Subgroups — #14577697

Order 2432.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927265	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927263	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927250	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927244	C₂	1	2	yes	maximal, complemented
5	#11927241	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927233	C₂	1	2	yes	maximal, complemented
7	#11927232	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927223	C₂	1	2	yes	maximal, complemented
9	#11927218	C₂	1	2	yes	maximal, complemented
10	#11927196	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927191	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927187	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927159	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927152	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927137	C₂	1	2	yes	maximal, complemented
16	#11927130	C₂	1	2	yes	maximal, complemented
17	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927077	C₂	1	2	yes	maximal, complemented
19	#126×D₁₉	C₂	1	2	yes	maximal, complemented
20	#11927026	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927016	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#64541	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#64545	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
26	C₂×#64541	C₂²	1	1	yes	characteristic
27	C₁₉×#126	C₂²	1	2	yes	complemented
28	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#124	C₂²	1	1	yes	characteristic
30	C₁₉×#123	C₂²	1	2	yes	complemented
31	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#121	C₂²	1	1	yes	characteristic
33	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
36	C₁₉×#117	C₂²	1	2	yes	complemented
37	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	#10597392	C₂²	1	1	yes	characteristic
39	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
40	#10597390	C₂²	1	1	yes	characteristic, complemented
41	#10597384	C₂²	1	2	yes	—
42	#10597384	C₂²	1	1	yes	characteristic
43	#10597384	C₂²	1	2	yes	complemented
44	#10597383	C₂²	1	2	yes	—
45	#10597382	C₂²	1	1	yes	characteristic
46	#10597381	C₂²	1	2	yes	complemented
47	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
48	#10597376	C₂²	1	1	yes	characteristic
49	#10597375	C₂²	1	1	yes	characteristic
50	#10597375	C₂²	1	1	yes	characteristic, complemented
51	#10597375	C₂²	1	2	yes	complemented
52	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
57	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
58	#10597372	C₂²	1	1	yes	characteristic, complemented
59	#10597370	C₂²	1	1	yes	characteristic, complemented
60	#10597370	C₂²	1	2	yes	complemented
61	#10597344	C₂²	1	2	yes	—
