Subgroups — #14577586

Order 2432.

1142 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	#11927262	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927259	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927257	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927223	C₂	1	2	yes	maximal, complemented
6	#11927220	C₂	1	2	yes	maximal, complemented
7	D₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927203	C₂	1	2	yes	maximal, complemented
9	#11927189	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927188	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927184	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927165	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927159	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927132	C₂	1	2	yes	maximal, complemented
16	#11927127	C₂	1	2	yes	maximal, complemented
17	#11927091	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927074	C₂	1	2	yes	maximal, complemented
19	#11927072	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10597331	C₂	1	2	yes	maximal, complemented
21	#11927016	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#64543	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
26	C₂×#64543	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
28	C₂×#64541	C₂²	1	2	yes	complemented
29	C₂²×Dic₃₈	C₂²	1	2	yes	complemented
30	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
35	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
40	#10597399	C₂²	1	2	yes	—
41	#10597399	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
43	#10597386	C₂²	1	1	yes	characteristic
44	#10597385	C₂²	1	2	yes	—
45	#10597385	C₂²	1	2	yes	complemented
46	#10597384	C₂²	1	1	yes	characteristic
47	#10597384	C₂²	1	1	yes	characteristic, complemented
48	#10597383	C₂²	1	2	yes	—
49	#10597382	C₂²	1	1	yes	characteristic, complemented
50	#10597381	C₂²	1	2	yes	complemented
51	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
52	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
53	#10597376	C₂²	1	1	yes	characteristic
54	#10597376	C₂²	1	2	yes	complemented
55	#10597376	C₂²	1	2	yes	complemented
56	#10597375	C₂²	1	2	yes	complemented
57	#10597375	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
64	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
65	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
66	#10597372	C₂²	1	2	yes	complemented
67	#10597370	C₂²	1	2	yes	complemented
68	#10597370	C₂²	1	2	yes	complemented
69	#10597370	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄×Dic₁₉	C₂²	1	2	yes	complemented
71	#10597344	C₂²	1	1	yes	characteristic, complemented
72	#10597344	C₂²	1	2	yes	complemented
73	#10597343	C₂²	1	1	yes	characteristic, complemented
74	#10597342	C₂²	1	1	yes	characteristic, complemented
75	#10597342	C₂²	1	2	yes	complemented
76	#10597341	C₂²	1	1	yes	characteristic, complemented
77	#10597340	C₂²	1	1	yes	characteristic, complemented
78	#10597339	C₂²	1	1	yes	characteristic, complemented
79	#10597338	C₂²	1	1	yes	characteristic, complemented
80	#10597338	C₂²	1	1	yes	characteristic, complemented
81	#10597335	C₂²	1	1	yes	characteristic, complemented
82	#10597334	C₂²	1	1	yes	characteristic, complemented
83	#10597334	C₂²	1	1	yes	characteristic, complemented
