Subgroups — #14577954

Order 2432.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927291	C₂	1	2	yes	maximal, complemented
2	#11927282	C₂	1	2	yes	maximal, complemented
3	#11927257	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927232	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927219	C₂	1	2	yes	maximal, complemented
6	#11927215	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927195	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927191	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927191	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927190	C₂	1	2	yes	maximal, complemented
11	D₄×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927159	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927150	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927145	C₂	1	2	yes	maximal, complemented
15	#11927133	C₂	1	2	yes	maximal, complemented
16	#11927125	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927110	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927110	C₂	1	2	yes	maximal, complemented
19	#11927105	C₂	1	2	yes	maximal, complemented
20	#11927056	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927053	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
28	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
29	C₂×#64541	C₂²	1	2	yes	complemented
30	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₇₆	C₂²	1	2	yes	—
32	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#126	C₂²	1	2	yes	complemented
34	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#123	C₂²	1	2	yes	complemented
36	C₁₉×#121	C₂²	1	1	yes	characteristic
37	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#121	C₂²	1	2	yes	complemented
39	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
41	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
44	#10597386	C₂²	1	2	yes	complemented
45	#10597386	C₂²	1	2	yes	complemented
46	#10597385	C₂²	1	1	yes	characteristic, complemented
47	#10597385	C₂²	1	2	yes	complemented
48	#10597384	C₂²	1	1	yes	characteristic
49	#10597384	C₂²	1	2	yes	complemented
50	#10597384	C₂²	1	2	yes	complemented
51	#10597383	C₂²	1	1	yes	characteristic, complemented
52	#10597383	C₂²	1	2	yes	complemented
53	#10597383	C₂²	1	2	yes	complemented
54	#10597383	C₂²	1	2	yes	complemented
55	#10597382	C₂²	1	1	yes	characteristic, complemented
56	#10597376	C₂²	1	2	yes	complemented
57	#10597376	C₂²	1	1	yes	characteristic, complemented
58	#10597376	C₂²	1	2	yes	complemented
59	#10597376	C₂²	1	2	yes	complemented
60	#10597376	C₂²	1	1	yes	characteristic, complemented
61	#10597375	C₂²	1	2	yes	complemented
62	#10597375	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
65	#10597370	C₂²	1	2	yes	complemented
66	#10597344	C₂²	1	2	yes	complemented
67	#10597343	C₂²	1	1	yes	characteristic, complemented