62	#10597344	C₂²	1	2	yes	—
63	#10597344	C₂²	1	2	yes	—
64	#10597343	C₂²	1	1	yes	characteristic
65	#10597343	C₂²	1	2	yes	complemented
66	#10597343	C₂²	1	1	yes	characteristic, complemented
67	#10597342	C₂²	1	2	yes	complemented
68	#10597342	C₂²	1	2	yes	complemented
69	#10597340	C₂²	1	2	yes	—
70	#10597340	C₂²	1	2	yes	complemented
71	#10597339	C₂²	1	1	yes	characteristic
72	#10597339	C₂²	1	1	yes	characteristic
73	#10597339	C₂²	1	2	yes	complemented
74	#10597338	C₂²	1	1	yes	characteristic
75	#10597338	C₂²	1	2	yes	complemented
76	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
78	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
80	#10597336	C₂²	1	2	yes	complemented
81	#10597336	C₂²	1	1	yes	characteristic, complemented
82	#10597335	C₂²	1	2	yes	complemented
83	#10597334	C₂²	1	1	yes	characteristic, complemented
84	#10597333	C₂²	1	2	yes	complemented
85	#10597331	C₂²	1	2	yes	—
86	#10597331	C₂²	1	2	yes	complemented
87	#10597330	C₂²	1	2	yes	—
88	#10597330	C₂²	1	2	yes	complemented
89	#10597329	C₂²	1	2	yes	—
90	#10597329	C₂²	1	2	yes	—
91	#10597329	C₂²	1	2	yes	complemented
92	#10597328	C₂²	1	2	yes	—
93	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
98	#10597325	C₂²	1	2	yes	complemented
99	#10597325	C₂²	1	2	yes	complemented
100	#10597325	C₂²	1	2	yes	complemented
101	#10597325	C₂²	1	2	yes	complemented
102	#10597325	C₂²	1	2	yes	complemented
103	#10597324	C₂²	1	2	yes	complemented
104	#10597323	C₂²	1	2	yes	complemented
105	#10597322	C₂²	1	1	yes	characteristic
106	#10597322	C₂²	1	2	yes	—
107	#10597322	C₂²	1	1	yes	characteristic, complemented
108	#10597321	C₂²	1	1	yes	characteristic
109	C₄×D₇₆	C₂²	1	1	yes	characteristic
110	C₄×D₇₆	C₂²	1	1	yes	characteristic
111	C₄×D₇₆	C₂²	1	1	yes	characteristic
112	C₄×D₇₆	C₂²	1	2	yes	complemented
113	#10597318	C₂²	1	1	yes	characteristic
114	#10597318	C₂²	1	1	yes	characteristic, complemented
115	#10597318	C₂²	1	2	yes	complemented
116	#10597318	C₂²	1	2	yes	complemented
117	C₄²×D₁₉	C₂²	1	2	yes	complemented
118	#10597316	C₂²	1	1	yes	characteristic, complemented
119	#10597316	C₂²	1	2	yes	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	C₂³×D₁₉	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₉	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
136	C₂²×Dic₁₉	C₂³	1	2	yes	—
137	#64545	—	2	4	no	—
138	D₄×D₁₉	—	2	4	no	—
139	#64541	—	2	4	no	—
140	C₂×D₇₆	C₂³	1	2	yes	—
141	C₂×D₇₆	C₂³	1	1	yes	characteristic
142	C₂×D₇₆	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₉	C₂³	1	2	yes	—
150	C₂×C₄×D₁₉	C₂³	1	2	yes	—
151	C₂×C₄×D₁₉	C₂³	1	2	yes	—
152	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
153	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