84	#10597333	C₂²	1	1	yes	characteristic, complemented
85	#10597332	C₂²	1	2	yes	complemented
86	#10597331	C₂²	1	1	yes	characteristic
87	#10597331	C₂²	1	2	yes	—
88	#10597331	C₂²	1	2	yes	complemented
89	#10597331	C₂²	1	2	yes	complemented
90	#10597331	C₂²	1	2	yes	complemented
91	#10597331	C₂²	1	2	yes	complemented
92	#10597331	C₂²	1	2	yes	complemented
93	#10597331	C₂²	1	2	yes	complemented
94	#10597331	C₂²	1	2	yes	complemented
95	#10597330	C₂²	1	1	yes	characteristic
96	#10597330	C₂²	1	2	yes	complemented
97	#10597330	C₂²	1	2	yes	complemented
98	#10597329	C₂²	1	1	yes	characteristic, complemented
99	#10597329	C₂²	1	2	yes	complemented
100	#10597329	C₂²	1	2	yes	complemented
101	#10597328	C₂²	1	2	yes	complemented
102	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
103	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
104	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
105	#10597325	C₂²	1	1	yes	characteristic, complemented
106	#10597325	C₂²	1	2	yes	complemented
107	#10597325	C₂²	1	2	yes	complemented
108	#10597324	C₂²	1	2	yes	complemented
109	#10597324	C₂²	1	2	yes	complemented
110	#10597323	C₂²	1	2	yes	complemented
111	#10597322	C₂²	1	2	yes	complemented
112	#10597321	C₂²	1	2	yes	complemented
113	#10597321	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
116	#10597318	C₂²	1	1	yes	characteristic, complemented
117	#10597318	C₂²	1	2	yes	complemented
118	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
119	#10597315	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	C₂²	1	2	yes	complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₉	C₂³	1	2	yes	—
124	C₂³×D₁₉	C₂³	1	2	yes	—
125	C₂×D₄×C₁₉	—	2	4	no	—
126	C₂×D₄×C₁₉	C₂³	1	2	yes	—
127	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₉	—	4	4	no	—
135	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
144	C₂²×Dic₁₉	C₂³	1	2	yes	—
145	C₂²×Dic₁₉	C₂³	1	2	yes	—
146	C₂²×Dic₁₉	C₂³	1	2	yes	—
147	#64543	—	2	4	no	—
148	D₄×D₁₉	—	2	4	no	—
149	#64541	—	4	4	no	—
150	C₂×D₇₆	C₂³	1	1	yes	characteristic
151	C₂×D₇₆	C₂³	1	1	yes	characteristic
152	C₂×D₇₆	C₂³	1	2	yes	—
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	2	yes	—
157	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₉	C₂³	1	2	yes	—
159	C₂×Dic₃₈	—	4	4	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	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
176	C₄²×C₁₉	C₂³	1	1	yes	characteristic
177	C₄²×C₁₉	C₂³	1	1	yes	characteristic
178	C₄²×C₁₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
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	2	yes	—
187	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₉)⋊C₄	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	1	yes	characteristic
194	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
202	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
203	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	C₄⋊Dic₁₉	C₂³	1	2	yes	—
206	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	2	yes	—
219	Dic₁₉⋊C₄	C₂³	1	2	yes	—
220	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₉	C₂³	1	2	yes	—
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	—	2	4	no	—
229	C₂³×C₁₉	—	4	2	no	—
230	C₂³×C₁₉	—	4	2	no	—
231	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₉	C₂⁴	1	2	yes	—
