Subgroups — #14577858

Order 2432.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 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	#11927290	C₂	1	2	yes	maximal, complemented
3	#11927255	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927249	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927203	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927200	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	#11927189	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927186	C₂	1	2	yes	maximal, complemented
11	#11927182	C₂	1	2	yes	maximal, complemented
12	#11927169	C₂	1	2	yes	maximal, complemented
13	#11927168	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927159	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927138	C₂	1	2	yes	maximal, complemented
16	#11927130	C₂	1	2	yes	maximal, complemented
17	#11927125	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927123	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927122	C₂	1	2	yes	maximal, complemented
20	#11927053	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#10597343	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₉	C₂²	1	2	yes	complemented
25	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₉	C₂²	1	2	yes	—
27	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
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×C₄×D₁₉	C₂²	1	1	yes	characteristic
32	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#123	C₂²	1	2	yes	complemented
35	C₁₉×#123	C₂²	1	2	yes	complemented
36	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₁₉×#121	C₂²	1	1	yes	characteristic
38	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	#10597393	C₂²	1	2	yes	complemented
44	#10597392	C₂²	1	2	yes	—
45	#10597392	C₂²	1	2	yes	complemented
46	#10597392	C₂²	1	2	yes	complemented
47	#10597385	C₂²	1	2	yes	—
48	#10597385	C₂²	1	1	yes	characteristic, complemented
49	#10597385	C₂²	1	2	yes	complemented
50	#10597385	C₂²	1	2	yes	complemented
51	#10597385	C₂²	1	2	yes	complemented
52	#10597384	C₂²	1	1	yes	characteristic
53	#10597384	C₂²	1	2	yes	complemented
54	#10597384	C₂²	1	2	yes	complemented
55	#10597383	C₂²	1	1	yes	characteristic
56	#10597383	C₂²	1	2	yes	—
57	#10597382	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₁₉	C₂²	1	2	yes	complemented
59	#10597376	C₂²	1	1	yes	characteristic
60	#10597376	C₂²	1	2	yes	complemented
61	#10597376	C₂²	1	2	yes	complemented
62	#10597376	C₂²	1	2	yes	complemented
63	#10597375	C₂²	1	2	yes	complemented
64	#10597375	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
67	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
68	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
69	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
