Subgroups — #18090366

Order 4864.

886 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597294	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926540	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926308	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926305	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#408	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	C₂×#10597294	—	2	2	no	—
13	C₂×#10597294	—	2	2	no	—
14	C₂×#10597294	—	2	2	no	—
15	#11926540	—	2	2	no	—
16	#11926540	—	2	2	no	—
17	C₂×#10597292	C₄	1	2	yes	complemented
18	C₂×#10597289	C₄	1	2	yes	complemented
19	#11926308	—	2	2	no	—
20	#11926305	—	2	2	no	—
21	#11926298	—	2	2	no	—
22	#11926298	—	2	2	no	—
23	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#408	—	2	2	no	—
27	C₁₉×#408	—	2	2	no	—
28	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	1	no	—
30	C₂×#41×C₁₉	—	2	1	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	D₄	1	2	yes	—
40	C₂×#41×C₁₉	D₄	1	2	yes	—
41	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×Dic₁₉	—	2	1	no	—
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	D₄	1	2	yes	—
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	—	2	1	no	—
60	C₂²×C₈×C₁₉	D₄	1	2	yes	—
61	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
62	#10597372	—	2	1	no	—
63	#10597372	—	2	1	no	—
64	#10597372	—	2	1	no	—
65	#10597372	—	2	1	no	—
66	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₄×Dic₁₉	—	2	1	no	—
68	C₂×C₄×Dic₁₉	—	2	1	no	—
69	C₂×C₄×Dic₁₉	—	2	1	no	—
70	C₂×C₄×Dic₁₉	—	2	1	no	—
71	C₂×C₄×Dic₁₉	—	2	1	no	—
72	C₂×C₄×Dic₁₉	—	2	1	no	—
73	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
74	C₂×#64520	—	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	D₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	—	2	1	no	—
81	C₂²×C₁₉⋊C₈	—	2	1	no	—
82	C₂²×C₁₉⋊C₈	—	2	1	no	—
83	C₂²×C₁₉⋊C₈	—	2	1	no	—
84	C₂²×C₁₉⋊C₈	—	2	1	no	—
85	C₂²×C₁₉⋊C₈	—	2	1	no	—
86	C₂²×C₁₉⋊C₈	—	2	1	no	—
87	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₉×C₂²⋊C₈	—	2	8	no	—
89	#10597294	—	2	8	no	—
90	#10597292	—	2	4	no	—
91	#10597289	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	1	no	—
93	C₂⁴×C₁₉	#41	1	1	yes	characteristic
94	#41×C₁₉	—	2	2	no	—
95	#41×C₁₉	—	2	2	no	—
96	#41×C₁₉	—	2	2	no	—
97	#41×C₁₉	—	2	2	no	—
98	#41×C₁₉	—	2	2	no	—
99	#41×C₁₉	—	2	2	no	—
100	#41×C₁₉	—	2	2	no	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	4	1	no	—
104	#41×C₁₉	—	4	1	no	—
105	#41×C₁₉	—	4	1	no	—
106	#41×C₁₉	—	4	1	no	—
107	#41×C₁₉	—	4	1	no	—
108	#41×C₁₉	—	4	1	no	—
109	#41×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	4	1	no	—
124	C₂×D₄×C₁₉	—	4	1	no	—
125	C₂×D₄×C₁₉	—	4	1	no	—
126	C₂×D₄×C₁₉	—	4	1	no	—
127	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	4	1	no	—
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
149	C₂²×Dic₁₉	—	2	4	no	—
150	C₂²×Dic₁₉	—	2	2	no	—
151	C₂²×Dic₁₉	—	2	2	no	—
152	C₂²×Dic₁₉	—	4	2	no	—
153	C₂²×Dic₁₉	—	4	1	no	—
154	C₂²×Dic₁₉	—	4	1	no	—
155	M₁₆×C₁₉	—	2	2	no	—
156	M₁₆×C₁₉	—	2	2	no	—
157	M₁₆×C₁₉	—	4	1	no	—
158	M₁₆×C₁₉	—	4	1	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	C₂×C₈×C₁₉	—	4	1	no	—
168	C₂×C₈×C₁₉	—	4	1	no	—
169	C₂²⋊Dic₁₉	—	4	1	no	—
170	C₂²⋊Dic₁₉	—	4	1	no	—
