Subgroups — #18087977

Order 4864.

1254 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11927024	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926526	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926517	C₂	1	1	yes	maximal, characteristic
4	#14563356	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563355	C₂	1	1	yes	maximal, characteristic, complemented
6	#14563344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	#11927024	—	2	2	no	—
11	#11927024	—	2	2	no	—
12	#11927024	—	2	2	no	—
13	#11927024	—	2	2	no	—
14	C₂×C₄×Dic₃₈	—	2	1	no	—
15	C₂×C₄×D₇₆	—	2	1	no	—
16	C₂×(C₂²⋊D₁₉)⋊C₄	—	2	2	no	—
17	C₂×#10597372	C₂²	1	1	yes	characteristic
18	C₂×#10597338	C₄	1	2	yes	complemented
19	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×D₁₉	C₄	1	2	yes	complemented
21	#11926526	—	2	2	no	—
22	#11926526	C₄	1	4	yes	complemented
23	C₂×#10597281	—	2	1	no	—
24	C₂×#10597280	—	2	1	no	—
25	#11926517	—	2	2	no	—
26	#11926517	C₄	1	4	yes	complemented
27	C₂×#10597263	—	2	2	no	—
28	#11926307	—	2	2	no	—
29	#11926306	—	2	2	no	—
30	#11926303	—	2	2	no	—
31	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
34	C₁₉×#339	—	2	2	no	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₂²⋊D₁₉	D₄	1	2	yes	—
37	C₂³×Dic₁₉	—	2	1	no	—
38	C₂×#64541	—	2	1	no	—
39	C₂×#64541	—	2	1	no	—
40	C₂×#64541	—	2	1	no	—
41	C₂×#64541	—	2	1	no	—
42	C₂×#64541	—	2	1	no	—
43	C₂×#64541	—	2	1	no	—
44	C₂×#64541	—	2	1	no	—
45	C₂×#64541	—	2	1	no	—
46	C₂×#64541	C₂×C₄	1	2	yes	—
47	C₂×#64541	C₂×C₄	1	2	yes	—
48	C₂×#64541	D₄	1	2	yes	—
49	C₂×#64541	Q₈	1	2	yes	—
50	C₂²×D₇₆	D₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₉	—	2	2	no	—
52	C₂²×C₄×D₁₉	C₂×C₄	1	2	yes	—
53	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
54	C₂×M₁₆×C₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₁₉×#117	—	2	1	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₁₉×#117	—	2	1	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	C₂×C₄	1	2	yes	complemented
67	C₁₉×#117	D₄	1	2	yes	—
68	C₁₉×#117	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄²×C₁₉	—	2	1	no	—
75	C₂×C₄²×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
77	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
78	#10597372	—	2	1	no	—
79	#10597372	—	2	1	no	—
80	#10597372	—	2	1	no	—
81	#10597372	C₂×C₄	1	2	yes	complemented
82	C₂×C₄⋊Dic₁₉	—	2	1	no	—
83	C₂×C₄⋊Dic₁₉	—	2	1	no	—
84	C₂×C₄⋊Dic₁₉	—	2	1	no	—
85	C₂×C₄⋊Dic₁₉	—	2	1	no	—
86	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
87	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
88	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
