Subgroups — #14577881

Order 2432.

1014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927298	C₂	1	2	yes	maximal, complemented
2	#11927296	C₂	1	2	yes	maximal, complemented
3	#11927233	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927232	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927229	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927218	C₂	1	2	yes	maximal, complemented
7	#11927217	C₂	1	2	yes	maximal, complemented
8	Q₈×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927207	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927207	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927174	C₂	1	2	yes	maximal, complemented
13	#11927172	C₂	1	2	yes	maximal, complemented
14	#11927157	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927152	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927138	C₂	1	2	yes	maximal, complemented
17	#11927135	C₂	1	2	yes	maximal, complemented
18	#11927120	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927117	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927053	C₂	1	1	yes	maximal, characteristic
21	C₂×#10597343	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#552	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×#64541	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
28	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
29	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#126	C₂²	1	2	yes	complemented
31	C₁₉×#125	C₂²	1	2	yes	complemented
32	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#123	C₂²	1	2	yes	—
34	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#117	C₂²	1	2	yes	—
39	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	#10597392	C₂²	1	1	yes	characteristic
42	#10597390	C₂²	1	1	yes	characteristic, complemented
43	#10597385	C₂²	1	1	yes	characteristic
44	#10597383	C₂²	1	1	yes	characteristic
45	D₄×Dic₁₉	C₂²	1	2	yes	—
46	#10597375	C₂²	1	2	yes	—
47	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
49	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
50	#10597372	C₂²	1	2	yes	—
51	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
52	#10597370	C₂²	1	1	yes	characteristic
53	#10597370	C₂²	1	1	yes	characteristic, complemented
54	#10597344	C₂²	1	2	yes	—
55	#10597344	C₂²	1	2	yes	—
56	#10597344	C₂²	1	2	yes	—
57	#10597344	C₂²	1	2	yes	complemented
58	#10597344	C₂²	1	2	yes	complemented
59	#10597343	C₂²	1	2	yes	—
60	#10597343	C₂²	1	1	yes	characteristic
61	#10597343	C₂²	1	1	yes	characteristic
62	#10597343	C₂²	1	2	yes	—
63	#10597343	C₂²	1	1	yes	characteristic
64	#10597343	C₂²	1	1	yes	characteristic
65	#10597343	C₂²	1	1	yes	characteristic
66	#10597343	C₂²	1	2	yes	—
67	#10597343	C₂²	1	2	yes	complemented
68	#10597343	C₂²	1	1	yes	characteristic, complemented
69	#10597343	C₂²	1	1	yes	characteristic, complemented
70	#10597342	C₂²	1	2	yes	—
71	#10597342	C₂²	1	1	yes	characteristic
72	#10597342	C₂²	1	2	yes	—
73	#10597342	C₂²	1	2	yes	complemented
74	#10597340	C₂²	1	1	yes	characteristic
75	#10597340	C₂²	1	2	yes	—
76	#10597340	C₂²	1	2	yes	—
77	#10597338	C₂²	1	2	yes	—