70	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
71	#10597370	C₂²	1	2	yes	complemented
72	#10597370	C₂²	1	2	yes	complemented
73	#10597370	C₂²	1	1	yes	characteristic, complemented
74	#10597344	C₂²	1	2	yes	complemented
75	#10597343	C₂²	1	2	yes	—
76	#10597343	C₂²	1	1	yes	characteristic
77	#10597343	C₂²	1	1	yes	characteristic
78	#10597343	C₂²	1	1	yes	characteristic, complemented
79	#10597343	C₂²	1	1	yes	characteristic, complemented
80	#10597343	C₂²	1	2	yes	complemented
81	#10597343	C₂²	1	2	yes	complemented
82	#10597343	C₂²	1	1	yes	characteristic, complemented
83	#10597342	C₂²	1	1	yes	characteristic
84	#10597342	C₂²	1	2	yes	—
85	#10597342	C₂²	1	2	yes	complemented
86	#10597342	C₂²	1	2	yes	complemented
87	#10597341	C₂²	1	1	yes	characteristic
88	#10597341	C₂²	1	2	yes	complemented
89	#10597341	C₂²	1	1	yes	characteristic, complemented
90	#10597340	C₂²	1	1	yes	characteristic, complemented
91	#10597340	C₂²	1	2	yes	complemented
92	#10597340	C₂²	1	2	yes	complemented
93	#10597339	C₂²	1	2	yes	—
94	#10597339	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
97	#10597336	C₂²	1	2	yes	complemented
98	#10597335	C₂²	1	2	yes	complemented
99	#10597334	C₂²	1	1	yes	characteristic, complemented
100	#10597333	C₂²	1	1	yes	characteristic, complemented
101	#10597332	C₂²	1	2	yes	complemented
102	#10597331	C₂²	1	2	yes	complemented
103	#10597331	C₂²	1	2	yes	complemented
104	#10597331	C₂²	1	2	yes	complemented
105	#10597330	C₂²	1	1	yes	characteristic
106	#10597330	C₂²	1	2	yes	—
107	#10597330	C₂²	1	2	yes	complemented
108	#10597329	C₂²	1	1	yes	characteristic, complemented
109	#10597329	C₂²	1	2	yes	complemented
110	#10597328	C₂²	1	1	yes	characteristic
111	#10597328	C₂²	1	2	yes	—
112	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
114	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
115	#10597325	C₂²	1	2	yes	complemented
116	#10597324	C₂²	1	1	yes	characteristic, complemented
117	#10597324	C₂²	1	2	yes	complemented
118	#10597324	C₂²	1	2	yes	complemented
119	#10597321	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₇₆	C₂²	1	1	yes	characteristic
121	#10597318	C₂²	1	1	yes	characteristic, 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	#41×C₁₉	—	4	4	no	—
126	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
127	C₂×D₄×C₁₉	C₂³	1	2	yes	—
128	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₉	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	1	yes	characteristic
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
145	C₂²×Dic₁₉	C₂³	1	2	yes	—
146	C₂²×Dic₁₉	C₂³	1	2	yes	—
147	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
148	#64543	—	4	2	no	—
149	D₄×D₁₉	—	4	2	no	—
150	D₄×D₁₉	—	4	4	no	—
151	#64541	—	4	2	no	—
152	#64541	—	4	2	no	—