89	C₂×Dic₁₉⋊C₄	—	2	2	no	—
90	C₂×C₄×Dic₁₉	—	2	2	no	—
91	C₂×C₄×Dic₁₉	—	2	1	no	—
92	C₂×#64520	—	2	1	no	—
93	C₂×#64520	—	2	1	no	—
94	C₂×#64520	—	2	1	no	—
95	C₂×#64520	—	2	1	no	—
96	C₂×#64520	—	2	1	no	—
97	C₂×#64520	C₂×C₄	1	2	yes	complemented
98	C₂²×C₁₉⋊C₈	—	2	1	no	—
99	#10597338	—	2	4	no	—
100	#10597338	—	2	4	no	—
101	C₄⋊C₄×D₁₉	—	2	4	no	—
102	C₄⋊C₄×D₁₉	—	2	4	no	—
103	(C₂²⋊D₁₉)⋊C₄	—	2	8	no	—
104	(C₂²⋊D₁₉)⋊C₄	—	2	8	no	—
105	C₄×D₇₆	—	2	4	no	—
106	C₄×D₇₆	—	2	4	no	—
107	C₄×Dic₃₈	—	2	4	no	—
108	C₄×Dic₃₈	—	2	4	no	—
109	#10597281	—	2	4	no	—
110	#10597280	—	2	4	no	—
111	#10597263	—	2	8	no	—
112	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂³×D₁₉	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	1	no	—
116	C₂²×C₄×C₁₉	—	4	1	no	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₉	—	2	2	no	—
132	C₂×C₂²⋊D₁₉	—	2	2	no	—
133	C₂×C₂²⋊D₁₉	—	2	2	no	—
134	C₂×C₂²⋊D₁₉	—	2	2	no	—
135	C₂×C₂²⋊D₁₉	C₂²⋊C₄	1	4	yes	—
136	C₂×C₂²⋊D₁₉	C₄⋊C₄	1	4	yes	—
137	C₂²×Dic₁₉	—	2	2	no	—
138	C₂²×Dic₁₉	—	2	2	no	—
139	C₂²×Dic₁₉	—	2	2	no	—
140	C₂²×Dic₁₉	—	4	1	no	—
141	C₂²×Dic₁₉	—	8	2	no	—
142	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
143	#64541	—	2	2	no	—
144	#64541	—	2	2	no	—
145	#64541	—	2	2	no	—
146	#64541	—	2	2	no	—
147	#64541	—	2	2	no	—
148	#64541	—	2	2	no	—
149	#64541	—	2	2	no	—
150	#64541	—	2	2	no	—
151	#64541	—	2	2	no	—
152	#64541	—	2	2	no	—
153	#64541	—	2	2	no	—
154	#64541	—	2	2	no	—
155	#64541	—	2	2	no	—
156	#64541	—	2	2	no	—
157	#64541	—	2	2	no	—
158	#64541	—	2	2	no	—
159	C₂×D₇₆	—	2	1	no	—
160	C₂×D₇₆	—	2	1	no	—
161	C₂×D₇₆	—	2	1	no	—
162	C₂×D₇₆	—	2	1	no	—
163	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
164	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
165	C₂×C₄×D₁₉	—	2	2	no	—
166	C₂×C₄×D₁₉	—	2	2	no	—
167	C₂×C₄×D₁₉	—	2	2	no	—
168	C₂×C₄×D₁₉	—	2	2	no	—
169	C₂×C₄×D₁₉	—	2	8	no	—
170	C₂×C₄×D₁₉	—	8	4	no	—
171	C₂×C₄×D₁₉	C₄²	1	4	yes	—
172	C₂×C₄×D₁₉	C₄⋊C₄	1	4	yes	—
173	C₂×Dic₃₈	—	2	1	no	—
174	C₂×Dic₃₈	—	2	1	no	—
175	C₂×Dic₃₈	—	2	1	no	—
176	C₂×Dic₃₈	—	2	1	no	—
177	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
178	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
179	M₁₆×C₁₉	—	2	2	no	—
180	M₁₆×C₁₉	—	2	2	no	—
181	M₁₆×C₁₉	—	4	1	no	—
182	M₁₆×C₁₉	—	4	1	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	4	1	no	—
185	C₂×C₈×C₁₉	—	4	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	4	1	no	—
190	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
191	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₄²×C₁₉	—	2	2	no	—
197	C₄²×C₁₉	—	2	2	no	—
198	C₄²×C₁₉	—	2	2	no	—
199	C₄²×C₁₉	—	4	1	no	—
200	C₂²⋊Dic₁₉	—	2	2	no	—
