Subgroups — #18090389

Order 4864.

822 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572152	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926541	C₂	1	1	yes	maximal, characteristic
3	#14572079	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926315	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926309	C₂	1	1	yes	maximal, characteristic, complemented
6	#14563344	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	#11926552	—	2	1	no	—
13	#11926548	—	2	1	no	—
14	#11926543	C₄	1	4	yes	complemented
15	#11926541	—	2	2	no	—
16	#11926541	—	2	2	no	—
17	#11926538	—	2	2	no	—
18	C₂×#10597273	—	2	1	no	—
19	C₂×#10597278	—	2	1	no	—
20	#11926512	—	2	2	no	—
21	#11926510	—	2	2	no	—
22	#11926507	—	2	2	no	—
23	#11926315	—	2	2	no	—
24	#11926309	—	2	2	no	—
25	#11926303	—	2	2	no	—
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₁₉×#336	—	2	2	no	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₂²⋊D₁₉	—	2	1	no	—
32	C₂×#64541	—	2	1	no	—
33	C₂×#64541	—	2	1	no	—
34	C₂×#64541	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
43	C₂×#64541	D₄	1	2	yes	—
44	C₂²×D₇₆	D₄	1	1	yes	characteristic
45	C₂²×C₄×D₁₉	—	2	1	no	—
46	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
47	C₂×M₁₆×C₁₉	—	2	1	no	—
48	C₂×M₁₆×C₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
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	D₄	1	2	yes	—
60	C₂²×C₈×C₁₉	D₄	1	2	yes	—
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	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
69	#10597372	—	2	1	no	—
70	#10597372	—	2	1	no	—
71	#10597372	—	2	1	no	—
72	#10597372	D₄	1	2	yes	—
73	C₂×C₄⋊Dic₁₉	—	2	1	no	—
74	C₂×C₄×Dic₁₉	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	—	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	C₂×C₄	1	2	yes	—
86	C₂×#64520	D₄	1	2	yes	—
87	C₂²×C₁₉⋊C₈	—	2	1	no	—
88	C₂²×C₁₉⋊C₈	—	2	1	no	—
89	#10597278	—	2	4	no	—
90	(C₂×D₁₉)⋊C₈	—	2	8	no	—
91	#10597273	—	2	4	no	—
92	#10597267	—	2	4	no	—
93	#10597266	—	2	4	no	—
94	C₂⁴×C₁₉	#41	1	1	yes	characteristic
95	C₂³×D₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂×C₂²⋊D₁₉	—	2	2	no	—
112	C₂×C₂²⋊D₁₉	—	2	2	no	—
113	C₂×C₂²⋊D₁₉	—	4	1	no	—
114	C₂×C₂²⋊D₁₉	—	4	1	no	—
115	C₂×C₂²⋊D₁₉	—	4	1	no	—
116	C₂×C₂²⋊D₁₉	—	4	1	no	—
117	C₂²×Dic₁₉	—	2	1	no	—
118	C₂²×Dic₁₉	—	4	1	no	—
119	#64541	—	2	2	no	—
120	#64541	—	2	2	no	—
121	#64541	—	2	2	no	—
122	#64541	—	2	2	no	—
123	#64541	—	2	2	no	—
124	#64541	—	2	2	no	—
125	#64541	—	2	2	no	—
126	#64541	—	2	2	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	C₂×D₇₆	—	2	1	no	—
136	C₂×D₇₆	—	2	1	no	—
137	C₂×D₇₆	—	2	1	no	—
138	C₂×D₇₆	—	2	1	no	—
139	C₂×D₇₆	—	2	1	no	—
140	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
141	C₂×C₄×D₁₉	—	2	2	no	—
142	C₂×C₄×D₁₉	—	2	2	no	—
143	C₂×C₄×D₁₉	—	4	1	no	—
144	C₂×C₄×D₁₉	—	4	1	no	—
145	C₂×C₄×D₁₉	—	4	1	no	—
146	C₂×C₄×D₁₉	—	4	1	no	—
147	C₂×Dic₃₈	—	2	1	no	—
