Subgroups — #14578225

Order 2432.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 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	#11927277	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927264	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927246	C₂	1	2	yes	maximal, complemented
6	#11927217	C₂	1	2	yes	maximal, complemented
7	#11927212	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927200	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927200	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927198	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927191	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927189	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927157	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927147	C₂	1	2	yes	maximal, complemented
15	#11927138	C₂	1	2	yes	maximal, complemented
16	#11927131	C₂	1	2	yes	maximal, complemented
17	#11927130	C₂	1	2	yes	maximal, complemented
18	#11927120	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927107	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927092	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927079	C₂	1	1	yes	maximal, characteristic, complemented
22	#11927072	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#540	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#64543	C₂²	1	1	yes	characteristic
25	C₂×#64543	C₂²	1	1	yes	characteristic
26	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
28	C₂×#64541	C₂²	1	1	yes	characteristic
29	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#127	C₂²	1	1	yes	characteristic
31	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#123	C₂²	1	2	yes	complemented
33	C₁₉×#123	C₂²	1	2	yes	complemented
34	C₁₉×#121	C₂²	1	1	yes	characteristic
35	C₁₉×#121	C₂²	1	2	yes	complemented
36	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#121	C₂²	1	2	yes	complemented
38	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
41	#10597386	C₂²	1	1	yes	characteristic
42	#10597386	C₂²	1	2	yes	complemented
43	#10597385	C₂²	1	2	yes	—
44	#10597385	C₂²	1	2	yes	—
45	#10597385	C₂²	1	2	yes	—
46	#10597385	C₂²	1	2	yes	complemented
47	#10597385	C₂²	1	2	yes	complemented
48	#10597384	C₂²	1	2	yes	—
49	#10597384	C₂²	1	2	yes	complemented
50	#10597384	C₂²	1	2	yes	complemented
51	#10597383	C₂²	1	2	yes	—
52	#10597383	C₂²	1	2	yes	—
53	#10597383	C₂²	1	2	yes	—
54	#10597382	C₂²	1	1	yes	characteristic
55	#10597382	C₂²	1	1	yes	characteristic
56	#10597382	C₂²	1	1	yes	characteristic, complemented
57	D₄×Dic₁₉	C₂²	1	2	yes	complemented
58	D₄×Dic₁₉	C₂²	1	2	yes	complemented
59	D₄×Dic₁₉	C₂²	1	2	yes	complemented
60	D₄×Dic₁₉	C₂²	1	2	yes	complemented
61	#10597376	C₂²	1	2	yes	—
62	#10597376	C₂²	1	2	yes	—
63	#10597375	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
66	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
67	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
68	#10597372	C₂²	1	2	yes	complemented
69	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
70	#10597370	C₂²	1	2	yes	complemented
71	#10597344	C₂²	1	1	yes	characteristic
72	#10597344	C₂²	1	2	yes	—
73	#10597344	C₂²	1	2	yes	—
