Subgroups — #18088128

Order 4864.

1204 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14576836	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926560	C₂	1	1	yes	maximal, characteristic
3	#14572155	C₂	1	1	yes	maximal, characteristic
4	#14563367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926301	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926301	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	#11927025	—	2	2	no	—
10	#11927024	—	2	2	no	—
11	#11927021	—	2	1	no	—
12	#11927018	—	2	1	no	—
13	#11927017	—	2	2	no	—
14	C₄×#64541	—	2	2	no	—
15	#11927012	C₄	1	4	yes	complemented
16	C₂×#10597372	C₂²	1	1	yes	characteristic
17	C₂×#10597372	C₂²	1	1	yes	characteristic
18	C₂×#10597372	C₂²	1	1	yes	characteristic
19	#117×D₁₉	—	2	2	no	—
20	#11926560	—	2	2	no	—
21	#11926560	—	2	2	no	—
22	C₂×#10597282	C₄	1	4	yes	complemented
23	#11926554	—	2	1	no	—
24	#11926550	—	2	1	no	—
25	#11926546	—	2	2	no	—
26	#11926541	C₄	1	4	yes	complemented
27	#11926310	—	2	2	no	—
28	#11926301	—	2	2	no	—
29	#11926301	—	2	2	no	—
30	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
33	C₁₉×#344	—	2	2	no	—
34	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×C₂²⋊D₁₉	—	2	1	no	—
36	C₂×#64541	—	2	1	no	—
37	C₂×#64541	—	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	C₂×C₄	1	2	yes	—
43	C₂×#64541	C₂×C₄	1	2	yes	—
44	C₂×#64541	C₂×C₄	1	2	yes	—
45	C₂×#64541	D₄	1	2	yes	—
46	C₂×#64541	D₄	1	2	yes	—
47	C₂×#64541	Q₈	1	2	yes	—
48	C₂²×D₇₆	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₉	—	2	1	no	—
50	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
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	—	2	1	no	—
60	C₂×M₁₆×C₁₉	—	2	1	no	—
61	C₂×M₁₆×C₁₉	—	2	1	no	—
62	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	complemented
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	C₂×C₄	1	2	yes	—
68	C₁₉×#117	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
73	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
74	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
75	C₄×C₂²⋊D₁₉	—	2	8	no	—
76	#10597372	—	2	1	no	—
77	#10597372	—	2	1	no	—
78	#10597372	—	2	1	no	—
79	#10597372	—	2	1	no	—
80	#10597372	—	2	1	no	—
81	#10597372	—	2	1	no	—
82	#10597372	—	2	1	no	—
83	#10597372	—	2	1	no	—
84	#10597372	—	2	1	no	—
85	#10597372	C₂×C₄	1	2	yes	complemented
86	#10597372	D₄	1	2	yes	—
87	#10597372	D₄	1	2	yes	—
88	C₂×C₄⋊Dic₁₉	—	2	1	no	—
89	C₂×C₄⋊Dic₁₉	—	2	1	no	—
90	C₂×C₄⋊Dic₁₉	—	2	1	no	—
91	C₂×C₄×Dic₁₉	—	2	1	no	—
92	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
93	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	complemented
94	#10597339	—	2	4	no	—
95	#10597338	—	2	4	no	—
96	C₄⋊C₄×D₁₉	—	2	4	no	—
97	#10597333	—	2	4	no	—
98	(C₂²⋊D₁₉)⋊C₄	—	2	8	no	—
99	C₂²⋊C₄×D₁₉	—	2	4	no	—
100	#10597323	—	2	4	no	—
101	C₄×D₇₆	—	2	4	no	—