233	C₂³×C₁₉	C₂⁴	1	2	yes	—
234	C₂²×D₁₉	—	2	4	no	—
235	C₂²×D₁₉	—	4	2	no	—
236	C₂²×D₁₉	—	4	2	no	—
237	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₉	C₂⁴	1	2	yes	—
239	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
240	D₄×C₁₉	—	2	4	no	—
241	D₄×C₁₉	—	2	2	no	—
242	D₄×C₁₉	#41	1	4	yes	complemented
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	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	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	4	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	C₂²⋊D₁₉	—	4	1	no	—
264	C₂²⋊D₁₉	—	4	2	no	—
265	C₂×Dic₁₉	—	2	4	no	—
266	C₂×Dic₁₉	—	2	4	no	—
267	C₂×Dic₁₉	—	4	2	no	—
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	2	yes	—
272	C₂×Dic₁₉	C₂⁴	1	2	yes	—
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₉	C₂⁴	1	2	yes	—
275	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
277	D₇₆	—	2	2	no	—
278	D₇₆	—	4	1	no	—
279	D₇₆	—	4	2	no	—
280	C₄×D₁₉	—	2	2	no	—
281	C₄×D₁₉	—	2	2	no	—
282	C₄×D₁₉	—	2	2	no	—
283	C₄×D₁₉	—	4	2	no	—
284	C₄×D₁₉	—	4	1	no	—
285	C₄×D₁₉	—	4	2	no	—
286	Dic₃₈	—	2	2	no	—
287	Dic₃₈	—	2	2	no	—
288	Dic₃₈	—	2	4	no	—
289	Dic₃₈	—	4	2	no	—
290	Dic₃₈	—	4	2	no	—
291	#3514	—	19	1	no	maximal, Sylow
292	C₂²×C₁₉	—	2	2	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	2	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	—	8	4	no	—
301	C₂²×C₁₉	C₂×#41	1	4	yes	—
302	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
303	C₂×D₁₉	—	2	1	no	—
304	C₂×D₁₉	—	2	1	no	—
305	C₂×D₁₉	—	2	2	no	—
306	C₂×D₁₉	—	2	1	no	—
307	C₂×D₁₉	—	2	2	no	—
308	C₂×D₁₉	—	2	1	no	—
309	C₂×D₁₉	—	2	1	no	—
310	C₂×D₁₉	—	2	2	no	—
311	C₂×D₁₉	—	2	1	no	—
312	C₂×D₁₉	—	8	4	no	—
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	1	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	1	no	—
325	Dic₁₉	—	2	2	no	—
326	Dic₁₉	—	2	2	no	—
327	Dic₁₉	—	2	1	no	—
328	Dic₁₉	—	2	1	no	—
329	Dic₁₉	H(5,𝔽₂)	1	2	yes	—
330	#559	—	19	1	no	—
331	#556	—	19	1	no	—
332	#555	—	19	1	no	—
333	#555	—	19	1	no	—
334	#551	—	19	2	no	—
335	#551	—	19	2	no	—
336	D₄×Q₈	—	19	1	no	—
337	#548	—	19	2	no	—
338	#546	—	19	1	no	—
339	#546	—	19	1	no	—
340	#546	—	19	2	no	—
341	D₄²	—	19	1	no	—
342	#542	—	19	1	no	—
343	#542	—	19	1	no	—
344	#538	—	19	2	no	—
345	#538	—	19	2	no	—
346	#532	—	19	1	no	—
347	#529	—	19	2	no	—
348	#529	—	19	1	no	—
349	C₂×#124	—	19	2	no	—
350	#518	—	19	1	no	—
351	#518	D₁₉	1	1	yes	characteristic, complemented
352	C₄×#41	—	19	1	no	—
353	C₂×C₁₉	—	2	4	no	—
354	C₂×C₁₉	—	4	2	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	—	4	1	no	—
360	D₁₉	—	4	2	no	—
361	D₁₉	—	4	1	no	—
362	C₂×#41	—	19	1	no	—
363	C₂×#41	—	19	2	no	—
364	C₂²×Q₈	—	19	2	no	—
365	C₂²×D₄	—	19	2	no	—
366	C₂²×D₄	—	19	1	no	—
367	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
368	C₄⋊Q₈	—	19	1	no	—
369	C₄⋊Q₈	—	19	1	no	—
370	C₄⋊Q₈	—	19	1	no	—
371	#127	—	19	1	no	—
372	#126	—	19	2	no	—
373	#126	—	19	1	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	#124	—	19	1	no	—
380	#124	—	19	1	no	—
381	#124	—	19	2	no	—
382	#124	—	19	2	no	—
383	#124	—	19	2	no	—
384	#124	—	19	2	no	—
385	#124	—	19	2	no	—
386	#124	—	19	2	no	—
387	#124	—	19	2	no	—
388	#124	—	19	2	no	—
389	#124	—	19	2	no	—
390	#124	—	19	1	no	—
391	#123	—	19	2	no	—