153	#64541	—	4	4	no	—
154	C₂×D₇₆	C₂³	1	1	yes	characteristic
155	C₂×D₇₆	C₂³	1	1	yes	characteristic
156	C₂×D₇₆	C₂³	1	2	yes	—
157	C₂×D₇₆	C₂³	1	2	yes	—
158	C₂×D₇₆	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₉	—	4	2	no	—
160	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₉	C₂³	1	2	yes	—
164	C₂×C₄×D₁₉	C₂³	1	2	yes	—
165	C₂×C₄×D₁₉	C₂³	1	2	yes	—
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×Dic₃₈	—	4	2	no	—
170	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
171	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
172	C₂×Dic₃₈	C₂³	1	2	yes	—
173	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
174	C₂×Dic₃₈	C₂³	1	2	yes	—
175	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
176	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
179	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
180	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
183	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
185	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
187	C₄²×C₁₉	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
194	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
200	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
204	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
207	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₉	C₂³	1	2	yes	—
213	C₄⋊Dic₁₉	C₂³	1	2	yes	—
214	C₄⋊Dic₁₉	C₂³	1	2	yes	—
215	C₄⋊Dic₁₉	C₂³	1	2	yes	—
216	C₄⋊Dic₁₉	C₂³	1	2	yes	—
217	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	2	yes	—
219	Dic₁₉⋊C₄	C₂³	1	2	yes	—
220	Dic₁₉⋊C₄	C₂³	1	2	yes	—
221	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₁₉⋊C₄	C₂³	1	2	yes	—
223	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
225	Dic₁₉⋊C₄	C₂³	1	2	yes	—
226	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
227	Dic₁₉⋊C₄	C₂³	1	2	yes	—
228	C₄×Dic₁₉	C₂³	1	2	yes	—
229	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
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	2	no	—
236	C₂²×D₁₉	—	2	4	no	—
237	C₂²×D₁₉	—	4	1	no	—
238	C₂²×D₁₉	—	4	2	no	—
239	C₂²×D₁₉	—	4	2	no	—
240	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₉	C₂⁴	1	2	yes	—
242	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
243	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
244	Q₈×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	2	4	no	—
246	D₄×C₁₉	—	2	2	no	—
247	D₄×C₁₉	—	2	2	no	—
248	D₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₁₉	—	2	2	no	—
263	C₂²⋊D₁₉	—	2	4	no	—
264	C₂²⋊D₁₉	—	2	2	no	—
265	C₂²⋊D₁₉	—	4	2	no	—
266	C₂²⋊D₁₉	—	4	1	no	—
267	C₂²⋊D₁₉	—	4	1	no	—
268	C₂²⋊D₁₉	—	4	2	no	—
269	C₂²⋊D₁₉	—	4	2	no	—
270	C₂²⋊D₁₉	—	4	2	no	—
271	C₂×Dic₁₉	—	4	2	no	—
272	C₂×Dic₁₉	—	4	1	no	—
273	C₂×Dic₁₉	—	4	2	no	—
274	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₉	C₂⁴	1	2	yes	—