78	#10597338	C₂²	1	1	yes	characteristic, complemented
79	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
80	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
81	#10597336	C₂²	1	2	yes	complemented
82	#10597336	C₂²	1	2	yes	complemented
83	#10597336	C₂²	1	2	yes	complemented
84	#10597336	C₂²	1	1	yes	characteristic, complemented
85	#10597335	C₂²	1	2	yes	complemented
86	#10597335	C₂²	1	2	yes	complemented
87	#10597334	C₂²	1	2	yes	complemented
88	#10597334	C₂²	1	2	yes	complemented
89	#10597334	C₂²	1	2	yes	complemented
90	#10597334	C₂²	1	2	yes	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	complemented
95	#10597331	C₂²	1	2	yes	—
96	#10597330	C₂²	1	1	yes	characteristic
97	#10597329	C₂²	1	1	yes	characteristic
98	#10597329	C₂²	1	2	yes	—
99	#10597329	C₂²	1	2	yes	complemented
100	#10597328	C₂²	1	1	yes	characteristic
101	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
103	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
104	#10597325	C₂²	1	2	yes	complemented
105	#10597324	C₂²	1	1	yes	characteristic
106	#10597324	C₂²	1	2	yes	—
107	#10597324	C₂²	1	2	yes	—
108	#10597324	C₂²	1	2	yes	—
109	#10597324	C₂²	1	2	yes	complemented
110	#10597324	C₂²	1	2	yes	complemented
111	#10597322	C₂²	1	2	yes	—
112	#10597321	C₂²	1	2	yes	—
113	C₄×D₇₆	C₂²	1	1	yes	characteristic
114	C₄×D₇₆	C₂²	1	2	yes	—
115	#10597318	C₂²	1	1	yes	characteristic
116	#10597318	C₂²	1	2	yes	—
117	#10597316	C₂²	1	2	yes	complemented
118	#10597316	C₂²	1	2	yes	complemented
119	#10597315	C₂²	1	2	yes	complemented
120	#10597315	C₂²	1	2	yes	complemented
121	#10597315	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₉	C₂³	1	2	yes	—
134	C₂²×Dic₁₉	C₂³	1	2	yes	—
135	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
136	Q₈×D₁₉	—	4	2	no	—
137	Q₈×D₁₉	—	4	2	no	—
138	#64541	—	4	2	no	—
139	C₂×D₇₆	C₂³	1	1	yes	characteristic
140	C₂×D₇₆	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₉	—	4	2	no	—
142	C₂×C₄×D₁₉	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	1	yes	characteristic
147	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₉	C₂³	1	2	yes	—
150	C₂×Dic₃₈	—	4	2	no	—
151	C₂×Dic₃₈	—	4	2	no	—
152	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
153	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
154	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
155	C₂×Dic₃₈	C₂³	1	2	yes	—
156	C₂×Dic₃₈	C₂³	1	2	yes	—
157	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
158	C₂×Dic₃₈	C₂³	1	2	yes	—
159	C₂×Dic₃₈	C₂³	1	2	yes	—
160	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
164	C₄⋊C₄×C₁₉	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	2	yes	—
168	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
174	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₄²×C₁₉	C₂³	1	2	yes	—
176	C₄²×C₁₉	C₂³	1	2	yes	—
177	C₄²×C₁₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
182	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₁₉)⋊C₄	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	2	yes	—
193	(C₂×D₁₉)⋊C₄	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	C₄⋊Dic₁₉	C₂³	1	2	yes	—