392	#123	—	19	2	no	—
393	#123	—	19	2	no	—
394	#123	—	19	1	no	—
395	#123	—	19	1	no	—
396	#123	—	19	2	no	—
397	#123	—	19	2	no	—
398	#123	—	19	2	no	—
399	C₂²⋊Q₈	—	19	2	no	—
400	C₂²⋊Q₈	—	19	1	no	—
401	C₂²⋊Q₈	—	19	2	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	2	no	—
407	#121	—	19	1	no	—
408	#121	—	19	1	no	—
409	#121	—	19	2	no	—
410	#121	—	19	2	no	—
411	#121	—	19	1	no	—
412	#121	—	19	2	no	—
413	#121	—	19	2	no	—
414	#121	—	19	1	no	—
415	#121	—	19	1	no	—
416	#121	—	19	2	no	—
417	#121	—	19	2	no	—
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	2	no	—
425	C₄×Q₈	—	19	1	no	—
426	C₄×D₄	—	19	1	no	—
427	C₄×D₄	—	19	1	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	2	no	—
433	C₄×D₄	—	19	2	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	—	19	2	no	—
436	C₄×D₄	—	19	2	no	—
437	C₄×D₄	—	19	1	no	—
438	C₄×D₄	—	19	1	no	—
439	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
440	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
441	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
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	2	no	—
446	#117	—	19	1	no	—
447	#117	—	19	1	no	—
448	#117	—	19	2	no	—
449	#117	—	19	1	no	—
450	#117	—	19	2	no	—
451	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
452	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
453	C₂×C₂²⋊C₄	—	19	2	no	—
454	C₂×C₂²⋊C₄	—	19	2	no	—
455	C₂×C₂²⋊C₄	—	19	2	no	—
456	C₂×C₂²⋊C₄	—	19	2	no	—
457	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	complemented
458	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	complemented
459	C₂×C₄²	—	19	2	no	—
460	C₂×C₄²	—	19	1	no	—
461	C₁₉	#3514	1	1	yes	characteristic, complemented, Sylow
462	C₂⁴	—	19	2	no	—
463	C₂⁴	C₂²×D₁₉	1	2	yes	—
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×Q₈	—	19	2	no	—
470	C₂×Q₈	—	19	2	no	—
471	C₂×Q₈	—	76	4	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	19	2	no	—
474	C₂×D₄	—	19	2	no	—
475	C₂×D₄	—	19	1	no	—
476	C₂×D₄	—	19	2	no	—
477	C₂×D₄	—	19	1	no	—
478	C₂×D₄	—	19	2	no	—
479	C₂×D₄	—	19	2	no	—
480	C₂×D₄	—	19	2	no	—
481	C₂×D₄	—	19	2	no	—
482	C₂×D₄	—	19	1	no	—
483	C₂×D₄	—	19	1	no	—
484	C₂×D₄	—	19	2	no	—
485	C₂×D₄	—	38	4	no	—
486	C₂×D₄	—	76	4	no	—
487	C₂×D₄	C₂²×D₁₉	1	2	yes	—
488	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
490	C₂²×C₄	—	19	2	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	—	19	1	no	—
496	C₂²×C₄	—	19	1	no	—
497	C₂²×C₄	—	19	2	no	—
498	C₂²×C₄	—	19	2	no	—
499	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
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	1	no	—
506	C₄⋊C₄	—	19	1	no	—
507	C₄⋊C₄	—	19	2	no	—
508	C₄⋊C₄	—	19	2	no	—
509	C₄⋊C₄	—	19	2	no	—
510	C₄⋊C₄	—	19	1	no	—
511	C₄⋊C₄	—	19	1	no	—
512	C₄⋊C₄	—	19	2	no	—
513	C₄⋊C₄	—	19	2	no	—
514	C₄⋊C₄	—	19	1	no	—
515	C₄⋊C₄	—	19	1	no	—
516	C₄⋊C₄	—	19	1	no	—
517	C₄⋊C₄	—	19	1	no	—
518	C₄⋊C₄	—	19	2	no	—
519	C₄⋊C₄	—	19	2	no	—
520	C₄⋊C₄	—	19	1	no	—
521	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
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	C₂²⋊C₄	—	19	1	no	—
526	C₂²⋊C₄	—	19	2	no	—
527	C₂²⋊C₄	—	19	2	no	—
528	C₂²⋊C₄	—	19	2	no	—
529	C₂²⋊C₄	—	19	2	no	—
530	C₂²⋊C₄	—	19	2	no	—
531	C₂²⋊C₄	—	19	2	no	—
532	C₂²⋊C₄	—	19	1	no	—
533	C₂²⋊C₄	—	19	2	no	—
534	C₂²⋊C₄	—	19	1	no	—
