Subgroups — #14577916

Order 2432.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927295	C₂	1	2	yes	maximal, complemented
2	#11927289	C₂	1	2	yes	maximal, complemented
3	#11927265	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927249	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927248	C₂	1	2	yes	maximal, complemented
6	#11927241	C₂	1	2	yes	maximal, complemented
7	#11927241	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927229	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927207	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927201	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927200	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927193	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927161	C₂	1	2	yes	maximal, complemented
14	#11927161	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927154	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927139	C₂	1	2	yes	maximal, complemented
17	#11927126	C₂	1	2	yes	maximal, complemented
18	#11927126	C₂	1	2	yes	maximal, complemented
19	#11927115	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927054	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927051	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#537	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
27	C₂×#64543	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₁₉×#121	C₂²	1	1	yes	characteristic
34	C₁₉×#121	C₂²	1	2	yes	—
35	C₁₉×#121	C₂²	1	2	yes	—
36	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#121	C₂²	1	2	yes	complemented
38	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	#10597392	C₂²	1	1	yes	characteristic
40	#10597392	C₂²	1	1	yes	characteristic
41	#10597392	C₂²	1	1	yes	characteristic
42	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
43	#10597390	C₂²	1	2	yes	complemented
44	#10597390	C₂²	1	1	yes	characteristic, complemented
45	#10597385	C₂²	1	2	yes	—
46	#10597385	C₂²	1	2	yes	—
47	#10597384	C₂²	1	1	yes	characteristic
48	#10597384	C₂²	1	1	yes	characteristic
49	#10597384	C₂²	1	1	yes	characteristic
50	#10597384	C₂²	1	2	yes	—
51	#10597384	C₂²	1	2	yes	—
52	#10597383	C₂²	1	1	yes	characteristic
53	#10597383	C₂²	1	1	yes	characteristic
54	#10597383	C₂²	1	2	yes	—
55	#10597382	C₂²	1	2	yes	—
56	#10597382	C₂²	1	2	yes	—
57	#10597382	C₂²	1	1	yes	characteristic, complemented
58	#10597382	C₂²	1	2	yes	complemented
59	#10597381	C₂²	1	1	yes	characteristic
60	#10597381	C₂²	1	1	yes	characteristic
61	#10597381	C₂²	1	2	yes	—
62	#10597381	C₂²	1	2	yes	—
63	#10597381	C₂²	1	2	yes	complemented
64	#10597381	C₂²	1	2	yes	complemented
65	#10597381	C₂²	1	2	yes	complemented
66	D₄×Dic₁₉	C₂²	1	2	yes	—
67	D₄×Dic₁₉	C₂²	1	2	yes	complemented
68	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
69	#10597375	C₂²	1	2	yes	—
70	#10597375	C₂²	1	2	yes	—
71	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
76	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
77	#10597372	C₂²	1	1	yes	characteristic
78	#10597372	C₂²	1	1	yes	characteristic, complemented