102	#10597318	—	2	4	no	—
103	C₄²×D₁₉	—	2	4	no	—
104	C₄×Dic₃₈	—	2	4	no	—
105	#10597282	—	2	8	no	—
106	#10597278	—	2	4	no	—
107	#10597273	—	2	4	no	—
108	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂³×D₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₁₉	—	2	2	no	—
126	C₂×C₂²⋊D₁₉	—	2	2	no	—
127	C₂×C₂²⋊D₁₉	—	2	2	no	—
128	C₂×C₂²⋊D₁₉	—	2	2	no	—
129	C₂×C₂²⋊D₁₉	—	2	2	no	—
130	C₂×C₂²⋊D₁₉	—	2	2	no	—
131	C₂²×Dic₁₉	—	2	1	no	—
132	C₂²×Dic₁₉	—	2	2	no	—
133	C₂²×Dic₁₉	—	2	2	no	—
134	C₂²×Dic₁₉	—	4	1	no	—
135	#64541	—	2	2	no	—
136	#64541	—	2	2	no	—
137	#64541	—	2	2	no	—
138	#64541	—	2	2	no	—
139	#64541	—	2	2	no	—
140	#64541	—	2	2	no	—
141	#64541	—	2	2	no	—
142	#64541	—	2	2	no	—
143	#64541	—	2	2	no	—
144	#64541	—	2	2	no	—
145	#64541	—	2	2	no	—
146	#64541	—	2	2	no	—
147	#64541	C₄²	1	4	yes	—
148	#64541	C₂²⋊C₄	1	4	yes	—
149	#64541	C₄⋊C₄	1	4	yes	—
150	#64541	C₄⋊C₄	1	4	yes	—
151	C₂×D₇₆	—	2	1	no	—
152	C₂×D₇₆	—	2	1	no	—
153	C₂×D₇₆	—	2	1	no	—
154	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
155	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
156	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
157	C₂×C₄×D₁₉	—	2	2	no	—
158	C₂×C₄×D₁₉	—	2	2	no	—
159	C₂×C₄×D₁₉	—	2	2	no	—
160	C₂×C₄×D₁₉	—	2	2	no	—
161	C₂×C₄×D₁₉	—	2	2	no	—
162	C₂×C₄×D₁₉	—	2	2	no	—
163	C₂×C₄×D₁₉	—	2	8	no	—
164	C₂×Dic₃₈	—	2	1	no	—
165	C₂×Dic₃₈	—	2	1	no	—
166	C₂×Dic₃₈	—	2	1	no	—
167	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
168	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
169	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
170	M₁₆×C₁₉	—	2	2	no	—
171	M₁₆×C₁₉	—	2	2	no	—
172	M₁₆×C₁₉	—	4	1	no	—
173	M₁₆×C₁₉	—	4	1	no	—
174	M₁₆×C₁₉	—	4	1	no	—
175	M₁₆×C₁₉	—	4	1	no	—
176	M₁₆×C₁₉	—	4	1	no	—
177	M₁₆×C₁₉	—	4	1	no	—
178	C₂×C₈×C₁₉	—	2	2	no	—
179	C₂×C₈×C₁₉	—	2	2	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	2	no	—
182	C₂×C₈×C₁₉	—	4	1	no	—
183	C₂×C₈×C₁₉	—	4	1	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₂²⋊Dic₁₉	—	2	2	no	—
191	C₂²⋊Dic₁₉	—	2	2	no	—
192	C₂²⋊Dic₁₉	—	2	2	no	—
193	C₂²⋊Dic₁₉	—	4	1	no	—
194	C₂²⋊Dic₁₉	—	4	1	no	—
195	C₂²⋊Dic₁₉	—	4	1	no	—
196	(C₂×D₁₉)⋊C₄	—	2	8	no	—
197	C₄⋊Dic₁₉	—	2	2	no	—
198	C₄⋊Dic₁₉	—	2	2	no	—
199	C₄⋊Dic₁₉	—	2	2	no	—
200	C₄⋊Dic₁₉	—	4	1	no	—
201	C₄⋊Dic₁₉	—	4	1	no	—
202	C₄⋊Dic₁₉	—	4	1	no	—
203	Dic₁₉⋊C₄	—	2	8	no	—
204	C₄×Dic₁₉	—	2	8	no	—
205	C₄×Dic₁₉	—	2	2	no	—
206	C₄×Dic₁₉	—	2	2	no	—
207	C₄×Dic₁₉	—	2	2	no	—
208	C₄×Dic₁₉	—	2	2	no	—
209	C₄×Dic₁₉	—	4	1	no	—
210	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
211	#10792	—	19	1	no	maximal, Sylow
212	C₂³×C₁₉	—	8	1	no	—
213	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
216	C₂³×C₁₉	#120	1	1	yes	characteristic
217	C₂³×C₁₉	#120	1	1	yes	characteristic
218	C₂³×C₁₉	#121	1	1	yes	characteristic
219	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
