Subgroups — #18089010

Order 4864.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926526	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926517	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926510	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926316	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926314	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×#64520	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926526	—	2	2	no	—
13	#11926526	—	2	2	no	—
14	C₂×#10597281	C₄	1	2	yes	complemented
15	C₂×#10597280	C₄	1	2	yes	complemented
16	#11926517	—	2	2	no	—
17	#11926517	—	2	2	no	—
18	C₂×#10597263	C₄	1	4	yes	—
19	#11926510	—	2	1	no	—
20	#11926510	—	2	1	no	—
21	#11926510	—	2	2	no	—
22	C₂×(C₂×D₁₉)⋊C₈	C₄	1	4	yes	complemented
23	#11926499	—	2	2	no	—
24	#11926499	—	2	2	no	—
25	C₂×#10597272	—	2	1	no	—
26	C₂×C₈×Dic₁₉	—	2	1	no	—
27	#11926316	—	2	2	no	—
28	#11926314	—	2	2	no	—
29	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
32	C₁₉×#336	—	2	2	no	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×C₂²⋊D₁₉	C₂×C₄	1	2	yes	—
35	C₂×#64541	—	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	—	2	1	no	—
43	C₂×#64541	—	2	1	no	—
44	C₂×#64541	—	2	1	no	—
45	C₂×#64541	—	2	1	no	—
46	C₂×#64541	—	2	1	no	—
47	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₉	C₂×C₄	1	2	yes	—
49	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
50	C₂×M₁₆×C₁₉	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
62	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	D₄	1	2	yes	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	1	no	—
67	C₁₉×#117	—	2	1	no	—
68	C₁₉×#117	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
73	#10597372	—	2	1	no	—
74	#10597372	—	2	1	no	—
75	#10597372	D₄	1	2	yes	—
76	#10597372	D₄	1	2	yes	—
77	C₂×C₄⋊Dic₁₉	—	2	1	no	—
78	C₂×C₄×Dic₁₉	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	—	2	1	no	—
83	C₂×#64520	—	2	1	no	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	—	2	1	no	—
88	C₂×#64520	C₂×C₄	1	2	yes	—
89	C₂×#64520	D₄	1	2	yes	—
90	C₂×#64520	D₄	1	2	yes	—
91	C₂²×C₁₉⋊C₈	—	2	1	no	—
92	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
93	#10597281	—	2	4	no	—
94	#10597280	—	2	4	no	—
95	(C₂×D₁₉)⋊C₈	—	2	4	no	—
96	(C₂×D₁₉)⋊C₈	—	2	4	no	—
97	#10597272	—	2	4	no	—
98	C₈×Dic₁₉	—	2	4	no	—
99	#10597263	—	2	8	no	—
100	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂³×D₁₉	C₄²	1	2	yes	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
117	C₂×C₂²⋊D₁₉	—	2	2	no	—
118	C₂×C₂²⋊D₁₉	—	2	2	no	—
119	C₂×C₂²⋊D₁₉	—	2	2	no	—
120	C₂×C₂²⋊D₁₉	—	2	2	no	—
121	C₂×C₂²⋊D₁₉	—	2	2	no	—
122	C₂×C₂²⋊D₁₉	—	2	2	no	—
123	C₂²×Dic₁₉	—	2	2	no	—
124	C₂²×Dic₁₉	C₄²	1	2	yes	—
125	#64541	—	4	1	no	—
126	#64541	—	4	1	no	—
127	#64541	—	4	1	no	—
128	#64541	—	4	1	no	—
129	#64541	—	4	1	no	—
130	#64541	—	4	1	no	—
131	#64541	—	4	1	no	—
132	#64541	—	4	1	no	—
133	#64541	—	4	1	no	—
134	#64541	—	4	1	no	—
135	#64541	—	4	1	no	—
136	#64541	—	4	1	no	—
137	#64541	—	4	1	no	—
138	#64541	—	4	1	no	—
139	#64541	—	4	1	no	—
140	#64541	—	4	1	no	—
141	C₂×D₇₆	—	2	1	no	—