74	#10597344	C₂²	1	2	yes	complemented
75	#10597343	C₂²	1	1	yes	characteristic
76	#10597343	C₂²	1	1	yes	characteristic
77	#10597343	C₂²	1	1	yes	characteristic, complemented
78	#10597343	C₂²	1	2	yes	complemented
79	#10597343	C₂²	1	2	yes	complemented
80	#10597342	C₂²	1	1	yes	characteristic, complemented
81	#10597341	C₂²	1	1	yes	characteristic
82	#10597340	C₂²	1	1	yes	characteristic
83	#10597340	C₂²	1	2	yes	complemented
84	#10597339	C₂²	1	1	yes	characteristic
85	#10597339	C₂²	1	2	yes	complemented
86	#10597338	C₂²	1	2	yes	complemented
87	#10597336	C₂²	1	2	yes	complemented
88	#10597336	C₂²	1	2	yes	complemented
89	#10597335	C₂²	1	1	yes	characteristic, complemented
90	#10597333	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	—
94	#10597332	C₂²	1	2	yes	—
95	#10597332	C₂²	1	2	yes	complemented
96	#10597332	C₂²	1	2	yes	complemented
97	#10597332	C₂²	1	2	yes	complemented
98	#10597331	C₂²	1	1	yes	characteristic
99	#10597331	C₂²	1	2	yes	—
100	#10597331	C₂²	1	2	yes	complemented
101	#10597331	C₂²	1	2	yes	complemented
102	#10597330	C₂²	1	1	yes	characteristic
103	#10597330	C₂²	1	2	yes	complemented
104	#10597329	C₂²	1	2	yes	—
105	#10597329	C₂²	1	1	yes	characteristic, complemented
106	#10597329	C₂²	1	2	yes	complemented
107	#10597328	C₂²	1	2	yes	—
108	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
110	#10597325	C₂²	1	1	yes	characteristic, complemented
111	#10597325	C₂²	1	2	yes	complemented
112	#10597325	C₂²	1	2	yes	complemented
113	#10597324	C₂²	1	2	yes	complemented
114	#10597324	C₂²	1	2	yes	complemented
115	#10597321	C₂²	1	1	yes	characteristic
116	#10597321	C₂²	1	1	yes	characteristic
117	C₄×D₇₆	C₂²	1	1	yes	characteristic
118	#10597318	C₂²	1	1	yes	characteristic
119	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
120	#10597315	C₂²	1	1	yes	characteristic, complemented
121	#10597315	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	2	yes	—
124	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₉	C₂³	1	2	yes	—
127	C₂×D₄×C₁₉	C₂³	1	2	yes	—
128	C₂×D₄×C₁₉	C₂³	1	2	yes	—
129	C₂×D₄×C₁₉	C₂³	1	2	yes	—
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	2	yes	—
135	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
142	C₂²×Dic₁₉	C₂³	1	2	yes	—
143	C₂²×Dic₁₉	C₂³	1	2	yes	—
144	C₂²×Dic₁₉	C₂³	1	2	yes	—
145	C₂²×Dic₁₉	C₂³	1	2	yes	—
146	#64543	—	4	2	no	—
147	#64543	—	4	2	no	—
148	#64543	—	4	2	no	—
149	D₄×D₁₉	—	4	2	no	—
150	#64541	—	4	2	no	—
151	C₂×D₇₆	C₂³	1	1	yes	characteristic
152	C₂×D₇₆	C₂³	1	1	yes	characteristic
153	C₂×D₇₆	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	1	yes	characteristic
158	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₉	C₂³	1	2	yes	—
160	C₂×Dic₃₈	—	4	2	no	—
161	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
162	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
163	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
164	C₂×Dic₃₈	C₂³	1	2	yes	—
165	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	2	yes	—
177	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₄²×C₁₉	C₂³	1	1	yes	characteristic
179	C₄²×C₁₉	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
188	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