220	C₂²×D₁₉	—	2	2	no	—
221	C₂²×D₁₉	—	2	2	no	—
222	C₂²×D₁₉	—	2	2	no	—
223	C₂²×D₁₉	—	8	2	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	8	2	no	—
226	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
254	C₂²⋊D₁₉	—	2	4	no	—
255	C₂²⋊D₁₉	—	2	4	no	—
256	C₂²⋊D₁₉	—	2	4	no	—
257	C₂²⋊D₁₉	—	2	4	no	—
258	C₂×Dic₁₉	—	2	2	no	—
259	C₂×Dic₁₉	—	2	2	no	—
260	C₂×Dic₁₉	—	2	2	no	—
261	C₂×Dic₁₉	—	2	4	no	—
262	C₂×Dic₁₉	—	4	2	no	—
263	C₂×Dic₁₉	—	4	2	no	—
264	C₂×Dic₁₉	—	8	2	no	—
265	C₂×Dic₁₉	—	8	2	no	—
266	C₂×Dic₁₉	—	8	2	no	—
267	D₇₆	—	2	2	no	—
268	D₇₆	—	2	2	no	—
269	D₇₆	—	2	2	no	—
270	D₇₆	#95	1	4	yes	—
271	C₄×D₁₉	—	2	4	no	—
272	C₄×D₁₉	—	2	4	no	—
273	C₄×D₁₉	—	2	4	no	—
274	C₄×D₁₉	—	2	4	no	—
275	C₄×D₁₉	—	8	8	no	—
276	Dic₃₈	—	2	2	no	—
277	Dic₃₈	—	2	2	no	—
278	Dic₃₈	—	2	2	no	—
279	Dic₃₈	#95	1	4	yes	—
280	C₈×C₁₉	—	4	2	no	—
281	C₈×C₁₉	—	4	2	no	—
282	#3428	—	19	1	no	—
283	C₂×#421	—	19	1	no	—
284	#2896	—	19	1	no	—
285	C₂×#344	D₁₉	1	1	yes	characteristic, complemented
286	#1740	—	19	1	no	—
287	C₂×H(3,ℤ/4)	—	19	1	no	—
288	C₂×H(3,ℤ/4)	—	19	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₁₉	#379	1	1	yes	characteristic
298	C₂²×C₁₉	#380	1	1	yes	characteristic
299	C₂²×C₁₉	#385	1	1	yes	characteristic
300	C₂²×C₁₉	#385	1	1	yes	characteristic
301	C₂²×C₁₉	#386	1	1	yes	characteristic
302	C₂²×C₁₉	#386	1	1	yes	characteristic
303	C₂×D₁₉	—	2	4	no	—
304	C₂×D₁₉	—	4	4	no	—
305	C₂×D₁₉	—	8	2	no	—
306	C₂×D₁₉	—	8	2	no	—
307	C₄×C₁₉	—	4	4	no	—
308	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
309	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
310	C₄×C₁₉	#380	1	1	yes	characteristic
311	C₄×C₁₉	#381	1	1	yes	characteristic
312	C₄×C₁₉	#385	1	1	yes	characteristic
313	C₄×C₁₉	#385	1	1	yes	characteristic
314	C₄×C₁₉	#386	1	1	yes	characteristic
315	C₄×C₁₉	#386	1	1	yes	characteristic
316	Dic₁₉	—	2	4	no	—
317	Dic₁₉	—	4	4	no	—
318	Dic₁₉	—	8	2	no	—
319	Dic₁₉	—	8	2	no	—
320	C₂²×#41	—	19	1	no	—
321	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
322	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
323	#520	—	38	2	no	—
324	#520	—	38	2	no	—
325	#519	—	38	1	no	—
326	#518	—	38	1	no	—
327	#518	—	38	2	no	—
328	C₄×#41	—	19	4	no	—
329	C₄×#41	—	38	2	no	—
330	C₂×#117	—	19	1	no	—
331	C₂×#117	—	19	1	no	—
332	C₂×#117	—	19	1	no	—
333	C₂×#117	—	38	2	no	—
334	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
335	#421	—	38	2	no	—
336	#421	—	38	2	no	—
337	C₂×#104	—	19	4	no	—
338	#419	—	38	1	no	—
339	#418	—	38	1	no	—
340	#417	—	38	2	no	—
341	#416	—	19	4	no	—
342	#344	—	2	2	no	—
343	#342	—	38	2	no	—
344	H(3,ℤ/4)	—	38	2	no	—
345	H(3,ℤ/4)	—	38	2	no	—
346	C₂×C₁₉	—	2	1	no	—
347	C₂×C₁₉	—	2	1	no	—
348	C₂×C₁₉	—	2	1	no	—
349	C₂×C₁₉	—	2	1	no	—
350	C₂×C₁₉	—	2	1	no	—
351	C₂×C₁₉	—	2	1	no	—
352	C₂×C₁₉	—	2	1	no	—
353	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
354	D₁₉	—	4	4	no	—
