Subgroups — #18088998

Order 4864.

990 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	C₂×#11926562	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926560	C₂	1	1	yes	maximal, characteristic
3	#14572053	C₂	1	1	yes	maximal, characteristic, complemented
4	#14566125	C₂	1	1	yes	maximal, characteristic
5	#14563367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926304	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926562	—	2	2	no	—
13	#11926562	C₄	1	4	yes	complemented
14	#11926560	—	2	2	no	—
15	#11926560	C₄	1	4	yes	complemented
16	C₂×#10597262	—	2	2	no	—
17	C₂×#10597282	—	2	2	no	—
18	#11926502	—	2	2	no	—
19	#11926499	—	2	2	no	—
20	M₁₆×Dic₁₉	—	2	2	no	—
21	#11926450	C₄	1	2	yes	complemented
22	#11926446	C₄	1	2	yes	complemented
23	#11926423	—	2	2	no	—
24	C₄×(C₂×D₁₉)⋊C₄	—	2	2	no	—
25	#11926310	—	2	2	no	—
26	#11926304	—	2	2	no	—
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#339	—	2	2	no	—
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₂²⋊D₁₉	—	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	—	2	1	no	—
43	C₂×#64541	—	2	1	no	—
44	C₂×#64541	C₂×C₄	1	2	yes	—
45	C₂×#64541	C₂×C₄	1	2	yes	—
46	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄×D₁₉	—	2	1	no	—
48	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
53	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
54	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₁₉×#117	—	2	1	no	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄²×C₁₉	—	2	1	no	—
63	C₂×C₄²×C₁₉	—	2	1	no	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
70	C₂×C₂²⋊Dic₁₉	D₄	1	2	yes	—
71	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
72	#10597372	—	2	1	no	—
73	#10597372	—	2	1	no	—
74	#10597372	—	2	1	no	—
75	#10597372	—	2	1	no	—
76	#10597372	—	2	1	no	—
77	#10597372	—	2	1	no	—
78	#10597372	—	2	1	no	—
79	#10597372	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊Dic₁₉	—	2	1	no	—
81	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
82	C₂×C₄×Dic₁₉	—	2	1	no	—
83	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	C₂×C₄	1	2	yes	—
88	C₂×#64520	D₄	1	2	yes	—
89	C₂×#64520	D₄	1	2	yes	—
90	C₂²×C₁₉⋊C₈	—	2	1	no	—
91	C₁₉⋊#95	—	2	4	no	—
92	#10597282	—	2	8	no	—
93	#10597272	—	2	4	no	—
94	C₈×Dic₁₉	—	2	4	no	—
95	#10597262	—	2	8	no	—
96	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂³×D₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	4	4	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	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	C₂²×C₄	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	—	4	1	no	—
120	C₂×C₂²⋊D₁₉	—	4	1	no	—
121	C₂×C₂²⋊D₁₉	—	4	1	no	—
122	C₂×C₂²⋊D₁₉	—	4	1	no	—
123	C₂²×Dic₁₉	—	2	1	no	—
124	C₂²×Dic₁₉	—	4	1	no	—
125	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
126	#64541	—	2	2	no	—
127	#64541	—	2	2	no	—
128	#64541	—	2	2	no	—
129	#64541	—	2	2	no	—
130	#64541	—	2	2	no	—
131	#64541	—	2	2	no	—
132	#64541	—	2	2	no	—