148	C₂×Dic₃₈	—	2	1	no	—
149	C₂×Dic₃₈	—	2	1	no	—
150	C₂×Dic₃₈	—	2	1	no	—
151	C₂×Dic₃₈	—	2	1	no	—
152	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
153	M₁₆×C₁₉	—	4	1	no	—
154	M₁₆×C₁₉	—	4	1	no	—
155	M₁₆×C₁₉	—	4	1	no	—
156	M₁₆×C₁₉	—	4	1	no	—
157	C₂×C₈×C₁₉	—	2	2	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	2	no	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	4	1	no	—
164	C₂×C₈×C₁₉	—	4	1	no	—
165	C₂×C₈×C₁₉	—	4	1	no	—
166	C₂×C₈×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	4	1	no	—
170	C₂²⋊C₄×C₁₉	—	4	1	no	—
171	C₄²×C₁₉	—	4	1	no	—
172	C₄²×C₁₉	—	4	1	no	—
173	C₂²⋊Dic₁₉	—	2	2	no	—
174	C₂²⋊Dic₁₉	—	4	1	no	—
175	C₄⋊Dic₁₉	—	2	2	no	—
176	C₄⋊Dic₁₉	—	4	1	no	—
177	C₄×Dic₁₉	—	2	2	no	—
178	C₄×Dic₁₉	—	4	1	no	—
179	#64520	—	2	2	no	—
180	#64520	—	2	2	no	—
181	#64520	—	2	2	no	—
182	#64520	—	2	2	no	—
183	#64520	—	4	1	no	—
184	#64520	—	4	1	no	—
185	#64520	—	4	1	no	—
186	#64520	—	4	1	no	—
187	C₂×C₁₉⋊C₈	—	2	2	no	—
188	C₂×C₁₉⋊C₈	—	2	2	no	—
189	C₂×C₁₉⋊C₈	—	4	1	no	—
190	C₂×C₁₉⋊C₈	—	4	1	no	—
191	C₂×C₁₉⋊C₈	—	4	1	no	—
192	C₂×C₁₉⋊C₈	—	4	1	no	—
193	#11194	—	19	1	no	maximal, Sylow
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
196	C₂³×C₁₉	#121	1	1	yes	characteristic
197	C₂³×C₁₉	#123	1	1	yes	characteristic
198	C₂³×C₁₉	#123	1	1	yes	characteristic
199	C₂³×C₁₉	#124	1	1	yes	characteristic
200	C₂³×C₁₉	#126	1	1	yes	characteristic
201	C₂³×C₁₉	#126	1	1	yes	characteristic
202	C₂²×D₁₉	—	2	2	no	—
203	C₂²×D₁₉	—	4	1	no	—
204	C₂²×D₁₉	—	4	1	no	—
205	C₂²×D₁₉	—	8	2	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
236	C₂²⋊D₁₉	—	4	2	no	—
237	C₂²⋊D₁₉	—	4	2	no	—
238	C₂²⋊D₁₉	—	4	2	no	—
239	C₂²⋊D₁₉	—	4	2	no	—
240	C₂×Dic₁₉	—	2	2	no	—
241	C₂×Dic₁₉	—	4	1	no	—
242	C₂×Dic₁₉	—	4	1	no	—
243	C₂×Dic₁₉	—	4	2	no	—
244	C₂×Dic₁₉	—	8	2	no	—
245	D₇₆	—	2	2	no	—
246	D₇₆	—	2	2	no	—
247	D₇₆	—	4	1	no	—
248	D₇₆	—	4	1	no	—
249	C₄×D₁₉	—	4	2	no	—
250	C₄×D₁₉	—	4	2	no	—
251	C₄×D₁₉	—	4	2	no	—
252	C₄×D₁₉	—	4	2	no	—
253	Dic₃₈	—	2	2	no	—
254	Dic₃₈	—	2	2	no	—
255	Dic₃₈	—	4	1	no	—
256	Dic₃₈	—	4	1	no	—
257	C₈×C₁₉	—	4	2	no	—
258	C₈×C₁₉	—	4	2	no	—
259	C₁₉⋊C₈	—	4	2	no	—
260	C₁₉⋊C₈	—	4	2	no	—
261	#2896	—	19	1	no	—
262	C₂×#416	—	19	1	no	—
263	#2879	—	19	1	no	—
264	C₂×#344	—	19	1	no	—
265	C₂×#341	—	19	1	no	—
266	#1733	—	19	1	no	—
267	#1729	D₁₉	1	1	yes	characteristic, complemented
268	C₂²×C₁₉	—	2	2	no	—
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	1	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	#386	1	1	yes	characteristic
276	C₂²×C₁₉	#388	1	1	yes	characteristic
277	C₂²×C₁₉	#388	1	1	yes	characteristic
278	C₂²×C₁₉	#394	1	1	yes	characteristic
279	C₂²×C₁₉	#397	1	1	yes	characteristic
280	C₂²×C₁₉	#397	1	1	yes	characteristic
281	C₂²×C₁₉	#397	1	1	yes	characteristic
282	C₂×D₁₉	—	4	4	no	—
283	C₂×D₁₉	—	4	2	no	—
284	C₂×D₁₉	—	8	2	no	—
285	C₂×D₁₉	—	8	2	no	—
286	C₄×C₁₉	—	8	2	no	—
287	C₄×C₁₉	#381	1	1	yes	characteristic