68	#10597343	C₂²	1	1	yes	characteristic, complemented
69	#10597343	C₂²	1	1	yes	characteristic, complemented
70	#10597343	C₂²	1	2	yes	complemented
71	#10597342	C₂²	1	1	yes	characteristic, complemented
72	#10597342	C₂²	1	2	yes	complemented
73	#10597341	C₂²	1	1	yes	characteristic
74	#10597341	C₂²	1	1	yes	characteristic, complemented
75	#10597341	C₂²	1	2	yes	complemented
76	#10597341	C₂²	1	2	yes	complemented
77	#10597341	C₂²	1	2	yes	complemented
78	#10597341	C₂²	1	1	yes	characteristic, complemented
79	#10597341	C₂²	1	1	yes	characteristic, complemented
80	#10597340	C₂²	1	2	yes	—
81	#10597340	C₂²	1	1	yes	characteristic, complemented
82	#10597340	C₂²	1	2	yes	complemented
83	#10597340	C₂²	1	2	yes	complemented
84	#10597340	C₂²	1	2	yes	complemented
85	#10597339	C₂²	1	2	yes	complemented
86	#10597339	C₂²	1	1	yes	characteristic, complemented
87	#10597339	C₂²	1	1	yes	characteristic, complemented
88	#10597338	C₂²	1	2	yes	complemented
89	#10597338	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
91	#10597336	C₂²	1	2	yes	complemented
92	#10597334	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	#10597331	C₂²	1	2	yes	complemented
97	#10597330	C₂²	1	1	yes	characteristic
98	#10597330	C₂²	1	2	yes	complemented
99	#10597330	C₂²	1	2	yes	complemented
100	#10597330	C₂²	1	2	yes	complemented
101	#10597330	C₂²	1	2	yes	complemented
102	#10597329	C₂²	1	1	yes	characteristic, complemented
103	#10597329	C₂²	1	2	yes	complemented
104	#10597329	C₂²	1	2	yes	complemented
105	#10597328	C₂²	1	1	yes	characteristic
106	#10597328	C₂²	1	2	yes	—
107	#10597328	C₂²	1	2	yes	complemented
108	#10597328	C₂²	1	2	yes	complemented
109	#10597328	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
113	#10597325	C₂²	1	2	yes	complemented
114	#10597324	C₂²	1	1	yes	characteristic, complemented
115	#10597321	C₂²	1	2	yes	complemented
116	#10597320	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₇₆	C₂²	1	1	yes	characteristic
118	C₄×D₇₆	C₂²	1	2	yes	complemented
119	C₄×D₇₆	C₂²	1	2	yes	complemented
120	#10597318	C₂²	1	1	yes	characteristic, complemented
121	#10597318	C₂²	1	2	yes	complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂³×D₁₉	C₂³	1	2	yes	—
125	C₂³×D₁₉	C₂³	1	2	yes	—
126	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₉	C₂³	1	2	yes	—
128	C₂×D₄×C₁₉	C₂³	1	2	yes	—
129	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
145	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
146	D₄×D₁₉	—	4	2	no	—
147	D₄×D₁₉	—	4	2	no	—
148	D₄×D₁₉	—	4	4	no	—
149	#64541	—	4	2	no	—
150	#64541	—	4	2	no	—
151	#64541	—	4	2	no	—
152	#64541	—	4	4	no	—
153	C₂×D₇₆	—	4	4	no	—
154	C₂×D₇₆	C₂³	1	1	yes	characteristic
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×D₇₆	C₂³	1	2	yes	—
159	C₂×D₇₆	C₂³	1	2	yes	—
160	C₂×D₇₆	C₂³	1	2	yes	—
161	C₂×D₇₆	C₂³	1	2	yes	—
162	C₂×D₇₆	C₂³	1	2	yes	—
