Subgroups — #18088207

Order 4864.

706 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926499	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926308	C₂	1	1	yes	maximal, characteristic
3	#14563351	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926499	—	2	2	no	—
13	#11926499	C₄	1	4	yes	complemented
14	C₂×#10597272	—	2	1	no	—
15	C₂×C₈×Dic₁₉	—	2	1	no	—
16	#11926308	—	2	2	no	—
17	#11926306	C₄	1	2	yes	complemented
18	#11926306	C₄	1	2	yes	complemented
19	#11926305	C₄	1	4	yes	complemented
20	#11926303	—	2	2	no	—
21	#11926298	—	2	2	no	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₁₉×#336	—	2	1	no	—
26	C₁₉×#336	—	2	1	no	—
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂³×Dic₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₉	D₄	1	2	yes	—
42	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	2	1	no	—
47	C₁₉×#117	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
52	#10597372	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	#10597372	C₂×C₄	1	2	yes	—
55	#10597372	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₉	—	2	1	no	—
59	C₂×C₄×Dic₁₉	—	2	1	no	—
60	C₂×C₄×Dic₁₉	—	2	1	no	—
61	C₂×C₄×Dic₁₉	—	2	1	no	—
62	C₂×C₄×Dic₁₉	—	2	1	no	—
63	C₂×C₄×Dic₁₉	—	2	1	no	—
64	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
65	C₂×#64520	—	2	1	no	—
66	C₂×#64520	—	2	1	no	—
67	C₂×#64520	—	2	1	no	—
68	C₂×#64520	C₂×C₄	1	2	yes	—
69	C₂×#64520	D₄	1	2	yes	—
70	C₂×#64520	Q₈	1	2	yes	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	—	2	1	no	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
79	#10597272	—	2	4	no	—
80	C₈×Dic₁₉	—	2	4	no	—
81	C₂⁴×C₁₉	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×Dic₁₉	—	2	4	no	—
98	C₂²×Dic₁₉	—	2	1	no	—
99	C₂²×Dic₁₉	—	2	1	no	—
100	C₂²×Dic₁₉	—	2	2	no	—
101	C₂²×Dic₁₉	—	4	2	no	—
102	C₂²×Dic₁₉	—	4	1	no	—
103	C₂²×Dic₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	2	2	no	—
105	M₁₆×C₁₉	—	2	2	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	1	no	—
111	C₂×C₈×C₁₉	—	2	1	no	—
112	C₂×C₈×C₁₉	—	2	1	no	—
113	C₂×C₈×C₁₉	—	2	1	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	4	1	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
120	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₂²⋊C₄×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₂²⋊Dic₁₉	—	2	2	no	—
128	C₂²⋊Dic₁₉	—	2	2	no	—
129	C₄⋊Dic₁₉	—	2	1	no	—
130	C₄⋊Dic₁₉	—	2	1	no	—
131	C₄⋊Dic₁₉	C₄²	1	2	yes	—
132	C₄⋊Dic₁₉	C₄²	1	2	yes	—
133	C₄×Dic₁₉	—	2	2	no	—
134	C₄×Dic₁₉	—	2	2	no	—
135	C₄×Dic₁₉	—	2	2	no	—
136	C₄×Dic₁₉	—	2	2	no	—
137	C₄×Dic₁₉	—	4	1	no	—
138	C₄×Dic₁₉	—	4	1	no	—
139	#64520	—	2	2	no	—
140	#64520	—	2	2	no	—
141	#64520	—	2	2	no	—
142	#64520	C₄⋊C₄	1	4	yes	—
143	C₂×C₁₉⋊C₈	—	2	2	no	—
144	C₂×C₁₉⋊C₈	—	2	2	no	—
145	C₂×C₁₉⋊C₈	—	2	2	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	4	1	no	—
150	C₂×C₁₉⋊C₈	—	4	1	no	—
151	C₂×C₁₉⋊C₈	—	4	1	no	—
152	C₂×C₁₉⋊C₈	—	4	1	no	—
153	#10809	—	19	1	no	maximal, Sylow