535	C₂²⋊C₄	—	19	2	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	1	no	—
538	C₂²⋊C₄	—	19	2	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	2	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	1	no	—
546	C₂²⋊C₄	—	19	2	no	—
547	C₂²⋊C₄	—	19	1	no	—
548	C₂²⋊C₄	—	19	1	no	—
549	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
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	2	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	—	19	1	no	—
564	C₄²	C₂²×D₁₉	1	1	yes	characteristic
565	C₄²	C₂²×D₁₉	1	2	yes	—
566	C₄²	C₂²×D₁₉	1	1	yes	characteristic
567	C₂³	—	2	4	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	19	1	no	—
571	C₂³	—	19	2	no	—
572	C₂³	—	19	1	no	—
573	C₂³	—	38	4	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	2	yes	—
579	Q₈	—	38	2	no	—
580	Q₈	—	38	4	no	—
581	Q₈	—	38	2	no	—
582	Q₈	—	76	2	no	—
583	Q₈	—	76	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	38	2	no	—
587	D₄	—	38	4	no	—
588	D₄	—	38	4	no	—
589	D₄	—	38	4	no	—
590	D₄	—	38	2	no	—
591	D₄	—	76	2	no	—
592	D₄	—	76	1	no	—
593	D₄	—	76	2	no	—
594	D₄	—	76	2	no	—
595	D₄	—	76	2	no	—
596	D₄	—	76	1	no	—
597	D₄	—	76	2	no	—
598	D₄	#64541	1	4	yes	complemented
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	19	1	no	—
605	C₂×C₄	—	19	1	no	—
606	C₂×C₄	—	19	2	no	—
607	C₂×C₄	—	19	1	no	—
608	C₂×C₄	—	19	1	no	—
609	C₂×C₄	—	19	2	no	—
610	C₂×C₄	—	19	1	no	—
611	C₂×C₄	—	19	1	no	—
612	C₂×C₄	—	19	2	no	—
613	C₂×C₄	—	38	2	no	—
614	C₂×C₄	—	38	4	no	—
615	C₂×C₄	—	38	4	no	—
616	C₂×C₄	—	38	2	no	—
617	C₂×C₄	—	38	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	2	yes	—
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	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₉	1	2	yes	—
629	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	8	4	no	—
639	C₂²	—	38	1	no	—
640	C₂²	—	38	1	no	—
641	C₂²	—	38	2	no	—
642	C₂²	—	38	1	no	—
643	C₂²	—	38	2	no	—
644	C₂²	—	38	1	no	—
645	C₂²	—	38	1	no	—
646	C₂²	—	38	2	no	—
647	C₂²	—	38	1	no	—
648	C₂²	—	152	4	no	—
649	C₂²	C₂×#64541	1	4	yes	—
650	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	19	2	no	—
659	C₄	—	38	1	no	—
660	C₄	—	38	1	no	—
661	C₄	—	38	2	no	—
662	C₄	—	38	2	no	—
663	C₄	—	38	2	no	—
664	C₄	—	38	1	no	—
665	C₄	—	38	1	no	—
666	C₄	—	38	1	no	—
667	C₄	C₂×#64541	1	2	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	2	no	—
671	C₂	—	76	1	no	—
672	C₂	—	76	2	no	—
673	C₂	—	76	1	no	—
674	C₂	C₂²×#64541	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
676	C₂	#11927379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#518	C₂
hypercenter	#518	D₁₉
hypocenter	C₁₉	#3514
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. #11927277	C₂	semidirect
2. #11927262	C₂	semidirect
3. #11927259	C₂	semidirect
4. #11927257	C₂	semidirect
5. #11927223	C₂	semidirect
6. #11927220	C₂	semidirect
7. D₄×Dic₃₈	C₂	semidirect
8. #11927203	C₂	semidirect
9. #11927189	C₂	semidirect
10. #11927188	C₂	semidirect
11. #11927184	C₂	semidirect
12. D₄×C₂²⋊D₁₉	C₂	semidirect
13. #11927165	C₂	semidirect
14. #11927159	C₂	semidirect
15. #11927132	C₂	semidirect
16. #11927127	C₂	semidirect
17. #11927091	C₂	semidirect
18. #11927074	C₂	semidirect
19. #11927072	C₂	semidirect
20. C₂×#10597331	C₂	semidirect
21. #11927016	C₂	semidirect
22. C₄×#64543	C₂	semidirect