171	C₄⋊Dic₁₉	—	2	2	no	—
172	C₄⋊Dic₁₉	—	2	2	no	—
173	C₄×Dic₁₉	—	2	2	no	—
174	C₄×Dic₁₉	—	2	2	no	—
175	C₄×Dic₁₉	—	4	1	no	—
176	C₄×Dic₁₉	—	4	1	no	—
177	C₄×Dic₁₉	—	4	1	no	—
178	C₄×Dic₁₉	—	4	1	no	—
179	#64520	—	2	2	no	—
180	#64520	—	2	2	no	—
181	#64520	—	4	1	no	—
182	#64520	—	4	1	no	—
183	C₂×C₁₉⋊C₈	—	2	2	no	—
184	C₂×C₁₉⋊C₈	—	2	2	no	—
185	C₂×C₁₉⋊C₈	—	2	2	no	—
186	C₂×C₁₉⋊C₈	—	2	2	no	—
187	C₂×C₁₉⋊C₈	—	4	1	no	—
188	C₂×C₁₉⋊C₈	—	4	1	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	#11191	—	19	1	no	maximal, Sylow
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
202	C₂³×C₁₉	#121	1	1	yes	characteristic
203	C₂³×C₁₉	#123	1	1	yes	characteristic
204	C₂³×C₁₉	#123	1	1	yes	characteristic
205	C₂³×C₁₉	#124	1	1	yes	characteristic
206	C₂³×C₁₉	#126	1	1	yes	characteristic
207	C₂³×C₁₉	#126	1	1	yes	characteristic
208	Q₈×C₁₉	—	2	2	no	—
209	Q₈×C₁₉	—	2	2	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	D₄×C₁₉	—	2	2	no	—
213	D₄×C₁₉	—	2	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	4	2	no	—
217	D₄×C₁₉	—	4	2	no	—
218	D₄×C₁₉	—	4	1	no	—
219	D₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
255	C₂×Dic₁₉	—	2	4	no	—
256	C₂×Dic₁₉	—	4	4	no	—
257	C₂×Dic₁₉	—	4	4	no	—
258	C₂×Dic₁₉	—	4	2	no	—
259	C₂×Dic₁₉	—	4	2	no	—
260	C₂×Dic₁₉	—	4	2	no	—
261	C₂×Dic₁₉	—	4	2	no	—
262	C₂×Dic₁₉	—	4	2	no	—
263	C₈×C₁₉	—	4	2	no	—
264	C₈×C₁₉	—	4	2	no	—
265	C₁₉⋊C₈	—	4	2	no	—
266	C₁₉⋊C₈	—	4	2	no	—
267	C₂²×#104	—	19	1	no	—
268	C₂×#416	—	19	1	no	—
269	C₂×#408	D₁₉	1	1	yes	characteristic
270	C₂×#341	—	19	1	no	—
271	C₂×#339	—	19	1	no	—
272	#1729	—	19	1	no	—
273	C₂×#336	—	19	1	no	—
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	2	2	no	—
276	C₂²×C₁₉	—	2	2	no	—
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	8	2	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	#386	1	1	yes	characteristic
288	C₂²×C₁₉	#388	1	1	yes	characteristic
289	C₂²×C₁₉	#388	1	1	yes	characteristic
290	C₂²×C₁₉	#394	1	1	yes	characteristic
291	C₂²×C₁₉	#397	1	1	yes	characteristic
292	C₂²×C₁₉	#397	1	1	yes	characteristic
293	C₂²×C₁₉	#397	1	1	yes	characteristic
294	C₂²×C₁₉	#443	1	2	yes	—
295	C₂²×C₁₉	#444	1	2	yes	—
296	C₄×C₁₉	—	4	2	no	—
297	C₄×C₁₉	#381	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	#394	1	1	yes	characteristic
302	C₄×C₁₉	#394	1	1	yes	characteristic
303	C₄×C₁₉	#394	1	1	yes	characteristic
304	C₄×C₁₉	#397	1	1	yes	characteristic
305	Dic₁₉	—	4	4	no	—
306	Dic₁₉	—	8	2	no	—
307	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
308	C₂²×M₁₆	—	19	1	no	—
309	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
310	C₂³×C₈	—	19	1	no	—
311	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
312	C₂×#117	—	19	1	no	—
313	C₂²×C₄²	—	19	1	no	—
314	C₂×#104	—	38	2	no	—
315	C₂×#104	—	38	2	no	—
316	C₂×#104	—	38	2	no	—
317	#416	—	38	2	no	—
318	#416	—	38	2	no	—
319	C₂×#103	—	19	2	no	—
320	C₂×#102	—	19	2	no	—
321	#408	—	2	2	no	—
322	#408	—	2	2	no	—
323	C₂×C₂²⋊C₈	—	2	2	no	—
324	#341	—	38	2	no	—
325	#339	—	38	2	no	—
326	#336	—	38	2	no	—
327	#336	—	38	2	no	—
328	C₂×C₁₉	—	2	1	no	—
329	C₂×C₁₉	—	2	1	no	—
330	C₂×C₁₉	—	2	1	no	—
331	C₂×C₁₉	—	2	1	no	—
332	C₂×C₁₉	—	8	2	no	—
333	C₂×C₁₉	#1440	1	1	yes	characteristic
334	C₂×C₁₉	#1876	1	2	yes	—
335	C₂×C₁₉	#1929	1	2	yes	—