198	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₉	C₂³	1	2	yes	—
200	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₉	C₂³	1	2	yes	—
202	C₄⋊Dic₁₉	C₂³	1	2	yes	—
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	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₁₉⋊C₄	C₂³	1	2	yes	—
217	Dic₁₉⋊C₄	C₂³	1	2	yes	—
218	Dic₁₉⋊C₄	C₂³	1	2	yes	—
219	Dic₁₉⋊C₄	C₂³	1	2	yes	—
220	Dic₁₉⋊C₄	C₂³	1	2	yes	—
221	Dic₁₉⋊C₄	C₂³	1	2	yes	—
222	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₉	—	2	2	no	—
231	C₂²×D₁₉	—	2	2	no	—
232	C₂²×D₁₉	—	4	1	no	—
233	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
236	Q₈×C₁₉	—	2	2	no	—
237	D₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₁₉	—	2	2	no	—
251	C₂²⋊D₁₉	—	2	2	no	—
252	C₂²⋊D₁₉	—	4	1	no	—
253	C₂²⋊D₁₉	—	4	1	no	—
254	C₂×Dic₁₉	—	4	2	no	—
255	C₂×Dic₁₉	—	4	2	no	—
256	C₂×Dic₁₉	—	4	1	no	—
257	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₉	C₂⁴	1	2	yes	—
260	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₉	C₂⁴	1	2	yes	—
262	C₂×Dic₁₉	C₂⁴	1	2	yes	—
263	C₂×Dic₁₉	C₂⁴	1	2	yes	—
264	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
266	D₇₆	—	2	2	no	—
267	D₇₆	—	4	1	no	—
268	C₄×D₁₉	—	2	4	no	—
269	C₄×D₁₉	—	2	2	no	—
270	C₄×D₁₉	—	2	2	no	—
271	C₄×D₁₉	—	2	2	no	—
272	C₄×D₁₉	—	4	1	no	—
273	C₄×D₁₉	—	4	1	no	—
274	C₄×D₁₉	—	4	2	no	—
275	C₄×D₁₉	—	4	2	no	—
276	Dic₃₈	—	2	2	no	—
277	Dic₃₈	—	2	2	no	—
278	Dic₃₈	—	2	2	no	—
279	Dic₃₈	—	4	2	no	—
280	Dic₃₈	—	4	2	no	—
281	Dic₃₈	—	4	1	no	—
282	Dic₃₈	—	4	2	no	—
283	Dic₃₈	—	4	2	no	—
284	#3538	—	19	1	no	maximal, Sylow
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
291	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
292	C₂×D₁₉	—	2	1	no	—
293	C₂×D₁₉	—	2	1	no	—
294	C₂×D₁₉	—	2	1	no	—
295	C₂×D₁₉	—	2	1	no	—
296	C₂×D₁₉	—	2	1	no	—
297	C₂×D₁₉	—	2	1	no	—
298	C₂×D₁₉	—	2	1	no	—
299	C₂×D₁₉	—	2	1	no	—
300	C₂×D₁₉	—	4	4	no	—
301	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	2	no	—
306	C₄×C₁₉	—	2	1	no	—
307	C₄×C₁₉	—	2	2	no	—
308	C₄×C₁₉	—	2	2	no	—
309	C₄×C₁₉	—	2	1	no	—
310	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
311	Dic₁₉	—	2	2	no	—
312	Dic₁₉	—	2	2	no	—
313	Dic₁₉	—	2	2	no	—
314	Dic₁₉	—	2	1	no	—
315	Dic₁₉	—	2	1	no	—
316	Dic₁₉	—	2	1	no	—
317	Dic₁₉	—	2	2	no	—
318	Dic₁₉	—	2	1	no	—
319	Dic₁₉	—	2	1	no	—
320	#563	—	19	2	no	—
321	#563	—	19	2	no	—
322	#552	—	19	1	no	—
323	#552	—	19	1	no	—
324	#552	—	19	1	no	—
325	#552	D₁₉	1	1	yes	characteristic, complemented
326	#551	—	19	2	no	—
327	#551	—	19	2	no	—
328	D₄×Q₈	—	19	1	no	—
329	D₄×Q₈	—	19	1	no	—
330	D₄×Q₈	—	19	1	no	—
331	D₄×Q₈	—	19	1	no	—
332	#544	—	19	2	no	—
333	#544	—	19	2	no	—
334	#541	—	19	1	no	—
335	#541	—	19	1	no	—
336	#539	—	19	2	no	—
337	#539	—	19	2	no	—
338	#536	—	19	1	no	—
339	#536	—	19	1	no	—
340	#525	—	19	1	no	—
341	C₂×C₂²⋊Q₈	—	19	1	no	—
342	C₂×C₂²⋊Q₈	—	19	1	no	—
343	C₂×C₁₉	—	2	2	no	—
344	C₂×C₁₉	—	4	1	no	—
345	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
347	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
348	D₁₉	—	2	2	no	—
349	D₁₉	—	4	1	no	—
350	D₁₉	—	4	1	no	—
351	C₂×#41	—	19	1	no	—
352	C₂²×Q₈	—	19	1	no	—