133	#64541	—	2	2	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	#64541	—	4	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×D₇₆	C₄²	1	2	yes	—
148	C₂×C₄×D₁₉	—	2	2	no	—
149	C₂×C₄×D₁₉	—	2	2	no	—
150	C₂×C₄×D₁₉	—	4	1	no	—
151	C₂×C₄×D₁₉	—	4	1	no	—
152	C₂×C₄×D₁₉	—	4	1	no	—
153	C₂×C₄×D₁₉	—	4	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	C₂×Dic₃₈	C₄²	1	2	yes	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	complemented
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	4	1	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	4	1	no	—
171	C₄²×C₁₉	—	2	2	no	—
172	C₄²×C₁₉	—	2	2	no	—
173	C₄²×C₁₉	—	2	2	no	—
174	C₄²×C₁₉	—	4	1	no	—
175	C₄²×C₁₉	—	4	1	no	—
176	C₄²×C₁₉	—	4	1	no	—
177	C₂²⋊Dic₁₉	—	2	2	no	—
178	C₂²⋊Dic₁₉	—	2	2	no	—
179	C₂²⋊Dic₁₉	—	2	2	no	—
180	C₂²⋊Dic₁₉	—	4	1	no	—
181	(C₂×D₁₉)⋊C₄	—	4	8	no	—
182	C₄⋊Dic₁₉	—	2	2	no	—
183	C₄⋊Dic₁₉	—	2	2	no	—
184	C₄⋊Dic₁₉	—	2	2	no	—
185	C₄⋊Dic₁₉	—	4	1	no	—
186	C₄×Dic₁₉	—	2	2	no	—
187	C₄×Dic₁₉	—	2	2	no	—
188	C₄×Dic₁₉	—	2	2	no	—
189	C₄×Dic₁₉	—	4	1	no	—
190	#64520	—	2	2	no	—
191	#64520	—	2	2	no	—
192	#64520	—	2	2	no	—
193	#64520	C₂²⋊C₄	1	4	yes	complemented
194	C₂×C₁₉⋊C₈	—	2	2	no	—
195	C₂×C₁₉⋊C₈	—	2	2	no	—
196	C₂×C₁₉⋊C₈	—	2	2	no	—
197	#10959	—	19	1	no	maximal, Sylow
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
201	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
202	C₂³×C₁₉	#121	1	1	yes	characteristic
203	C₂³×C₁₉	#121	1	1	yes	characteristic
204	C₂³×C₁₉	#124	1	1	yes	characteristic
205	C₂³×C₁₉	#127	1	1	yes	characteristic
206	C₂²×D₁₉	—	2	2	no	—
207	C₂²×D₁₉	—	4	4	no	—
208	C₂²×D₁₉	—	4	1	no	—
209	C₂²×D₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	4	no	—
213	C₂×C₄×C₁₉	—	4	4	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	8	2	no	—
217	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#117	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	C₄×D₄	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	#121	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	#123	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#126	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	4	no	—
251	C₂×Dic₁₉	—	4	1	no	—
252	C₂×Dic₁₉	—	4	1	no	—
253	C₂×Dic₁₉	—	4	4	no	—
254	C₂×Dic₁₉	—	4	2	no	—
255	C₂×Dic₁₉	—	8	2	no	—
256	D₇₆	—	2	2	no	—
257	D₇₆	—	2	2	no	—
258	D₇₆	—	4	1	no	—
259	D₇₆	—	4	1	no	—
260	C₄×D₁₉	—	4	2	no	—
261	C₄×D₁₉	—	4	2	no	—
262	C₄×D₁₉	—	4	2	no	—
263	C₄×D₁₉	—	4	2	no	—
264	Dic₃₈	—	2	2	no	—
265	Dic₃₈	—	2	2	no	—
266	Dic₃₈	—	4	1	no	—
267	Dic₃₈	—	4	1	no	—
268	C₈×C₁₉	—	2	4	no	—
269	C₁₉⋊C₈	—	2	4	no	—
270	C₂×#421	—	19	1	no	—
271	C₂×#421	—	19	1	no	—
272	#2873	—	19	1	no	—
273	#2297	—	19	1	no	—
274	#1740	—	19	1	no	—
275	C₂×#339	—	19	1	no	—
276	C₂×#339	D₁₉	1	1	yes	characteristic, complemented
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	2	no	—
279	C₂²×C₁₉	—	2	2	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
285	C₂²×C₁₉	#386	1	1	yes	characteristic
286	C₂²×C₁₉	#388	1	1	yes	characteristic
287	C₂²×C₁₉	#388	1	1	yes	characteristic