163	C₂×D₇₆	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₉	—	4	2	no	—
165	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₉	C₂³	1	2	yes	—
169	C₂×C₄×D₁₉	C₂³	1	2	yes	—
170	C₂×C₄×D₁₉	C₂³	1	2	yes	—
171	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₁₉	C₂³	1	2	yes	—
174	C₂×C₄×D₁₉	C₂³	1	2	yes	—
175	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
176	C₂×Dic₃₈	C₂³	1	2	yes	—
177	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
181	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
183	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
187	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
190	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
191	C₄²×C₁₉	C₂³	1	2	yes	—
192	C₄²×C₁₉	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
195	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
196	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
197	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
198	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
206	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
207	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
215	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₁₉	C₂³	1	2	yes	—
219	C₄⋊Dic₁₉	C₂³	1	2	yes	—
220	C₄⋊Dic₁₉	C₂³	1	2	yes	—
221	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₁₉⋊C₄	C₂³	1	2	yes	—
223	Dic₁₉⋊C₄	C₂³	1	2	yes	—
224	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
225	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
226	Dic₁₉⋊C₄	C₂³	1	2	yes	—
227	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₉	C₂³	1	2	yes	—
230	C₄×Dic₁₉	C₂³	1	2	yes	—
231	C₂³×C₁₉	C₂⁴	1	2	yes	—
232	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₉	—	2	2	no	—
235	C₂²×D₁₉	—	2	4	no	—
236	C₂²×D₁₉	—	4	1	no	—
237	C₂²×D₁₉	—	4	1	no	—
238	C₂²×D₁₉	—	4	2	no	—
239	C₂²×D₁₉	—	4	2	no	—
240	C₂²×D₁₉	—	4	2	no	—
241	C₂²×D₁₉	—	4	2	no	—
242	C₂²×D₁₉	—	4	2	no	—
243	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
245	C₂²×D₁₉	C₂⁴	1	2	yes	—
246	C₂²×D₁₉	C₂⁴	1	2	yes	—
247	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
248	D₄×C₁₉	—	2	2	no	—
249	D₄×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	4	2	no	—
251	D₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	—	4	2	no	—
256	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₁₉	—	2	2	no	—
265	C₂²⋊D₁₉	—	4	2	no	—
266	C₂²⋊D₁₉	—	4	2	no	—
267	C₂²⋊D₁₉	—	4	1	no	—
268	C₂²⋊D₁₉	—	4	1	no	—
269	C₂²⋊D₁₉	—	4	2	no	—
270	C₂²⋊D₁₉	—	4	2	no	—
271	C₂²⋊D₁₉	—	4	2	no	—
272	C₂²⋊D₁₉	—	4	2	no	—
273	C₂²⋊D₁₉	—	4	2	no	—
274	C₂²⋊D₁₉	—	4	1	no	—
275	C₂×Dic₁₉	—	4	1	no	—
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	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
283	D₇₆	—	2	2	no	—
284	D₇₆	—	2	4	no	—
285	D₇₆	—	2	2	no	—
286	D₇₆	—	2	2	no	—
287	D₇₆	—	4	2	no	—
288	D₇₆	—	4	2	no	—
289	D₇₆	—	4	2	no	—
290	D₇₆	—	4	2	no	—