355	C₂×#41	—	19	2	no	—
356	C₂×#41	—	19	2	no	—
357	C₂×#41	—	19	2	no	—
358	C₂×#41	—	19	2	no	—
359	C₂×#41	—	19	2	no	—
360	C₂×#41	—	19	2	no	—
361	C₂×#41	—	38	1	no	—
362	C₂×#41	—	38	1	no	—
363	C₂×#41	—	38	1	no	—
364	C₂×#41	—	38	1	no	—
365	C₂×#41	—	38	1	no	—
366	C₂×#41	—	38	1	no	—
367	C₂²×Q₈	—	19	1	no	—
368	C₂²×D₄	—	19	1	no	—
369	C₂²×D₄	—	38	1	no	—
370	C₂³×C₄	—	38	1	no	—
371	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	C₄×D₁₉	1	2	yes	complemented
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	C₄×D₁₉	1	2	yes	complemented
386	C₄×Q₈	—	38	4	no	—
387	C₄×Q₈	—	38	4	no	—
388	C₄×D₄	—	38	4	no	—
389	C₄×D₄	—	38	4	no	—
390	C₄×D₄	—	38	8	no	—
391	C₄×D₄	—	38	8	no	—
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	#117	—	19	2	no	—
395	#117	—	19	2	no	—
396	#117	—	19	2	no	—
397	#117	—	38	4	no	—
398	#117	—	38	4	no	—
399	#117	—	38	4	no	—
400	#117	—	38	1	no	—
401	#117	—	38	1	no	—
402	#117	—	38	1	no	—
403	#117	—	38	1	no	—
404	#117	—	38	1	no	—
405	#117	—	38	1	no	—
406	#117	—	38	1	no	—
407	#117	—	38	1	no	—
408	#117	—	38	1	no	—
409	#117	C₄×D₁₉	1	2	yes	—
410	#117	C₂²⋊D₁₉	1	2	yes	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	38	4	no	—
413	C₂×C₄⋊C₄	—	38	1	no	—
414	C₂×C₄⋊C₄	—	38	1	no	—
415	C₂×C₄⋊C₄	—	38	1	no	—
416	C₂×C₂²⋊C₄	—	38	4	no	—
417	C₂×C₂²⋊C₄	—	38	1	no	—
418	C₂×C₂²⋊C₄	—	38	1	no	—
419	C₂×C₂²⋊C₄	—	38	1	no	—
420	C₂×C₂²⋊C₄	D₇₆	1	2	yes	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	19	2	no	—
423	C₂×C₄²	—	19	2	no	—
424	C₂×C₄²	—	38	4	no	—
425	C₂×C₄²	—	38	1	no	—
426	#104	—	38	8	no	—
427	#103	—	38	4	no	—
428	#102	—	38	4	no	—
429	C₁₉	#10792	1	1	yes	characteristic, complemented, Sylow
430	C₂⁴	—	38	1	no	—
431	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
432	#41	—	19	4	no	—
433	#41	—	19	4	no	—
434	#41	—	19	4	no	—
435	#41	—	19	4	no	—
436	#41	—	38	2	no	—
437	#41	—	38	2	no	—
438	#41	—	38	2	no	—
439	#41	—	38	2	no	—
440	#41	—	38	2	no	—
441	#41	—	38	2	no	—
442	#41	—	38	2	no	—
443	#41	—	38	2	no	—
444	#41	—	38	2	no	—
445	#41	—	38	2	no	—
446	#41	—	38	2	no	—
447	#41	—	38	2	no	—
448	C₂×Q₈	—	19	2	no	—
449	C₂×Q₈	—	19	2	no	—
450	C₂×Q₈	—	19	2	no	—
451	C₂×Q₈	—	38	1	no	—
452	C₂×Q₈	—	38	1	no	—
453	C₂×Q₈	—	38	1	no	—
454	C₂×D₄	—	19	2	no	—
455	C₂×D₄	—	19	2	no	—
456	C₂×D₄	—	19	2	no	—
457	C₂×D₄	—	38	2	no	—
458	C₂×D₄	—	38	2	no	—
459	C₂×D₄	—	38	2	no	—
460	C₂×D₄	—	38	2	no	—
461	C₂×D₄	—	38	2	no	—
462	C₂×D₄	—	38	2	no	—
463	C₂×D₄	—	38	1	no	—
464	C₂×D₄	—	38	1	no	—
465	C₂×D₄	—	38	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	38	8	no	—
468	C₂²×C₄	—	38	1	no	—
469	C₂²×C₄	—	38	2	no	—
470	C₂²×C₄	—	38	2	no	—
471	C₂²×C₄	—	38	2	no	—
472	C₂²×C₄	—	38	2	no	—
473	C₂²×C₄	—	38	2	no	—
474	C₂²×C₄	—	38	2	no	—
475	C₂²×C₄	—	38	2	no	—
476	C₂²×C₄	—	38	2	no	—
477	C₂²×C₄	—	76	1	no	—
478	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