288	C₄×C₁₉	#386	1	1	yes	characteristic
289	C₄×C₁₉	#388	1	1	yes	characteristic
290	C₄×C₁₉	#388	1	1	yes	characteristic
291	C₄×C₁₉	#394	1	1	yes	characteristic
292	C₄×C₁₉	#394	1	1	yes	characteristic
293	C₄×C₁₉	#394	1	1	yes	characteristic
294	C₄×C₁₉	#397	1	1	yes	characteristic
295	Dic₁₉	—	4	2	no	—
296	Dic₁₉	—	8	2	no	—
297	C₂²×#41	—	19	1	no	—
298	C₂²×M₁₆	—	19	1	no	—
299	C₂²×M₁₆	—	19	1	no	—
300	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
301	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
302	C₂×#117	—	19	1	no	—
303	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
304	#419	—	38	1	no	—
305	#418	—	38	1	no	—
306	#417	—	19	4	no	—
307	#416	—	38	2	no	—
308	#416	—	38	2	no	—
309	#416	—	38	2	no	—
310	C₂×#103	—	38	1	no	—
311	C₂×#102	—	38	1	no	—
312	#408	—	38	2	no	—
313	#408	—	38	2	no	—
314	#407	—	38	2	no	—
315	#344	—	38	2	no	—
316	#341	—	38	2	no	—
317	#339	—	38	2	no	—
318	#336	—	2	2	no	—
319	C₂×C₁₉	—	2	1	no	—
320	C₂×C₁₉	—	2	1	no	—
321	C₂×C₁₉	—	2	1	no	—
322	C₂×C₁₉	—	2	1	no	—
323	C₂×C₁₉	—	2	1	no	—
324	C₂×C₁₉	—	2	1	no	—
325	C₂×C₁₉	#1440	1	1	yes	characteristic
326	C₂×C₁₉	#1881	1	2	yes	—
327	D₁₉	—	8	2	no	—
328	C₂×#41	—	19	2	no	—
329	C₂×#41	—	19	2	no	—
330	C₂×#41	—	38	1	no	—
331	C₂×#41	—	38	1	no	—
332	C₂×#41	—	38	1	no	—
333	C₂×#41	—	38	1	no	—
334	C₂×#41	—	38	1	no	—
335	C₂×#41	—	38	1	no	—
336	C₂×#41	—	38	1	no	—
337	C₂×#41	—	38	1	no	—
338	C₂×#41	—	38	1	no	—
339	C₂×#41	—	38	1	no	—
340	C₂²×Q₈	—	19	1	no	—
341	C₂²×D₄	—	19	1	no	—
342	C₂²×D₄	—	38	1	no	—
343	C₂³×C₄	—	38	1	no	—
344	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	19	2	no	—
352	C₂×M₁₆	—	19	2	no	—
353	C₂×M₁₆	—	38	1	no	—
354	C₂×M₁₆	—	38	1	no	—
355	C₂×M₁₆	—	38	1	no	—
356	C₂×M₁₆	—	38	1	no	—
357	C₂×M₁₆	—	38	1	no	—
358	C₂×M₁₆	—	38	1	no	—
359	C₂×M₁₆	—	38	1	no	—
360	C₂×M₁₆	—	38	1	no	—
361	C₂×M₁₆	—	38	1	no	—
362	C₂×M₁₆	—	38	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	38	1	no	—
370	C₂²×C₈	—	38	1	no	—
371	C₂²×C₈	D₇₆	1	2	yes	—
372	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	19	2	no	—
378	#117	—	38	1	no	—
379	#117	—	38	1	no	—
380	#117	—	38	1	no	—
381	C₂×C₄⋊C₄	—	38	1	no	—
382	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	38	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	38	1	no	—
387	#103	—	38	4	no	—
388	#103	—	38	4	no	—
389	#102	—	38	4	no	—
390	#102	—	38	4	no	—
391	C₂²⋊C₈	—	38	8	no	—
392	C₁₉	#11194	1	1	yes	characteristic, complemented, Sylow
393	C₂⁴	—	38	1	no	—
394	C₂⁴	#64541	1	1	yes	characteristic
395	#41	—	38	2	no	—
396	#41	—	38	2	no	—
397	#41	—	38	2	no	—
398	#41	—	38	2	no	—
399	#41	—	38	2	no	—
400	#41	—	38	2	no	—
401	#41	—	38	2	no	—
402	#41	—	38	2	no	—
403	#41	—	76	1	no	—
404	#41	—	76	1	no	—
405	#41	—	76	1	no	—
406	#41	—	76	1	no	—
407	#41	—	76	1	no	—
408	#41	—	76	1	no	—
409	#41	—	76	1	no	—
410	#41	—	76	1	no	—
411	C₂×Q₈	—	19	2	no	—
412	C₂×Q₈	—	38	1	no	—
413	C₂×Q₈	—	38	1	no	—
414	C₂×Q₈	—	38	1	no	—
415	C₂×Q₈	—	38	1	no	—