201	C₂²⋊Dic₁₉	—	4	1	no	—
202	(C₂×D₁₉)⋊C₄	—	2	8	no	—
203	C₄⋊Dic₁₉	—	2	2	no	—
204	C₄⋊Dic₁₉	—	2	2	no	—
205	C₄⋊Dic₁₉	—	2	2	no	—
206	C₄⋊Dic₁₉	—	2	2	no	—
207	C₄⋊Dic₁₉	—	4	1	no	—
208	C₄⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
209	Dic₁₉⋊C₄	—	2	8	no	—
210	C₄×Dic₁₉	—	2	8	no	—
211	C₄×Dic₁₉	—	2	2	no	—
212	C₄×Dic₁₉	—	4	1	no	—
213	#64520	—	2	2	no	—
214	#64520	—	2	2	no	—
215	#64520	—	4	1	no	—
216	#64520	—	4	1	no	—
217	C₂×C₁₉⋊C₈	—	2	2	no	—
218	C₂×C₁₉⋊C₈	—	4	1	no	—
219	C₂×C₁₉⋊C₈	—	4	1	no	—
220	#10765	—	19	1	no	maximal, Sylow
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂³×C₁₉	#120	1	1	yes	characteristic
227	C₂³×C₁₉	#120	1	1	yes	characteristic
228	C₂³×C₁₉	#123	1	1	yes	characteristic
229	C₂³×C₁₉	#123	1	1	yes	characteristic
230	C₂²×D₁₉	—	2	2	no	—
231	C₂²×D₁₉	—	2	2	no	—
232	C₂²×D₁₉	—	4	2	no	—
233	C₂²×D₁₉	—	4	2	no	—
234	C₂²×D₁₉	#95	1	4	yes	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	8	1	no	—
241	C₂×C₄×C₁₉	—	8	1	no	—
242	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
270	C₂²⋊D₁₉	—	2	4	no	—
271	C₂²⋊D₁₉	—	2	4	no	—
272	C₂²⋊D₁₉	—	2	4	no	—
273	C₂²⋊D₁₉	—	2	4	no	—
274	C₂×Dic₁₉	—	2	2	no	—
275	C₂×Dic₁₉	—	2	2	no	—
276	C₂×Dic₁₉	—	2	4	no	—
277	C₂×Dic₁₉	—	4	4	no	—
278	C₂×Dic₁₉	—	4	2	no	—
279	C₂×Dic₁₉	—	8	2	no	—
280	C₂×Dic₁₉	—	8	2	no	—
281	C₂×Dic₁₉	—	8	1	no	—
282	C₂×Dic₁₉	—	8	1	no	—
283	C₂×Dic₁₉	#95	1	4	yes	—
284	D₇₆	—	2	2	no	—
285	D₇₆	—	2	2	no	—
286	D₇₆	—	2	2	no	—
287	D₇₆	—	2	2	no	—
288	C₄×D₁₉	—	2	4	no	—
289	C₄×D₁₉	—	2	4	no	—
290	C₄×D₁₉	—	2	4	no	—
291	C₄×D₁₉	—	2	4	no	—
292	C₄×D₁₉	—	8	8	no	—
293	Dic₃₈	—	2	2	no	—
294	Dic₃₈	—	2	2	no	—
295	Dic₃₈	—	2	2	no	—
296	Dic₃₈	—	2	2	no	—
297	C₈×C₁₉	—	4	2	no	—
298	C₁₉⋊C₈	—	4	2	no	—
299	C₂×#520	—	19	1	no	—
300	C₂×#413	—	19	1	no	—
301	C₂×#410	—	19	1	no	—
302	#1736	—	19	1	no	—
303	#1736	—	19	1	no	—
304	#1733	—	19	1	no	—
305	#1733	D₁₉	1	1	yes	characteristic, complemented
306	C₂²×C₁₉	—	2	1	no	—
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	1	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	4	1	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	4	1	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
317	C₂²×C₁₉	#379	1	1	yes	characteristic
318	C₂²×C₁₉	#381	1	1	yes	characteristic
319	C₂²×C₁₉	#385	1	1	yes	characteristic
320	C₂²×C₁₉	#385	1	1	yes	characteristic
321	C₂²×C₁₉	#386	1	1	yes	characteristic
322	C₂²×C₁₉	#386	1	1	yes	characteristic
323	C₂×D₁₉	—	2	4	no	—
324	C₂×D₁₉	—	4	4	no	—
325	C₂×D₁₉	—	4	2	no	—
326	C₂×D₁₉	—	4	2	no	—
327	C₂×D₁₉	—	4	4	no	—
328	C₄×C₁₉	—	4	2	no	—
329	C₄×C₁₉	—	4	2	no	—
330	C₄×C₁₉	—	8	2	no	—
331	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