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	#117	1	1	yes	characteristic
157	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
158	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
159	C₂³×C₁₉	#124	1	1	yes	characteristic
160	C₂³×C₁₉	#125	1	1	yes	characteristic
161	C₂³×C₁₉	#126	1	1	yes	characteristic
162	C₂³×C₁₉	#126	1	1	yes	characteristic
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
194	C₂×Dic₁₉	—	2	4	no	—
195	C₂×Dic₁₉	—	2	2	no	—
196	C₂×Dic₁₉	—	2	2	no	—
197	C₂×Dic₁₉	—	4	4	no	—
198	C₂×Dic₁₉	—	4	4	no	—
199	C₂×Dic₁₉	—	4	2	no	—
200	C₂×Dic₁₉	—	4	2	no	—
201	C₂×Dic₁₉	—	4	2	no	—
202	C₂×Dic₁₉	—	4	2	no	—
203	C₈×C₁₉	—	2	2	no	—
204	C₈×C₁₉	—	2	2	no	—
205	C₈×C₁₉	—	4	2	no	—
206	C₁₉⋊C₈	—	2	4	no	—
207	C₁₉⋊C₈	—	4	2	no	—
208	C₂×#405	—	19	1	no	—
209	C₂×#341	—	19	1	no	—
210	#1735	—	19	1	no	—
211	C₂×#339	—	19	1	no	—
212	C₂×#339	—	19	1	no	—
213	#1729	D₁₉	1	1	yes	characteristic
214	C₂×#336	—	19	1	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	2	1	no	—
223	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×C₁₉	#382	1	1	yes	characteristic
225	C₂²×C₁₉	#383	1	1	yes	characteristic
226	C₂²×C₁₉	#387	1	1	yes	characteristic
227	C₂²×C₁₉	#387	1	1	yes	characteristic
228	C₂²×C₁₉	#388	1	1	yes	characteristic
229	C₂²×C₁₉	#388	1	1	yes	characteristic
230	C₂²×C₁₉	#443	1	2	yes	—
231	C₂²×C₁₉	#444	1	2	yes	—
232	C₄×C₁₉	—	8	2	no	—
233	C₄×C₁₉	#376	1	1	yes	characteristic
234	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
235	C₄×C₁₉	#380	1	1	yes	characteristic
236	C₄×C₁₉	#381	1	1	yes	characteristic
237	C₄×C₁₉	#387	1	1	yes	characteristic
238	C₄×C₁₉	#387	1	1	yes	characteristic
239	C₄×C₁₉	#388	1	1	yes	characteristic
240	C₄×C₁₉	#388	1	1	yes	characteristic
241	Dic₁₉	—	4	4	no	—
242	Dic₁₉	—	4	2	no	—
243	Dic₁₉	—	4	2	no	—
244	C₂²×M₁₆	—	19	1	no	—
245	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
246	C₂³×C₈	—	19	1	no	—
247	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
248	C₂×#117	—	19	1	no	—
249	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
250	C₂²×C₄²	—	19	1	no	—
251	#405	—	19	4	no	—
252	#405	—	38	2	no	—
253	C₂×#97	—	38	1	no	—
254	C₂×C₄×C₈	—	38	1	no	—
255	#341	—	38	2	no	—
256	#340	—	19	2	no	—
257	#340	—	19	2	no	—
258	#339	—	19	4	no	—
259	#339	—	38	2	no	—
260	#336	—	2	1	no	—
261	#336	—	2	1	no	—
262	#336	—	38	2	no	—
263	C₂×C₁₉	—	2	1	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	#1434	1	1	yes	characteristic
268	C₂×C₁₉	#1764	1	1	yes	characteristic
269	C₂×C₁₉	#1765	1	1	yes	characteristic
270	C₂×C₁₉	#1922	1	2	yes	—
271	C₂×C₁₉	#1929	1	2	yes	—
272	C₂³×C₄	—	38	1	no	—
273	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	19	2	no	—
280	C₂×M₁₆	—	19	2	no	—
281	C₂×M₁₆	—	19	2	no	—
282	C₂×M₁₆	—	38	1	no	—
283	C₂×M₁₆	—	38	1	no	—
284	C₂×M₁₆	—	38	1	no	—
285	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	19	2	no	—
292	C₂²×C₈	—	38	1	no	—
293	C₂²×C₈	—	38	1	no	—
294	C₂²×C₈	—	38	1	no	—
295	C₂²×C₈	—	38	1	no	—