291	D₇₆	—	4	1	no	—
292	D₇₆	—	4	2	no	—
293	C₄×D₁₉	—	2	4	no	—
294	C₄×D₁₉	—	2	2	no	—
295	C₄×D₁₉	—	2	2	no	—
296	C₄×D₁₉	—	2	2	no	—
297	C₄×D₁₉	—	4	1	no	—
298	C₄×D₁₉	—	4	1	no	—
299	C₄×D₁₉	—	4	2	no	—
300	C₄×D₁₉	—	4	2	no	—
301	C₄×D₁₉	—	4	2	no	—
302	C₄×D₁₉	—	4	2	no	—
303	Dic₃₈	—	2	2	no	—
304	Dic₃₈	—	4	2	no	—
305	Dic₃₈	—	4	1	no	—
306	#3542	—	19	1	no	maximal, Sylow
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	2	2	no	—
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	2	2	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	2	no	—
316	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
317	C₂×D₁₉	—	2	1	no	—
318	C₂×D₁₉	—	2	1	no	—
319	C₂×D₁₉	—	2	1	no	—
320	C₂×D₁₉	—	2	1	no	—
321	C₂×D₁₉	—	2	2	no	—
322	C₂×D₁₉	—	2	2	no	—
323	C₂×D₁₉	—	2	2	no	—
324	C₂×D₁₉	—	2	1	no	—
325	C₂×D₁₉	—	2	2	no	—
326	C₂×D₁₉	—	2	1	no	—
327	C₂×D₁₉	—	2	2	no	—
328	C₂×D₁₉	—	2	1	no	—
329	C₂×D₁₉	—	2	2	no	—
330	C₂×D₁₉	—	2	1	no	—
331	C₂×D₁₉	—	4	4	no	—
332	C₂×D₁₉	—	8	4	no	—
333	C₂×D₁₉	—	8	4	no	—
334	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	2	2	no	—
337	C₄×C₁₉	—	2	2	no	—
338	C₄×C₁₉	—	2	1	no	—
339	C₄×C₁₉	—	2	1	no	—
340	C₄×C₁₉	—	2	2	no	—
341	C₄×C₁₉	—	2	1	no	—
342	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
343	Dic₁₉	—	2	2	no	—
344	Dic₁₉	—	2	1	no	—
345	Dic₁₉	—	2	1	no	—
346	Dic₁₉	—	2	2	no	—
347	Dic₁₉	—	2	1	no	—
348	Dic₁₉	—	2	1	no	—
349	Dic₁₉	—	2	1	no	—
350	#562	—	19	2	no	—
351	#560	—	19	2	no	—
352	#555	—	19	1	no	—
353	#553	D₁₉	1	1	yes	characteristic, complemented
354	#552	—	19	1	no	—
355	#551	—	19	2	no	—
356	#550	—	19	1	no	—
357	#547	—	19	1	no	—
358	#546	—	19	1	no	—
359	#546	—	19	1	no	—
360	#546	—	19	2	no	—
361	D₄²	—	19	1	no	—
362	#542	—	19	1	no	—
363	#540	—	19	1	no	—
364	#540	—	19	2	no	—
365	#538	—	19	2	no	—
366	#537	—	19	1	no	—
367	#535	—	19	2	no	—
368	#535	—	19	1	no	—
369	#534	—	19	2	no	—
370	#525	—	19	1	no	—
371	#525	—	19	1	no	—
372	C₂×#121	—	19	1	no	—
373	C₂×C₁₉	—	4	1	no	—
374	C₂×C₁₉	—	4	2	no	—
375	C₂×C₁₉	—	4	1	no	—
376	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₁₉	#585	1	1	yes	characteristic
379	D₁₉	—	2	2	no	—
380	D₁₉	—	4	1	no	—
381	D₁₉	—	4	2	no	—
382	D₁₉	—	4	2	no	—
383	D₁₉	—	4	1	no	—
384	C₂×#41	—	19	1	no	—
385	C₂×#41	—	19	1	no	—
386	C₂×#41	—	19	2	no	—
387	C₂×#41	—	19	1	no	—
388	C₂²×D₄	—	19	2	no	—
389	C₂²×D₄	—	19	1	no	—
390	C₂²×D₄	—	19	1	no	—
391	C₂²×D₄	—	19	2	no	—
392	C₂³×C₄	—	19	1	no	—
393	C₄⋊Q₈	—	19	1	no	—
394	#127	—	19	2	no	—
395	#127	—	19	2	no	—
396	#127	—	19	1	no	—
397	#126	—	19	2	no	—
398	#126	—	19	2	no	—
399	#126	C₂×D₁₉	1	2	yes	complemented
400	#125	—	19	2	no	—
401	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
402	#124	—	19	1	no	—
403	#124	—	19	2	no	—
404	#124	—	19	2	no	—
405	#124	—	19	2	no	—
406	#124	—	19	2	no	—
407	#123	—	19	2	no	—
408	#123	—	19	2	no	—
409	#123	—	19	1	no	—
410	#123	—	19	2	no	—
411	#123	—	19	2	no	—
412	#123	—	19	2	no	—