481	C₂²×C₄	#64541	1	1	yes	characteristic
482	C₂²×C₄	#64541	1	1	yes	characteristic
483	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
484	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
485	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
486	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
487	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
488	C₂²×C₄	#64543	1	1	yes	characteristic
489	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
490	C₂²×C₄	#64545	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	4	1	no	—
495	M₁₆	—	4	1	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	4	1	no	—
498	M₁₆	—	4	1	no	—
499	M₁₆	—	4	1	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	4	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	38	8	no	—
509	C₄⋊C₄	—	38	2	no	—
510	C₄⋊C₄	—	38	2	no	—
511	C₄⋊C₄	—	38	2	no	—
512	C₄⋊C₄	—	76	1	no	—
513	C₄⋊C₄	—	76	1	no	—
514	C₄⋊C₄	—	76	1	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	38	8	no	—
517	C₂²⋊C₄	—	38	2	no	—
518	C₂²⋊C₄	—	38	2	no	—
519	C₂²⋊C₄	—	38	2	no	—
520	C₂²⋊C₄	—	76	1	no	—
521	C₂²⋊C₄	—	76	1	no	—
522	C₂²⋊C₄	—	76	1	no	—
523	C₂²⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	19	4	no	—
527	C₄²	—	38	8	no	—
528	C₄²	—	38	2	no	—
529	C₄²	—	38	2	no	—
530	C₄²	—	38	2	no	—
531	C₄²	—	38	2	no	—
532	C₄²	—	76	1	no	—
533	C₂³	—	8	1	no	—
534	C₂³	—	38	2	no	—
535	C₂³	—	38	2	no	—
536	C₂³	—	38	2	no	—
537	C₂³	—	152	2	no	—
538	C₂³	C₄×D₇₆	1	1	yes	characteristic
539	C₂³	C₄×D₇₆	1	1	yes	characteristic
540	C₂³	#10597328	1	1	yes	characteristic
541	C₂³	#10597328	1	1	yes	characteristic
542	C₂³	#10597341	1	1	yes	characteristic
543	C₂³	#10597343	1	1	yes	characteristic
544	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
545	Q₈	—	19	4	no	—
546	Q₈	—	38	2	no	—
547	Q₈	—	38	2	no	—
548	Q₈	—	38	2	no	—
549	D₄	—	19	4	no	—
550	D₄	—	38	4	no	—
551	D₄	—	38	4	no	—
552	D₄	—	38	4	no	—
553	D₄	—	38	4	no	—
554	D₄	—	38	2	no	—
555	D₄	—	38	2	no	—
556	D₄	—	38	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	—	38	2	no	—
560	C₂×C₄	—	38	2	no	—
561	C₂×C₄	—	38	2	no	—
562	C₂×C₄	—	38	4	no	—
563	C₂×C₄	—	38	4	no	—
564	C₂×C₄	—	38	4	no	—
565	C₂×C₄	—	38	4	no	—
566	C₂×C₄	—	38	4	no	—
567	C₂×C₄	—	76	2	no	—
568	C₂×C₄	—	76	2	no	—
569	C₂×C₄	—	152	8	no	—
570	C₂×C₄	—	152	2	no	—
571	C₂×C₄	—	152	2	no	—
572	C₂×C₄	—	152	2	no	—
573	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
574	C₂×C₄	#10597318	1	1	yes	characteristic
575	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
576	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
577	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
578	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
579	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
580	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
581	C₂×C₄	#10597329	1	1	yes	characteristic