199	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₉	C₂³	1	2	yes	—
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	C₄⋊Dic₁₉	C₂³	1	2	yes	—
206	C₄⋊Dic₁₉	C₂³	1	2	yes	—
207	C₄⋊Dic₁₉	C₂³	1	2	yes	—
208	C₄⋊Dic₁₉	C₂³	1	2	yes	—
209	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₉	C₂³	1	2	yes	—
211	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
212	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₁₉⋊C₄	C₂³	1	2	yes	—
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	2	yes	—
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
229	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₉	C₂⁴	1	2	yes	—
231	C₂²×D₁₉	—	4	2	no	—
232	C₂²×D₁₉	—	4	2	no	—
233	C₂²×D₁₉	—	4	2	no	—
234	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₉	C₂⁴	1	2	yes	—
236	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
237	D₄×C₁₉	—	2	2	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₁₉	—	4	2	no	—
255	C₂²⋊D₁₉	—	4	2	no	—
256	C₂²⋊D₁₉	—	4	2	no	—
257	C₂²⋊D₁₉	—	4	2	no	—
258	C₂²⋊D₁₉	—	4	2	no	—
259	C₂²⋊D₁₉	—	4	1	no	—
260	C₂²⋊D₁₉	—	4	2	no	—
261	C₂²⋊D₁₉	—	4	1	no	—
262	C₂²⋊D₁₉	—	4	2	no	—
263	C₂×Dic₁₉	—	4	2	no	—
264	C₂×Dic₁₉	—	4	2	no	—
265	C₂×Dic₁₉	—	4	2	no	—
266	C₂×Dic₁₉	—	4	2	no	—
267	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
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	C₂×Dic₁₉	C₂⁴	1	2	yes	—
274	C₂×Dic₁₉	C₂⁴	1	2	yes	—
275	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
276	D₇₆	—	2	2	no	—
277	D₇₆	—	4	1	no	—
278	D₇₆	—	4	2	no	—
279	C₄×D₁₉	—	2	2	no	—
280	C₄×D₁₉	—	2	2	no	—
281	C₄×D₁₉	—	4	1	no	—
282	C₄×D₁₉	—	4	2	no	—
283	C₄×D₁₉	—	4	1	no	—
284	C₄×D₁₉	—	4	2	no	—
285	Dic₃₈	—	2	2	no	—
286	Dic₃₈	—	2	2	no	—
287	Dic₃₈	—	2	2	no	—
288	Dic₃₈	—	4	2	no	—
289	Dic₃₈	—	4	1	no	—
290	#3562	—	19	1	no	maximal, Sylow
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
301	C₂×D₁₉	—	2	1	no	—
302	C₂×D₁₉	—	2	1	no	—
303	C₂×D₁₉	—	2	2	no	—
304	C₂×D₁₉	—	2	1	no	—
305	C₂×D₁₉	—	2	1	no	—
306	C₂×D₁₉	—	2	2	no	—
307	C₂×D₁₉	—	2	2	no	—
308	C₂×D₁₉	—	2	1	no	—
309	C₂×D₁₉	—	2	1	no	—
310	C₂×D₁₉	—	8	4	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	1	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
319	Dic₁₉	—	2	2	no	—
320	Dic₁₉	—	2	2	no	—
321	Dic₁₉	—	2	2	no	—
322	Dic₁₉	—	2	1	no	—
323	Dic₁₉	—	2	1	no	—
324	Dic₁₉	—	2	1	no	—
325	Dic₁₉	—	2	1	no	—
326	Dic₁₉	—	2	1	no	—
327	Dic₁₉	—	2	1	no	—
328	#562	—	19	2	no	—
329	#560	—	19	2	no	—
330	#559	—	19	1	no	—
331	#556	—	19	1	no	—
332	#553	—	19	2	no	—
333	#551	—	19	2	no	—
334	#550	—	19	1	no	—
335	#548	—	19	1	no	—
336	#548	—	19	1	no	—
337	#547	—	19	1	no	—
338	#546	—	19	1	no	—
339	#546	—	19	1	no	—
340	#541	—	19	1	no	—
341	#540	—	19	2	no	—
342	#540	D₁₉	1	1	yes	characteristic, complemented
343	#539	—	19	2	no	—
344	#538	—	19	2	no	—
345	#538	—	19	2	no	—
346	#536	—	19	1	no	—
347	#535	—	19	1	no	—
348	#532	—	19	1	no	—
349	#529	—	19	1	no	—
350	#529	—	19	1	no	—
351	C₂×C₁₉	—	4	2	no	—
352	C₂×C₁₉	—	4	1	no	—
353	C₂×C₁₉	—	4	2	no	—
354	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₁₉	#585	1	1	yes	characteristic
356	C₂×C₁₉	#585	1	1	yes	characteristic
357	D₁₉	—	4	1	no	—
358	D₁₉	—	4	2	no	—
359	D₁₉	—	4	1	no	—
360	C₂×#41	—	19	1	no	—