413	#123	—	19	2	no	—
414	#123	—	19	1	no	—
415	#123	—	19	2	no	—
416	#123	—	19	2	no	—
417	#123	—	19	2	no	—
418	#123	C₂×D₁₉	1	2	yes	complemented
419	C₂²⋊Q₈	—	19	2	no	—
420	C₂²⋊Q₈	—	19	1	no	—
421	C₂²⋊Q₈	—	19	1	no	—
422	C₂²⋊Q₈	—	19	1	no	—
423	C₂²⋊Q₈	—	19	1	no	—
424	C₂²⋊Q₈	—	19	2	no	—
425	C₂²⋊Q₈	—	19	2	no	—
426	C₂²⋊Q₈	—	19	1	no	—
427	#121	—	19	1	no	—
428	#121	—	19	2	no	—
429	#121	—	19	2	no	—
430	#121	—	19	2	no	—
431	#121	—	19	1	no	—
432	#121	—	19	1	no	—
433	#121	—	19	2	no	—
434	#121	—	19	1	no	—
435	#121	—	19	2	no	—
436	#121	—	19	2	no	—
437	#121	—	19	1	no	—
438	#121	—	19	1	no	—
439	#121	—	19	1	no	—
440	#121	—	19	2	no	—
441	#121	—	19	2	no	—
442	#121	—	19	2	no	—
443	#121	—	19	1	no	—
444	#121	—	19	2	no	—
445	#121	—	19	1	no	—
446	#121	—	19	2	no	—
447	#121	—	19	2	no	—
448	#121	—	19	2	no	—
449	#121	C₂×D₁₉	1	1	yes	characteristic
450	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
451	#121	C₂×D₁₉	1	2	yes	complemented
452	#120	—	19	1	no	—
453	#120	—	19	2	no	—
454	#120	—	19	2	no	—
455	#120	—	19	2	no	—
456	#120	—	19	1	no	—
457	#120	—	19	2	no	—
458	#120	—	19	2	no	—
459	#120	—	19	2	no	—
460	#120	—	19	2	no	—
461	C₄×Q₈	—	19	1	no	—
462	C₄×D₄	—	19	1	no	—
463	C₄×D₄	—	19	1	no	—
464	C₄×D₄	—	19	2	no	—
465	C₄×D₄	—	19	1	no	—
466	C₄×D₄	—	19	1	no	—
467	C₄×D₄	—	19	2	no	—
468	C₄×D₄	—	19	1	no	—
469	C₄×D₄	—	19	2	no	—
470	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
471	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
472	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
473	#117	—	19	2	no	—
474	#117	—	19	1	no	—
475	#117	—	19	1	no	—
476	#117	—	19	2	no	—
477	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
478	C₂×C₄⋊C₄	—	19	1	no	—
479	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
480	C₂×C₂²⋊C₄	—	19	2	no	—
481	C₂×C₂²⋊C₄	—	19	2	no	—
482	C₂×C₂²⋊C₄	—	19	2	no	—
483	C₁₉	#3542	1	1	yes	characteristic, complemented, Sylow
484	C₂⁴	—	19	2	no	—
485	C₂⁴	—	19	1	no	—
486	C₂⁴	—	19	2	no	—
487	#41	—	76	2	no	—
488	#41	—	76	2	no	—
489	#41	—	76	2	no	—
490	#41	—	76	4	no	—
491	C₂×Q₈	—	19	1	no	—
492	C₂×Q₈	—	19	1	no	—
493	C₂×Q₈	—	19	2	no	—
494	C₂×D₄	—	19	1	no	—
495	C₂×D₄	—	19	1	no	—
496	C₂×D₄	—	19	1	no	—
497	C₂×D₄	—	19	2	no	—
498	C₂×D₄	—	19	2	no	—
499	C₂×D₄	—	19	2	no	—
500	C₂×D₄	—	19	2	no	—
501	C₂×D₄	—	19	2	no	—
502	C₂×D₄	—	19	1	no	—
503	C₂×D₄	—	19	2	no	—
504	C₂×D₄	—	19	2	no	—
505	C₂×D₄	—	19	2	no	—
506	C₂×D₄	—	19	1	no	—
507	C₂×D₄	—	19	1	no	—
508	C₂×D₄	—	19	1	no	—
509	C₂×D₄	—	19	2	no	—
510	C₂×D₄	—	19	2	no	—
511	C₂×D₄	—	19	1	no	—
512	C₂×D₄	—	19	2	no	—
513	C₂×D₄	—	19	2	no	—
514	C₂×D₄	—	19	2	no	—
515	C₂×D₄	—	76	4	no	—
516	C₂×D₄	—	76	2	no	—
517	C₂×D₄	—	76	2	no	—
518	C₂×D₄	—	76	4	no	—
519	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₁₉	1	2	yes	—
521	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₁₉	1	2	yes	—
523	C₂²×C₄	—	19	1	no	—
524	C₂²×C₄	—	19	2	no	—