296	C₂²×C₈	—	38	1	no	—
297	C₂²×C₈	—	38	1	no	—
298	C₂²×C₈	—	38	1	no	—
299	C₂²×C₈	C₄×D₁₉	1	2	yes	—
300	C₂²×C₈	D₇₆	1	2	yes	—
301	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
302	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	—	2	1	no	—
306	#117	—	2	1	no	—
307	#117	—	19	2	no	—
308	#117	—	19	2	no	—
309	#117	—	38	1	no	—
310	#117	—	38	1	no	—
311	C₂×C₄⋊C₄	—	19	1	no	—
312	C₂×C₄⋊C₄	—	19	1	no	—
313	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	38	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	19	2	no	—
318	C₂×C₄²	—	38	1	no	—
319	C₂×C₄²	—	38	1	no	—
320	C₂×C₄²	—	38	1	no	—
321	C₂×C₄²	—	38	1	no	—
322	C₂×C₄²	—	38	1	no	—
323	C₂×C₄²	—	38	1	no	—
324	#97	—	38	4	no	—
325	C₄×C₈	—	38	4	no	—
326	C₁₉	#10809	1	1	yes	characteristic, complemented, Sylow
327	C₂⁴	#64541	1	1	yes	characteristic
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	38	4	no	—
330	C₂²×C₄	—	38	2	no	—
331	C₂²×C₄	—	38	1	no	—
332	C₂²×C₄	—	38	1	no	—
333	C₂²×C₄	—	76	2	no	—
334	C₂²×C₄	—	76	1	no	—
335	C₂²×C₄	—	76	1	no	—
336	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
340	C₂²×C₄	#64541	1	1	yes	characteristic
341	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
342	C₂²×C₄	#64543	1	1	yes	characteristic
343	C₂²×C₄	#64543	1	1	yes	characteristic
344	C₂²×C₄	#64543	1	1	yes	characteristic
345	C₂²×C₄	#64543	1	1	yes	characteristic
346	C₂²×C₄	#64543	1	1	yes	characteristic
347	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
348	C₂²×C₄	#64545	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	4	1	no	—
353	M₁₆	—	4	1	no	—
354	M₁₆	—	19	4	no	—
355	M₁₆	—	38	2	no	—
356	M₁₆	—	38	2	no	—
357	M₁₆	—	38	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	38	2	no	—
370	C₂×C₈	—	38	2	no	—
371	C₂×C₈	—	38	2	no	—
372	C₂×C₈	—	38	2	no	—
373	C₂×C₈	—	38	2	no	—
374	C₂×C₈	—	38	2	no	—
375	C₂×C₈	—	76	1	no	—
376	C₂×C₈	—	76	1	no	—
377	C₂×C₈	—	76	1	no	—
378	C₂×C₈	—	76	1	no	—
379	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
380	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	19	2	no	—
384	C₄⋊C₄	—	19	2	no	—
385	C₄⋊C₄	—	38	1	no	—
386	C₄⋊C₄	—	38	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	38	2	no	—
390	C₂²⋊C₄	—	38	2	no	—
391	C₄²	—	4	1	no	—
392	C₄²	—	4	1	no	—
393	C₄²	—	38	2	no	—
394	C₄²	—	38	2	no	—
395	C₄²	—	38	2	no	—
396	C₄²	—	38	2	no	—
397	C₄²	—	76	1	no	—
398	C₄²	—	76	1	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	#10597318	1	1	yes	characteristic
402	C₂³	C₄×D₇₆	1	1	yes	characteristic
403	C₂³	#10597325	1	1	yes	characteristic
404	C₂³	#10597331	1	1	yes	characteristic
405	C₂³	#10597335	1	1	yes	characteristic
406	C₂³	#10597344	1	1	yes	characteristic
407	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	38	4	no	—
412	C₂×C₄	—	38	2	no	—
413	C₂×C₄	—	38	2	no	—
414	C₂×C₄	—	76	4	no	—
415	C₂×C₄	—	76	2	no	—
416	C₂×C₄	—	76	4	no	—
417	C₂×C₄	—	76	2	no	—
418	C₂×C₄	—	76	2	no	—
419	C₂×C₄	—	76	2	no	—
420	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