276	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₉	C₂⁴	1	2	yes	—
278	C₂×Dic₁₉	C₂⁴	1	2	yes	—
279	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
282	D₇₆	—	2	2	no	—
283	D₇₆	—	2	2	no	—
284	D₇₆	—	4	1	no	—
285	D₇₆	—	4	2	no	—
286	D₇₆	—	4	2	no	—
287	C₄×D₁₉	—	2	2	no	—
288	C₄×D₁₉	—	2	2	no	—
289	C₄×D₁₉	—	2	2	no	—
290	C₄×D₁₉	—	4	1	no	—
291	C₄×D₁₉	—	4	1	no	—
292	C₄×D₁₉	—	4	2	no	—
293	C₄×D₁₉	—	4	2	no	—
294	C₄×D₁₉	—	4	2	no	—
295	C₄×D₁₉	—	4	2	no	—
296	Dic₃₈	—	2	2	no	—
297	Dic₃₈	—	2	2	no	—
298	Dic₃₈	—	4	2	no	—
299	Dic₃₈	—	4	2	no	—
300	Dic₃₈	—	4	1	no	—
301	#3536	—	19	1	no	maximal, Sylow
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	2	no	—
305	C₂²×C₁₉	—	2	1	no	—
306	C₂²×C₁₉	—	2	2	no	—
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	2	no	—
310	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
311	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
312	C₂×D₁₉	—	2	1	no	—
313	C₂×D₁₉	—	2	1	no	—
314	C₂×D₁₉	—	2	1	no	—
315	C₂×D₁₉	—	2	1	no	—
316	C₂×D₁₉	—	2	1	no	—
317	C₂×D₁₉	—	2	2	no	—
318	C₂×D₁₉	—	2	2	no	—
319	C₂×D₁₉	—	2	1	no	—
320	C₂×D₁₉	—	2	1	no	—
321	C₂×D₁₉	—	2	1	no	—
322	C₂×D₁₉	—	2	2	no	—
323	C₂×D₁₉	—	4	4	no	—
324	C₂×D₁₉	—	8	4	no	—
325	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
326	C₄×C₁₉	—	2	1	no	—
327	C₄×C₁₉	—	2	1	no	—
328	C₄×C₁₉	—	2	2	no	—
329	C₄×C₁₉	—	2	2	no	—
330	C₄×C₁₉	—	2	2	no	—
331	C₄×C₁₉	—	2	1	no	—
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
334	Dic₁₉	—	2	2	no	—
335	Dic₁₉	—	2	2	no	—
336	Dic₁₉	—	2	1	no	—
337	Dic₁₉	—	2	1	no	—
338	Dic₁₉	—	2	1	no	—
339	Dic₁₉	—	2	2	no	—
340	Dic₁₉	—	2	1	no	—
341	Dic₁₉	—	2	1	no	—
342	#562	—	19	2	no	—
343	#562	—	19	2	no	—
344	#554	—	19	1	no	—
345	#554	—	19	1	no	—
346	#548	—	19	1	no	—
347	#548	—	19	1	no	—
348	#547	—	19	1	no	—
349	#547	D₁₉	1	1	yes	characteristic, complemented
350	#546	—	19	2	no	—
351	#546	—	19	2	no	—
352	#546	—	19	1	no	—
353	#546	—	19	1	no	—
354	#543	—	19	2	no	—
355	#542	—	19	1	no	—
356	#542	—	19	1	no	—
357	#539	—	19	2	no	—
358	#538	—	19	2	no	—
359	#537	—	19	2	no	—
360	#537	—	19	1	no	—
361	#537	—	19	1	no	—
362	#525	—	19	1	no	—
363	C₂×C₂²⋊Q₈	—	19	1	no	—
364	C₂×#121	—	19	1	no	—
365	C₂×C₁₉	—	2	2	no	—
366	C₂×C₁₉	—	4	2	no	—
367	C₂×C₁₉	—	4	1	no	—
368	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
371	D₁₉	—	2	2	no	—
372	D₁₉	—	4	1	no	—
373	D₁₉	—	4	1	no	—
374	D₁₉	—	4	2	no	—
375	C₂×#41	—	19	1	no	—
376	C₂×#41	—	19	1	no	—
377	C₂×#41	—	19	2	no	—
378	C₂×#41	—	19	1	no	—
379	C₂×#41	C₂×D₁₉	1	2	yes	complemented
380	C₂²×Q₈	—	19	1	no	—
381	C₂²×D₄	—	19	1	no	—
382	C₂²×D₄	—	19	2	no	—
383	C₂³×C₄	—	19	1	no	—
384	C₄⋊Q₈	—	19	1	no	—
385	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
386	#126	—	19	2	no	—
387	#126	—	19	2	no	—
388	#125	—	19	2	no	—