353	C₂²×Q₈	—	19	1	no	—
354	C₂²×Q₈	—	19	1	no	—
355	C₂²×Q₈	—	19	1	no	—
356	C₂³×C₄	—	19	1	no	—
357	C₄⋊Q₈	—	19	1	no	—
358	C₄⋊Q₈	—	19	2	no	—
359	C₄⋊Q₈	—	19	2	no	—
360	C₄⋊Q₈	—	19	2	no	—
361	C₄⋊Q₈	—	19	2	no	—
362	C₄⋊Q₈	—	19	2	no	—
363	C₄⋊Q₈	—	19	1	no	—
364	C₄⋊Q₈	—	19	2	no	—
365	#126	—	19	2	no	—
366	#126	—	19	2	no	—
367	#126	—	19	2	no	—
368	#126	—	19	2	no	—
369	#126	—	19	2	no	—
370	#126	—	19	2	no	—
371	#126	—	19	2	no	—
372	#126	C₂×D₁₉	1	2	yes	complemented
373	#125	—	19	2	no	—
374	#125	—	19	2	no	—
375	#125	—	19	2	no	—
376	#125	—	19	1	no	—
377	#125	—	19	2	no	—
378	#125	—	19	2	no	—
379	#125	—	19	2	no	—
380	#125	—	19	2	no	—
381	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
382	#125	C₂×D₁₉	1	2	yes	complemented
383	#124	—	19	2	no	—
384	#124	—	19	2	no	—
385	#123	—	19	2	no	—
386	#123	—	19	1	no	—
387	#123	—	19	2	no	—
388	#123	—	19	2	no	—
389	#123	—	19	1	no	—
390	#123	—	19	2	no	—
391	#123	—	19	2	no	—
392	#123	—	19	2	no	—
393	#123	—	19	2	no	—
394	#123	C₂×D₁₉	1	2	yes	—
395	C₂²⋊Q₈	—	19	1	no	—
396	C₂²⋊Q₈	—	19	1	no	—
397	C₂²⋊Q₈	—	19	1	no	—
398	C₂²⋊Q₈	—	19	1	no	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	1	no	—
401	C₂²⋊Q₈	—	19	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	1	no	—
407	C₂²⋊Q₈	—	19	1	no	—
408	C₂²⋊Q₈	—	19	1	no	—
409	C₂²⋊Q₈	—	19	2	no	—
410	C₂²⋊Q₈	—	19	2	no	—
411	C₂²⋊Q₈	—	19	2	no	—
412	C₂²⋊Q₈	—	19	2	no	—
413	C₂²⋊Q₈	—	19	2	no	—
414	C₂²⋊Q₈	—	19	1	no	—
415	C₂²⋊Q₈	—	19	2	no	—
416	C₂²⋊Q₈	—	19	2	no	—
417	C₂²⋊Q₈	—	19	2	no	—
418	C₂²⋊Q₈	—	19	2	no	—
419	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
420	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
421	#121	—	19	1	no	—
422	#121	—	19	1	no	—
423	#120	—	19	1	no	—
424	#120	—	19	1	no	—
425	C₄×Q₈	—	19	1	no	—
426	C₄×Q₈	—	19	1	no	—
427	C₄×Q₈	—	19	1	no	—
428	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
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	C₂×D₁₉	1	1	yes	characteristic
437	#117	—	19	2	no	—
438	#117	—	19	1	no	—
439	#117	—	19	2	no	—
440	#117	—	19	1	no	—
441	#117	—	19	2	no	—
442	#117	C₂×D₁₉	1	2	yes	—
443	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
444	C₂×C₄⋊C₄	—	19	2	no	—
445	C₂×C₄⋊C₄	—	19	2	no	—
446	C₂×C₄⋊C₄	—	19	1	no	—
447	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	—	19	2	no	—
449	C₂×C₂²⋊C₄	—	19	2	no	—
450	C₁₉	#3538	1	1	yes	characteristic, complemented, Sylow
451	C₂⁴	—	19	1	no	—
452	#41	—	76	2	no	—
453	C₂×Q₈	—	19	1	no	—
454	C₂×Q₈	—	19	1	no	—
455	C₂×Q₈	—	19	1	no	—
456	C₂×Q₈	—	19	2	no	—
457	C₂×Q₈	—	19	2	no	—
458	C₂×Q₈	—	19	2	no	—
459	C₂×Q₈	—	19	2	no	—
460	C₂×Q₈	—	19	1	no	—
461	C₂×Q₈	—	76	2	no	—
462	C₂×Q₈	—	76	2	no	—
463	C₂×Q₈	—	76	2	no	—
464	C₂×Q₈	—	76	2	no	—
465	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
466	C₂×D₄	—	19	1	no	—
467	C₂×D₄	—	19	1	no	—
468	C₂×D₄	—	19	1	no	—
469	C₂×D₄	—	19	1	no	—
470	C₂×D₄	—	19	1	no	—
471	C₂×D₄	—	19	1	no	—
472	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
473	C₂²×C₄	—	19	2	no	—
474	C₂²×C₄	—	19	1	no	—
475	C₂²×C₄	—	19	2	no	—
476	C₂²×C₄	—	19	2	no	—
477	C₂²×C₄	—	19	1	no	—
478	C₂²×C₄	—	19	1	no	—
479	C₂²×C₄	—	19	1	no	—