361	C₂×#41	—	19	1	no	—
362	C₂×#41	—	19	1	no	—
363	C₂×#41	—	19	1	no	—
364	C₂²×Q₈	—	19	1	no	—
365	C₂²×D₄	—	19	1	no	—
366	C₄⋊Q₈	—	19	1	no	—
367	C₄⋊Q₈	—	19	1	no	—
368	#127	—	19	1	no	—
369	#127	—	19	2	no	—
370	#127	C₂×D₁₉	1	1	yes	characteristic
371	#126	—	19	2	no	—
372	#126	—	19	1	no	—
373	#126	—	19	2	no	—
374	#126	—	19	2	no	—
375	#126	—	19	1	no	—
376	#126	—	19	2	no	—
377	#126	—	19	2	no	—
378	#125	—	19	1	no	—
379	#125	—	19	2	no	—
380	#125	—	19	2	no	—
381	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
382	#124	—	19	1	no	—
383	#124	—	19	1	no	—
384	#124	—	19	1	no	—
385	#124	—	19	1	no	—
386	#124	—	19	2	no	—
387	#124	—	19	2	no	—
388	#124	—	19	2	no	—
389	#124	—	19	1	no	—
390	#124	—	19	1	no	—
391	#123	—	19	2	no	—
392	#123	—	19	1	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	—	19	2	no	—
399	#123	—	19	2	no	—
400	#123	—	19	2	no	—
401	#123	—	19	2	no	—
402	#123	C₂×D₁₉	1	2	yes	complemented
403	#123	C₂×D₁₉	1	2	yes	complemented
404	C₂²⋊Q₈	—	19	2	no	—
405	C₂²⋊Q₈	—	19	1	no	—
406	C₂²⋊Q₈	—	19	1	no	—
407	C₂²⋊Q₈	—	19	2	no	—
408	C₂²⋊Q₈	—	19	2	no	—
409	C₂²⋊Q₈	—	19	1	no	—
410	C₂²⋊Q₈	—	19	1	no	—
411	C₂²⋊Q₈	—	19	2	no	—
412	C₂²⋊Q₈	—	19	2	no	—
413	#121	—	19	2	no	—
414	#121	—	19	2	no	—
415	#121	—	19	2	no	—
416	#121	—	19	2	no	—
417	#121	—	19	2	no	—
418	#121	—	19	2	no	—
419	#121	—	19	2	no	—
420	#121	—	19	2	no	—
421	#121	—	19	2	no	—
422	#121	—	19	2	no	—
423	#121	—	19	1	no	—
424	#121	—	19	1	no	—
425	#121	—	19	2	no	—
426	#121	C₂×D₁₉	1	1	yes	characteristic
427	#121	C₂×D₁₉	1	2	yes	complemented
428	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
429	#121	C₂×D₁₉	1	2	yes	complemented
430	#120	—	19	2	no	—
431	#120	—	19	2	no	—
432	#120	—	19	2	no	—
433	#120	—	19	2	no	—
434	C₄×Q₈	—	19	1	no	—
435	C₄×Q₈	—	19	1	no	—
436	C₄×Q₈	—	19	1	no	—
437	C₄×Q₈	—	19	1	no	—
438	C₄×D₄	—	19	2	no	—
439	C₄×D₄	—	19	2	no	—
440	C₄×D₄	—	19	2	no	—
441	C₄×D₄	—	19	2	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	1	no	—
447	C₄×D₄	—	19	2	no	—
448	C₄×D₄	—	19	1	no	—
449	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
450	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
451	#117	—	19	2	no	—
452	#117	—	19	2	no	—
453	#117	—	19	1	no	—
454	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	—	19	2	no	—
456	C₂×C₂²⋊C₄	—	19	2	no	—
457	C₂×C₂²⋊C₄	—	19	2	no	—
458	C₂×C₄²	—	19	1	no	—
459	C₁₉	#3562	1	1	yes	characteristic, complemented, Sylow
460	C₂⁴	—	19	2	no	—
461	#41	—	76	2	no	—
462	#41	—	76	2	no	—
463	#41	—	76	2	no	—
464	#41	—	76	2	no	—
465	C₂×Q₈	—	19	1	no	—
466	C₂×Q₈	—	19	1	no	—
467	C₂×Q₈	—	19	1	no	—
468	C₂×Q₈	—	19	1	no	—
469	C₂×Q₈	—	19	2	no	—
470	C₂×Q₈	—	76	2	no	—
471	C₂×D₄	—	19	1	no	—
472	C₂×D₄	—	19	2	no	—
473	C₂×D₄	—	19	2	no	—
474	C₂×D₄	—	19	1	no	—
475	C₂×D₄	—	19	2	no	—
476	C₂×D₄	—	19	2	no	—
477	C₂×D₄	—	19	2	no	—
478	C₂×D₄	—	19	2	no	—
479	C₂×D₄	—	19	2	no	—
480	C₂×D₄	—	19	1	no	—
481	C₂×D₄	—	19	1	no	—
482	C₂×D₄	—	19	2	no	—
483	C₂×D₄	—	76	2	no	—
484	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₁₉	1	2	yes	—
487	C₂×D₄	C₂²×D₁₉	1	2	yes	—
488	C₂×D₄	C₂²×D₁₉	1	2	yes	—
489	C₂×D₄	C₂²×D₁₉	1	2	yes	—
490	C₂²×C₄	—	19	2	no	—
491	C₂²×C₄	—	19	2	no	—
492	C₂²×C₄	—	19	2	no	—
493	C₂²×C₄	—	19	2	no	—
