Subgroups — #14577582

Order 2432.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 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	#11927250	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927244	C₂	1	2	yes	maximal, complemented
4	#11927233	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927222	C₂	1	2	yes	maximal, complemented
6	#11927219	C₂	1	2	yes	maximal, complemented
7	#11927195	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927191	C₂	1	2	yes	maximal, complemented
9	#11927191	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927190	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927178	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927161	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927147	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927135	C₂	1	2	yes	maximal, complemented
15	#11927126	C₂	1	2	yes	maximal, complemented
16	#11927079	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927076	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927053	C₂	1	2	yes	maximal, complemented
19	#123×D₁₉	C₂	1	2	yes	maximal, complemented
20	#11927025	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927018	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×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	—
26	C₂×#64541	C₂²	1	1	yes	characteristic
27	C₂×#64541	C₂²	1	2	yes	complemented
28	C₂²×D₇₆	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	C₂²	1	2	yes	complemented
30	C₁₉×#126	C₂²	1	2	yes	complemented
31	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#123	C₂²	1	2	yes	complemented
33	C₁₉×#121	C₂²	1	1	yes	characteristic
34	C₁₉×#121	C₂²	1	2	yes	complemented
35	C₁₉×#121	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	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	#10597386	C₂²	1	1	yes	characteristic
42	#10597385	C₂²	1	2	yes	complemented
43	#10597384	C₂²	1	1	yes	characteristic
44	#10597384	C₂²	1	2	yes	complemented
45	#10597384	C₂²	1	2	yes	complemented
46	#10597383	C₂²	1	2	yes	—
47	#10597383	C₂²	1	2	yes	complemented
48	#10597383	C₂²	1	2	yes	complemented
49	#10597382	C₂²	1	1	yes	characteristic, complemented
50	#10597382	C₂²	1	2	yes	complemented
51	#10597382	C₂²	1	1	yes	characteristic, complemented
52	#10597381	C₂²	1	2	yes	complemented
53	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
54	#10597376	C₂²	1	1	yes	characteristic, complemented
55	#10597375	C₂²	1	2	yes	complemented
56	#10597375	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
61	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
63	#10597372	C₂²	1	1	yes	characteristic, complemented
64	#10597372	C₂²	1	1	yes	characteristic, complemented
65	#10597370	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
70	#10597342	C₂²	1	2	yes	complemented
71	#10597342	C₂²	1	2	yes	complemented