154	C₂×Dic₃₈	C₂³	1	2	yes	—
155	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₄²×C₁₉	C₂³	1	1	yes	characteristic
167	C₄²×C₁₉	C₂³	1	1	yes	characteristic
168	C₄²×C₁₉	C₂³	1	1	yes	characteristic
169	C₄²×C₁₉	C₂³	1	1	yes	characteristic
170	C₄²×C₁₉	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
178	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₉	C₂³	1	2	yes	—
198	C₄⋊Dic₁₉	C₂³	1	2	yes	—
199	C₄⋊Dic₁₉	C₂³	1	2	yes	—
200	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₉	C₂³	1	2	yes	—
202	Dic₁₉⋊C₄	C₂³	1	2	yes	—
203	Dic₁₉⋊C₄	C₂³	1	2	yes	—
204	Dic₁₉⋊C₄	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
206	Dic₁₉⋊C₄	C₂³	1	2	yes	—
207	Dic₁₉⋊C₄	C₂³	1	2	yes	—
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	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	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₉	C₂³	1	2	yes	—
221	C₄×Dic₁₉	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	2	yes	—
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₂³×C₁₉	C₂⁴	1	2	yes	—
226	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₉	—	2	4	no	—
228	C₂²×D₁₉	—	4	2	no	—
229	C₂²×D₁₉	—	4	2	no	—
230	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₉	C₂⁴	1	2	yes	—
233	Q₈×C₁₉	—	2	2	no	—
234	D₄×C₁₉	—	2	2	no	—
235	D₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₉	—	2	4	no	—
250	C₂²⋊D₁₉	—	2	4	no	—
251	C₂²⋊D₁₉	—	4	1	no	—
252	C₂²⋊D₁₉	—	4	2	no	—
253	C₂²⋊D₁₉	—	4	1	no	—
254	C₂×Dic₁₉	—	4	2	no	—
255	C₂×Dic₁₉	C₂⁴	1	2	yes	—
256	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₉	C₂⁴	1	2	yes	—
259	C₂×Dic₁₉	C₂⁴	1	2	yes	—
260	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
264	D₇₆	—	2	4	no	—
265	D₇₆	—	4	1	no	—
266	D₇₆	#41	1	4	yes	—
267	C₄×D₁₉	—	2	4	no	—
268	C₄×D₁₉	—	2	4	no	—
269	C₄×D₁₉	—	2	2	no	—
270	C₄×D₁₉	—	2	2	no	—
271	C₄×D₁₉	—	4	2	no	—
272	C₄×D₁₉	—	4	2	no	—
273	C₄×D₁₉	—	4	2	no	—
274	C₄×D₁₉	—	4	2	no	—
275	C₄×D₁₉	—	4	2	no	—
276	Dic₃₈	—	2	2	no	—
277	Dic₃₈	—	4	2	no	—
278	Dic₃₈	—	4	1	no	—
279	#3521	—	19	1	no	maximal, Sylow
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	2	2	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
287	C₂×D₁₉	—	2	2	no	—
288	C₂×D₁₉	—	2	2	no	—
289	C₂×D₁₉	—	2	1	no	—
290	C₂×D₁₉	—	2	1	no	—
291	C₂×D₁₉	—	2	1	no	—
292	C₂×D₁₉	—	2	1	no	—
293	C₂×D₁₉	—	2	1	no	—
294	C₂×D₁₉	—	2	1	no	—
295	C₂×D₁₉	—	8	4	no	—
296	C₂×D₁₉	C₂×#41	1	4	yes	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	2	no	—
299	C₄×C₁₉	—	2	2	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	2	no	—
304	C₄×C₁₉	—	2	1	no	—
305	C₄×C₁₉	C₂×#41	1	2	yes	—
306	Dic₁₉	—	2	2	no	—
307	Dic₁₉	—	2	1	no	—
308	Dic₁₉	—	2	1	no	—
309	Dic₁₉	—	2	1	no	—
310	Dic₁₉	—	2	1	no	—
311	Dic₁₉	—	2	2	no	—
312	Dic₁₉	—	2	1	no	—
313	Dic₁₉	—	2	2	no	—