336	C₂×C₁₉	#1937	1	1	yes	characteristic
337	C₂×C₁₉	#1938	1	1	yes	characteristic
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	D₇₆	1	2	yes	—
349	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
350	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	38	1	no	—
355	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	19	2	no	—
362	C₂×M₁₆	—	38	1	no	—
363	C₂×M₁₆	—	38	1	no	—
364	C₂×M₁₆	—	38	1	no	—
365	C₂×M₁₆	—	38	1	no	—
366	C₂×M₁₆	—	38	1	no	—
367	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	19	2	no	—
376	C₂²×C₈	—	38	1	no	—
377	C₂²×C₈	—	38	1	no	—
378	C₂²×C₈	—	38	1	no	—
379	C₂²×C₈	—	38	1	no	—
380	C₂²×C₈	—	38	1	no	—
381	C₂²×C₈	—	38	1	no	—
382	C₂²×C₈	—	38	1	no	—
383	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
384	#117	—	38	1	no	—
385	#117	—	38	1	no	—
386	#117	—	38	1	no	—
387	#117	—	38	1	no	—
388	C₂×C₄⋊C₄	—	19	2	no	—
389	C₂×C₂²⋊C₄	—	38	1	no	—
390	C₂×C₄²	—	19	2	no	—
391	C₂×C₄²	—	38	1	no	—
392	C₂×C₄²	—	38	1	no	—
393	C₂×C₄²	—	38	1	no	—
394	C₂×C₄²	—	38	1	no	—
395	C₂×C₄²	—	38	1	no	—
396	C₂×C₄²	—	38	1	no	—
397	#104	—	38	8	no	—
398	#103	—	38	4	no	—
399	#102	—	38	4	no	—
400	C₂²⋊C₈	—	2	8	no	—
401	C₁₉	#11191	1	1	yes	characteristic, complemented, Sylow
402	C₂⁴	—	2	1	no	—
403	C₂⁴	#64541	1	1	yes	characteristic
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	4	1	no	—
413	#41	—	4	1	no	—
414	#41	—	4	1	no	—
415	#41	—	4	1	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂×D₄	—	4	1	no	—
437	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	38	4	no	—
446	C₂²×C₄	—	38	2	no	—
447	C₂²×C₄	—	38	2	no	—
448	C₂²×C₄	—	76	2	no	—
449	C₂²×C₄	—	76	1	no	—
450	C₂²×C₄	—	76	1	no	—
451	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
453	C₂²×C₄	#64541	1	1	yes	characteristic
454	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
455	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
456	C₂²×C₄	#64543	1	1	yes	characteristic
457	C₂²×C₄	#64543	1	1	yes	characteristic
458	C₂²×C₄	#64543	1	1	yes	characteristic
459	C₂²×C₄	#64543	1	1	yes	characteristic
460	C₂²×C₄	#64543	1	1	yes	characteristic
461	C₂²×C₄	#64543	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	4	1	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	38	2	no	—
470	M₁₆	—	38	2	no	—
471	M₁₆	—	76	1	no	—
472	M₁₆	—	76	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	38	2	no	—
484	C₂×C₈	—	38	2	no	—
485	C₂×C₈	—	38	2	no	—
486	C₂×C₈	—	38	2	no	—
487	C₂×C₈	—	76	1	no	—
488	C₂×C₈	—	76	1	no	—
489	C₂×C₈	—	76	1	no	—
490	C₂×C₈	—	76	1	no	—
491	C₂×C₈	—	76	1	no	—
492	C₂×C₈	—	76	1	no	—
493	C₄⋊C₄	—	38	2	no	—
494	C₄⋊C₄	—	38	2	no	—
495	C₂²⋊C₄	—	76	1	no	—
496	C₂²⋊C₄	—	76	1	no	—
497	C₄²	—	38	2	no	—
498	C₄²	—	38	2	no	—
499	C₄²	—	76	1	no	—
500	C₄²	—	76	1	no	—
501	C₄²	—	76	1	no	—
502	C₄²	—	76	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	#10597325	1	1	yes	characteristic
511	C₂³	#10597325	1	1	yes	characteristic
512	C₂³	#10597329	1	1	yes	characteristic
513	C₂³	#10597331	1	1	yes	characteristic
514	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
515	C₂³	#10597375	1	1	yes	characteristic
516	C₂³	#10597376	1	1	yes	characteristic
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	38	4	no	—
537	C₂×C₄	—	76	4	no	—