416	C₂×Q₈	—	38	1	no	—
417	C₂×D₄	—	19	2	no	—
418	C₂×D₄	—	38	2	no	—
419	C₂×D₄	—	38	2	no	—
420	C₂×D₄	—	38	1	no	—
421	C₂×D₄	—	38	1	no	—
422	C₂×D₄	—	38	1	no	—
423	C₂×D₄	—	38	1	no	—
424	C₂×D₄	—	38	1	no	—
425	C₂×D₄	—	76	1	no	—
426	C₂×D₄	—	76	1	no	—
427	C₂×D₄	—	76	1	no	—
428	C₂×D₄	—	76	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	38	1	no	—
431	C₂²×C₄	—	38	2	no	—
432	C₂²×C₄	—	38	2	no	—
433	C₂²×C₄	—	76	1	no	—
434	C₂²×C₄	—	76	1	no	—
435	C₂²×C₄	—	76	1	no	—
436	C₂²×C₄	—	76	1	no	—
437	C₂²×C₄	—	76	1	no	—
438	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
440	C₂²×C₄	#64541	1	1	yes	characteristic
441	C₂²×C₄	#64541	1	1	yes	characteristic
442	C₂²×C₄	#64541	1	1	yes	characteristic
443	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
444	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
445	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
446	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
447	C₂²×C₄	#64543	1	1	yes	characteristic
448	C₂²×C₄	#64543	1	1	yes	characteristic
449	C₂²×C₄	#64545	1	1	yes	characteristic
450	C₂²×C₄	#64545	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
452	M₁₆	—	4	1	no	—
453	M₁₆	—	4	1	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	—	4	1	no	—
456	M₁₆	—	38	2	no	—
457	M₁₆	—	38	2	no	—
458	M₁₆	—	38	2	no	—
459	M₁₆	—	38	2	no	—
460	M₁₆	—	76	1	no	—
461	M₁₆	—	76	1	no	—
462	M₁₆	—	76	1	no	—
463	M₁₆	—	76	1	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	4	1	no	—
471	C₂×C₈	—	4	1	no	—
472	C₂×C₈	—	4	1	no	—
473	C₂×C₈	—	4	1	no	—
474	C₂×C₈	—	38	2	no	—
475	C₂×C₈	—	38	2	no	—
476	C₂×C₈	—	76	1	no	—
477	C₂×C₈	—	76	1	no	—
478	C₂×C₈	—	76	1	no	—
479	C₂×C₈	—	76	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	38	2	no	—
483	C₄⋊C₄	—	76	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	38	2	no	—
487	C₂²⋊C₄	—	76	1	no	—
488	C₄²	—	4	1	no	—
489	C₄²	—	4	1	no	—
490	C₄²	—	38	2	no	—
491	C₄²	—	76	1	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	38	2	no	—
494	C₂³	—	76	1	no	—
495	C₂³	—	76	1	no	—
496	C₂³	—	152	2	no	—
497	C₂³	#10597321	1	1	yes	characteristic
498	C₂³	#10597322	1	1	yes	characteristic
499	C₂³	#10597329	1	1	yes	characteristic
500	C₂³	#10597330	1	1	yes	characteristic
501	C₂³	#10597340	1	1	yes	characteristic
502	C₂³	#10597344	1	1	yes	characteristic
503	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
504	Q₈	—	38	2	no	—
505	Q₈	—	38	2	no	—
506	Q₈	—	76	1	no	—
507	Q₈	—	76	1	no	—
508	D₄	—	38	2	no	—
509	D₄	—	38	2	no	—
510	D₄	—	76	2	no	—
511	D₄	—	76	2	no	—
512	D₄	—	76	2	no	—
513	D₄	—	76	2	no	—
514	D₄	—	76	1	no	—
515	D₄	—	76	1	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	38	2	no	—
519	C₂×C₄	—	76	1	no	—
520	C₂×C₄	—	76	1	no	—
521	C₂×C₄	—	76	2	no	—
522	C₂×C₄	—	76	2	no	—
523	C₂×C₄	—	76	2	no	—
524	C₂×C₄	—	76	2	no	—
525	C₂×C₄	—	76	2	no	—
526	C₂×C₄	—	152	2	no	—
527	C₂×C₄	#10597318	1	1	yes	characteristic