480	C₂²×C₄	—	19	2	no	—
481	C₂²×C₄	—	19	1	no	—
482	C₂²×C₄	—	19	2	no	—
483	C₂²×C₄	—	19	1	no	—
484	C₂²×C₄	—	76	2	no	—
485	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
486	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	1	no	—
493	C₄⋊C₄	—	19	2	no	—
494	C₄⋊C₄	—	19	2	no	—
495	C₄⋊C₄	—	19	2	no	—
496	C₄⋊C₄	—	19	2	no	—
497	C₄⋊C₄	—	19	1	no	—
498	C₄⋊C₄	—	19	1	no	—
499	C₄⋊C₄	—	19	2	no	—
500	C₄⋊C₄	—	19	2	no	—
501	C₄⋊C₄	—	19	2	no	—
502	C₄⋊C₄	—	19	1	no	—
503	C₄⋊C₄	—	19	2	no	—
504	C₄⋊C₄	—	19	2	no	—
505	C₄⋊C₄	—	19	2	no	—
506	C₄⋊C₄	—	19	2	no	—
507	C₄⋊C₄	—	19	2	no	—
508	C₄⋊C₄	—	19	2	no	—
509	C₄⋊C₄	—	19	2	no	—
510	C₄⋊C₄	—	19	2	no	—
511	C₄⋊C₄	—	19	2	no	—
512	C₄⋊C₄	—	19	2	no	—
513	C₄⋊C₄	—	19	1	no	—
514	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
516	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
521	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
524	C₂²⋊C₄	—	19	2	no	—
525	C₂²⋊C₄	—	19	1	no	—
526	C₂²⋊C₄	—	19	1	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	2	no	—
533	C₂²⋊C₄	—	19	2	no	—
534	C₂²⋊C₄	—	19	1	no	—
535	C₂²⋊C₄	—	19	1	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	1	no	—
538	C₂²⋊C₄	—	19	2	no	—
539	C₂²⋊C₄	—	19	1	no	—
540	C₂²⋊C₄	—	19	1	no	—
541	C₂²⋊C₄	—	19	2	no	—
542	C₂²⋊C₄	—	19	2	no	—
543	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
548	C₄²	—	19	2	no	—
549	C₄²	—	19	1	no	—
550	C₄²	—	19	2	no	—
551	C₄²	—	19	2	no	—
552	C₄²	—	19	2	no	—
553	C₄²	C₂²×D₁₉	1	2	yes	—
554	C₄²	C₂²×D₁₉	1	1	yes	characteristic
555	C₄²	C₂²×D₁₉	1	2	yes	—
556	C₂³	—	19	1	no	—
557	C₂³	—	19	1	no	—
558	C₂³	—	19	1	no	—
559	C₂³	—	38	2	no	—
560	C₂³	—	38	2	no	—
561	C₂³	—	76	1	no	—
562	C₂³	C₂³×D₁₉	1	1	yes	characteristic
563	C₂³	C₂³×D₁₉	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	38	2	no	—
566	Q₈	—	38	2	no	—
567	Q₈	—	38	2	no	—
568	Q₈	—	76	2	no	—
569	Q₈	—	76	2	no	—
570	Q₈	—	76	2	no	—
571	Q₈	—	76	2	no	—
572	Q₈	—	76	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	38	2	no	—
575	D₄	—	38	2	no	—
576	D₄	—	38	2	no	—
577	D₄	—	76	1	no	—
578	D₄	—	76	1	no	—
579	D₄	—	76	1	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	19	1	no	—
584	C₂×C₄	—	19	1	no	—
585	C₂×C₄	—	19	2	no	—
586	C₂×C₄	—	19	1	no	—
587	C₂×C₄	—	19	2	no	—
588	C₂×C₄	—	19	2	no	—
589	C₂×C₄	—	19	2	no	—
590	C₂×C₄	—	19	1	no	—
591	C₂×C₄	—	19	1	no	—
592	C₂×C₄	—	38	4	no	—
593	C₂×C₄	—	38	2	no	—
594	C₂×C₄	—	38	2	no	—
595	C₂×C₄	—	38	2	no	—
596	C₂×C₄	—	76	1	no	—
597	C₂×C₄	—	76	1	no	—
598	C₂×C₄	—	76	2	no	—
599	C₂×C₄	—	76	2	no	—
600	C₂×C₄	—	76	1	no	—
601	C₂×C₄	—	76	2	no	—
602	C₂×C₄	—	76	2	no	—
603	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₁₉	1	2	yes	—
605	C₂×C₄	C₂³×D₁₉	1	2	yes	—
606	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₉	1	2	yes	—
608	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₉	1	2	yes	—
610	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	19	2	no	—
618	C₂²	—	38	1	no	—
619	C₂²	—	38	1	no	—
620	C₂²	—	38	1	no	—
621	C₂²	—	38	1	no	—
622	C₂²	—	38	1	no	—
623	C₂²	—	38	1	no	—
624	C₂²	—	38	1	no	—
625	C₂²	—	38	1	no	—
626	C₂²	—	76	4	no	—
627	C₂²	#10597436	1	2	yes	—