389	#125	—	19	2	no	—
390	#124	—	19	2	no	—
391	#124	—	19	1	no	—
392	#124	—	19	2	no	—
393	#124	—	19	2	no	—
394	#124	—	19	2	no	—
395	#124	—	19	1	no	—
396	#123	—	19	2	no	—
397	#123	—	19	2	no	—
398	#123	—	19	1	no	—
399	#123	—	19	2	no	—
400	#123	—	19	2	no	—
401	#123	—	19	1	no	—
402	#123	—	19	2	no	—
403	#123	—	19	2	no	—
404	#123	C₂×D₁₉	1	2	yes	complemented
405	#123	C₂×D₁₉	1	2	yes	complemented
406	C₂²⋊Q₈	—	19	2	no	—
407	C₂²⋊Q₈	—	19	2	no	—
408	C₂²⋊Q₈	—	19	2	no	—
409	C₂²⋊Q₈	—	19	2	no	—
410	C₂²⋊Q₈	—	19	1	no	—
411	C₂²⋊Q₈	—	19	2	no	—
412	C₂²⋊Q₈	—	19	1	no	—
413	C₂²⋊Q₈	—	19	1	no	—
414	C₂²⋊Q₈	—	19	2	no	—
415	C₂²⋊Q₈	—	19	1	no	—
416	C₂²⋊Q₈	—	19	1	no	—
417	C₂²⋊Q₈	—	19	2	no	—
418	C₂²⋊Q₈	—	19	1	no	—
419	C₂²⋊Q₈	—	19	2	no	—
420	C₂²⋊Q₈	—	19	1	no	—
421	C₂²⋊Q₈	—	19	2	no	—
422	C₂²⋊Q₈	—	19	2	no	—
423	C₂²⋊Q₈	—	19	2	no	—
424	C₂²⋊Q₈	—	19	1	no	—
425	C₂²⋊Q₈	—	19	2	no	—
426	C₂²⋊Q₈	—	19	2	no	—
427	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
428	#121	—	19	1	no	—
429	#121	—	19	2	no	—
430	#121	—	19	2	no	—
431	#121	—	19	2	no	—
432	#121	—	19	1	no	—
433	#121	—	19	2	no	—
434	#121	—	19	2	no	—
435	#121	—	19	2	no	—
436	#121	—	19	1	no	—
437	#121	—	19	2	no	—
438	#121	—	19	2	no	—
439	#121	—	19	2	no	—
440	#121	—	19	1	no	—
441	#121	—	19	1	no	—
442	#121	—	19	2	no	—
443	#121	—	19	2	no	—
444	#121	—	19	1	no	—
445	#121	—	19	2	no	—
446	#121	C₂×D₁₉	1	1	yes	characteristic
447	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
448	#120	—	19	1	no	—
449	#120	—	19	2	no	—
450	#120	—	19	1	no	—
451	#120	—	19	2	no	—
452	C₄×Q₈	—	19	1	no	—
453	C₄×Q₈	—	19	1	no	—
454	C₄×D₄	—	19	2	no	—
455	C₄×D₄	—	19	1	no	—
456	C₄×D₄	—	19	1	no	—
457	C₄×D₄	—	19	2	no	—
458	C₄×D₄	—	19	2	no	—
459	C₄×D₄	—	19	1	no	—
460	C₄×D₄	—	19	2	no	—
461	C₄×D₄	—	19	1	no	—
462	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
463	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
464	#117	—	19	1	no	—
465	C₂×C₄⋊C₄	—	19	2	no	—
466	C₂×C₄⋊C₄	—	19	1	no	—
467	C₂×C₄⋊C₄	—	19	1	no	—
468	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
469	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
470	C₂×C₂²⋊C₄	—	19	2	no	—
471	C₂×C₂²⋊C₄	—	19	2	no	—
472	C₂×C₂²⋊C₄	—	19	2	no	—
473	C₂×C₂²⋊C₄	—	19	2	no	—
474	C₁₉	#3536	1	1	yes	characteristic, complemented, Sylow
475	C₂⁴	—	19	1	no	—
476	C₂⁴	—	19	2	no	—
477	#41	—	4	4	no	—
478	#41	—	76	2	no	—
479	#41	—	76	4	no	—
480	#41	—	76	2	no	—
481	#41	—	76	2	no	—
482	C₂×Q₈	—	19	1	no	—
483	C₂×Q₈	—	19	1	no	—
484	C₂×Q₈	—	19	1	no	—
485	C₂×Q₈	—	19	2	no	—
486	C₂×Q₈	—	19	2	no	—
487	C₂×Q₈	—	76	2	no	—
488	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
489	C₂×D₄	—	19	1	no	—
490	C₂×D₄	—	19	1	no	—
491	C₂×D₄	—	19	2	no	—
492	C₂×D₄	—	19	1	no	—
493	C₂×D₄	—	19	2	no	—
494	C₂×D₄	—	19	2	no	—
495	C₂×D₄	—	19	1	no	—