421	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
422	C₂×C₄	#10597323	1	1	yes	characteristic
423	C₂×C₄	#10597323	1	1	yes	characteristic
424	C₂×C₄	#10597323	1	1	yes	characteristic
425	C₂×C₄	#10597323	1	1	yes	characteristic
426	C₂×C₄	#10597325	1	1	yes	characteristic
427	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
428	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
429	C₂×C₄	#10597331	1	1	yes	characteristic
430	C₂×C₄	#10597332	1	1	yes	characteristic
431	C₂×C₄	#10597332	1	1	yes	characteristic
432	C₂×C₄	#10597333	1	1	yes	characteristic
433	C₂×C₄	#10597333	1	1	yes	characteristic
434	C₂×C₄	#10597335	1	1	yes	characteristic
435	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
436	C₂×C₄	#10597338	1	1	yes	characteristic
437	C₂×C₄	#10597338	1	1	yes	characteristic
438	C₂×C₄	#10597338	1	1	yes	characteristic
439	C₂×C₄	#10597341	1	1	yes	characteristic
440	C₂×C₄	#10597343	1	1	yes	characteristic
441	C₂×C₄	#10597344	1	1	yes	characteristic
442	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
443	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
444	C₂×C₄	#10597381	1	1	yes	characteristic
445	C₂×C₄	#10597381	1	1	yes	characteristic
446	C₂×C₄	#10597384	1	1	yes	characteristic
447	C₂×C₄	#10597392	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	—	4	2	no	—
451	C₈	—	38	4	no	—
452	C₈	—	76	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
462	C₂²	#11926408	1	1	yes	characteristic
463	C₂²	#11926411	1	1	yes	characteristic
464	C₂²	#11926425	1	1	yes	characteristic
465	C₂²	#11926429	1	1	yes	characteristic
466	C₂²	#11926432	1	1	yes	characteristic
467	C₂²	#11926436	1	1	yes	characteristic
468	C₂²	#11926659	1	2	yes	—
469	C₂²	#11926664	1	2	yes	—
470	C₄	—	8	2	no	—
471	C₄	—	76	4	no	—
472	C₄	—	76	2	no	—
473	C₄	—	76	2	no	—
474	C₄	#11926389	1	1	yes	characteristic
475	C₄	#11926395	1	1	yes	characteristic
476	C₄	#11926401	1	1	yes	characteristic
477	C₄	#11926405	1	1	yes	characteristic
478	C₄	#11926425	1	1	yes	characteristic
479	C₄	#11926429	1	1	yes	characteristic
480	C₄	#11926432	1	1	yes	characteristic
481	C₄	#11926436	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	#14561859	1	1	yes	characteristic
487	C₂	#14563474	1	1	yes	characteristic
488	C₂	#14563481	1	1	yes	characteristic
489	C₂	#14564231	1	2	yes	—
490	C₂	#14564280	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1729	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1729	D₁₉
hypocenter	C₁₉	#10809
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ #1729

Complements

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

N	H ≅ G/N	type
13. #11926499	C₄	semidirect
17. #11926306	C₄	semidirect
18. #11926306	C₄	semidirect
19. #11926305	C₄	semidirect
326. C₁₉	#10809	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926499	2
C₂×#11926308	2
#14563351	2
C₂×#11926305	2
C₂×#11926303	2
C₂×#11926298	2
C₁₉×#1729	2
#10809	19