538	C₂×C₄	—	76	4	no	—
539	C₂×C₄	—	76	2	no	—
540	C₂×C₄	—	76	2	no	—
541	C₂×C₄	—	76	2	no	—
542	C₂×C₄	—	76	2	no	—
543	C₂×C₄	—	76	2	no	—
544	C₂×C₄	#10597323	1	1	yes	characteristic
545	C₂×C₄	#10597323	1	1	yes	characteristic
546	C₂×C₄	#10597325	1	1	yes	characteristic
547	C₂×C₄	#10597325	1	1	yes	characteristic
548	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
549	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
550	C₂×C₄	#10597328	1	1	yes	characteristic
551	C₂×C₄	#10597329	1	1	yes	characteristic
552	C₂×C₄	#10597331	1	1	yes	characteristic
553	C₂×C₄	#10597332	1	1	yes	characteristic
554	C₂×C₄	#10597332	1	1	yes	characteristic
555	C₂×C₄	#10597332	1	1	yes	characteristic
556	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
557	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
558	C₂×C₄	#10597376	1	1	yes	characteristic
559	C₂×C₄	#10597381	1	1	yes	characteristic
560	C₂×C₄	#10597381	1	1	yes	characteristic
561	C₂×C₄	#10597381	1	1	yes	characteristic
562	C₂×C₄	#10597381	1	1	yes	characteristic
563	C₂×C₄	#10597382	1	1	yes	characteristic
564	C₂×C₄	#10597382	1	1	yes	characteristic
565	C₂×C₄	#10597384	1	1	yes	characteristic
566	C₂×C₄	#10597384	1	1	yes	characteristic
567	C₂×C₄	#10597385	1	1	yes	characteristic
568	C₂×C₄	#10597385	1	1	yes	characteristic
569	C₂×C₄	#10597385	1	1	yes	characteristic
570	C₂×C₄	#10597385	1	1	yes	characteristic
571	C₂×C₄	#10597399	1	1	yes	characteristic
572	C₈	—	4	2	no	—
573	C₈	—	4	2	no	—
574	C₈	—	76	2	no	—
575	C₈	—	76	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	8	2	no	—
587	C₂²	—	8	1	no	—
588	C₂²	—	8	1	no	—
589	C₂²	#11926423	1	1	yes	characteristic
590	C₂²	#11926432	1	1	yes	characteristic
591	C₂²	#11926438	1	1	yes	characteristic
592	C₂²	#11926460	1	1	yes	characteristic
593	C₂²	#11926469	1	1	yes	characteristic
594	C₂²	#11926472	1	1	yes	characteristic
595	C₂²	#11926472	1	1	yes	characteristic
596	C₂²	#11926659	1	2	yes	—
597	C₂²	#11926664	1	2	yes	—
598	C₄	—	4	2	no	—
599	C₄	—	76	4	no	—
600	C₄	—	152	2	no	—
601	C₄	#11926405	1	1	yes	characteristic
602	C₄	#11926421	1	1	yes	characteristic
603	C₄	#11926432	1	1	yes	characteristic
604	C₄	#11926438	1	1	yes	characteristic
605	C₄	#11926458	1	1	yes	characteristic
606	C₄	#11926458	1	1	yes	characteristic
607	C₄	#11926460	1	1	yes	characteristic
608	C₄	#11926469	1	1	yes	characteristic
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	8	2	no	—
614	C₂	#14561882	1	1	yes	characteristic
615	C₂	#14563962	1	2	yes	—
616	C₂	#14564280	1	2	yes	—
617	C₂	#14564342	1	1	yes	characteristic
618	C₂	#14564349	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#408	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#408	D₁₉
hypocenter	C₁₉	#11191
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂×#408

Complements

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

N	H ≅ G/N	type
3. C₂×#11926308	C₂	semidirect
4. C₂×#11926305	C₂	semidirect
5. #14563331	C₂	semidirect
6. C₂×#11926298	C₂	semidirect
17. C₂×#10597292	C₄	semidirect
18. C₂×#10597289	C₄	semidirect
401. C₁₉	#11191	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597294	2
C₂×#11926540	2
C₂×#11926308	2
C₂×#11926305	2
#14563331	2
C₂×#11926298	2
C₂×C₁₉×#408	2
#11191	19