142	C₂×D₇₆	—	2	1	no	—
143	C₂×D₇₆	—	2	1	no	—
144	C₂×D₇₆	—	2	1	no	—
145	C₂×D₇₆	—	2	1	no	—
146	C₂×D₇₆	—	2	1	no	—
147	C₂×C₄×D₁₉	—	2	2	no	—
148	C₂×C₄×D₁₉	—	2	2	no	—
149	C₂×C₄×D₁₉	—	2	2	no	—
150	C₂×C₄×D₁₉	—	2	2	no	—
151	C₂×C₄×D₁₉	—	2	2	no	—
152	C₂×C₄×D₁₉	—	2	2	no	—
153	C₂×Dic₃₈	—	2	1	no	—
154	C₂×Dic₃₈	—	2	1	no	—
155	C₂×Dic₃₈	—	2	1	no	—
156	C₂×Dic₃₈	—	2	1	no	—
157	C₂×Dic₃₈	—	2	1	no	—
158	C₂×Dic₃₈	—	2	1	no	—
159	M₁₆×C₁₉	—	2	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	4	1	no	—
162	M₁₆×C₁₉	—	4	1	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	1	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	4	1	no	—
173	C₂×C₈×C₁₉	—	4	1	no	—
174	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
175	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
176	C₄⋊C₄×C₁₉	—	4	1	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₄²×C₁₉	—	4	1	no	—
181	C₄²×C₁₉	—	4	1	no	—
182	C₂²⋊Dic₁₉	—	2	2	no	—
183	C₂²⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
184	C₄⋊Dic₁₉	—	2	2	no	—
185	C₄⋊Dic₁₉	—	2	2	no	—
186	C₄×Dic₁₉	—	2	2	no	—
187	C₄×Dic₁₉	—	2	2	no	—
188	#64520	—	2	2	no	—
189	#64520	—	2	2	no	—
190	#64520	—	2	2	no	—
191	#64520	—	4	1	no	—
192	#64520	—	4	1	no	—
193	#64520	—	4	1	no	—
194	#64520	—	4	1	no	—
195	#64520	C₂²⋊C₄	1	4	yes	—
196	C₂×C₁₉⋊C₈	—	2	2	no	—
197	C₂×C₁₉⋊C₈	—	2	2	no	—
198	C₂×C₁₉⋊C₈	—	2	2	no	—
199	C₂×C₁₉⋊C₈	—	2	2	no	—
200	C₂×C₁₉⋊C₈	—	2	2	no	—
201	C₂×C₁₉⋊C₈	—	2	2	no	—
202	#10961	—	19	1	no	maximal, Sylow
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
205	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₁₉	#117	1	1	yes	characteristic
207	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
208	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
211	C₂²×D₁₉	—	2	2	no	—
212	C₂²×D₁₉	—	2	2	no	—
213	C₂²×D₁₉	—	2	2	no	—
214	C₂²×D₁₉	—	4	4	no	—
215	C₂×C₄×C₁₉	—	4	4	no	—
216	C₂×C₄×C₁₉	—	4	2	no	—
217	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
245	C₂²⋊D₁₉	—	4	2	no	—
246	C₂²⋊D₁₉	—	4	2	no	—
247	C₂²⋊D₁₉	—	4	2	no	—
248	C₂²⋊D₁₉	—	4	2	no	—
249	C₂×Dic₁₉	—	2	2	no	—
250	C₂×Dic₁₉	—	2	2	no	—
251	C₂×Dic₁₉	—	2	2	no	—
252	C₂×Dic₁₉	—	2	4	no	—
253	C₂×Dic₁₉	—	4	4	no	—
254	D₇₆	—	4	1	no	—
255	D₇₆	—	4	1	no	—
256	D₇₆	—	4	1	no	—
257	D₇₆	—	4	1	no	—
258	C₄×D₁₉	—	4	2	no	—
259	C₄×D₁₉	—	4	2	no	—
260	C₄×D₁₉	—	4	2	no	—
261	C₄×D₁₉	—	4	2	no	—
262	Dic₃₈	—	4	1	no	—
263	Dic₃₈	—	4	1	no	—
264	Dic₃₈	—	4	1	no	—
265	Dic₃₈	—	4	1	no	—
266	C₈×C₁₉	—	2	2	no	—
267	C₈×C₁₉	—	2	2	no	—
268	C₈×C₁₉	—	4	2	no	—
269	C₁₉⋊C₈	—	2	4	no	—
270	C₁₉⋊C₈	—	4	2	no	—
271	C₂×#413	—	19	1	no	—
272	C₂×#410	—	19	1	no	—
273	C₂×#408	—	19	1	no	—
274	C₂×#405	—	19	1	no	—
275	C₂×#344	—	19	1	no	—
276	C₂×#344	—	19	1	no	—
277	#1729	D₁₉	1	1	yes	characteristic, complemented
278	C₂²×C₁₉	—	2	2	no	—
279	C₂²×C₁₉	—	2	2	no	—
280	C₂²×C₁₉	—	2	2	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
288	C₂²×C₁₉	#386	1	1	yes	characteristic
289	C₂²×C₁₉	#388	1	1	yes	characteristic
290	C₂²×C₁₉	#388	1	1	yes	characteristic
291	C₂²×C₁₉	#390	1	1	yes	characteristic
292	C₂×D₁₉	—	4	2	no	—
293	C₂×D₁₉	—	4	4	no	—
294	C₂×D₁₉	—	8	2	no	—