525	C₂²×C₄	—	19	1	no	—
526	C₂²×C₄	—	19	1	no	—
527	C₂²×C₄	—	19	1	no	—
528	C₂²×C₄	—	19	1	no	—
529	C₂²×C₄	—	19	2	no	—
530	C₂²×C₄	—	19	2	no	—
531	C₂²×C₄	—	19	2	no	—
532	C₂²×C₄	—	19	2	no	—
533	C₂²×C₄	—	19	1	no	—
534	C₂²×C₄	—	76	2	no	—
535	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
538	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
539	C₄⋊C₄	—	19	2	no	—
540	C₄⋊C₄	—	19	1	no	—
541	C₄⋊C₄	—	19	1	no	—
542	C₄⋊C₄	—	19	1	no	—
543	C₄⋊C₄	—	19	2	no	—
544	C₄⋊C₄	—	19	1	no	—
545	C₄⋊C₄	—	19	2	no	—
546	C₄⋊C₄	—	19	1	no	—
547	C₄⋊C₄	—	19	2	no	—
548	C₄⋊C₄	—	19	1	no	—
549	C₄⋊C₄	—	19	2	no	—
550	C₄⋊C₄	—	19	2	no	—
551	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
552	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
553	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
554	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
556	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
558	C₂²⋊C₄	—	19	2	no	—
559	C₂²⋊C₄	—	19	2	no	—
560	C₂²⋊C₄	—	19	2	no	—
561	C₂²⋊C₄	—	19	1	no	—
562	C₂²⋊C₄	—	19	1	no	—
563	C₂²⋊C₄	—	19	1	no	—
564	C₂²⋊C₄	—	19	1	no	—
565	C₂²⋊C₄	—	19	2	no	—
566	C₂²⋊C₄	—	19	2	no	—
567	C₂²⋊C₄	—	19	2	no	—
568	C₂²⋊C₄	—	19	2	no	—
569	C₂²⋊C₄	—	19	1	no	—
570	C₂²⋊C₄	—	19	2	no	—
571	C₂²⋊C₄	—	19	2	no	—
572	C₂²⋊C₄	—	19	1	no	—
573	C₂²⋊C₄	—	19	1	no	—
574	C₂²⋊C₄	—	19	1	no	—
575	C₂²⋊C₄	—	19	2	no	—
576	C₂²⋊C₄	—	19	2	no	—
577	C₂²⋊C₄	—	19	2	no	—
578	C₂²⋊C₄	—	19	2	no	—
579	C₂²⋊C₄	—	19	2	no	—
580	C₂²⋊C₄	—	19	2	no	—
581	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
584	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
585	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
586	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
587	C₄²	—	19	2	no	—
588	C₄²	—	19	1	no	—
589	C₄²	—	19	2	no	—
590	C₄²	C₂²×D₁₉	1	2	yes	—
591	C₄²	C₂²×D₁₉	1	1	yes	characteristic
592	C₂³	—	19	1	no	—
593	C₂³	—	19	1	no	—
594	C₂³	—	19	2	no	—
595	C₂³	—	19	1	no	—
596	C₂³	—	19	2	no	—
597	C₂³	—	38	2	no	—
598	C₂³	—	38	4	no	—
599	C₂³	—	76	1	no	—
600	C₂³	—	76	1	no	—
601	C₂³	—	76	2	no	—
602	C₂³	—	76	2	no	—
603	C₂³	—	76	2	no	—
604	C₂³	—	76	2	no	—
605	C₂³	—	76	2	no	—
606	C₂³	C₂³×D₁₉	1	2	yes	—
607	C₂³	C₂³×D₁₉	1	1	yes	characteristic
608	C₂³	C₂³×D₁₉	1	1	yes	characteristic
609	Q₈	—	38	2	no	—
610	Q₈	—	76	2	no	—
611	Q₈	—	76	1	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	1	no	—
616	D₄	—	38	2	no	—
617	D₄	—	38	4	no	—
618	D₄	—	38	2	no	—
619	D₄	—	38	2	no	—
620	D₄	—	38	2	no	—
621	D₄	—	76	2	no	—
622	D₄	—	76	2	no	—
623	D₄	—	76	2	no	—
624	D₄	—	76	1	no	—
625	D₄	—	76	2	no	—
626	D₄	—	76	2	no	—
627	D₄	—	76	2	no	—
628	D₄	—	76	2	no	—
629	D₄	—	76	2	no	—
630	D₄	—	76	2	no	—
631	D₄	—	76	2	no	—
632	D₄	—	76	1	no	—
633	D₄	—	76	1	no	—
634	D₄	—	76	2	no	—
635	D₄	—	76	2	no	—
636	D₄	—	76	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	19	2	no	—
642	C₂×C₄	—	19	1	no	—