628	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	38	1	no	—
638	C₄	—	38	1	no	—
639	C₄	—	38	1	no	—
640	C₄	—	38	2	no	—
641	C₄	—	38	2	no	—
642	C₄	—	38	2	no	—
643	C₄	—	38	2	no	—
644	C₄	—	38	1	no	—
645	C₄	—	38	1	no	—
646	C₄	#10597435	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	38	2	no	—
650	C₂	—	76	1	no	—
651	C₂	—	76	1	no	—
652	C₂	C₂×#10597435	1	1	yes	characteristic
653	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
654	C₂	C₂×#10597436	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#552	C₂
prime radical	#11927053	C₂
hypercenter	#552	D₁₉
hypocenter	C₁₉	#3538
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #11927298	C₂	semidirect
2. #11927296	C₂	semidirect
3. #11927233	C₂	semidirect
4. #11927232	C₂	semidirect
5. #11927229	C₂	semidirect
6. #11927218	C₂	semidirect
7. #11927217	C₂	semidirect
8. Q₈×D₇₆	C₂	semidirect
9. D₄×Dic₃₈	C₂	semidirect
10. #11927207	C₂	semidirect
11. #11927207	C₂	semidirect
12. #11927174	C₂	semidirect
13. #11927172	C₂	semidirect
14. #11927157	C₂	semidirect
15. #11927152	C₂	semidirect
16. #11927138	C₂	semidirect
17. #11927135	C₂	semidirect
18. #11927120	C₂	semidirect
19. #11927117	C₂	semidirect
21. C₂×#10597343	C₂	semidirect
22. C₂²⋊Q₈×D₁₉	C₂	semidirect
23. C₁₉×#552	C₂	semidirect
25. C₂×Q₈×D₁₉	C₂²	semidirect
29. C₂²×Dic₃₈	C₂²	semidirect
30. C₁₉×#126	C₂²	semidirect
31. C₁₉×#125	C₂²	semidirect
32. C₁₉×#125	C₂²	semidirect
35. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₉	C₂²	semidirect
39. C₁₉×#117	C₂²	semidirect
42. #10597390	C₂²	semidirect
53. #10597370	C₂²	semidirect
57. #10597344	C₂²	semidirect
58. #10597344	C₂²	semidirect
67. #10597343	C₂²	semidirect
68. #10597343	C₂²	semidirect
69. #10597343	C₂²	semidirect
73. #10597342	C₂²	semidirect
78. #10597338	C₂²	semidirect
81. #10597336	C₂²	semidirect
82. #10597336	C₂²	semidirect
83. #10597336	C₂²	semidirect
84. #10597336	C₂²	semidirect
85. #10597335	C₂²	semidirect
86. #10597335	C₂²	semidirect
87. #10597334	C₂²	semidirect
88. #10597334	C₂²	semidirect
89. #10597334	C₂²	semidirect
90. #10597334	C₂²	semidirect
91. #10597333	C₂²	semidirect
92. #10597333	C₂²	semidirect
94. #10597332	C₂²	semidirect
99. #10597329	C₂²	semidirect
104. #10597325	C₂²	semidirect
109. #10597324	C₂²	semidirect
110. #10597324	C₂²	semidirect
117. #10597316	C₂²	semidirect
118. #10597316	C₂²	semidirect
119. #10597315	C₂²	semidirect
120. #10597315	C₂²	semidirect
121. #10597315	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
325. #552	D₁₉	semidirect
372. #126	C₂×D₁₉	semidirect
381. #125	C₂×D₁₉	semidirect
382. #125	C₂×D₁₉	semidirect
420. C₂²⋊Q₈	C₂×D₁₉	semidirect
428. C₄×Q₈	C₂×D₁₉	semidirect
443. #117	C₂×D₁₉	semidirect
450. C₁₉	#3538	semidirect

Maximal subgroups

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

subgroup	index
#11927298	2
#11927296	2
#11927233	2
#11927232	2
#11927229	2
#11927218	2
#11927217	2
Q₈×D₇₆	2
D₄×Dic₃₈	2
#11927207	2
#11927174	2
#11927172	2
#11927157	2
#11927152	2
#11927138	2
#11927135	2
#11927120	2
#11927117	2
#11927053	2
C₂×#10597343	2
C₂²⋊Q₈×D₁₉	2
C₁₉×#552	2
#3538	19