295	C₂×D₁₉	—	8	2	no	—
296	C₄×C₁₉	—	8	2	no	—
297	C₄×C₁₉	#386	1	1	yes	characteristic
298	C₄×C₁₉	#386	1	1	yes	characteristic
299	C₄×C₁₉	#388	1	1	yes	characteristic
300	C₄×C₁₉	#388	1	1	yes	characteristic
301	C₄×C₁₉	#388	1	1	yes	characteristic
302	C₄×C₁₉	#388	1	1	yes	characteristic
303	C₄×C₁₉	#390	1	1	yes	characteristic
304	C₄×C₁₉	#390	1	1	yes	characteristic
305	Dic₁₉	—	4	4	no	—
306	Dic₁₉	—	4	2	no	—
307	C₂²×#41	—	19	1	no	—
308	C₂²×M₁₆	—	19	1	no	—
309	C₂²×M₁₆	—	19	1	no	—
310	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
311	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
312	C₂×#117	—	19	1	no	—
313	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
314	#413	—	38	2	no	—
315	#413	—	38	2	no	—
316	C₂×#101	—	19	2	no	—
317	C₂×#100	—	19	2	no	—
318	#410	—	38	2	no	—
319	#410	—	38	2	no	—
320	C₂×#99	—	19	4	no	—
321	#408	—	38	1	no	—
322	#408	—	38	1	no	—
323	#408	—	38	2	no	—
324	C₂×C₂²⋊C₈	—	19	4	no	—
325	#405	—	38	2	no	—
326	#405	—	38	2	no	—
327	C₂×#97	—	38	1	no	—
328	C₂×C₄×C₈	—	38	1	no	—
329	#344	—	38	2	no	—
330	#344	—	38	2	no	—
331	#336	—	2	2	no	—
332	C₂×C₁₉	—	2	1	no	—
333	C₂×C₁₉	—	2	1	no	—
334	C₂×C₁₉	—	2	1	no	—
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	2	1	no	—
337	C₂×C₁₉	—	2	1	no	—
338	C₂×C₁₉	#1437	1	1	yes	characteristic
339	C₂×C₁₉	#1757	1	2	yes	—
340	D₁₉	—	8	2	no	—
341	C₂×#41	—	38	1	no	—
342	C₂×#41	—	38	1	no	—
343	C₂×#41	—	38	1	no	—
344	C₂×#41	—	38	1	no	—
345	C₂×#41	—	38	1	no	—
346	C₂×#41	—	38	1	no	—
347	C₂×#41	—	38	1	no	—
348	C₂×#41	—	38	1	no	—
349	C₂×#41	—	38	1	no	—
350	C₂×#41	—	38	1	no	—
351	C₂×#41	—	38	1	no	—
352	C₂×#41	—	38	1	no	—
353	C₂²×Q₈	—	19	1	no	—
354	C₂²×D₄	—	19	2	no	—
355	C₂²×D₄	—	19	1	no	—
356	C₂³×C₄	—	19	2	no	—
357	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	19	2	no	—
364	C₂×M₁₆	—	19	2	no	—
365	C₂×M₁₆	—	19	2	no	—
366	C₂×M₁₆	—	38	1	no	—
367	C₂×M₁₆	—	38	1	no	—
368	C₂×M₁₆	—	38	1	no	—
369	C₂×M₁₆	—	38	1	no	—
370	C₂×M₁₆	—	38	1	no	—
371	C₂×M₁₆	—	38	1	no	—
372	C₂×M₁₆	—	38	1	no	—
373	C₂×M₁₆	—	38	1	no	—
374	C₂×M₁₆	—	38	1	no	—
375	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	19	2	no	—
382	C₂²×C₈	—	38	1	no	—
383	C₂²×C₈	C₄×D₁₉	1	2	yes	—
384	C₂²×C₈	D₇₆	1	1	yes	characteristic
385	C₂²×C₈	D₇₆	1	1	yes	characteristic
386	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
387	#117	—	2	1	no	—
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	#117	—	19	2	no	—
392	#117	—	19	2	no	—
393	#117	—	38	1	no	—
394	#117	—	38	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	38	1	no	—
397	C₂×C₂²⋊C₄	—	19	2	no	—
398	C₂×C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	38	1	no	—
401	#101	—	38	4	no	—
402	#100	—	38	4	no	—
403	#99	—	38	8	no	—
404	C₂²⋊C₈	—	38	4	no	—
405	C₂²⋊C₈	—	38	4	no	—
406	#97	—	38	4	no	—
407	C₄×C₈	—	38	4	no	—
408	C₁₉	#10961	1	1	yes	characteristic, complemented, Sylow
409	C₂⁴	—	19	2	no	—
410	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
411	#41	—	76	1	no	—
412	#41	—	76	1	no	—
413	#41	—	76	1	no	—
414	#41	—	76	1	no	—
415	#41	—	76	1	no	—
416	#41	—	76	1	no	—
417	#41	—	76	1	no	—