314	Dic₁₉	—	2	1	no	—
315	#556	—	19	1	no	—
316	#556	—	19	1	no	—
317	#554	—	19	1	no	—
318	#553	—	19	1	no	—
319	#553	—	19	2	no	—
320	#552	—	19	1	no	—
321	#552	—	19	2	no	—
322	#551	—	19	2	no	—
323	#551	—	19	2	no	—
324	#547	—	19	1	no	—
325	#546	—	19	1	no	—
326	#546	—	19	1	no	—
327	#542	—	19	1	no	—
328	#541	—	19	1	no	—
329	#539	—	19	2	no	—
330	#538	—	19	2	no	—
331	#529	—	19	2	no	—
332	#529	—	19	1	no	—
333	#529	D₁₉	1	1	yes	characteristic, complemented
334	C₂×#126	—	19	2	no	—
335	#520	—	19	1	no	—
336	#518	—	19	1	no	—
337	C₄×#41	—	19	1	no	—
338	C₂×C₁₉	—	4	2	no	—
339	C₂×C₁₉	—	4	1	no	—
340	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
341	C₂×C₁₉	#585	1	1	yes	characteristic
342	C₂×C₁₉	#585	1	1	yes	characteristic
343	D₁₉	—	2	4	no	—
344	D₁₉	—	4	1	no	—
345	D₁₉	—	4	1	no	—
346	C₂×#41	—	19	1	no	—
347	C₂×#41	—	19	1	no	—
348	C₂²×D₄	—	19	1	no	—
349	C₄⋊Q₈	—	19	1	no	—
350	C₄⋊Q₈	—	19	1	no	—
351	#126	—	19	2	no	—
352	#126	—	19	2	no	—
353	#126	—	19	2	no	—
354	#126	—	19	2	no	—
355	#126	—	19	2	no	—
356	#126	—	19	2	no	—
357	#126	—	19	2	no	—
358	#126	—	19	2	no	—
359	#126	—	19	1	no	—
360	#126	—	19	1	no	—
361	#126	—	19	2	no	—
362	#126	C₂×D₁₉	1	2	yes	complemented
363	#125	—	19	2	no	—
364	#125	—	19	2	no	—
365	#125	—	19	1	no	—
366	#125	—	19	1	no	—
367	#125	—	19	2	no	—
368	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
369	#124	—	19	1	no	—
370	#124	—	19	2	no	—
371	#124	—	19	2	no	—
372	#124	—	19	1	no	—
373	#124	C₂×D₁₉	1	1	yes	characteristic
374	#123	—	19	2	no	—
375	#123	—	19	1	no	—
376	#123	—	19	1	no	—
377	#123	—	19	2	no	—
378	#123	—	19	2	no	—
379	#123	—	19	2	no	—
380	#123	—	19	2	no	—
381	#123	—	19	2	no	—
382	#123	—	19	2	no	—
383	#123	C₂×D₁₉	1	2	yes	complemented
384	C₂²⋊Q₈	—	19	1	no	—
385	C₂²⋊Q₈	—	19	1	no	—
386	C₂²⋊Q₈	—	19	2	no	—
387	C₂²⋊Q₈	—	19	2	no	—
388	C₂²⋊Q₈	—	19	2	no	—
389	C₂²⋊Q₈	—	19	2	no	—
390	C₂²⋊Q₈	—	19	1	no	—
391	C₂²⋊Q₈	—	19	1	no	—
392	C₂²⋊Q₈	—	19	2	no	—
393	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
394	#121	—	19	2	no	—
395	#121	—	19	1	no	—
396	#121	—	19	2	no	—
397	#121	—	19	1	no	—
398	#121	—	19	2	no	—
399	#121	—	19	2	no	—
400	#121	C₂×D₁₉	1	1	yes	characteristic
401	#120	—	19	2	no	—
402	#120	—	19	2	no	—
403	C₄×Q₈	—	19	1	no	—
404	C₄×Q₈	—	19	2	no	—
405	C₄×Q₈	—	19	1	no	—
406	C₄×Q₈	—	19	1	no	—
407	C₄×Q₈	—	19	1	no	—
408	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
409	C₄×D₄	—	19	1	no	—
410	C₄×D₄	—	19	2	no	—
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	—	19	2	no	—
413	C₄×D₄	—	19	1	no	—
414	C₄×D₄	—	19	1	no	—
415	C₄×D₄	—	19	1	no	—
416	C₄×D₄	—	19	2	no	—
417	C₄×D₄	—	19	1	no	—
418	C₄×D₄	—	19	2	no	—
419	C₄×D₄	—	19	2	no	—
420	C₄×D₄	—	19	1	no	—
421	C₄×D₄	—	19	1	no	—
422	C₄×D₄	—	19	2	no	—