72	#10597342	C₂²	1	2	yes	complemented
73	#10597341	C₂²	1	1	yes	characteristic
74	#10597340	C₂²	1	2	yes	complemented
75	#10597340	C₂²	1	2	yes	complemented
76	#10597340	C₂²	1	2	yes	complemented
77	#10597339	C₂²	1	1	yes	characteristic
78	#10597339	C₂²	1	1	yes	characteristic
79	#10597339	C₂²	1	1	yes	characteristic
80	#10597339	C₂²	1	1	yes	characteristic, complemented
81	#10597339	C₂²	1	2	yes	complemented
82	#10597339	C₂²	1	1	yes	characteristic, complemented
83	#10597338	C₂²	1	2	yes	complemented
84	#10597338	C₂²	1	2	yes	complemented
85	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
86	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
87	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
88	#10597336	C₂²	1	1	yes	characteristic, complemented
89	#10597336	C₂²	1	1	yes	characteristic, complemented
90	#10597334	C₂²	1	1	yes	characteristic, complemented
91	#10597333	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	#10597330	C₂²	1	2	yes	—
96	#10597330	C₂²	1	2	yes	complemented
97	#10597329	C₂²	1	1	yes	characteristic
98	#10597329	C₂²	1	2	yes	—
99	#10597329	C₂²	1	1	yes	characteristic, complemented
100	#10597329	C₂²	1	2	yes	complemented
101	#10597329	C₂²	1	2	yes	complemented
102	#10597329	C₂²	1	2	yes	complemented
103	#10597328	C₂²	1	2	yes	—
104	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
110	#10597325	C₂²	1	1	yes	characteristic, complemented
111	#10597325	C₂²	1	1	yes	characteristic, complemented
112	#10597325	C₂²	1	2	yes	complemented
113	#10597325	C₂²	1	2	yes	complemented
114	#10597324	C₂²	1	2	yes	complemented
115	#10597321	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₇₆	C₂²	1	1	yes	characteristic
117	C₄×D₇₆	C₂²	1	2	yes	complemented
118	C₄×D₇₆	C₂²	1	2	yes	complemented
119	#10597318	C₂²	1	2	yes	complemented
120	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
121	#10597316	C₂²	1	2	yes	complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	2	yes	—
124	C₂³×D₁₉	C₂³	1	2	yes	—
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₉	C₂³	1	2	yes	—
127	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
140	C₂²×Dic₁₉	C₂³	1	2	yes	—
141	D₄×D₁₉	—	2	4	no	—
142	D₄×D₁₉	—	4	4	no	—
143	#64541	—	2	4	no	—
144	#64541	—	4	4	no	—
145	C₂×D₇₆	—	2	4	no	—
146	C₂×D₇₆	C₂³	1	1	yes	characteristic
147	C₂×D₇₆	C₂³	1	2	yes	—
148	C₂×D₇₆	C₂³	1	2	yes	—
149	C₂×D₇₆	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₉	—	4	4	no	—
151	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₉	C₂³	1	2	yes	—
157	C₂×C₄×D₁₉	C₂³	1	2	yes	—
158	C₂×C₄×D₁₉	C₂³	1	2	yes	—
159	C₂×C₄×D₁₉	C₂³	1	2	yes	—
160	C₂×C₄×D₁₉	C₂³	1	2	yes	—
161	C₂×C₄×D₁₉	C₂³	1	2	yes	—
162	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
163	C₂×Dic₃₈	C₂³	1	2	yes	—
164	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
170	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