79	#10597372	C₂²	1	2	yes	complemented
80	#10597370	C₂²	1	1	yes	characteristic
81	#10597370	C₂²	1	1	yes	characteristic
82	#10597370	C₂²	1	1	yes	characteristic, complemented
83	#10597370	C₂²	1	1	yes	characteristic, complemented
84	#10597370	C₂²	1	2	yes	complemented
85	#10597370	C₂²	1	2	yes	complemented
86	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
87	#10597344	C₂²	1	2	yes	—
88	#10597344	C₂²	1	2	yes	—
89	#10597343	C₂²	1	1	yes	characteristic
90	#10597343	C₂²	1	1	yes	characteristic
91	#10597342	C₂²	1	2	yes	—
92	#10597342	C₂²	1	2	yes	—
93	#10597342	C₂²	1	2	yes	—
94	#10597338	C₂²	1	1	yes	characteristic
95	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
96	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
97	#10597336	C₂²	1	1	yes	characteristic, complemented
98	#10597336	C₂²	1	2	yes	complemented
99	#10597335	C₂²	1	2	yes	complemented
100	#10597335	C₂²	1	2	yes	complemented
101	#10597335	C₂²	1	2	yes	complemented
102	#10597334	C₂²	1	2	yes	complemented
103	#10597334	C₂²	1	1	yes	characteristic, complemented
104	#10597333	C₂²	1	1	yes	characteristic, complemented
105	#10597333	C₂²	1	1	yes	characteristic, complemented
106	#10597333	C₂²	1	2	yes	complemented
107	#10597331	C₂²	1	2	yes	—
108	#10597331	C₂²	1	2	yes	—
109	#10597329	C₂²	1	2	yes	—
110	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
111	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
112	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
113	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
114	#10597325	C₂²	1	2	yes	—
115	#10597325	C₂²	1	2	yes	—
116	#10597325	C₂²	1	2	yes	complemented
117	#10597325	C₂²	1	2	yes	complemented
118	#10597325	C₂²	1	2	yes	complemented
119	#10597324	C₂²	1	2	yes	—
120	#10597324	C₂²	1	2	yes	complemented
121	#10597324	C₂²	1	2	yes	complemented
122	#10597324	C₂²	1	2	yes	complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	#41×C₁₉	—	4	2	no	—
125	#41×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₉	C₂³	1	2	yes	—
130	C₂×D₄×C₁₉	C₂³	1	2	yes	—
131	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₉	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	1	yes	characteristic
143	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
146	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₉	C₂³	1	2	yes	—
148	C₂²×Dic₁₉	C₂³	1	2	yes	—
149	C₂²×Dic₁₉	C₂³	1	2	yes	—
150	Q₈×D₁₉	—	4	2	no	—
151	#64543	—	4	2	no	—
152	C₂×C₄×D₁₉	—	4	2	no	—
153	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₉	C₂³	1	2	yes	—
158	C₂×C₄×D₁₉	C₂³	1	2	yes	—
159	C₂×Dic₃₈	—	4	2	no	—
160	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
161	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
162	C₂×Dic₃₈	C₂³	1	2	yes	—
163	C₂×Dic₃₈	C₂³	1	2	yes	—
164	C₂×Dic₃₈	C₂³	1	2	yes	—
165	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₉	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	1	yes	characteristic
184	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
189	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
197	C₄⋊Dic₁₉	C₂³	1	2	yes	—