288	C₂²×C₁₉	#390	1	1	yes	characteristic
289	C₂²×C₁₉	#390	1	1	yes	characteristic
290	C₂²×C₁₉	#390	1	1	yes	characteristic
291	C₂×D₁₉	—	4	4	no	—
292	C₂×D₁₉	—	4	2	no	—
293	C₂×D₁₉	—	8	2	no	—
294	C₂×D₁₉	—	8	2	no	—
295	C₄×C₁₉	—	4	4	no	—
296	C₄×C₁₉	—	8	2	no	—
297	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
298	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
299	C₄×C₁₉	#386	1	1	yes	characteristic
300	C₄×C₁₉	#386	1	1	yes	characteristic
301	C₄×C₁₉	#388	1	1	yes	characteristic
302	C₄×C₁₉	#388	1	1	yes	characteristic
303	C₄×C₁₉	#388	1	1	yes	characteristic
304	C₄×C₁₉	#388	1	1	yes	characteristic
305	Dic₁₉	—	4	4	no	—
306	Dic₁₉	—	4	2	no	—
307	Dic₁₉	—	8	2	no	—
308	C₂²×#41	—	19	1	no	—
309	C₂²×M₁₆	—	19	1	no	—
310	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
311	C₂×#117	—	19	1	no	—
312	C₂×#117	—	19	1	no	—
313	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
314	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
315	#421	—	19	4	no	—
316	#421	—	19	4	no	—
317	#421	—	38	2	no	—
318	#421	—	38	2	no	—
319	C₂×#104	—	38	2	no	—
320	C₂×#104	—	38	2	no	—
321	#405	—	38	2	no	—
322	#405	—	38	2	no	—
323	C₄×M₁₆	—	38	2	no	—
324	#391	—	19	2	no	—
325	#390	—	19	2	no	—
326	#386	—	38	2	no	—
327	C₄×C₂²⋊C₄	—	38	2	no	—
328	#342	—	38	2	no	—
329	#339	—	2	2	no	—
330	#339	—	38	2	no	—
331	C₂×C₁₉	—	2	1	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	#1437	1	1	yes	characteristic
338	C₂×C₁₉	#1884	1	2	yes	—
339	D₁₉	—	8	2	no	—
340	C₂×#41	—	19	2	no	—
341	C₂×#41	—	19	2	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	C₂²×Q₈	—	19	1	no	—
353	C₂²×D₄	—	19	1	no	—
354	C₂²×D₄	—	38	1	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	—	38	1	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	—	19	2	no	—
362	C₂×M₁₆	—	19	2	no	—
363	C₂×M₁₆	—	19	2	no	—
364	C₂×M₁₆	—	38	1	no	—
365	C₂×M₁₆	—	38	1	no	—
366	C₂×M₁₆	—	38	1	no	—
367	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
368	C₂×M₁₆	D₇₆	1	2	yes	—
369	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	38	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	19	2	no	—
376	#117	—	38	1	no	—
377	#117	—	38	1	no	—
378	#117	—	38	1	no	—
379	#117	—	38	1	no	—
380	#117	—	38	1	no	—
381	#117	—	38	1	no	—
382	#117	—	38	1	no	—
383	#117	C₄×D₁₉	1	2	yes	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	19	2	no	—
386	C₂×C₄⋊C₄	—	38	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	19	2	no	—
389	C₂×C₂²⋊C₄	—	38	1	no	—
390	C₂×C₂²⋊C₄	—	38	4	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	19	2	no	—
398	C₂×C₄²	—	38	1	no	—
399	C₂×C₄²	C₄×D₁₉	1	2	yes	—
400	#104	—	38	8	no	—
401	#104	—	38	8	no	—
402	#97	—	38	4	no	—
403	C₄×C₈	—	38	4	no	—
404	#95	—	38	4	no	—
405	C₁₉	#10959	1	1	yes	characteristic, complemented, Sylow
406	C₂⁴	—	38	1	no	—
407	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
408	#41	—	38	2	no	—
409	#41	—	38	2	no	—
410	#41	—	38	2	no	—
411	#41	—	38	2	no	—
412	#41	—	38	2	no	—
413	#41	—	38	2	no	—
414	#41	—	38	2	no	—