174	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
177	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₄²×C₁₉	C₂³	1	2	yes	—
179	C₄²×C₁₉	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₉	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	1	yes	characteristic
186	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
190	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
197	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
203	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₉	C₂³	1	2	yes	—
206	C₄⋊Dic₁₉	C₂³	1	2	yes	—
207	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
225	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₉	C₂⁴	1	2	yes	—
230	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₉	—	2	4	no	—
232	C₂²×D₁₉	—	2	4	no	—
233	C₂²×D₁₉	—	2	4	no	—
234	C₂²×D₁₉	—	4	2	no	—
235	C₂²×D₁₉	—	4	2	no	—
236	C₂²×D₁₉	—	4	2	no	—
237	C₂²×D₁₉	C₂⁴	1	2	yes	—
238	C₂²×D₁₉	C₂⁴	1	2	yes	—
239	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
240	D₄×C₁₉	—	2	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₁₉	—	2	4	no	—
257	C₂²⋊D₁₉	—	2	4	no	—
258	C₂²⋊D₁₉	—	2	2	no	—
259	C₂²⋊D₁₉	—	2	2	no	—
260	C₂²⋊D₁₉	—	4	2	no	—
261	C₂²⋊D₁₉	—	4	2	no	—
262	C₂²⋊D₁₉	—	4	2	no	—
263	C₂×Dic₁₉	—	4	2	no	—
264	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₉	C₂⁴	1	2	yes	—
268	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₉	C₂⁴	1	2	yes	—
273	D₇₆	—	2	4	no	—
274	D₇₆	—	2	4	no	—
275	D₇₆	—	2	2	no	—
276	D₇₆	#41	1	4	yes	complemented
277	C₄×D₁₉	—	2	4	no	—
278	C₄×D₁₉	—	2	2	no	—
279	C₄×D₁₉	—	2	4	no	—
280	C₄×D₁₉	—	2	2	no	—
281	C₄×D₁₉	—	4	2	no	—
282	C₄×D₁₉	—	4	2	no	—
283	C₄×D₁₉	—	4	2	no	—
284	C₄×D₁₉	—	4	1	no	—
285	C₄×D₁₉	—	4	2	no	—
286	C₄×D₁₉	—	4	2	no	—
287	C₄×D₁₉	—	4	2	no	—
288	Dic₃₈	—	2	2	no	—
289	Dic₃₈	—	4	1	no	—
290	Dic₃₈	—	4	2	no	—
291	#3513	—	19	1	no	maximal, Sylow
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
302	C₂×D₁₉	—	2	1	no	—
303	C₂×D₁₉	—	2	2	no	—
304	C₂×D₁₉	—	2	1	no	—
305	C₂×D₁₉	—	2	2	no	—
306	C₂×D₁₉	—	2	2	no	—
307	C₂×D₁₉	—	2	2	no	—
308	C₂×D₁₉	—	2	2	no	—
309	C₂×D₁₉	—	4	8	no	—
310	C₂×D₁₉	—	8	4	no	—
311	C₂×D₁₉	C₂×#41	1	4	yes	—
312	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	—	2	2	no	—
320	C₄×C₁₉	C₂×#41	1	2	yes	—
321	Dic₁₉	—	2	2	no	—
322	Dic₁₉	—	2	1	no	—
323	Dic₁₉	—	2	1	no	—
324	Dic₁₉	—	2	2	no	—
325	Dic₁₉	—	2	1	no	—
326	Dic₁₉	—	2	1	no	—
327	Dic₁₉	—	2	1	no	—
328	Dic₁₉	—	2	1	no	—
329	Dic₁₉	—	2	1	no	—
330	#559	—	19	1	no	—
331	#554	—	19	1	no	—
332	#553	—	19	2	no	—
333	#553	D₁₉	1	1	yes	characteristic, complemented
334	#552	—	19	1	no	—
335	#551	—	19	2	no	—
336	#551	—	19	2	no	—
337	#547	—	19	1	no	—
338	#546	—	19	2	no	—
339	#546	—	19	1	no	—
340	#546	—	19	1	no	—
341	D₄²	—	19	1	no	—
342	#542	—	19	1	no	—
343	#540	—	19	1	no	—
344	#539	—	19	2	no	—
345	#538	—	19	2	no	—
346	#529	—	19	1	no	—
347	#529	—	19	1	no	—