418	#41	—	76	1	no	—
419	#41	—	76	1	no	—
420	#41	—	76	1	no	—
421	#41	—	76	1	no	—
422	#41	—	76	1	no	—
423	#41	—	76	1	no	—
424	#41	—	76	1	no	—
425	#41	—	76	1	no	—
426	#41	—	76	1	no	—
427	C₂×Q₈	—	38	1	no	—
428	C₂×Q₈	—	38	1	no	—
429	C₂×Q₈	—	38	1	no	—
430	C₂×Q₈	—	38	1	no	—
431	C₂×Q₈	—	38	1	no	—
432	C₂×Q₈	—	38	1	no	—
433	C₂×D₄	—	38	2	no	—
434	C₂×D₄	—	38	2	no	—
435	C₂×D₄	—	38	2	no	—
436	C₂×D₄	—	38	2	no	—
437	C₂×D₄	—	38	2	no	—
438	C₂×D₄	—	38	2	no	—
439	C₂×D₄	—	38	1	no	—
440	C₂×D₄	—	38	1	no	—
441	C₂×D₄	—	38	1	no	—
442	C₂×D₄	—	38	1	no	—
443	C₂×D₄	—	38	1	no	—
444	C₂×D₄	—	38	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	19	2	no	—
447	C₂²×C₄	—	38	2	no	—
448	C₂²×C₄	—	38	2	no	—
449	C₂²×C₄	—	38	2	no	—
450	C₂²×C₄	—	38	2	no	—
451	C₂²×C₄	—	38	2	no	—
452	C₂²×C₄	—	38	2	no	—
453	C₂²×C₄	—	38	2	no	—
454	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
457	C₂²×C₄	#64541	1	1	yes	characteristic
458	C₂²×C₄	#64541	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
460	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
461	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
462	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
463	C₂²×C₄	#64543	1	1	yes	characteristic
464	C₂²×C₄	#64543	1	1	yes	characteristic
465	C₂²×C₄	#64545	1	1	yes	characteristic
466	C₂²×C₄	#64545	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	4	1	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	19	4	no	—
473	M₁₆	—	38	2	no	—
474	M₁₆	—	38	2	no	—
475	M₁₆	—	38	2	no	—
476	M₁₆	—	76	1	no	—
477	M₁₆	—	76	1	no	—
478	M₁₆	—	76	1	no	—
479	M₁₆	—	76	1	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	4	1	no	—
490	C₂×C₈	—	4	1	no	—
491	C₂×C₈	—	38	2	no	—
492	C₂×C₈	—	38	2	no	—
493	C₂×C₈	—	38	2	no	—
494	C₂×C₈	—	38	2	no	—
495	C₂×C₈	—	38	2	no	—
496	C₂×C₈	—	38	2	no	—
497	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
498	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	38	2	no	—
502	C₄⋊C₄	—	38	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	19	4	no	—
506	C₂²⋊C₄	—	38	2	no	—
507	C₄²	—	4	1	no	—
508	C₄²	—	4	1	no	—
509	C₄²	—	38	2	no	—
510	C₄²	—	38	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	38	2	no	—
513	C₂³	—	38	2	no	—
514	C₂³	—	38	2	no	—
515	C₂³	—	76	4	no	—
516	C₂³	C₄²×D₁₉	1	1	yes	characteristic
517	C₂³	C₄×D₇₆	1	1	yes	characteristic
518	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
519	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
520	C₂³	#10597338	1	1	yes	characteristic
521	C₂³	#10597339	1	1	yes	characteristic
522	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
523	Q₈	—	76	1	no	—
524	Q₈	—	76	1	no	—
525	Q₈	—	76	1	no	—
526	Q₈	—	76	1	no	—
527	D₄	—	76	2	no	—
528	D₄	—	76	2	no	—
529	D₄	—	76	2	no	—
530	D₄	—	76	2	no	—
531	D₄	—	76	1	no	—
532	D₄	—	76	1	no	—
533	D₄	—	76	1	no	—
534	D₄	—	76	1	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	38	2	no	—
538	C₂×C₄	—	38	2	no	—
539	C₂×C₄	—	38	2	no	—
540	C₂×C₄	—	38	4	no	—
541	C₂×C₄	—	76	4	no	—
542	C₂×C₄	—	76	2	no	—
543	C₂×C₄	—	76	2	no	—
544	C₂×C₄	—	76	2	no	—
545	C₂×C₄	—	76	2	no	—
546	C₂×C₄	#10597318	1	1	yes	characteristic
