—
630	C₂×C₄	—	38	2	no	—
631	C₂×C₄	—	76	2	no	—
632	C₂×C₄	—	76	2	no	—
633	C₂×C₄	—	76	2	no	—
634	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₉	1	2	yes	—
636	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₁₉	1	2	yes	—
640	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
641	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	8	no	—
650	C₂²	—	19	2	no	—
651	C₂²	—	38	1	no	—
652	C₂²	—	38	1	no	—
653	C₂²	—	38	1	no	—
654	C₂²	—	38	2	no	—
655	C₂²	—	38	1	no	—
656	C₂²	—	38	2	no	—
657	C₂²	—	38	2	no	—
658	C₂²	—	38	1	no	—
659	C₂²	—	76	8	no	—
660	C₂²	C₂×#64541	1	4	yes	—
661	C₂²	#41×D₁₉	1	2	yes	—
662	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	19	2	no	—
670	C₄	—	38	2	no	—
671	C₄	—	38	1	no	—
672	C₄	—	38	1	no	—
673	C₄	—	38	1	no	—
674	C₄	—	38	2	no	—
675	C₄	—	38	1	no	—
676	C₄	—	38	2	no	—
677	C₄	—	38	1	no	—
678	C₄	C₂×#64541	1	2	yes	—
679	C₄	#10597430	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	2	4	no	—
682	C₂	—	4	2	no	—
683	C₂	—	38	2	no	—
684	C₂	—	76	2	no	—
685	C₂	—	76	1	no	—
686	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
687	C₂	C₂²×#64541	1	1	yes	characteristic
688	C₂	C₂×#10597430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂×C₄×D₄×C₁₉	C₂
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#3481
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #11927277	C₂	semidirect
2. #11927253	C₂	semidirect
3. #11927249	C₂	semidirect
4. #11927244	C₂	semidirect
5. #11927243	C₂	semidirect
6. #11927242	C₂	semidirect
7. #11927223	C₂	semidirect
8. #11927220	C₂	semidirect
9. #11927189	C₂	semidirect
10. #11927188	C₂	semidirect
11. #11927184	C₂	semidirect
12. D₄×C₂²⋊D₁₉	C₂	semidirect
13. #11927091	C₂	semidirect
14. #11927078	C₂	semidirect
15. #11927076	C₂	semidirect
16. #11927074	C₂	semidirect
17. #11927055	C₂	semidirect
18. #11927053	C₂	semidirect
19. C₄×#64541	C₂	semidirect
20. C₄×#64543	C₂	semidirect
21. C₂×C₄×C₂²⋊D₁₉	C₂	semidirect
22. C₄×D₄×D₁₉	C₂	semidirect
23. C₂×C₄×D₄×C₁₉	C₂	semidirect
25. C₂³×C₄×C₁₉	C₂²	semidirect
30. C₂×#64541	C₂²	semidirect
31. C₂²×C₄×D₁₉	C₂²	semidirect
34. C₄×D₄×C₁₉	C₂²	semidirect
35. C₄×D₄×C₁₉	C₂²	semidirect
36. C₄×D₄×C₁₉	C₂²	semidirect
37. C₄×D₄×C₁₉	C₂²	semidirect
38. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
39. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
40. C₂×C₄²×C₁₉	C₂²	semidirect
42. #10597399	C₂²	semidirect
43. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
46. #10597385	C₂²	semidirect
48. #10597384	C₂²	semidirect
50. #10597382	C₂²	semidirect
51. #10597381	C₂²	semidirect
55. #10597376	C₂²	semidirect
56. #10597376	C₂²	semidirect
57. #10597375	C₂²	semidirect