348	#525	—	19	2	no	—
349	C₂×#123	—	19	2	no	—
350	#520	—	19	1	no	—
351	#518	—	19	1	no	—
352	C₂×C₄×D₄	—	19	1	no	—
353	C₂×C₁₉	—	4	2	no	—
354	C₂×C₁₉	—	4	1	no	—
355	C₂×C₁₉	—	4	1	no	—
356	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
357	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₁₉	#585	1	1	yes	characteristic
359	D₁₉	—	2	2	no	—
360	D₁₉	—	2	4	no	—
361	D₁₉	—	4	2	no	—
362	C₂×#41	—	19	1	no	—
363	C₂×#41	—	19	2	no	—
364	C₂²×D₄	—	19	1	no	—
365	C₂²×D₄	—	19	2	no	—
366	C₂²×D₄	—	19	1	no	—
367	C₂³×C₄	—	19	2	no	—
368	C₄⋊Q₈	—	19	1	no	—
369	#127	—	19	1	no	—
370	#126	—	19	2	no	—
371	#126	—	19	1	no	—
372	#126	—	19	1	no	—
373	#126	—	19	2	no	—
374	#126	—	19	2	no	—
375	#126	C₂×D₁₉	1	2	yes	complemented
376	#125	—	19	1	no	—
377	#125	—	19	1	no	—
378	#125	—	19	2	no	—
379	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
380	#124	—	19	1	no	—
381	#124	—	19	2	no	—
382	#124	—	19	1	no	—
383	#124	—	19	2	no	—
384	#124	—	19	1	no	—
385	#123	—	19	2	no	—
386	#123	—	19	2	no	—
387	#123	—	19	2	no	—
388	#123	—	19	2	no	—
389	#123	—	19	2	no	—
390	#123	—	19	2	no	—
391	#123	—	19	1	no	—
392	#123	—	19	2	no	—
393	#123	—	19	2	no	—
394	#123	—	19	1	no	—
395	#123	—	19	2	no	—
396	#123	—	19	2	no	—
397	#123	—	19	2	no	—
398	#123	C₂×D₁₉	1	2	yes	complemented
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	2	no	—
401	C₂²⋊Q₈	—	19	1	no	—
402	C₂²⋊Q₈	—	19	1	no	—
403	C₂²⋊Q₈	—	19	2	no	—
404	C₂²⋊Q₈	—	19	2	no	—
405	C₂²⋊Q₈	—	19	2	no	—
406	C₂²⋊Q₈	—	19	2	no	—
407	#121	—	19	1	no	—
408	#121	—	19	2	no	—
409	#121	—	19	2	no	—
410	#121	—	19	2	no	—
411	#121	—	19	1	no	—
412	#121	—	19	1	no	—
413	#121	—	19	2	no	—
414	#121	—	19	2	no	—
415	#121	C₂×D₁₉	1	1	yes	characteristic
416	#121	C₂×D₁₉	1	2	yes	complemented
417	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
418	#120	—	19	2	no	—
419	#120	—	19	2	no	—
420	#120	—	19	2	no	—
421	#120	—	19	2	no	—
422	C₄×Q₈	—	19	1	no	—
423	C₄×Q₈	—	19	1	no	—
424	C₄×Q₈	—	19	1	no	—
425	C₄×D₄	—	19	1	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	1	no	—
431	C₄×D₄	—	19	1	no	—
432	C₄×D₄	—	19	1	no	—
433	C₄×D₄	—	19	1	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	—	19	1	no	—
436	C₄×D₄	—	19	1	no	—
437	C₄×D₄	—	19	2	no	—
438	C₄×D₄	—	19	2	no	—
439	C₄×D₄	—	19	1	no	—
440	C₄×D₄	—	19	2	no	—
441	C₄×D₄	—	19	2	no	—
442	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
443	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
444	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
445	#117	—	19	1	no	—
446	#117	—	19	1	no	—
447	#117	—	19	2	no	—
448	#117	—	19	2	no	—
449	#117	—	19	2	no	—
450	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
451	C₂×C₄⋊C₄	—	19	1	no	—
452	C₂×C₄⋊C₄	—	19	2	no	—
453	C₂×C₄⋊C₄	—	19	2	no	—
454	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
455	C₂×C₂²⋊C₄	—	19	2	no	—
456	C₂×C₂²⋊C₄	—	19	2	no	—
457	C₂×C₂²⋊C₄	—	19	2	no	—