423	C₄×D₄	—	19	1	no	—
424	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
426	#117	—	19	1	no	—
427	#117	—	19	1	no	—
428	#117	—	19	2	no	—
429	#117	—	19	2	no	—
430	#117	—	19	2	no	—
431	#117	—	19	1	no	—
432	#117	—	19	1	no	—
433	#117	—	19	2	no	—
434	#117	C₂×D₁₉	1	2	yes	complemented
435	C₂×C₄⋊C₄	—	19	2	no	—
436	C₂×C₄⋊C₄	—	19	1	no	—
437	C₂×C₄⋊C₄	—	19	2	no	—
438	C₂×C₄⋊C₄	—	19	2	no	—
439	C₂×C₂²⋊C₄	—	19	2	no	—
440	C₂×C₂²⋊C₄	—	19	2	no	—
441	C₂×C₂²⋊C₄	—	19	2	no	—
442	C₂×C₂²⋊C₄	—	19	2	no	—
443	C₂×C₄²	—	19	2	no	—
444	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
445	C₁₉	#3521	1	1	yes	characteristic, complemented, Sylow
446	C₂⁴	—	19	2	no	—
447	#41	—	38	4	no	—
448	#41	—	38	4	no	—
449	C₂×Q₈	—	19	1	no	—
450	C₂×Q₈	—	19	1	no	—
451	C₂×Q₈	—	19	2	no	—
452	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
453	C₂×D₄	—	19	2	no	—
454	C₂×D₄	—	19	2	no	—
455	C₂×D₄	—	19	1	no	—
456	C₂×D₄	—	19	2	no	—
457	C₂×D₄	—	19	1	no	—
458	C₂×D₄	—	19	1	no	—
459	C₂×D₄	—	19	2	no	—
460	C₂×D₄	—	19	1	no	—
461	C₂×D₄	—	38	4	no	—
462	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
463	C₂×D₄	C₂²×D₁₉	1	2	yes	—
464	C₂²×C₄	—	19	2	no	—
465	C₂²×C₄	—	19	2	no	—
466	C₂²×C₄	—	19	2	no	—
467	C₂²×C₄	—	19	1	no	—
468	C₂²×C₄	—	19	1	no	—
469	C₂²×C₄	—	19	2	no	—
470	C₂²×C₄	—	19	2	no	—
471	C₂²×C₄	—	19	2	no	—
472	C₂²×C₄	—	19	2	no	—
473	C₂²×C₄	—	19	2	no	—
474	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
478	C₄⋊C₄	—	19	1	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	1	no	—
481	C₄⋊C₄	—	19	1	no	—
482	C₄⋊C₄	—	19	2	no	—
483	C₄⋊C₄	—	19	2	no	—
484	C₄⋊C₄	—	19	1	no	—
485	C₄⋊C₄	—	19	1	no	—
486	C₄⋊C₄	—	19	1	no	—
487	C₄⋊C₄	—	19	1	no	—
488	C₄⋊C₄	—	19	2	no	—
489	C₄⋊C₄	—	19	2	no	—
490	C₄⋊C₄	—	19	2	no	—
491	C₄⋊C₄	—	19	1	no	—
492	C₄⋊C₄	—	19	2	no	—
493	C₄⋊C₄	—	19	2	no	—
494	C₄⋊C₄	—	19	1	no	—
495	C₄⋊C₄	—	19	2	no	—
496	C₄⋊C₄	—	19	2	no	—
497	C₄⋊C₄	—	19	2	no	—
498	C₄⋊C₄	—	19	1	no	—
499	C₄⋊C₄	—	19	2	no	—
500	C₄⋊C₄	—	19	1	no	—
501	C₄⋊C₄	—	19	1	no	—
502	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
506	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
508	C₂²⋊C₄	—	19	2	no	—
509	C₂²⋊C₄	—	19	2	no	—
510	C₂²⋊C₄	—	19	2	no	—
511	C₂²⋊C₄	—	19	2	no	—
512	C₂²⋊C₄	—	19	2	no	—
513	C₂²⋊C₄	—	19	1	no	—
514	C₂²⋊C₄	—	19	1	no	—
515	C₂²⋊C₄	—	19	1	no	—
516	C₂²⋊C₄	—	19	2	no	—
517	C₂²⋊C₄	—	19	1	no	—
518	C₂²⋊C₄	—	19	1	no	—
519	C₂²⋊C₄	—	19	1	no	—
520	C₂²⋊C₄	—	19	2	no	—
521	C₂²⋊C₄	—	19	2	no	—
522	C₂²⋊C₄	—	19	2	no	—
523	C₂²⋊C₄	—	19	2	no	—
524	C₂²⋊C₄	—	19	1	no	—
525	C₂²⋊C₄	—	19	2	no	—
526	C₂²⋊C₄	—	19	2	no	—
527	C₂²⋊C₄	—	19	1	no	—
528	C₂²⋊C₄	—	19	1	no	—
529	C₂²⋊C₄	—	19	2	no	—
530	C₂²⋊C₄	—	19	1	no	—
531	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
536	C₄²	—	19	2	no	—