496	C₂×D₄	—	19	2	no	—
497	C₂×D₄	—	19	2	no	—
498	C₂×D₄	—	19	1	no	—
499	C₂×D₄	—	19	1	no	—
500	C₂×D₄	—	19	2	no	—
501	C₂×D₄	—	19	1	no	—
502	C₂×D₄	—	19	2	no	—
503	C₂×D₄	—	76	2	no	—
504	C₂×D₄	—	76	4	no	—
505	C₂×D₄	C₂²×D₁₉	1	2	yes	—
506	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
507	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₁₉	1	2	yes	—
509	C₂²×C₄	—	19	2	no	—
510	C₂²×C₄	—	19	2	no	—
511	C₂²×C₄	—	19	1	no	—
512	C₂²×C₄	—	19	1	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	2	no	—
518	C₂²×C₄	—	19	2	no	—
519	C₂²×C₄	—	19	2	no	—
520	C₂²×C₄	—	19	1	no	—
521	C₂²×C₄	—	76	2	no	—
522	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
523	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
526	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
527	C₄⋊C₄	—	19	2	no	—
528	C₄⋊C₄	—	19	2	no	—
529	C₄⋊C₄	—	19	1	no	—
530	C₄⋊C₄	—	19	1	no	—
531	C₄⋊C₄	—	19	2	no	—
532	C₄⋊C₄	—	19	1	no	—
533	C₄⋊C₄	—	19	1	no	—
534	C₄⋊C₄	—	19	2	no	—
535	C₄⋊C₄	—	19	2	no	—
536	C₄⋊C₄	—	19	2	no	—
537	C₄⋊C₄	—	19	1	no	—
538	C₄⋊C₄	—	19	2	no	—
539	C₄⋊C₄	—	19	2	no	—
540	C₄⋊C₄	—	19	2	no	—
541	C₄⋊C₄	—	19	2	no	—
542	C₄⋊C₄	—	19	2	no	—
543	C₄⋊C₄	—	19	1	no	—
544	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
548	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
549	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
550	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
551	C₂²⋊C₄	—	19	2	no	—
552	C₂²⋊C₄	—	19	2	no	—
553	C₂²⋊C₄	—	19	1	no	—
554	C₂²⋊C₄	—	19	2	no	—
555	C₂²⋊C₄	—	19	1	no	—
556	C₂²⋊C₄	—	19	2	no	—
557	C₂²⋊C₄	—	19	2	no	—
558	C₂²⋊C₄	—	19	2	no	—
559	C₂²⋊C₄	—	19	1	no	—
560	C₂²⋊C₄	—	19	1	no	—
561	C₂²⋊C₄	—	19	2	no	—
562	C₂²⋊C₄	—	19	2	no	—
563	C₂²⋊C₄	—	19	2	no	—
564	C₂²⋊C₄	—	19	2	no	—
565	C₂²⋊C₄	—	19	2	no	—
566	C₂²⋊C₄	—	19	2	no	—
567	C₂²⋊C₄	—	19	1	no	—
568	C₂²⋊C₄	—	19	1	no	—
569	C₂²⋊C₄	—	19	2	no	—
570	C₂²⋊C₄	—	19	2	no	—
571	C₂²⋊C₄	—	19	1	no	—
572	C₂²⋊C₄	—	19	2	no	—
573	C₂²⋊C₄	—	19	1	no	—
574	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
577	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
578	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
579	C₄²	—	19	1	no	—
580	C₄²	—	19	2	no	—
581	C₄²	—	19	2	no	—
582	C₄²	C₂²×D₁₉	1	1	yes	characteristic
583	C₂³	—	19	1	no	—
584	C₂³	—	19	2	no	—
585	C₂³	—	19	1	no	—
586	C₂³	—	19	1	no	—
587	C₂³	—	38	2	no	—
588	C₂³	—	38	4	no	—
589	C₂³	—	38	2	no	—
590	C₂³	—	76	1	no	—
591	C₂³	—	76	2	no	—
592	C₂³	—	76	2	no	—
593	C₂³	C₂³×D₁₉	1	2	yes	—
594	C₂³	C₂³×D₁₉	1	1	yes	characteristic
595	C₂³	C₂³×D₁₉	1	1	yes	characteristic
596	Q₈	—	4	2	no	—
597	Q₈	—	38	2	no	—
598	Q₈	—	38	2	no	—
599	Q₈	—	76	2	no	—
600	Q₈	—	76	2	no	—
601	Q₈	—	76	1	no	—
602	D₄	—	2	4	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	38	2	no	—
607	D₄	—	38	2	no	—