198	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₉	C₂³	1	2	yes	—
200	C₄⋊Dic₁₉	C₂³	1	2	yes	—
201	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
206	Dic₁₉⋊C₄	C₂³	1	2	yes	—
207	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	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	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	2	yes	—
222	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
228	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₉	C₂⁴	1	2	yes	—
232	C₂²×D₁₉	—	2	2	no	—
233	C₂²×D₁₉	—	4	1	no	—
234	C₂²×D₁₉	—	4	1	no	—
235	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₉	—	2	2	no	—
238	Q₈×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	2	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	1	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	1	no	—
245	D₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
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	C₂²⋊D₁₉	—	2	2	no	—
259	C₂²⋊D₁₉	—	2	4	no	—
260	C₂²⋊D₁₉	—	2	2	no	—
261	C₂²⋊D₁₉	—	4	2	no	—
262	C₂²⋊D₁₉	—	4	1	no	—
263	C₂²⋊D₁₉	—	4	1	no	—
264	C₂×Dic₁₉	—	4	2	no	—
265	C₂×Dic₁₉	—	4	1	no	—
266	C₂×Dic₁₉	—	4	2	no	—
267	C₂×Dic₁₉	—	4	2	no	—
268	C₂×Dic₁₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₉	C₂⁴	1	2	yes	—
275	C₂×Dic₁₉	C₂⁴	1	2	yes	—
276	C₂×Dic₁₉	C₂⁴	1	2	yes	—
277	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
278	C₄×D₁₉	—	2	2	no	—
279	C₄×D₁₉	—	2	2	no	—
280	C₄×D₁₉	—	4	1	no	—
281	C₄×D₁₉	—	4	1	no	—
282	C₄×D₁₉	—	4	2	no	—
283	C₄×D₁₉	—	4	2	no	—
284	Dic₃₈	—	2	2	no	—
285	Dic₃₈	—	2	2	no	—
286	Dic₃₈	—	4	2	no	—
287	Dic₃₈	—	4	2	no	—
288	Dic₃₈	—	4	2	no	—
289	#3541	—	19	1	no	maximal, Sylow
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	2	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	—	2	1	no	—
302	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
303	C₂×D₁₉	—	2	1	no	—
304	C₂×D₁₉	—	2	1	no	—
305	C₂×D₁₉	—	2	1	no	—
306	C₂×D₁₉	—	2	1	no	—
307	C₂×D₁₉	—	2	1	no	—
308	C₂×D₁₉	—	4	4	no	—
309	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
310	C₄×C₁₉	—	2	1	no	—
311	C₄×C₁₉	—	2	2	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	2	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
317	Dic₁₉	—	2	2	no	—
318	Dic₁₉	—	2	2	no	—
319	Dic₁₉	—	2	1	no	—
320	Dic₁₉	—	2	1	no	—
321	Dic₁₉	—	2	2	no	—
322	Dic₁₉	—	2	1	no	—
323	Dic₁₉	—	2	1	no	—
324	Dic₁₉	—	2	1	no	—
325	Dic₁₉	—	2	2	no	—
326	Dic₁₉	—	2	1	no	—
327	#563	—	19	2	no	—
328	#562	—	19	2	no	—
329	#556	—	19	1	no	—
330	#554	—	19	2	no	—
331	#554	—	19	1	no	—
332	#553	—	19	1	no	—
333	#553	—	19	2	no	—
334	#552	—	19	1	no	—
335	D₄×Q₈	—	19	1	no	—
336	#548	—	19	1	no	—
337	#548	—	19	1	no	—
338	#547	—	19	1	no	—
339	#542	—	19	1	no	—
340	#542	—	19	2	no	—
341	#541	—	19	1	no	—
342	#539	—	19	2	no	—
343	#538	—	19	2	no	—
344	#538	—	19	2	no	—
345	#537	D₁₉	1	1	yes	characteristic, complemented
346	#536	—	19	1	no	—
347	#525	—	19	1	no	—
348	#525	—	19	1	no	—
349	C₂×C₂²⋊Q₈	—	19	1	no	—
350	C₂×C₁₉	—	4	1	no	—
351	C₂×C₁₉	—	4	1	no	—
352	C₂×C₁₉	—	4	2	no	—
353	C₂×C₁₉	—	4	1	no	—