332	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
333	C₄×C₁₉	#380	1	1	yes	characteristic
334	C₄×C₁₉	#380	1	1	yes	characteristic
335	C₄×C₁₉	#385	1	1	yes	characteristic
336	C₄×C₁₉	#385	1	1	yes	characteristic
337	C₄×C₁₉	#386	1	1	yes	characteristic
338	C₄×C₁₉	#386	1	1	yes	characteristic
339	Dic₁₉	—	2	4	no	—
340	Dic₁₉	—	4	4	no	—
341	Dic₁₉	—	8	2	no	—
342	C₂²×#41	—	19	1	no	—
343	C₂²×M₁₆	—	19	1	no	—
344	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
345	#520	—	38	2	no	—
346	#520	—	38	2	no	—
347	#520	—	38	2	no	—
348	#520	—	38	2	no	—
349	C₂×C₄×Q₈	—	38	1	no	—
350	C₂×C₄×D₄	—	38	1	no	—
351	C₂×C₄×D₄	—	38	2	no	—
352	C₂×#117	—	19	2	no	—
353	C₂×#117	—	19	1	no	—
354	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
355	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	—	19	1	no	—
357	C₂²×C₄⋊C₄	—	19	2	no	—
358	#413	—	19	4	no	—
359	#413	—	38	2	no	—
360	C₂×#101	—	38	1	no	—
361	C₂×#100	—	38	1	no	—
362	#410	—	19	4	no	—
363	#410	—	38	2	no	—
364	C₂×#99	—	38	2	no	—
365	#340	—	38	2	no	—
366	#340	—	38	2	no	—
367	#339	—	2	2	no	—
368	#339	—	38	2	no	—
369	C₂×C₁₉	—	2	1	no	—
370	C₂×C₁₉	—	2	1	no	—
371	C₂×C₁₉	—	2	1	no	—
372	C₂×C₁₉	—	2	1	no	—
373	C₂×C₁₉	—	2	1	no	—
374	C₂×C₁₉	—	2	1	no	—
375	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
376	C₂×C₁₉	#1795	1	1	yes	characteristic
377	C₂×C₁₉	#1796	1	1	yes	characteristic
378	D₁₉	—	4	4	no	—
379	C₂×#41	—	19	2	no	—
380	C₂×#41	—	19	2	no	—
381	C₂×#41	—	19	2	no	—
382	C₂×#41	—	19	2	no	—
383	C₂×#41	—	38	1	no	—
384	C₂×#41	—	38	1	no	—
385	C₂×#41	—	38	1	no	—
386	C₂×#41	—	38	1	no	—
387	C₂×#41	—	38	1	no	—
388	C₂×#41	—	38	1	no	—
389	C₂×#41	—	38	1	no	—
390	C₂×#41	—	38	1	no	—
391	C₂²×Q₈	—	19	1	no	—
392	C₂²×D₄	—	19	2	no	—
393	C₂²×D₄	—	19	1	no	—
394	C₂³×C₄	—	19	2	no	—
395	C₂³×C₄	—	38	2	no	—
396	C₂³×C₄	—	38	1	no	—
397	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
398	C₂×M₁₆	—	2	1	no	—
399	C₂×M₁₆	—	2	1	no	—
400	C₂×M₁₆	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	—	2	1	no	—
403	C₂×M₁₆	—	19	2	no	—
404	C₂×M₁₆	—	38	1	no	—
405	C₂×M₁₆	—	38	1	no	—
406	C₂×M₁₆	—	38	1	no	—
407	C₂×M₁₆	—	38	1	no	—
408	C₂×M₁₆	—	38	1	no	—
409	C₂×M₁₆	C₄×D₁₉	1	2	yes	complemented
410	C₂²×C₈	—	2	1	no	—
411	C₂²×C₈	—	38	1	no	—
412	C₄×Q₈	—	38	4	no	—
413	C₄×Q₈	—	38	4	no	—
414	C₄×D₄	—	38	4	no	—
415	C₄×D₄	—	38	4	no	—
416	C₄×D₄	—	38	8	no	—
417	C₄×D₄	—	38	8	no	—
418	#117	—	2	1	no	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	—	2	1	no	—
423	#117	—	19	2	no	—
424	#117	—	38	4	no	—
425	#117	—	38	4	no	—
426	#117	—	38	1	no	—
427	#117	—	38	1	no	—
428	#117	—	38	1	no	—
429	#117	C₄×D₁₉	1	2	yes	complemented