415	#41	—	38	2	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	C₂×Q₈	—	19	2	no	—
425	C₂×Q₈	—	38	1	no	—
426	C₂×Q₈	—	38	1	no	—
427	C₂×Q₈	—	38	1	no	—
428	C₂×Q₈	—	38	1	no	—
429	C₂×Q₈	—	38	1	no	—
430	C₂×D₄	—	19	2	no	—
431	C₂×D₄	—	38	2	no	—
432	C₂×D₄	—	38	2	no	—
433	C₂×D₄	—	38	1	no	—
434	C₂×D₄	—	38	1	no	—
435	C₂×D₄	—	38	1	no	—
436	C₂×D₄	—	38	1	no	—
437	C₂×D₄	—	38	1	no	—
438	C₂×D₄	—	76	1	no	—
439	C₂×D₄	—	76	1	no	—
440	C₂×D₄	—	76	1	no	—
441	C₂×D₄	—	76	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	19	4	no	—
448	C₂²×C₄	—	38	1	no	—
449	C₂²×C₄	—	38	2	no	—
450	C₂²×C₄	—	38	2	no	—
451	C₂²×C₄	—	76	1	no	—
452	C₂²×C₄	—	76	1	no	—
453	C₂²×C₄	—	76	1	no	—
454	C₂²×C₄	—	76	1	no	—
455	C₂²×C₄	—	76	1	no	—
456	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
460	C₂²×C₄	#64541	1	1	yes	characteristic
461	C₂²×C₄	#64541	1	1	yes	characteristic
462	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
463	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
464	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
465	C₂²×C₄	#64543	1	1	yes	characteristic
466	C₂²×C₄	#64543	1	1	yes	characteristic
467	C₂²×C₄	#64545	1	1	yes	characteristic
468	C₂²×C₄	#64545	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
470	M₁₆	—	2	2	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	19	4	no	—
474	M₁₆	—	38	2	no	—
475	M₁₆	—	38	2	no	—
476	M₁₆	—	38	2	no	—
477	M₁₆	(C₂×D₁₉)⋊C₄	1	4	yes	complemented
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	38	2	no	—
482	C₂×C₈	—	38	2	no	—
483	C₂×C₈	—	38	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	38	2	no	—
487	C₄⋊C₄	—	38	2	no	—
488	C₄⋊C₄	—	38	2	no	—
489	C₄⋊C₄	—	76	1	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	38	2	no	—
493	C₂²⋊C₄	—	38	2	no	—
494	C₂²⋊C₄	—	38	2	no	—
495	C₂²⋊C₄	—	76	8	no	—
496	C₂²⋊C₄	—	76	1	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	4	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	—	4	1	no	—
503	C₄²	—	38	2	no	—
504	C₄²	—	38	2	no	—
505	C₄²	—	38	2	no	—
506	C₄²	—	76	1	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	38	2	no	—
509	C₂³	—	76	4	no	—
510	C₂³	—	76	1	no	—
511	C₂³	—	76	1	no	—
512	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
513	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
514	C₂³	#10597330	1	1	yes	characteristic
515	C₂³	#10597331	1	1	yes	characteristic
516	C₂³	#10597339	1	1	yes	characteristic
517	C₂³	#10597341	1	1	yes	characteristic
518	C₂³	#10597386	1	1	yes	characteristic
519	Q₈	—	38	2	no	—
520	Q₈	—	38	2	no	—
521	Q₈	—	76	1	no	—
522	Q₈	—	76	1	no	—
523	D₄	—	38	2	no	—
524	D₄	—	38	2	no	—
525	D₄	—	76	2	no	—
526	D₄	—	76	2	no	—
527	D₄	—	76	2	no	—
528	D₄	—	76	2	no	—
529	D₄	—	76	1	no	—
530	D₄	—	76	1	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	—	38	2	no	—
539	C₂×C₄	—	38	4	no	—
540	C₂×C₄	—	76	1	no	—
541	C₂×C₄	—	76	1	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	—	76	4	no	—
547	C₂×C₄	—	76	2	no	—
548	C₂×C₄	—	152	2	no	—