354	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂×C₁₉	#585	1	1	yes	characteristic
357	D₁₉	—	2	2	no	—
358	D₁₉	—	4	1	no	—
359	C₂×#41	—	19	1	no	—
360	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
361	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
362	C₂²×Q₈	—	19	1	no	—
363	C₂²×Q₈	—	19	1	no	—
364	C₂³×C₄	—	19	1	no	—
365	C₄⋊Q₈	—	19	2	no	—
366	C₄⋊Q₈	—	19	1	no	—
367	C₄⋊Q₈	—	19	2	no	—
368	C₄⋊Q₈	—	19	1	no	—
369	#126	—	19	2	no	—
370	#126	—	19	2	no	—
371	#126	—	19	2	no	—
372	#126	—	19	2	no	—
373	#126	—	19	2	no	—
374	#126	—	19	2	no	—
375	#126	—	19	2	no	—
376	#125	—	19	2	no	—
377	#125	—	19	2	no	—
378	#125	—	19	1	no	—
379	#125	—	19	2	no	—
380	#125	—	19	2	no	—
381	#124	—	19	2	no	—
382	#124	—	19	2	no	—
383	#124	—	19	1	no	—
384	#124	—	19	2	no	—
385	#124	—	19	2	no	—
386	#124	—	19	2	no	—
387	#123	—	19	1	no	—
388	#123	—	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	1	no	—
398	C₂²⋊Q₈	—	19	1	no	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	1	no	—
401	C₂²⋊Q₈	—	19	1	no	—
402	C₂²⋊Q₈	—	19	1	no	—
403	C₂²⋊Q₈	—	19	1	no	—
404	C₂²⋊Q₈	—	19	2	no	—
405	C₂²⋊Q₈	—	19	2	no	—
406	C₂²⋊Q₈	—	19	1	no	—
407	C₂²⋊Q₈	—	19	2	no	—
408	C₂²⋊Q₈	—	19	1	no	—
409	C₂²⋊Q₈	—	19	2	no	—
410	C₂²⋊Q₈	—	19	2	no	—
411	C₂²⋊Q₈	—	19	2	no	—
412	C₂²⋊Q₈	—	19	2	no	—
413	C₂²⋊Q₈	—	19	2	no	—
414	C₂²⋊Q₈	—	19	2	no	—
415	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
416	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
418	#121	—	19	1	no	—
419	#121	—	19	1	no	—
420	#121	—	19	1	no	—
421	#121	—	19	2	no	—
422	#121	—	19	2	no	—
423	#121	—	19	2	no	—
424	#121	—	19	2	no	—
425	#121	C₂×D₁₉	1	1	yes	characteristic
426	#121	C₂×D₁₉	1	2	yes	—
427	#121	C₂×D₁₉	1	2	yes	—
428	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
429	#121	C₂×D₁₉	1	2	yes	complemented
430	#120	—	19	1	no	—
431	#120	—	19	1	no	—
432	#120	—	19	2	no	—
433	C₄×Q₈	—	19	1	no	—
434	C₄×Q₈	—	19	1	no	—
435	C₄×Q₈	—	19	1	no	—
436	C₄×Q₈	—	19	2	no	—
437	C₄×D₄	—	19	2	no	—
438	C₄×D₄	—	19	2	no	—
439	C₄×D₄	—	19	1	no	—
440	C₄×D₄	—	19	1	no	—
441	C₄×D₄	—	19	1	no	—
442	C₄×D₄	—	19	1	no	—
443	C₄×D₄	—	19	1	no	—
444	C₄×D₄	—	19	2	no	—
445	C₄×D₄	—	19	2	no	—
446	C₄×D₄	—	19	2	no	—
447	C₄×D₄	—	19	2	no	—
448	C₄×D₄	—	19	2	no	—
449	#117	—	19	1	no	—
450	#117	—	19	1	no	—
451	#117	—	19	2	no	—
452	#117	—	19	1	no	—
453	C₂×C₄⋊C₄	—	19	2	no	—
454	C₂×C₄⋊C₄	—	19	2	no	—
455	C₂×C₄⋊C₄	—	19	1	no	—
456	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
457	C₂×C₂²⋊C₄	—	19	2	no	—
458	C₁₉	#3541	1	1	yes	characteristic, complemented, Sylow
459	C₂⁴	—	19	1	no	—
460	#41	—	4	2	no	—
461	#41	—	4	2	no	—
462	#41	—	76	2	no	—
463	C₂×Q₈	—	19	1	no	—
464	C₂×Q₈	—	19	1	no	—
465	C₂×Q₈	—	19	2	no	—
466	C₂×Q₈	—	19	2	no	—
467	C₂×Q₈	—	19	2	no	—
468	C₂×Q₈	—	76	2	no	—
469	C₂×Q₈	—	76	2	no	—
470	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
472	C₂×D₄	—	19	1	no	—
473	C₂×D₄	—	19	1	no	—
474	C₂×D₄	—	19	2	no	—
475	C₂×D₄	—	19	1	no	—
476	C₂×D₄	—	19	1	no	—
477	C₂×D₄	—	19	2	no	—
478	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₁₉	1	2	yes	—
480	C₂×D₄	C₂²×D₁₉	1	2	yes	—