430	#117	D₇₆	1	2	yes	—
431	#117	C₂²⋊D₁₉	1	2	yes	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	19	2	no	—
434	C₂×C₄⋊C₄	—	19	2	no	—
435	C₂×C₄⋊C₄	—	19	2	no	—
436	C₂×C₄⋊C₄	—	38	4	no	—
437	C₂×C₄⋊C₄	—	38	2	no	—
438	C₂×C₄⋊C₄	—	38	1	no	—
439	C₂×C₄⋊C₄	—	38	1	no	—
440	C₂×C₄⋊C₄	—	38	1	no	—
441	C₂×C₄⋊C₄	—	38	4	no	—
442	C₂×C₄⋊C₄	—	38	1	no	—
443	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	38	2	no	—
448	C₂×C₂²⋊C₄	—	38	1	no	—
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	38	2	no	—
452	C₂×C₄²	—	38	1	no	—
453	#101	—	38	4	no	—
454	#100	—	38	4	no	—
455	#99	—	38	8	no	—
456	C₁₉	#10765	1	1	yes	characteristic, complemented, Sylow
457	C₂⁴	—	19	2	no	—
458	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
459	#41	—	38	2	no	—
460	#41	—	38	2	no	—
461	#41	—	38	2	no	—
462	#41	—	38	2	no	—
463	#41	—	38	2	no	—
464	#41	—	38	2	no	—
465	#41	—	38	2	no	—
466	#41	—	38	2	no	—
467	#41	—	38	2	no	—
468	#41	—	38	2	no	—
469	#41	—	38	2	no	—
470	#41	—	38	2	no	—
471	#41	—	38	2	no	—
472	#41	—	38	2	no	—
473	#41	—	38	2	no	—
474	#41	—	38	2	no	—
475	C₂×Q₈	—	19	2	no	—
476	C₂×Q₈	—	19	2	no	—
477	C₂×Q₈	—	38	1	no	—
478	C₂×Q₈	—	38	1	no	—
479	C₂×Q₈	—	38	1	no	—
480	C₂×Q₈	—	38	1	no	—
481	C₂×D₄	—	19	4	no	—
482	C₂×D₄	—	19	4	no	—
483	C₂×D₄	—	19	2	no	—
484	C₂×D₄	—	19	2	no	—
485	C₂×D₄	—	38	2	no	—
486	C₂×D₄	—	38	2	no	—
487	C₂×D₄	—	38	2	no	—
488	C₂×D₄	—	38	2	no	—
489	C₂×D₄	—	38	1	no	—
490	C₂×D₄	—	38	1	no	—
491	C₂×D₄	—	38	1	no	—
492	C₂×D₄	—	38	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	19	2	no	—
497	C₂²×C₄	—	19	4	no	—
498	C₂²×C₄	—	19	4	no	—
499	C₂²×C₄	—	38	8	no	—
500	C₂²×C₄	—	38	2	no	—
501	C₂²×C₄	—	38	2	no	—
502	C₂²×C₄	—	38	2	no	—
503	C₂²×C₄	—	38	2	no	—
504	C₂²×C₄	—	38	2	no	—
505	C₂²×C₄	—	38	2	no	—
506	C₂²×C₄	—	38	2	no	—
507	C₂²×C₄	—	76	1	no	—
508	C₂²×C₄	—	152	4	no	—
509	C₂²×C₄	—	152	2	no	—
510	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
514	C₂²×C₄	#64541	1	1	yes	characteristic
515	C₂²×C₄	#64541	1	1	yes	characteristic
516	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
517	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
518	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
519	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
520	C₂²×C₄	#64543	1	1	yes	characteristic
521	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
522	C₂²×C₄	#64545	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
524	M₁₆	—	2	2	no	—
525	M₁₆	—	2	2	no	—
526	M₁₆	—	4	1	no	—
527	M₁₆	—	4	1	no	—
528	M₁₆	—	38	2	no	—
529	M₁₆	—	38	2	no	—
530	M₁₆	—	76	1	no	—
531	M₁₆	—	76	1	no	—
532	C₂×C₈	—	2	2	no	—
533	C₂×C₈	—	4	1	no	—
534	C₂×C₈	—	4	1	no	—