608	D₄	—	38	4	no	—
609	D₄	—	38	2	no	—
610	D₄	—	38	2	no	—
611	D₄	—	76	2	no	—
612	D₄	—	76	2	no	—
613	D₄	—	76	1	no	—
614	D₄	—	76	2	no	—
615	D₄	—	76	2	no	—
616	D₄	—	76	1	no	—
617	D₄	—	76	1	no	—
618	D₄	—	76	2	no	—
619	D₄	—	76	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	19	1	no	—
626	C₂×C₄	—	19	1	no	—
627	C₂×C₄	—	19	2	no	—
628	C₂×C₄	—	19	2	no	—
629	C₂×C₄	—	19	2	no	—
630	C₂×C₄	—	19	1	no	—
631	C₂×C₄	—	19	1	no	—
632	C₂×C₄	—	19	1	no	—
633	C₂×C₄	—	38	2	no	—
634	C₂×C₄	—	38	2	no	—
635	C₂×C₄	—	38	2	no	—
636	C₂×C₄	—	76	1	no	—
637	C₂×C₄	—	76	1	no	—
638	C₂×C₄	—	76	2	no	—
639	C₂×C₄	—	76	2	no	—
640	C₂×C₄	—	76	2	no	—
641	C₂×C₄	—	76	2	no	—
642	C₂×C₄	—	76	1	no	—
643	C₂×C₄	—	76	2	no	—
644	C₂×C₄	—	76	2	no	—
645	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₉	1	2	yes	—
647	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₉	1	2	yes	—
650	C₂×C₄	C₂³×D₁₉	1	2	yes	—
651	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	19	2	no	—
662	C₂²	—	38	1	no	—
663	C₂²	—	38	1	no	—
664	C₂²	—	38	1	no	—
665	C₂²	—	38	2	no	—
666	C₂²	—	38	1	no	—
667	C₂²	—	38	1	no	—
668	C₂²	—	38	1	no	—
669	C₂²	—	38	2	no	—
670	C₂²	—	38	1	no	—
671	C₂²	—	38	1	no	—
672	C₂²	—	38	2	no	—
673	C₂²	—	76	4	no	—
674	C₂²	—	152	4	no	—
675	C₂²	#10597430	1	2	yes	—
676	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	38	2	no	—
685	C₄	—	38	1	no	—
686	C₄	—	38	1	no	—
687	C₄	—	38	1	no	—
688	C₄	—	38	1	no	—
689	C₄	—	38	2	no	—
690	C₄	—	38	2	no	—
691	C₄	—	38	1	no	—
692	C₄	#10597435	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	4	1	no	—
696	C₂	—	38	2	no	—
697	C₂	—	76	1	no	—
698	C₂	—	76	2	no	—
699	C₂	—	76	1	no	—
700	C₂	C₂×#10597430	1	1	yes	characteristic
701	C₂	C₂×#10597435	1	1	yes	characteristic
702	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#547	C₂
hypercenter	#547	D₁₉
hypocenter	C₁₉	#3536
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #11927291	C₂	semidirect
2. #11927290	C₂	semidirect
3. #11927255	C₂	semidirect
4. #11927249	C₂	semidirect
5. #11927203	C₂	semidirect
6. #11927200	C₂	semidirect
7. #11927195	C₂	semidirect
8. #11927191	C₂	semidirect
9. #11927189	C₂	semidirect
10. #11927186	C₂	semidirect
11. #11927182	C₂	semidirect
12. #11927169	C₂	semidirect
13. #11927168	C₂	semidirect
14. #11927159	C₂	semidirect
15. #11927138	C₂	semidirect
16. #11927130	C₂	semidirect
17. #11927125	C₂	semidirect
18. #11927123	C₂	semidirect
19. #11927122	C₂	semidirect
20. #11927053	C₂	semidirect
21. C₂×#10597343	C₂	semidirect
22. #121×D₁₉	C₂	semidirect
23. C₁₉×#547	C₂	semidirect
24. C₂×#41×C₁₉	C₂²	semidirect
25. C₂×#64543	C₂²	semidirect
28. C₂×#64541	C₂²	semidirect
29. C₂×#64541	C₂²	semidirect
30. C₂×#64541	C₂²	semidirect
32. C₂²×Dic₃₈	C₂²	semidirect
33. C₁₉×C₄⋊Q₈	C₂²	semidirect
34. C₁₉×#123	C₂²	semidirect