458	C₂×C₂²⋊C₄	—	19	2	no	—
459	C₂×C₂²⋊C₄	—	19	2	no	—
460	C₂×C₄²	—	19	1	no	—
461	C₁₉	#3513	1	1	yes	characteristic, complemented, Sylow
462	C₂⁴	—	19	2	no	—
463	C₂⁴	—	19	2	no	—
464	#41	—	38	4	no	—
465	#41	—	76	4	no	—
466	C₂×Q₈	—	19	1	no	—
467	C₂×Q₈	—	19	1	no	—
468	C₂×Q₈	—	19	2	no	—
469	C₂×D₄	—	19	2	no	—
470	C₂×D₄	—	19	2	no	—
471	C₂×D₄	—	19	1	no	—
472	C₂×D₄	—	19	1	no	—
473	C₂×D₄	—	19	2	no	—
474	C₂×D₄	—	19	2	no	—
475	C₂×D₄	—	19	2	no	—
476	C₂×D₄	—	19	1	no	—
477	C₂×D₄	—	19	2	no	—
478	C₂×D₄	—	19	1	no	—
479	C₂×D₄	—	19	2	no	—
480	C₂×D₄	—	38	4	no	—
481	C₂×D₄	—	38	4	no	—
482	C₂×D₄	—	76	4	no	—
483	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₁₉	1	2	yes	—
486	C₂×D₄	C₂²×D₁₉	1	2	yes	—
487	C₂²×C₄	—	19	2	no	—
488	C₂²×C₄	—	19	1	no	—
489	C₂²×C₄	—	19	1	no	—
490	C₂²×C₄	—	19	2	no	—
491	C₂²×C₄	—	19	2	no	—
492	C₂²×C₄	—	19	1	no	—
493	C₂²×C₄	—	19	2	no	—
494	C₂²×C₄	—	19	2	no	—
495	C₂²×C₄	—	19	2	no	—
496	C₂²×C₄	—	19	2	no	—
497	C₂²×C₄	—	19	2	no	—
498	C₂²×C₄	—	19	2	no	—
499	C₂²×C₄	—	76	4	no	—
500	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
503	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
504	C₄⋊C₄	—	19	1	no	—
505	C₄⋊C₄	—	19	2	no	—
506	C₄⋊C₄	—	19	2	no	—
507	C₄⋊C₄	—	19	2	no	—
508	C₄⋊C₄	—	19	2	no	—
509	C₄⋊C₄	—	19	2	no	—
510	C₄⋊C₄	—	19	2	no	—
511	C₄⋊C₄	—	19	1	no	—
512	C₄⋊C₄	—	19	1	no	—
513	C₄⋊C₄	—	19	1	no	—
514	C₄⋊C₄	—	19	1	no	—
515	C₄⋊C₄	—	19	1	no	—
516	C₄⋊C₄	—	19	2	no	—
517	C₄⋊C₄	—	19	1	no	—
518	C₄⋊C₄	—	19	1	no	—
519	C₄⋊C₄	—	19	1	no	—
520	C₄⋊C₄	—	19	2	no	—
521	C₄⋊C₄	—	19	1	no	—
522	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
529	C₂²⋊C₄	—	19	1	no	—
530	C₂²⋊C₄	—	19	1	no	—
531	C₂²⋊C₄	—	19	2	no	—
532	C₂²⋊C₄	—	19	2	no	—
533	C₂²⋊C₄	—	19	2	no	—
534	C₂²⋊C₄	—	19	1	no	—
535	C₂²⋊C₄	—	19	1	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	2	no	—
538	C₂²⋊C₄	—	19	1	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	1	no	—
541	C₂²⋊C₄	—	19	2	no	—
542	C₂²⋊C₄	—	19	2	no	—
543	C₂²⋊C₄	—	19	2	no	—
544	C₂²⋊C₄	—	19	2	no	—
545	C₂²⋊C₄	—	19	2	no	—
546	C₂²⋊C₄	—	19	2	no	—
547	C₂²⋊C₄	—	19	2	no	—
548	C₂²⋊C₄	—	19	1	no	—
549	C₂²⋊C₄	—	19	2	no	—
550	C₂²⋊C₄	—	19	2	no	—
551	C₂²⋊C₄	—	19	2	no	—
552	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
557	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
558	C₄²	—	19	1	no	—
559	C₄²	—	19	1	no	—
560	C₄²	—	19	1	no	—
561	C₄²	—	19	2	no	—
562	C₄²	—	19	2	no	—
563	C₄²	—	19	1	no	—
564	C₄²	—	19	1	no	—
565	C₄²	C₂²×D₁₉	1	1	yes	characteristic
566	C₄²	C₂²×D₁₉	1	2	yes	—
567	C₂³	—	19	2	no	—
568	C₂³	—	19	1	no	—
569	C₂³	—	19	2	no	—
570	C₂³	—	38	4	no	—
571	C₂³	—	38	4	no	—
572	C₂³	—	38	4	no	—
573	C₂³	—	76	2	no	—
574	C₂³	—	76	2	no	—
575	C₂³	—	76	2	no	—
576	C₂³	C₂³×D₁₉	1	1	yes	characteristic
577	C₂³	C₂³×D₁₉	1	2	yes	—
578	C₂³	C₂³×D₁₉	1	1	yes	characteristic
579	Q₈	—	38	2	no	—
580	Q₈	—	76	2	no	—