481	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₉	1	2	yes	—
484	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
485	C₂²×C₄	—	19	2	no	—
486	C₂²×C₄	—	19	2	no	—
487	C₂²×C₄	—	19	2	no	—
488	C₂²×C₄	—	19	1	no	—
489	C₂²×C₄	—	19	1	no	—
490	C₂²×C₄	—	19	1	no	—
491	C₂²×C₄	—	19	2	no	—
492	C₂²×C₄	—	19	2	no	—
493	C₂²×C₄	—	19	1	no	—
494	C₂²×C₄	—	19	1	no	—
495	C₂²×C₄	—	76	2	no	—
496	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
500	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
501	C₄⋊C₄	—	19	1	no	—
502	C₄⋊C₄	—	19	2	no	—
503	C₄⋊C₄	—	19	2	no	—
504	C₄⋊C₄	—	19	2	no	—
505	C₄⋊C₄	—	19	2	no	—
506	C₄⋊C₄	—	19	2	no	—
507	C₄⋊C₄	—	19	1	no	—
508	C₄⋊C₄	—	19	1	no	—
509	C₄⋊C₄	—	19	2	no	—
510	C₄⋊C₄	—	19	2	no	—
511	C₄⋊C₄	—	19	1	no	—
512	C₄⋊C₄	—	19	2	no	—
513	C₄⋊C₄	—	19	2	no	—
514	C₄⋊C₄	—	19	2	no	—
515	C₄⋊C₄	—	19	2	no	—
516	C₄⋊C₄	—	19	2	no	—
517	C₄⋊C₄	—	19	2	no	—
518	C₄⋊C₄	—	19	1	no	—
519	C₄⋊C₄	—	19	1	no	—
520	C₄⋊C₄	—	19	1	no	—
521	C₄⋊C₄	—	19	1	no	—
522	C₄⋊C₄	—	19	2	no	—
523	C₄⋊C₄	—	19	2	no	—
524	C₄⋊C₄	—	19	2	no	—
525	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
530	C₂²⋊C₄	—	19	2	no	—
531	C₂²⋊C₄	—	19	1	no	—
532	C₂²⋊C₄	—	19	1	no	—
533	C₂²⋊C₄	—	19	1	no	—
534	C₂²⋊C₄	—	19	2	no	—
535	C₂²⋊C₄	—	19	2	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	1	no	—
550	C₂²⋊C₄	—	19	2	no	—
551	C₂²⋊C₄	—	19	1	no	—
552	C₂²⋊C₄	—	19	1	no	—
553	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
557	C₄²	—	19	2	no	—
558	C₄²	—	19	1	no	—
559	C₄²	—	19	1	no	—
560	C₄²	—	19	2	no	—
561	C₄²	—	19	2	no	—
562	C₄²	—	19	2	no	—
563	C₄²	—	19	2	no	—
564	C₂³	—	19	1	no	—
565	C₂³	—	19	1	no	—
566	C₂³	—	38	2	no	—
567	C₂³	—	76	1	no	—
568	C₂³	—	76	1	no	—
569	C₂³	C₂³×D₁₉	1	1	yes	characteristic
570	C₂³	C₂³×D₁₉	1	1	yes	characteristic
571	C₂³	C₂³×D₁₉	1	1	yes	characteristic
572	C₂³	C₂³×D₁₉	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	38	2	no	—
576	Q₈	—	38	2	no	—
577	Q₈	—	76	2	no	—
578	Q₈	—	76	2	no	—
579	Q₈	—	76	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	38	2	no	—
588	D₄	—	38	2	no	—
589	D₄	—	38	4	no	—
590	D₄	—	76	2	no	—
591	D₄	—	76	1	no	—
592	D₄	—	76	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	19	2	no	—
599	C₂×C₄	—	19	1	no	—
600	C₂×C₄	—	19	1	no	—
601	C₂×C₄	—	19	1	no	—
602	C₂×C₄	—	19	1	no	—
603	C₂×C₄	—	19	2	no	—
604	C₂×C₄	—	19	2	no	—
605	C₂×C₄	—	19	1	no	—
606	C₂×C₄	—	19	2	no	—
607	C₂×C₄	—	19	1	no	—
608	C₂×C₄	—	38	2	no	—
609	C₂×C₄	—	38	2	no	—
610	C₂×C₄	—	76	1	no	—
611	C₂×C₄	—	76	1	no	—
612	C₂×C₄	—	76	2	no	—
613	C₂×C₄	—	76	2	no	—
614	C₂×C₄	—	76	1	no	—
615	C₂×C₄	—	76	2	no	—
616	C₂×C₄	—	76	2	no	—
617	C₂×C₄	—	76	2	no	—
618	C₂×C₄	C₂³×D₁₉	1	2	yes	—
619	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₉	1	2	yes	—
621	C₂×C₄	C₂³×D₁₉	1	2	yes	—
622	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	19	2	no	—
638	C₂²	—	38	1	no	—
639	C₂²	—	38	1	no	—
640	C₂²	—	38	1	no	—
641	C₂²	—	38	1	no	—
642	C₂²	—	38	1	no	—
643	C₂²	—	76	4	no	—
644	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	38	1	no	—
652	C₄	—	38	1	no	—
653	C₄	—	38	2	no	—