35. C₁₉×#123	C₂²	semidirect
36. C₁₉×C₂²⋊Q₈	C₂²	semidirect
38. C₁₉×#121	C₂²	semidirect
39. C₄×D₄×C₁₉	C₂²	semidirect
40. C₄×D₄×C₁₉	C₂²	semidirect
41. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
42. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
43. #10597393	C₂²	semidirect
45. #10597392	C₂²	semidirect
46. #10597392	C₂²	semidirect
48. #10597385	C₂²	semidirect
49. #10597385	C₂²	semidirect
50. #10597385	C₂²	semidirect
51. #10597385	C₂²	semidirect
53. #10597384	C₂²	semidirect
54. #10597384	C₂²	semidirect
57. #10597382	C₂²	semidirect
58. D₄×Dic₁₉	C₂²	semidirect
60. #10597376	C₂²	semidirect
61. #10597376	C₂²	semidirect
62. #10597376	C₂²	semidirect
63. #10597375	C₂²	semidirect
64. #10597375	C₂²	semidirect
67. C₄×C₂²⋊D₁₉	C₂²	semidirect
70. C₂×C₄⋊Dic₁₉	C₂²	semidirect
71. #10597370	C₂²	semidirect
72. #10597370	C₂²	semidirect
73. #10597370	C₂²	semidirect
74. #10597344	C₂²	semidirect
78. #10597343	C₂²	semidirect
79. #10597343	C₂²	semidirect
80. #10597343	C₂²	semidirect
81. #10597343	C₂²	semidirect
82. #10597343	C₂²	semidirect
85. #10597342	C₂²	semidirect
86. #10597342	C₂²	semidirect
88. #10597341	C₂²	semidirect
89. #10597341	C₂²	semidirect
90. #10597340	C₂²	semidirect
91. #10597340	C₂²	semidirect
92. #10597340	C₂²	semidirect
94. #10597339	C₂²	semidirect
96. C₄⋊C₄×D₁₉	C₂²	semidirect
97. #10597336	C₂²	semidirect
98. #10597335	C₂²	semidirect
99. #10597334	C₂²	semidirect
100. #10597333	C₂²	semidirect
101. #10597332	C₂²	semidirect
102. #10597331	C₂²	semidirect
103. #10597331	C₂²	semidirect
104. #10597331	C₂²	semidirect
107. #10597330	C₂²	semidirect
108. #10597329	C₂²	semidirect
109. #10597329	C₂²	semidirect
112. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
115. #10597325	C₂²	semidirect
116. #10597324	C₂²	semidirect
117. #10597324	C₂²	semidirect
118. #10597324	C₂²	semidirect
119. #10597321	C₂²	semidirect
121. #10597318	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
349. #547	D₁₉	semidirect
379. C₂×#41	C₂×D₁₉	semidirect
385. C₄⋊Q₈	C₂×D₁₉	semidirect
404. #123	C₂×D₁₉	semidirect
405. #123	C₂×D₁₉	semidirect
427. C₂²⋊Q₈	C₂×D₁₉	semidirect
447. #121	C₂×D₁₉	semidirect
462. C₄×D₄	C₂×D₁₉	semidirect
463. C₄×D₄	C₂×D₁₉	semidirect
468. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
469. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
474. C₁₉	#3536	semidirect

Maximal subgroups

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

subgroup	index
#11927291	2
#11927290	2
#11927255	2
#11927249	2
#11927203	2
#11927200	2
#11927195	2
#11927191	2
#11927189	2
#11927186	2
#11927182	2
#11927169	2
#11927168	2
#11927159	2
#11927138	2
#11927130	2
#11927125	2
#11927123	2
#11927122	2
#11927053	2
C₂×#10597343	2
#121×D₁₉	2
C₁₉×#547	2
#3536	19