581	Q₈	—	76	1	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	1	no	—
586	D₄	—	19	4	no	—
587	D₄	—	38	4	no	—
588	D₄	—	38	4	no	—
589	D₄	—	38	4	no	—
590	D₄	—	38	2	no	—
591	D₄	—	38	4	no	—
592	D₄	—	38	2	no	—
593	D₄	—	38	2	no	—
594	D₄	—	76	2	no	—
595	D₄	—	76	2	no	—
596	D₄	—	76	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	19	1	no	—
602	C₂×C₄	—	19	1	no	—
603	C₂×C₄	—	19	2	no	—
604	C₂×C₄	—	19	1	no	—
605	C₂×C₄	—	19	1	no	—
606	C₂×C₄	—	19	1	no	—
607	C₂×C₄	—	19	1	no	—
608	C₂×C₄	—	19	1	no	—
609	C₂×C₄	—	19	2	no	—
610	C₂×C₄	—	38	2	no	—
611	C₂×C₄	—	38	4	no	—
612	C₂×C₄	—	38	4	no	—
613	C₂×C₄	—	38	2	no	—
614	C₂×C₄	—	76	2	no	—
615	C₂×C₄	—	76	2	no	—
616	C₂×C₄	—	76	2	no	—
617	C₂×C₄	—	76	2	no	—
618	C₂×C₄	—	76	2	no	—
619	C₂×C₄	—	76	2	no	—
620	C₂×C₄	—	76	1	no	—
621	C₂×C₄	—	76	2	no	—
622	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₉	1	2	yes	—
625	C₂×C₄	C₂³×D₁₉	1	2	yes	—
626	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₉	1	2	yes	—
628	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	19	4	no	—
640	C₂²	—	19	2	no	—
641	C₂²	—	38	1	no	—
642	C₂²	—	38	2	no	—
643	C₂²	—	38	1	no	—
644	C₂²	—	38	2	no	—
645	C₂²	—	38	2	no	—
646	C₂²	—	38	2	no	—
647	C₂²	—	38	2	no	—
648	C₂²	—	76	8	no	—
649	C₂²	—	152	4	no	—
650	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	38	1	no	—
659	C₄	—	38	2	no	—
660	C₄	—	38	1	no	—
661	C₄	—	38	2	no	—
662	C₄	—	38	1	no	—
663	C₄	—	38	1	no	—
664	C₄	—	38	1	no	—
665	C₄	—	38	1	no	—
666	C₄	—	38	1	no	—
667	C₄	#41×D₁₉	1	2	yes	—
668	C₂	—	4	2	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	1	no	—
671	C₂	—	38	2	no	—
672	C₂	—	38	4	no	—
673	C₂	—	76	2	no	—
674	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
676	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	#3513
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. #11927277	C₂	semidirect
2. #11927250	C₂	semidirect
3. #11927244	C₂	semidirect
4. #11927233	C₂	semidirect
5. #11927222	C₂	semidirect
6. #11927219	C₂	semidirect
7. #11927195	C₂	semidirect
8. #11927191	C₂	semidirect
9. #11927191	C₂	semidirect
10. #11927190	C₂	semidirect
11. #11927178	C₂	semidirect
12. #11927161	C₂	semidirect
13. #11927147	C₂	semidirect
14. #11927135	C₂	semidirect
15. #11927126	C₂	semidirect
16. #11927079	C₂	semidirect
17. #11927076	C₂	semidirect
18. #11927053	C₂	semidirect
19. #123×D₁₉	C₂	semidirect
20. #11927025	C₂	semidirect
21. #11927018	C₂	semidirect
22. C₄×D₄×D₁₉	C₂	semidirect
23. C₁₉×#553	C₂	semidirect
27. C₂×#64541	C₂²	semidirect
29. C₂²×C₄×D₁₉	C₂²	semidirect
30. C₁₉×#126	C₂²	semidirect
31. C₁₉×#125	C₂²	semidirect
32. C₁₉×#123	C₂²	semidirect
34. C₁₉×#121	C₂²	semidirect
35. C₁₉×#121	C₂²	semidirect
36. C₄×D₄×C₁₉	C₂²	semidirect
37. C₄×D₄×C₁₉	C₂²	semidirect
38. C₄×D₄×C₁₉	C₂²	semidirect
39. C₁₉×#117	C₂²	semidirect
40. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
42. #10597385	C₂²	semidirect