535	C₂×C₈	—	38	2	no	—
536	C₂×C₈	—	76	1	no	—
537	C₂×C₈	—	76	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	—	19	4	no	—
543	C₄⋊C₄	—	38	8	no	—
544	C₄⋊C₄	—	38	2	no	—
545	C₄⋊C₄	—	38	2	no	—
546	C₄⋊C₄	—	38	2	no	—
547	C₄⋊C₄	—	38	2	no	—
548	C₄⋊C₄	—	76	1	no	—
549	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
550	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	38	8	no	—
556	C₂²⋊C₄	—	38	2	no	—
557	C₂²⋊C₄	—	76	1	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	2	no	—
560	C₄²	—	2	2	no	—
561	C₄²	—	4	1	no	—
562	C₄²	—	38	8	no	—
563	C₄²	—	38	2	no	—
564	C₄²	—	76	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	19	4	no	—
568	C₂³	—	38	2	no	—
569	C₂³	—	38	2	no	—
570	C₂³	—	76	2	no	—
571	C₂³	—	76	2	no	—
572	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
573	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
574	C₂³	#10597328	1	1	yes	characteristic
575	C₂³	#10597329	1	1	yes	characteristic
576	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
577	C₂³	#10597340	1	1	yes	characteristic
578	C₂³	#10597383	1	1	yes	characteristic
579	Q₈	—	38	2	no	—
580	Q₈	—	38	2	no	—
581	Q₈	—	38	2	no	—
582	Q₈	—	38	2	no	—
583	D₄	—	38	4	no	—
584	D₄	—	38	4	no	—
585	D₄	—	38	4	no	—
586	D₄	—	38	4	no	—
587	D₄	—	38	2	no	—
588	D₄	—	38	2	no	—
589	D₄	—	38	2	no	—
590	D₄	—	38	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	8	1	no	—
597	C₂×C₄	—	8	1	no	—
598	C₂×C₄	—	19	4	no	—
599	C₂×C₄	—	38	2	no	—
600	C₂×C₄	—	38	2	no	—
601	C₂×C₄	—	38	4	no	—
602	C₂×C₄	—	38	4	no	—
603	C₂×C₄	—	38	4	no	—
604	C₂×C₄	—	38	4	no	—
605	C₂×C₄	—	38	4	no	—
606	C₂×C₄	—	76	4	no	—
607	C₂×C₄	—	76	2	no	—
608	C₂×C₄	—	152	8	no	—
609	C₂×C₄	—	152	2	no	—
610	C₂×C₄	—	152	2	no	—
611	C₂×C₄	—	152	1	no	—
612	C₂×C₄	—	152	1	no	—
613	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
614	C₂×C₄	#10597318	1	1	yes	characteristic
615	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
616	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
617	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
618	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
619	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
620	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
621	C₂×C₄	#10597328	1	1	yes	characteristic
622	C₂×C₄	#10597329	1	1	yes	characteristic
623	C₂×C₄	#10597330	1	1	yes	characteristic
624	C₂×C₄	#10597330	1	1	yes	characteristic
625	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
626	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
627	C₂×C₄	#10597338	1	1	yes	characteristic
628	C₂×C₄	#10597339	1	1	yes	characteristic
629	C₂×C₄	#10597339	1	1	yes	characteristic