537	C₄²	—	19	2	no	—
538	C₄²	—	19	2	no	—
539	C₄²	—	19	2	no	—
540	C₄²	—	19	2	no	—
541	C₄²	—	19	1	no	—
542	C₄²	—	19	1	no	—
543	C₄²	C₂²×D₁₉	1	1	yes	characteristic
544	C₄²	C₂²×D₁₉	1	1	yes	characteristic
545	C₄²	C₂²×D₁₉	1	1	yes	characteristic
546	C₄²	C₂²×D₁₉	1	1	yes	characteristic
547	C₄²	C₂²×D₁₉	1	2	yes	—
548	C₂³	—	19	2	no	—
549	C₂³	—	19	1	no	—
550	C₂³	—	19	1	no	—
551	C₂³	—	38	4	no	—
552	C₂³	—	76	2	no	—
553	C₂³	—	76	2	no	—
554	C₂³	C₂³×D₁₉	1	2	yes	—
555	C₂³	C₂³×D₁₉	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	38	2	no	—
558	Q₈	—	76	2	no	—
559	Q₈	—	76	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	19	4	no	—
563	D₄	—	38	4	no	—
564	D₄	—	38	4	no	—
565	D₄	—	38	4	no	—
566	D₄	—	76	1	no	—
567	D₄	—	76	1	no	—
568	D₄	—	76	2	no	—
569	D₄	—	76	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	19	2	no	—
575	C₂×C₄	—	19	1	no	—
576	C₂×C₄	—	19	2	no	—
577	C₂×C₄	—	19	2	no	—
578	C₂×C₄	—	19	1	no	—
579	C₂×C₄	—	19	1	no	—
580	C₂×C₄	—	19	1	no	—
581	C₂×C₄	—	19	1	no	—
582	C₂×C₄	—	19	1	no	—
583	C₂×C₄	—	38	4	no	—
584	C₂×C₄	—	38	4	no	—
585	C₂×C₄	—	38	2	no	—
586	C₂×C₄	—	38	2	no	—
587	C₂×C₄	—	76	2	no	—
588	C₂×C₄	—	76	2	no	—
589	C₂×C₄	—	76	2	no	—
590	C₂×C₄	—	76	2	no	—
591	C₂×C₄	—	76	2	no	—
592	C₂×C₄	—	76	2	no	—
593	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₉	1	2	yes	—
597	C₂×C₄	C₂³×D₁₉	1	2	yes	—
598	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₉	1	2	yes	—
601	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
602	C₂²	—	2	1	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	19	4	no	—
609	C₂²	—	38	2	no	—
610	C₂²	—	38	2	no	—
611	C₂²	—	38	1	no	—
612	C₂²	—	38	1	no	—
613	C₂²	—	38	1	no	—
614	C₂²	—	38	1	no	—
615	C₂²	—	38	1	no	—
616	C₂²	—	38	1	no	—
617	C₂²	—	152	4	no	—
618	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	38	1	no	—
628	C₄	—	38	1	no	—
629	C₄	—	38	2	no	—
630	C₄	—	38	2	no	—
631	C₄	—	38	1	no	—
632	C₄	—	38	1	no	—
633	C₄	—	38	1	no	—
634	C₄	—	38	2	no	—
635	C₄	—	38	1	no	—
636	C₄	#41×D₁₉	1	2	yes	—
637	C₂	—	4	2	no	—
638	C₂	—	4	1	no	—
639	C₂	—	38	4	no	—
640	C₂	—	76	1	no	—
641	C₂	—	76	1	no	—
642	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
643	C₂	#11927380	1	1	yes	characteristic
644	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#529	C₂
hypercenter	#529	D₁₉
hypocenter	C₁₉	#3521
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #11927265	C₂	semidirect
2. #11927263	C₂	semidirect
3. #11927250	C₂	semidirect
4. #11927244	C₂	semidirect
5. #11927241	C₂	semidirect
6. #11927233	C₂	semidirect
7. #11927232	C₂	semidirect
8. #11927223	C₂	semidirect
9. #11927218	C₂	semidirect
10. #11927196	C₂	semidirect
11. #11927191	C₂	semidirect
12. #11927187	C₂	semidirect
13. #11927159	C₂	semidirect