44. #10597384	C₂²	semidirect
45. #10597384	C₂²	semidirect
47. #10597383	C₂²	semidirect
48. #10597383	C₂²	semidirect
49. #10597382	C₂²	semidirect
50. #10597382	C₂²	semidirect
51. #10597382	C₂²	semidirect
52. #10597381	C₂²	semidirect
53. D₄×Dic₁₉	C₂²	semidirect
54. #10597376	C₂²	semidirect
55. #10597375	C₂²	semidirect
56. #10597375	C₂²	semidirect
58. C₄×C₂²⋊D₁₉	C₂²	semidirect
59. C₄×C₂²⋊D₁₉	C₂²	semidirect
60. C₄×C₂²⋊D₁₉	C₂²	semidirect
61. C₄×C₂²⋊D₁₉	C₂²	semidirect
62. C₄×C₂²⋊D₁₉	C₂²	semidirect
63. #10597372	C₂²	semidirect
64. #10597372	C₂²	semidirect
65. #10597370	C₂²	semidirect
66. #10597344	C₂²	semidirect
67. #10597343	C₂²	semidirect
68. #10597343	C₂²	semidirect
69. #10597343	C₂²	semidirect
70. #10597342	C₂²	semidirect
71. #10597342	C₂²	semidirect
72. #10597342	C₂²	semidirect
74. #10597340	C₂²	semidirect
75. #10597340	C₂²	semidirect
76. #10597340	C₂²	semidirect
80. #10597339	C₂²	semidirect
81. #10597339	C₂²	semidirect
82. #10597339	C₂²	semidirect
83. #10597338	C₂²	semidirect
84. #10597338	C₂²	semidirect
85. C₄⋊C₄×D₁₉	C₂²	semidirect
86. C₄⋊C₄×D₁₉	C₂²	semidirect
87. C₄⋊C₄×D₁₉	C₂²	semidirect
88. #10597336	C₂²	semidirect
89. #10597336	C₂²	semidirect
90. #10597334	C₂²	semidirect
91. #10597333	C₂²	semidirect
92. #10597333	C₂²	semidirect
93. #10597332	C₂²	semidirect
94. #10597331	C₂²	semidirect
96. #10597330	C₂²	semidirect
99. #10597329	C₂²	semidirect
100. #10597329	C₂²	semidirect
101. #10597329	C₂²	semidirect
102. #10597329	C₂²	semidirect
104. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
105. C₂²⋊C₄×D₁₉	C₂²	semidirect
106. C₂²⋊C₄×D₁₉	C₂²	semidirect
107. C₂²⋊C₄×D₁₉	C₂²	semidirect
108. C₂²⋊C₄×D₁₉	C₂²	semidirect
109. C₂²⋊C₄×D₁₉	C₂²	semidirect
110. #10597325	C₂²	semidirect
111. #10597325	C₂²	semidirect
112. #10597325	C₂²	semidirect
113. #10597325	C₂²	semidirect
114. #10597324	C₂²	semidirect
115. #10597321	C₂²	semidirect
117. C₄×D₇₆	C₂²	semidirect
118. C₄×D₇₆	C₂²	semidirect
119. #10597318	C₂²	semidirect
120. C₄²×D₁₉	C₂²	semidirect
121. #10597316	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
276. D₇₆	#41	semidirect
333. #553	D₁₉	semidirect
375. #126	C₂×D₁₉	semidirect
379. #125	C₂×D₁₉	semidirect
398. #123	C₂×D₁₉	semidirect
416. #121	C₂×D₁₉	semidirect
417. #121	C₂×D₁₉	semidirect
442. C₄×D₄	C₂×D₁₉	semidirect
443. C₄×D₄	C₂×D₁₉	semidirect
444. C₄×D₄	C₂×D₁₉	semidirect
450. #117	C₂×D₁₉	semidirect
454. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
461. C₁₉	#3513	semidirect

Maximal subgroups

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

subgroup	index
#11927277	2
#11927250	2
#11927244	2
#11927233	2
#11927222	2
#11927219	2
#11927195	2
#11927191	2
#11927190	2
#11927178	2
#11927161	2
#11927147	2
#11927135	2
#11927126	2
#11927079	2
#11927076	2
#11927053	2
#123×D₁₉	2
#11927025	2
#11927018	2
C₄×D₄×D₁₉	2
C₁₉×#553	2
#3513	19