494	C₂²×C₄	—	19	1	no	—
495	C₂²×C₄	—	19	1	no	—
496	C₂²×C₄	—	19	1	no	—
497	C₂²×C₄	—	19	1	no	—
498	C₂²×C₄	—	19	2	no	—
499	C₂²×C₄	—	19	2	no	—
500	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
503	C₄⋊C₄	—	19	1	no	—
504	C₄⋊C₄	—	19	1	no	—
505	C₄⋊C₄	—	19	1	no	—
506	C₄⋊C₄	—	19	1	no	—
507	C₄⋊C₄	—	19	1	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	2	no	—
514	C₄⋊C₄	—	19	2	no	—
515	C₄⋊C₄	—	19	2	no	—
516	C₄⋊C₄	—	19	1	no	—
517	C₄⋊C₄	—	19	2	no	—
518	C₄⋊C₄	—	19	2	no	—
519	C₄⋊C₄	—	19	2	no	—
520	C₄⋊C₄	—	19	2	no	—
521	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
527	C₂²⋊C₄	—	19	2	no	—
528	C₂²⋊C₄	—	19	2	no	—
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	2	no	—
535	C₂²⋊C₄	—	19	1	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	2	no	—
538	C₂²⋊C₄	—	19	2	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	2	no	—
541	C₂²⋊C₄	—	19	1	no	—
542	C₂²⋊C₄	—	19	1	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	1	no	—
548	C₂²⋊C₄	—	19	2	no	—
549	C₂²⋊C₄	—	19	1	no	—
550	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
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	C₄²	—	19	1	no	—
557	C₄²	—	19	1	no	—
558	C₄²	—	19	1	no	—
559	C₄²	—	19	2	no	—
560	C₄²	—	19	1	no	—
561	C₄²	—	19	2	no	—
562	C₄²	—	19	2	no	—
563	C₄²	C₂²×D₁₉	1	1	yes	characteristic
564	C₄²	C₂²×D₁₉	1	1	yes	characteristic
565	C₂³	—	19	1	no	—
566	C₂³	—	19	2	no	—
567	C₂³	—	19	1	no	—
568	C₂³	—	76	2	no	—
569	C₂³	—	76	2	no	—
570	C₂³	—	76	2	no	—
571	C₂³	C₂³×D₁₉	1	2	yes	—
572	C₂³	C₂³×D₁₉	1	1	yes	characteristic
573	C₂³	C₂³×D₁₉	1	2	yes	—
574	Q₈	—	38	2	no	—
575	Q₈	—	38	2	no	—
576	Q₈	—	38	2	no	—
577	Q₈	—	76	2	no	—
578	Q₈	—	76	1	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	38	2	no	—
586	D₄	—	76	1	no	—
587	D₄	—	76	2	no	—
588	D₄	—	76	2	no	—
589	D₄	—	76	2	no	—
590	D₄	—	76	2	no	—
591	D₄	—	76	2	no	—
592	D₄	—	76	2	no	—
593	D₄	—	76	1	no	—
594	D₄	—	76	2	no	—
595	D₄	—	76	1	no	—
596	D₄	—	76	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	19	1	no	—
601	C₂×C₄	—	19	1	no	—
602	C₂×C₄	—	19	1	no	—
603	C₂×C₄	—	19	1	no	—
604	C₂×C₄	—	19	1	no	—
605	C₂×C₄	—	19	2	no	—
606	C₂×C₄	—	19	2	no	—
607	C₂×C₄	—	19	2	no	—
608	C₂×C₄	—	19	1	no	—
609	C₂×C₄	—	38	2	no	—
610	C₂×C₄	—	38	2	no	—
611	C₂×C₄	—	76	2	no	—
612	C₂×C₄	—	76	2	no	—
613	C₂×C₄	—	76	1	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	—	76	2	no	—
619	C₂×C₄	C₂³×D₁₉	1	2	yes	—
620	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₉	1	2	yes	—
623	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	38	1	no	—
637	C₂²	—	38	1	no	—
638	C₂²	—	38	2	no	—
639	C₂²	—	38	1	no	—
640	C₂²	—	38	1	no	—
641	C₂²	—	38	2	no	—
642	C₂²	—	38	2	no	—
643	C₂²	—	38	1	no	—
644	C₂²	—	38	1	no	—
645	C₂²	—	152	4	no	—
646	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	38	1	no	—
655	C₄	—	38	1	no	—
656	C₄	—	38	2	no	—
657	C₄	—	38	2	no	—
658	C₄	—	38	2	no	—
659	C₄	—	38	1	no	—
660	C₄	—	38	1	no	—
661	C₄	—	38	1	no	—
662	C₄	—	38	1	no	—
663	C₄	#10597435	1	2	yes	—
664	C₂	—	4	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	76	1	no	—
668	C₂	—	76	2	no	—
669	C₂	—	76	1	no	—
670	C₂	C₂×#10597435	1	1	yes	characteristic
671	C₂	#11927379	1	1	yes	characteristic