58. #10597375	C₂²	semidirect
59. #10597375	C₂²	semidirect
63. C₄×C₂²⋊D₁₉	C₂²	semidirect
64. C₄×C₂²⋊D₁₉	C₂²	semidirect
65. C₄×C₂²⋊D₁₉	C₂²	semidirect
66. C₄×C₂²⋊D₁₉	C₂²	semidirect
67. C₄×C₂²⋊D₁₉	C₂²	semidirect
68. C₄×C₂²⋊D₁₉	C₂²	semidirect
69. C₄×C₂²⋊D₁₉	C₂²	semidirect
70. C₄×C₂²⋊D₁₉	C₂²	semidirect
71. C₄×C₂²⋊D₁₉	C₂²	semidirect
72. C₄×C₂²⋊D₁₉	C₂²	semidirect
73. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
74. #10597372	C₂²	semidirect
75. #10597372	C₂²	semidirect
76. #10597370	C₂²	semidirect
77. #10597370	C₂²	semidirect
78. #10597370	C₂²	semidirect
79. C₂×Dic₁₉⋊C₄	C₂²	semidirect
80. C₂×C₄×Dic₁₉	C₂²	semidirect
81. #10597344	C₂²	semidirect
82. #10597343	C₂²	semidirect
83. #10597342	C₂²	semidirect
84. #10597341	C₂²	semidirect
85. #10597340	C₂²	semidirect
86. #10597339	C₂²	semidirect
87. #10597338	C₂²	semidirect
88. C₄⋊C₄×D₁₉	C₂²	semidirect
89. #10597336	C₂²	semidirect
90. #10597335	C₂²	semidirect
91. #10597334	C₂²	semidirect
92. #10597333	C₂²	semidirect
93. #10597332	C₂²	semidirect
94. #10597331	C₂²	semidirect
95. #10597331	C₂²	semidirect
96. #10597330	C₂²	semidirect
97. #10597330	C₂²	semidirect
98. #10597329	C₂²	semidirect
99. #10597329	C₂²	semidirect
100. #10597328	C₂²	semidirect
101. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
103. C₂²⋊C₄×D₁₉	C₂²	semidirect
104. #10597325	C₂²	semidirect
105. #10597325	C₂²	semidirect
106. #10597324	C₂²	semidirect
107. #10597324	C₂²	semidirect
108. #10597323	C₂²	semidirect
109. #10597322	C₂²	semidirect
110. #10597321	C₂²	semidirect
111. C₄×D₇₆	C₂²	semidirect
112. C₄×D₇₆	C₂²	semidirect
113. C₄×D₇₆	C₂²	semidirect
114. #10597318	C₂²	semidirect
115. #10597318	C₂²	semidirect
116. #10597318	C₂²	semidirect
117. C₄²×D₁₉	C₂²	semidirect
118. C₄²×D₁₉	C₂²	semidirect
119. #10597316	C₂²	semidirect
120. C₄×Dic₃₈	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
244. D₄×C₁₉	#41	semidirect
269. C₂²⋊D₁₉	#41	semidirect
358. C₂×C₄×D₄	D₁₉	semidirect
375. C₂³×C₄	C₂×D₁₉	semidirect
445. C₄×D₄	C₂×D₁₉	semidirect
446. C₄×D₄	C₂×D₁₉	semidirect
447. C₄×D₄	C₂×D₁₉	semidirect
448. C₄×D₄	C₂×D₁₉	semidirect
458. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
462. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
466. C₂×C₄²	C₂×D₁₉	semidirect
467. C₁₉	#3481	semidirect
604. D₄	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927277	2
#11927253	2
#11927249	2
#11927244	2
#11927243	2
#11927242	2
#11927223	2
#11927220	2
#11927189	2
#11927188	2
#11927184	2
D₄×C₂²⋊D₁₉	2
#11927091	2
#11927078	2
#11927076	2
#11927074	2
#11927055	2
#11927053	2
C₄×#64541	2
C₄×#64543	2
C₂×C₄×C₂²⋊D₁₉	2
C₄×D₄×D₁₉	2
C₂×C₄×D₄×C₁₉	2
#3481	19