547	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
548	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
549	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
550	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
551	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
552	C₂×C₄	#10597328	1	1	yes	characteristic
553	C₂×C₄	#10597330	1	1	yes	characteristic
554	C₂×C₄	#10597330	1	1	yes	characteristic
555	C₂×C₄	#10597331	1	1	yes	characteristic
556	C₂×C₄	#10597331	1	1	yes	characteristic
557	C₂×C₄	#10597332	1	1	yes	characteristic
558	C₂×C₄	#10597338	1	1	yes	characteristic
559	C₂×C₄	#10597339	1	1	yes	characteristic
560	C₂×C₄	#10597339	1	1	yes	characteristic
561	C₂×C₄	#10597339	1	1	yes	characteristic
562	C₂×C₄	#10597340	1	1	yes	characteristic
563	C₂×C₄	#10597340	1	1	yes	characteristic
564	C₂×C₄	#10597341	1	1	yes	characteristic
565	C₂×C₄	#10597341	1	1	yes	characteristic
566	C₂×C₄	#10597344	1	1	yes	characteristic
567	C₂×C₄	#10597344	1	1	yes	characteristic
568	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
569	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
570	C₂×C₄	#10597385	1	1	yes	characteristic
571	C₂×C₄	#10597385	1	1	yes	characteristic
572	C₂×C₄	#10597386	1	1	yes	characteristic
573	C₂×C₄	#10597393	1	1	yes	characteristic
574	C₈	—	2	2	no	—
575	C₈	—	2	2	no	—
576	C₈	—	4	2	no	—
577	C₈	—	38	4	no	—
578	C₈	—	76	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	76	2	no	—
587	C₂²	—	76	4	no	—
588	C₂²	—	152	2	no	—
589	C₂²	—	152	2	no	—
590	C₂²	#11926391	1	1	yes	characteristic
591	C₂²	#11926391	1	1	yes	characteristic
592	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
593	C₂²	#11926422	1	1	yes	characteristic
594	C₂²	#11926434	1	1	yes	characteristic
595	C₂²	#11926436	1	1	yes	characteristic
596	C₂²	#11926444	1	1	yes	characteristic
597	C₄	—	8	2	no	—
598	C₄	—	76	4	no	—
599	C₄	—	76	2	no	—
600	C₄	#11926421	1	1	yes	characteristic
601	C₄	#11926422	1	1	yes	characteristic
602	C₄	#11926433	1	1	yes	characteristic
603	C₄	#11926433	1	1	yes	characteristic
604	C₄	#11926434	1	1	yes	characteristic
605	C₄	#11926436	1	1	yes	characteristic
606	C₄	#11926444	1	1	yes	characteristic
607	C₄	#11926445	1	1	yes	characteristic
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	152	2	no	—
615	C₂	#14561871	1	1	yes	characteristic
616	C₂	#14563436	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1729	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1729	D₁₉
hypocenter	C₁₉	#10961
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ #1729

Complements

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

N	H ≅ G/N	type
4. C₂×#11926499	C₂	semidirect
5. C₂×#11926316	C₂	semidirect
6. C₂×#11926314	C₂	semidirect
7. C₁₉×#1729	C₂	semidirect
14. C₂×#10597281	C₄	semidirect
15. C₂×#10597280	C₄	semidirect
22. C₂×(C₂×D₁₉)⋊C₈	C₄	semidirect
277. #1729	D₁₉	semidirect
408. C₁₉	#10961	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926526	2
C₂×#11926517	2
C₂×#11926510	2
C₂×#11926499	2
C₂×#11926316	2
C₂×#11926314	2
C₁₉×#1729	2
#10961	19