630	C₂×C₄	#10597340	1	1	yes	characteristic
631	C₂×C₄	#10597341	1	1	yes	characteristic
632	C₂×C₄	#10597342	1	1	yes	characteristic
633	C₂×C₄	#10597342	1	1	yes	characteristic
634	C₂×C₄	#10597343	1	1	yes	characteristic
635	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
636	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
637	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
638	C₂×C₄	#10597383	1	1	yes	characteristic
639	C₂×C₄	#10597384	1	1	yes	characteristic
640	C₂×C₄	#10597392	1	1	yes	characteristic
641	C₈	—	4	2	no	—
642	C₈	—	76	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	38	4	no	—
654	C₂²	—	76	4	no	—
655	C₂²	—	76	4	no	—
656	C₂²	—	76	2	no	—
657	C₂²	—	76	2	no	—
658	C₂²	#95×D₁₉	1	1	yes	characteristic
659	C₂²	#11926399	1	1	yes	characteristic
660	C₂²	#11926406	1	1	yes	characteristic
661	C₂²	#11926415	1	1	yes	characteristic
662	C₂²	#11926418	1	1	yes	characteristic
663	C₂²	#11926420	1	1	yes	characteristic
664	C₂²	#11926422	1	1	yes	characteristic
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	8	2	no	—
668	C₄	—	38	4	no	—
669	C₄	—	76	4	no	—
670	C₄	—	152	2	no	—
671	C₄	#11926391	1	1	yes	characteristic
672	C₄	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
673	C₄	#11926401	1	1	yes	characteristic
674	C₄	#11926403	1	1	yes	characteristic
675	C₄	#11926415	1	1	yes	characteristic
676	C₄	#11926418	1	1	yes	characteristic
677	C₄	#11926420	1	1	yes	characteristic
678	C₄	#11926422	1	1	yes	characteristic
679	C₂	—	2	1	no	—
680	C₂	—	2	1	no	—
681	C₂	—	2	1	no	—
682	C₂	—	2	1	no	—
683	C₂	—	2	1	no	—
684	C₂	—	2	1	no	—
685	C₂	—	76	4	no	—
686	C₂	(C₂×D₁₉)⋊#95	1	1	yes	characteristic
687	C₂	#14563604	1	1	yes	characteristic
688	C₂	#14563609	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926399
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1733	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1733	D₁₉
hypocenter	C₁₉	#10765
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
4. #14563356	C₂	semidirect
5. #14563355	C₂	semidirect
6. #14563344	C₂	semidirect
7. C₁₉×#1733	C₂	semidirect
18. C₂×#10597338	C₄	semidirect
20. C₂×C₄⋊C₄×D₁₉	C₄	semidirect
22. #11926526	C₄	semidirect
26. #11926517	C₄	semidirect
59. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
66. C₁₉×#117	C₂×C₄	semidirect
81. #10597372	C₂×C₄	semidirect
97. C₂×#64520	C₂×C₄	semidirect
305. #1733	D₁₉	semidirect
409. C₂×M₁₆	C₄×D₁₉	semidirect
429. #117	C₄×D₁₉	semidirect
456. C₁₉	#10765	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11927024	2
C₂×#11926526	2
C₂×#11926517	2
#14563356	2
#14563355	2
#14563344	2
C₁₉×#1733	2
#10765	19