643	C₂×C₄	—	19	1	no	—
644	C₂×C₄	—	19	1	no	—
645	C₂×C₄	—	19	2	no	—
646	C₂×C₄	—	19	1	no	—
647	C₂×C₄	—	19	1	no	—
648	C₂×C₄	—	38	4	no	—
649	C₂×C₄	—	38	2	no	—
650	C₂×C₄	—	38	2	no	—
651	C₂×C₄	—	38	2	no	—
652	C₂×C₄	—	76	1	no	—
653	C₂×C₄	—	76	1	no	—
654	C₂×C₄	—	76	2	no	—
655	C₂×C₄	—	76	2	no	—
656	C₂×C₄	—	76	2	no	—
657	C₂×C₄	—	76	2	no	—
658	C₂×C₄	—	76	1	no	—
659	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₁₉	1	2	yes	—
661	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₉	1	2	yes	—
663	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₉	1	2	yes	—
666	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	19	2	no	—
677	C₂²	—	38	1	no	—
678	C₂²	—	38	1	no	—
679	C₂²	—	38	2	no	—
680	C₂²	—	38	1	no	—
681	C₂²	—	38	1	no	—
682	C₂²	—	38	2	no	—
683	C₂²	—	38	1	no	—
684	C₂²	—	38	1	no	—
685	C₂²	—	38	2	no	—
686	C₂²	—	38	2	no	—
687	C₂²	—	38	2	no	—
688	C₂²	—	38	1	no	—
689	C₂²	—	38	2	no	—
690	C₂²	—	38	1	no	—
691	C₂²	—	76	4	no	—
692	C₂²	—	152	4	no	—
693	C₂²	—	152	4	no	—
694	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	1	no	—
702	C₄	—	38	2	no	—
703	C₄	—	38	1	no	—
704	C₄	—	38	1	no	—
705	C₄	—	38	1	no	—
706	C₄	—	38	1	no	—
707	C₄	—	38	2	no	—
708	C₄	—	38	1	no	—
709	C₄	#10597435	1	2	yes	—
710	C₂	—	4	1	no	—
711	C₂	—	4	2	no	—
712	C₂	—	4	1	no	—
713	C₂	—	38	2	no	—
714	C₂	—	76	1	no	—
715	C₂	—	76	1	no	—
716	C₂	—	76	2	no	—
717	C₂	—	76	2	no	—
718	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
719	C₂	C₂×#10597435	1	1	yes	characteristic
720	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#553	C₂
hypercenter	#553	D₁₉
hypocenter	C₁₉	#3542
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #11927291	C₂	semidirect
2. #11927282	C₂	semidirect
3. #11927257	C₂	semidirect
4. #11927232	C₂	semidirect
5. #11927219	C₂	semidirect
6. #11927215	C₂	semidirect
7. #11927195	C₂	semidirect
8. #11927191	C₂	semidirect
9. #11927191	C₂	semidirect
10. #11927190	C₂	semidirect
11. D₄×D₇₆	C₂	semidirect
12. #11927159	C₂	semidirect
13. #11927150	C₂	semidirect
14. #11927145	C₂	semidirect
15. #11927133	C₂	semidirect
16. #11927125	C₂	semidirect
17. #11927110	C₂	semidirect
18. #11927110	C₂	semidirect
19. #11927105	C₂	semidirect
20. #11927056	C₂	semidirect
21. #11927053	C₂	semidirect
22. #121×D₁₉	C₂	semidirect
23. C₁₉×#553	C₂	semidirect
25. C₂×D₄×D₁₉	C₂²	semidirect
26. C₂×D₄×D₁₉	C₂²	semidirect
27. C₂×#64541	C₂²	semidirect
28. C₂×#64541	C₂²	semidirect
29. C₂×#64541	C₂²	semidirect
30. C₂×#64541	C₂²	semidirect
32. C₂²×C₄×D₁₉	C₂²	semidirect
33. C₁₉×#126	C₂²	semidirect
34. C₁₉×#125	C₂²	semidirect
35. C₁₉×#123	C₂²	semidirect
37. C₁₉×#121	C₂²	semidirect
38. C₁₉×#121	C₂²	semidirect
39. C₄×D₄×C₁₉	C₂²	semidirect
40. C₄×D₄×C₁₉	C₂²	semidirect
41. C₄×D₄×C₁₉	C₂²	semidirect
42. C₁₉×#117	C₂²	semidirect
43. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
44. #10597386	C₂²	semidirect
45. #10597386	C₂²	semidirect