549	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
550	C₂×C₄	#10597318	1	1	yes	characteristic
551	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
552	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
553	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
554	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
555	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
556	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
557	C₂×C₄	#10597328	1	1	yes	characteristic
558	C₂×C₄	#10597330	1	1	yes	characteristic
559	C₂×C₄	#10597331	1	1	yes	characteristic
560	C₂×C₄	#10597332	1	1	yes	characteristic
561	C₂×C₄	#10597338	1	1	yes	characteristic
562	C₂×C₄	#10597338	1	1	yes	characteristic
563	C₂×C₄	#10597339	1	1	yes	characteristic
564	C₂×C₄	#10597339	1	1	yes	characteristic
565	C₂×C₄	#10597339	1	1	yes	characteristic
566	C₂×C₄	#10597340	1	1	yes	characteristic
567	C₂×C₄	#10597340	1	1	yes	characteristic
568	C₂×C₄	#10597341	1	1	yes	characteristic
569	C₂×C₄	#10597344	1	1	yes	characteristic
570	C₂×C₄	#10597344	1	1	yes	characteristic
571	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
573	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
574	C₂×C₄	#10597385	1	1	yes	characteristic
575	C₂×C₄	#10597385	1	1	yes	characteristic
576	C₂×C₄	#10597393	1	1	yes	characteristic
577	C₈	—	2	4	no	—
578	C₈	—	38	4	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	4	no	—
587	C₂²	—	76	2	no	—
588	C₂²	—	152	2	no	—
589	C₂²	—	152	2	no	—
590	C₂²	#11926391	1	1	yes	characteristic
591	C₂²	#11926422	1	1	yes	characteristic
592	C₂²	#11926433	1	1	yes	characteristic
593	C₂²	#11926436	1	1	yes	characteristic
594	C₂²	#11926444	1	1	yes	characteristic
595	C₂²	#11926444	1	1	yes	characteristic
596	C₂²	#11926445	1	1	yes	characteristic
597	C₄	—	4	4	no	—
598	C₄	—	8	2	no	—
599	C₄	—	76	2	no	—
600	C₄	—	76	4	no	—
601	C₄	—	152	2	no	—
602	C₄	#11926391	1	1	yes	characteristic
603	C₄	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
604	C₄	#11926421	1	1	yes	characteristic
605	C₄	#11926422	1	1	yes	characteristic
606	C₄	#11926433	1	1	yes	characteristic
607	C₄	#11926434	1	1	yes	characteristic
608	C₄	#11926434	1	1	yes	characteristic
609	C₄	#11926436	1	1	yes	characteristic
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	152	2	no	—
617	C₂	#14561871	1	1	yes	characteristic
618	C₂	#14564017	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#10959
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
3. #14572053	C₂	semidirect
5. #14563367	C₂	semidirect
6. C₂×#11926304	C₂	semidirect
7. C₂×C₁₉×#339	C₂	semidirect
13. #11926562	C₄	semidirect
15. #11926560	C₄	semidirect
21. #11926450	C₄	semidirect
22. #11926446	C₄	semidirect
163. M₁₆×C₁₉	C₂²⋊C₄	semidirect
193. #64520	C₂²⋊C₄	semidirect
276. C₂×#339	D₁₉	semidirect
405. C₁₉	#10959	semidirect
477. M₁₆	(C₂×D₁₉)⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926562	2
C₂×#11926560	2
#14572053	2
#14566125	2
#14563367	2
C₂×#11926304	2
C₂×C₁₉×#339	2
#10959	19