528	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
529	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
530	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	#10597328	1	1	yes	characteristic
532	C₂×C₄	#10597329	1	1	yes	characteristic
533	C₂×C₄	#10597329	1	1	yes	characteristic
534	C₂×C₄	#10597330	1	1	yes	characteristic
535	C₂×C₄	#10597330	1	1	yes	characteristic
536	C₂×C₄	#10597331	1	1	yes	characteristic
537	C₂×C₄	#10597331	1	1	yes	characteristic
538	C₂×C₄	#10597332	1	1	yes	characteristic
539	C₂×C₄	#10597338	1	1	yes	characteristic
540	C₂×C₄	#10597339	1	1	yes	characteristic
541	C₂×C₄	#10597340	1	1	yes	characteristic
542	C₂×C₄	#10597340	1	1	yes	characteristic
543	C₂×C₄	#10597340	1	1	yes	characteristic
544	C₂×C₄	#10597340	1	1	yes	characteristic
545	C₂×C₄	#10597341	1	1	yes	characteristic
546	C₂×C₄	#10597341	1	1	yes	characteristic
547	C₂×C₄	#10597344	1	1	yes	characteristic
548	C₂×C₄	#10597344	1	1	yes	characteristic
549	C₂×C₄	#10597375	1	1	yes	characteristic
550	C₂×C₄	#10597376	1	1	yes	characteristic
551	C₂×C₄	#10597383	1	1	yes	characteristic
552	C₂×C₄	#10597384	1	1	yes	characteristic
553	C₂×C₄	#10597385	1	1	yes	characteristic
554	C₂×C₄	#10597393	1	1	yes	characteristic
555	C₈	—	4	2	no	—
556	C₈	—	4	2	no	—
557	C₈	—	76	2	no	—
558	C₈	—	76	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	76	2	no	—
567	C₂²	—	76	4	no	—
568	C₂²	—	152	2	no	—
569	C₂²	—	152	2	no	—
570	C₂²	#11926420	1	1	yes	characteristic
571	C₂²	#11926434	1	1	yes	characteristic
572	C₂²	#11926435	1	1	yes	characteristic
573	C₂²	#11926462	1	1	yes	characteristic
574	C₂²	#11926471	1	1	yes	characteristic
575	C₂²	#11926473	1	1	yes	characteristic
576	C₂²	#11926473	1	1	yes	characteristic
577	C₄	—	8	2	no	—
578	C₄	—	76	2	no	—
579	C₄	—	152	2	no	—
580	C₄	#11926406	1	1	yes	characteristic
581	C₄	#11926422	1	1	yes	characteristic
582	C₄	#11926433	1	1	yes	characteristic
583	C₄	#11926436	1	1	yes	characteristic
584	C₄	#11926459	1	1	yes	characteristic
585	C₄	#11926460	1	1	yes	characteristic
586	C₄	#11926461	1	1	yes	characteristic
587	C₄	#11926470	1	1	yes	characteristic
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	152	2	no	—
595	C₂	#14561883	1	1	yes	characteristic
596	C₂	#14564000	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1729	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1729	D₁₉
hypocenter	C₁₉	#11194
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1729

Complements

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

N	H ≅ G/N	type
4. C₂×#11926315	C₂	semidirect
5. C₂×#11926309	C₂	semidirect
6. #14563344	C₂	semidirect
7. C₁₉×#1729	C₂	semidirect
14. #11926543	C₄	semidirect
267. #1729	D₁₉	semidirect
392. C₁₉	#11194	semidirect

Maximal subgroups

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

subgroup	index
#14572152	2
C₂×#11926541	2
#14572079	2
C₂×#11926315	2
C₂×#11926309	2
#14563344	2
C₁₉×#1729	2
#11194	19