654	C₄	—	38	2	no	—
655	C₄	—	38	2	no	—
656	C₄	—	38	1	no	—
657	C₄	—	38	1	no	—
658	C₄	—	38	1	no	—
659	C₄	—	38	2	no	—
660	C₄	—	38	1	no	—
661	C₄	#10597430	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	2	no	—
666	C₂	—	38	2	no	—
667	C₂	—	76	1	no	—
668	C₂	C₂×#10597430	1	1	yes	characteristic
669	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
670	C₂	#11927379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#537	C₂
hypercenter	#537	D₁₉
hypocenter	C₁₉	#3541
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. #11927295	C₂	semidirect
2. #11927289	C₂	semidirect
3. #11927265	C₂	semidirect
4. #11927249	C₂	semidirect
5. #11927248	C₂	semidirect
6. #11927241	C₂	semidirect
7. #11927241	C₂	semidirect
8. #11927229	C₂	semidirect
9. #11927207	C₂	semidirect
10. #11927201	C₂	semidirect
11. #11927200	C₂	semidirect
12. #11927193	C₂	semidirect
13. #11927161	C₂	semidirect
14. #11927161	C₂	semidirect
15. #11927154	C₂	semidirect
16. #11927139	C₂	semidirect
17. #11927126	C₂	semidirect
18. #11927126	C₂	semidirect
19. #11927115	C₂	semidirect
20. #11927054	C₂	semidirect
21. #11927051	C₂	semidirect
22. C₂²⋊Q₈×D₁₉	C₂	semidirect
23. C₁₉×#537	C₂	semidirect
25. C₂×#41×C₁₉	C₂²	semidirect
29. C₂²×Dic₃₈	C₂²	semidirect
31. C₁₉×C₂²⋊Q₈	C₂²	semidirect
32. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₁₉×#121	C₂²	semidirect
37. C₁₉×#121	C₂²	semidirect
38. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
42. Q₈×Dic₁₉	C₂²	semidirect
43. #10597390	C₂²	semidirect
44. #10597390	C₂²	semidirect
57. #10597382	C₂²	semidirect
58. #10597382	C₂²	semidirect
63. #10597381	C₂²	semidirect
64. #10597381	C₂²	semidirect
65. #10597381	C₂²	semidirect
67. D₄×Dic₁₉	C₂²	semidirect
68. D₄×Dic₁₉	C₂²	semidirect
78. #10597372	C₂²	semidirect
79. #10597372	C₂²	semidirect
82. #10597370	C₂²	semidirect
83. #10597370	C₂²	semidirect
84. #10597370	C₂²	semidirect
85. #10597370	C₂²	semidirect
86. C₂×Dic₁₉⋊C₄	C₂²	semidirect
97. #10597336	C₂²	semidirect
98. #10597336	C₂²	semidirect
99. #10597335	C₂²	semidirect
100. #10597335	C₂²	semidirect
101. #10597335	C₂²	semidirect
102. #10597334	C₂²	semidirect
103. #10597334	C₂²	semidirect
104. #10597333	C₂²	semidirect
105. #10597333	C₂²	semidirect
106. #10597333	C₂²	semidirect
116. #10597325	C₂²	semidirect
117. #10597325	C₂²	semidirect
118. #10597325	C₂²	semidirect
120. #10597324	C₂²	semidirect
121. #10597324	C₂²	semidirect
122. #10597324	C₂²	semidirect
345. #537	D₁₉	semidirect
361. C₂×#41	C₂×D₁₉	semidirect
416. C₂²⋊Q₈	C₂×D₁₉	semidirect
417. C₂²⋊Q₈	C₂×D₁₉	semidirect
428. #121	C₂×D₁₉	semidirect
429. #121	C₂×D₁₉	semidirect
456. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
458. C₁₉	#3541	semidirect

Maximal subgroups

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

subgroup	index
#11927295	2
#11927289	2
#11927265	2
#11927249	2
#11927248	2
#11927241	2
#11927229	2
#11927207	2
#11927201	2
#11927200	2
#11927193	2
#11927161	2
#11927154	2
#11927139	2
#11927126	2
#11927115	2
#11927054	2
#11927051	2
C₂²⋊Q₈×D₁₉	2
C₁₉×#537	2
#3541	19