14. #11927152	C₂	semidirect
15. #11927137	C₂	semidirect
16. #11927130	C₂	semidirect
17. #11927078	C₂	semidirect
18. #11927077	C₂	semidirect
19. #126×D₁₉	C₂	semidirect
20. #11927026	C₂	semidirect
21. #11927016	C₂	semidirect
22. C₄×#64541	C₂	semidirect
23. C₁₉×#529	C₂	semidirect
27. C₁₉×#126	C₂²	semidirect
28. C₁₉×#125	C₂²	semidirect
30. C₁₉×#123	C₂²	semidirect
31. C₁₉×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₁₉	C₂²	semidirect
35. C₄×D₄×C₁₉	C₂²	semidirect
36. C₁₉×#117	C₂²	semidirect
37. C₂×C₄²×C₁₉	C₂²	semidirect
39. Q₈×Dic₁₉	C₂²	semidirect
40. #10597390	C₂²	semidirect
43. #10597384	C₂²	semidirect
46. #10597381	C₂²	semidirect
50. #10597375	C₂²	semidirect
51. #10597375	C₂²	semidirect
54. C₄×C₂²⋊D₁₉	C₂²	semidirect
55. C₄×C₂²⋊D₁₉	C₂²	semidirect
56. C₄×C₂²⋊D₁₉	C₂²	semidirect
58. #10597372	C₂²	semidirect
59. #10597370	C₂²	semidirect
60. #10597370	C₂²	semidirect
65. #10597343	C₂²	semidirect
66. #10597343	C₂²	semidirect
67. #10597342	C₂²	semidirect
68. #10597342	C₂²	semidirect
70. #10597340	C₂²	semidirect
73. #10597339	C₂²	semidirect
75. #10597338	C₂²	semidirect
76. C₄⋊C₄×D₁₉	C₂²	semidirect
77. C₄⋊C₄×D₁₉	C₂²	semidirect
78. C₄⋊C₄×D₁₉	C₂²	semidirect
79. C₄⋊C₄×D₁₉	C₂²	semidirect
80. #10597336	C₂²	semidirect
81. #10597336	C₂²	semidirect
82. #10597335	C₂²	semidirect
83. #10597334	C₂²	semidirect
84. #10597333	C₂²	semidirect
86. #10597331	C₂²	semidirect
88. #10597330	C₂²	semidirect
91. #10597329	C₂²	semidirect
94. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
98. #10597325	C₂²	semidirect
99. #10597325	C₂²	semidirect
100. #10597325	C₂²	semidirect
101. #10597325	C₂²	semidirect
102. #10597325	C₂²	semidirect
103. #10597324	C₂²	semidirect
104. #10597323	C₂²	semidirect
107. #10597322	C₂²	semidirect
112. C₄×D₇₆	C₂²	semidirect
114. #10597318	C₂²	semidirect
115. #10597318	C₂²	semidirect
116. #10597318	C₂²	semidirect
117. C₄²×D₁₉	C₂²	semidirect
118. #10597316	C₂²	semidirect
119. #10597316	C₂²	semidirect
120. C₄×Dic₃₈	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
333. #529	D₁₉	semidirect
362. #126	C₂×D₁₉	semidirect
368. #125	C₂×D₁₉	semidirect
383. #123	C₂×D₁₉	semidirect
393. C₂²⋊Q₈	C₂×D₁₉	semidirect
408. C₄×Q₈	C₂×D₁₉	semidirect
425. C₄×D₄	C₂×D₁₉	semidirect
434. #117	C₂×D₁₉	semidirect
444. C₂×C₄²	C₂×D₁₉	semidirect
445. C₁₉	#3521	semidirect

Maximal subgroups

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

subgroup	index
#11927265	2
#11927263	2
#11927250	2
#11927244	2
#11927241	2
#11927233	2
#11927232	2
#11927223	2
#11927218	2
#11927196	2
#11927191	2
#11927187	2
#11927159	2
#11927152	2
#11927137	2
#11927130	2
#11927078	2
#11927077	2
#126×D₁₉	2
#11927026	2
#11927016	2
C₄×#64541	2
C₁₉×#529	2
#3521	19