582	C₂×C₄	#10597329	1	1	yes	characteristic
583	C₂×C₄	#10597330	1	1	yes	characteristic
584	C₂×C₄	#10597330	1	1	yes	characteristic
585	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
586	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
587	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
588	C₂×C₄	#10597338	1	1	yes	characteristic
589	C₂×C₄	#10597339	1	1	yes	characteristic
590	C₂×C₄	#10597339	1	1	yes	characteristic
591	C₂×C₄	#10597340	1	1	yes	characteristic
592	C₂×C₄	#10597340	1	1	yes	characteristic
593	C₂×C₄	#10597342	1	1	yes	characteristic
594	C₂×C₄	#10597342	1	1	yes	characteristic
595	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
596	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
597	C₂×C₄	#10597383	1	1	yes	characteristic
598	C₂×C₄	#10597383	1	1	yes	characteristic
599	C₂×C₄	#10597384	1	1	yes	characteristic
600	C₂×C₄	#10597392	1	1	yes	characteristic
601	C₈	—	4	2	no	—
602	C₈	—	4	2	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	38	4	no	—
611	C₂²	—	76	4	no	—
612	C₂²	—	152	2	no	—
613	C₂²	—	152	2	no	—
614	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
615	C₂²	#11926399	1	1	yes	characteristic
616	C₂²	#11926401	1	1	yes	characteristic
617	C₂²	#11926418	1	1	yes	characteristic
618	C₂²	#11926418	1	1	yes	characteristic
619	C₂²	#11926422	1	1	yes	characteristic
620	C₂²	#11926422	1	1	yes	characteristic
621	C₄	—	4	4	no	—
622	C₄	—	38	4	no	—
623	C₄	—	76	4	no	—
624	C₄	—	152	2	no	—
625	C₄	—	152	2	no	—
626	C₄	#95×D₁₉	1	1	yes	characteristic
627	C₄	#11926391	1	1	yes	characteristic
628	C₄	#11926403	1	1	yes	characteristic
629	C₄	#11926406	1	1	yes	characteristic
630	C₄	#11926415	1	1	yes	characteristic
631	C₄	#11926415	1	1	yes	characteristic
632	C₄	#11926420	1	1	yes	characteristic
633	C₄	#11926420	1	1	yes	characteristic
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	76	4	no	—
642	C₂	(C₂×D₁₉)⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926391
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#344	C₂
socle	C₂×C₁₉	C₂²⋊#95
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#344	D₁₉
hypocenter	C₁₉	#10792
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
4. #14563367	C₂	semidirect
5. C₂×#11926301	C₂	semidirect
6. C₂×#11926301	C₂	semidirect
7. C₂×C₁₉×#344	C₂	semidirect
15. #11927012	C₄	semidirect
22. C₂×#10597282	C₄	semidirect
26. #11926541	C₄	semidirect
62. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
64. C₂²×C₈×C₁₉	C₂×C₄	semidirect
85. #10597372	C₂×C₄	semidirect
93. C₂×C₄×Dic₁₉	C₂×C₄	semidirect
285. C₂×#344	D₁₉	semidirect
383. C₂×M₁₆	C₄×D₁₉	semidirect
385. C₂²×C₈	C₄×D₁₉	semidirect
429. C₁₉	#10792	semidirect

Maximal subgroups

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

subgroup	index
#14576836	2
C₂×#11926560	2
#14572155	2
#14563367	2
C₂×#11926301	2
C₂×C₁₉×#344	2
#10792	19