672	C₂	#11927379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#540	C₂
hypercenter	#540	D₁₉
hypocenter	C₁₉	#3562
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #540

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. #11927277	C₂	semidirect
4. #11927264	C₂	semidirect
5. #11927246	C₂	semidirect
6. #11927217	C₂	semidirect
7. #11927212	C₂	semidirect
8. #11927200	C₂	semidirect
9. #11927200	C₂	semidirect
10. #11927198	C₂	semidirect
11. #11927191	C₂	semidirect
12. #11927189	C₂	semidirect
13. #11927157	C₂	semidirect
14. #11927147	C₂	semidirect
15. #11927138	C₂	semidirect
16. #11927131	C₂	semidirect
17. #11927130	C₂	semidirect
18. #11927120	C₂	semidirect
19. #11927107	C₂	semidirect
20. #11927092	C₂	semidirect
21. #11927079	C₂	semidirect
22. #11927072	C₂	semidirect
23. C₁₉×#540	C₂	semidirect
26. C₂×#64543	C₂²	semidirect
29. C₂²×Dic₃₈	C₂²	semidirect
31. C₁₉×#125	C₂²	semidirect
32. C₁₉×#123	C₂²	semidirect
33. C₁₉×#123	C₂²	semidirect
35. C₁₉×#121	C₂²	semidirect
36. C₁₉×#121	C₂²	semidirect
37. C₁₉×#121	C₂²	semidirect
39. C₄×D₄×C₁₉	C₂²	semidirect
40. C₁₉×#117	C₂²	semidirect
42. #10597386	C₂²	semidirect
46. #10597385	C₂²	semidirect
47. #10597385	C₂²	semidirect
49. #10597384	C₂²	semidirect
50. #10597384	C₂²	semidirect
56. #10597382	C₂²	semidirect
57. D₄×Dic₁₉	C₂²	semidirect
58. D₄×Dic₁₉	C₂²	semidirect
59. D₄×Dic₁₉	C₂²	semidirect
60. D₄×Dic₁₉	C₂²	semidirect
63. #10597375	C₂²	semidirect
65. C₄×C₂²⋊D₁₉	C₂²	semidirect
66. C₄×C₂²⋊D₁₉	C₂²	semidirect
68. #10597372	C₂²	semidirect
69. C₂×C₄⋊Dic₁₉	C₂²	semidirect
70. #10597370	C₂²	semidirect
74. #10597344	C₂²	semidirect
77. #10597343	C₂²	semidirect
78. #10597343	C₂²	semidirect
79. #10597343	C₂²	semidirect
80. #10597342	C₂²	semidirect
83. #10597340	C₂²	semidirect
85. #10597339	C₂²	semidirect
86. #10597338	C₂²	semidirect
87. #10597336	C₂²	semidirect
88. #10597336	C₂²	semidirect
89. #10597335	C₂²	semidirect
90. #10597333	C₂²	semidirect
91. #10597333	C₂²	semidirect
92. #10597333	C₂²	semidirect
95. #10597332	C₂²	semidirect
96. #10597332	C₂²	semidirect
97. #10597332	C₂²	semidirect
100. #10597331	C₂²	semidirect
101. #10597331	C₂²	semidirect
103. #10597330	C₂²	semidirect
105. #10597329	C₂²	semidirect
106. #10597329	C₂²	semidirect
108. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
110. #10597325	C₂²	semidirect
111. #10597325	C₂²	semidirect
112. #10597325	C₂²	semidirect
113. #10597324	C₂²	semidirect
114. #10597324	C₂²	semidirect
119. C₄²×D₁₉	C₂²	semidirect
120. #10597315	C₂²	semidirect
121. #10597315	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
342. #540	D₁₉	semidirect
381. #125	C₂×D₁₉	semidirect
402. #123	C₂×D₁₉	semidirect
403. #123	C₂×D₁₉	semidirect
427. #121	C₂×D₁₉	semidirect
428. #121	C₂×D₁₉	semidirect
429. #121	C₂×D₁₉	semidirect
450. C₄×D₄	C₂×D₁₉	semidirect
454. #117	C₂×D₁₉	semidirect
459. C₁₉	#3562	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
#11927277	2
#11927264	2
#11927246	2
#11927217	2
#11927212	2
#11927200	2
#11927198	2
#11927191	2
#11927189	2
#11927157	2
#11927147	2
#11927138	2
#11927131	2
#11927130	2
#11927120	2
#11927107	2
#11927092	2
#11927079	2
#11927072	2
C₁₉×#540	2
#3562	19