46. #10597385	C₂²	semidirect
47. #10597385	C₂²	semidirect
49. #10597384	C₂²	semidirect
50. #10597384	C₂²	semidirect
51. #10597383	C₂²	semidirect
52. #10597383	C₂²	semidirect
53. #10597383	C₂²	semidirect
54. #10597383	C₂²	semidirect
55. #10597382	C₂²	semidirect
56. #10597376	C₂²	semidirect
57. #10597376	C₂²	semidirect
58. #10597376	C₂²	semidirect
59. #10597376	C₂²	semidirect
60. #10597376	C₂²	semidirect
61. #10597375	C₂²	semidirect
62. #10597375	C₂²	semidirect
63. C₄×C₂²⋊D₁₉	C₂²	semidirect
64. C₄×C₂²⋊D₁₉	C₂²	semidirect
65. #10597370	C₂²	semidirect
66. #10597344	C₂²	semidirect
67. #10597343	C₂²	semidirect
68. #10597343	C₂²	semidirect
69. #10597343	C₂²	semidirect
70. #10597343	C₂²	semidirect
71. #10597342	C₂²	semidirect
72. #10597342	C₂²	semidirect
74. #10597341	C₂²	semidirect
75. #10597341	C₂²	semidirect
76. #10597341	C₂²	semidirect
77. #10597341	C₂²	semidirect
78. #10597341	C₂²	semidirect
79. #10597341	C₂²	semidirect
81. #10597340	C₂²	semidirect
82. #10597340	C₂²	semidirect
83. #10597340	C₂²	semidirect
84. #10597340	C₂²	semidirect
85. #10597339	C₂²	semidirect
86. #10597339	C₂²	semidirect
87. #10597339	C₂²	semidirect
88. #10597338	C₂²	semidirect
89. #10597338	C₂²	semidirect
90. C₄⋊C₄×D₁₉	C₂²	semidirect
91. #10597336	C₂²	semidirect
92. #10597334	C₂²	semidirect
93. #10597332	C₂²	semidirect
94. #10597331	C₂²	semidirect
95. #10597331	C₂²	semidirect
96. #10597331	C₂²	semidirect
98. #10597330	C₂²	semidirect
99. #10597330	C₂²	semidirect
100. #10597330	C₂²	semidirect
101. #10597330	C₂²	semidirect
102. #10597329	C₂²	semidirect
103. #10597329	C₂²	semidirect
104. #10597329	C₂²	semidirect
107. #10597328	C₂²	semidirect
108. #10597328	C₂²	semidirect
109. #10597328	C₂²	semidirect
110. C₂²⋊C₄×D₁₉	C₂²	semidirect
111. C₂²⋊C₄×D₁₉	C₂²	semidirect
112. C₂²⋊C₄×D₁₉	C₂²	semidirect
113. #10597325	C₂²	semidirect
114. #10597324	C₂²	semidirect
115. #10597321	C₂²	semidirect
116. #10597320	C₂²	semidirect
118. C₄×D₇₆	C₂²	semidirect
119. C₄×D₇₆	C₂²	semidirect
120. #10597318	C₂²	semidirect
121. #10597318	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
353. #553	D₁₉	semidirect
399. #126	C₂×D₁₉	semidirect
401. #125	C₂×D₁₉	semidirect
418. #123	C₂×D₁₉	semidirect
450. #121	C₂×D₁₉	semidirect
451. #121	C₂×D₁₉	semidirect
470. C₄×D₄	C₂×D₁₉	semidirect
471. C₄×D₄	C₂×D₁₉	semidirect
472. C₄×D₄	C₂×D₁₉	semidirect
477. #117	C₂×D₁₉	semidirect
479. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
483. C₁₉	#3542	semidirect

Maximal subgroups

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

subgroup	index
#11927291	2
#11927282	2
#11927257	2
#11927232	2
#11927219	2
#11927215	2
#11927195	2
#11927191	2
#11927190	2
D₄×D₇₆	2
#11927159	2
#11927150	2
#11927145	2
#11927133	2
#11927125	2
#11927110	2
#11927105	2
#11927056	2
#11927053	2
#121×D₁₉	2
C₁₉×#553	2
#3542	19