23. C₁₉×#518	C₂	semidirect
28. C₂×#64541	C₂²	semidirect
29. C₂²×Dic₃₈	C₂²	semidirect
32. C₄×D₄×C₁₉	C₂²	semidirect
33. C₄×D₄×C₁₉	C₂²	semidirect
34. C₄×D₄×C₁₉	C₂²	semidirect
35. C₄×D₄×C₁₉	C₂²	semidirect
36. C₁₉×#117	C₂²	semidirect
37. C₁₉×#117	C₂²	semidirect
38. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
39. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
41. #10597399	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
45. #10597385	C₂²	semidirect
47. #10597384	C₂²	semidirect
49. #10597382	C₂²	semidirect
50. #10597381	C₂²	semidirect
54. #10597376	C₂²	semidirect
55. #10597376	C₂²	semidirect
56. #10597375	C₂²	semidirect
57. #10597375	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. C₄×C₂²⋊D₁₉	C₂²	semidirect
64. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
65. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
66. #10597372	C₂²	semidirect
67. #10597370	C₂²	semidirect
68. #10597370	C₂²	semidirect
69. #10597370	C₂²	semidirect
70. C₂×C₄×Dic₁₉	C₂²	semidirect
71. #10597344	C₂²	semidirect
72. #10597344	C₂²	semidirect
73. #10597343	C₂²	semidirect
74. #10597342	C₂²	semidirect
75. #10597342	C₂²	semidirect
76. #10597341	C₂²	semidirect
77. #10597340	C₂²	semidirect
78. #10597339	C₂²	semidirect
79. #10597338	C₂²	semidirect
80. #10597338	C₂²	semidirect
81. #10597335	C₂²	semidirect
82. #10597334	C₂²	semidirect
83. #10597334	C₂²	semidirect
84. #10597333	C₂²	semidirect
85. #10597332	C₂²	semidirect
88. #10597331	C₂²	semidirect
89. #10597331	C₂²	semidirect
90. #10597331	C₂²	semidirect
91. #10597331	C₂²	semidirect
92. #10597331	C₂²	semidirect
93. #10597331	C₂²	semidirect
94. #10597331	C₂²	semidirect
96. #10597330	C₂²	semidirect
97. #10597330	C₂²	semidirect
98. #10597329	C₂²	semidirect
99. #10597329	C₂²	semidirect
100. #10597329	C₂²	semidirect
101. #10597328	C₂²	semidirect
102. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
103. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
104. C₂²⋊C₄×D₁₉	C₂²	semidirect
105. #10597325	C₂²	semidirect
106. #10597325	C₂²	semidirect
107. #10597325	C₂²	semidirect
108. #10597324	C₂²	semidirect
109. #10597324	C₂²	semidirect
110. #10597323	C₂²	semidirect
111. #10597322	C₂²	semidirect
112. #10597321	C₂²	semidirect
113. #10597321	C₂²	semidirect
114. C₄×D₇₆	C₂²	semidirect
115. C₄×D₇₆	C₂²	semidirect
116. #10597318	C₂²	semidirect
117. #10597318	C₂²	semidirect
118. C₄²×D₁₉	C₂²	semidirect
119. #10597315	C₂²	semidirect
120. C₄×Dic₃₈	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
242. D₄×C₁₉	#41	semidirect
351. #518	D₁₉	semidirect
441. C₄×D₄	C₂×D₁₉	semidirect
442. C₄×D₄	C₂×D₁₉	semidirect
443. C₄×D₄	C₂×D₁₉	semidirect
444. C₄×D₄	C₂×D₁₉	semidirect
451. #117	C₂×D₁₉	semidirect
452. #117	C₂×D₁₉	semidirect
457. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
458. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
461. C₁₉	#3514	semidirect
598. D₄	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927277	2
#11927262	2
#11927259	2
#11927257	2
#11927223	2
#11927220	2
D₄×Dic₃₈	2
#11927203	2
#11927189	2
#11927188	2
#11927184	2
D₄×C₂²⋊D₁₉	2
#11927165	2
#11927159	2
#11927132	2
#11927127	2
#11927091	2
#11927074	2
#11927072	2
C₂×#10597331	2
#11927016	2
C₄×#64543	2
C₁₉×#518	2
#3514	19