Subgroups — #18088987

Order 4864.

918 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926561	C₂	1	1	yes	maximal, characteristic
2	#14572154	C₂	1	1	yes	maximal, characteristic
3	#14572053	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926315	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926309	C₂	1	1	yes	maximal, characteristic, complemented
6	#14563352	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	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926561	—	2	2	no	—
13	#11926561	C₄	1	4	yes	complemented
14	C₂×#10597294	—	2	2	no	—
15	#11926553	C₄	1	2	yes	complemented
16	#11926549	C₄	1	2	yes	complemented
17	#11926545	—	2	2	no	—
18	#11926540	—	2	2	no	—
19	#11926502	—	2	2	no	—
20	#11926499	—	2	2	no	—
21	M₁₆×Dic₁₉	—	2	2	no	—
22	#11926315	—	2	2	no	—
23	#11926309	—	2	2	no	—
24	#11926307	—	2	2	no	—
25	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#408	—	2	2	no	—
29	C₁₉×#408	C₄	1	4	yes	complemented
30	C₂×C₁₉×C₂²⋊C₈	—	2	2	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	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
53	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₁₉	D₄	1	2	yes	—
62	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
63	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
64	#10597372	—	2	1	no	—
65	#10597372	—	2	1	no	—
66	#10597372	—	2	1	no	—
67	#10597372	—	2	1	no	—
68	#10597372	—	2	1	no	—
69	#10597372	C₂×C₄	1	2	yes	—
70	#10597372	C₂×C₄	1	2	yes	—
71	#10597372	D₄	1	2	yes	—
72	C₂×C₄⋊Dic₁₉	—	2	1	no	—
73	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
74	C₂×C₄×Dic₁₉	—	2	1	no	—
75	C₂×C₄×Dic₁₉	—	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	C₂×C₄	1	2	yes	—
85	C₂×#64520	C₂×C₄	1	2	yes	—
86	C₂×#64520	D₄	1	2	yes	—
87	C₂×#64520	D₄	1	2	yes	—
88	C₂²×C₁₉⋊C₈	—	2	1	no	—
89	C₂²×C₁₉⋊C₈	—	2	1	no	—
90	C₁₉×C₂²⋊C₈	—	2	8	no	—
91	#10597294	—	2	8	no	—
92	#10597292	—	2	4	no	—
93	#10597289	—	2	4	no	—
94	#10597272	—	2	4	no	—
95	C₈×Dic₁₉	—	2	4	no	—
96	C₂⁴×C₁₉	—	2	1	no	—
97	C₂⁴×C₁₉	#41	1	1	yes	characteristic
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	—	2	2	no	—
103	#41×C₁₉	—	2	2	no	—
104	#41×C₁₉	—	2	2	no	—
105	#41×C₁₉	—	2	2	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	#41×C₁₉	—	4	1	no	—
111	#41×C₁₉	—	4	1	no	—
112	#41×C₁₉	—	4	1	no	—
113	#41×C₁₉	—	4	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	C₄²	1	2	yes	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
153	C₂²×Dic₁₉	—	2	2	no	—
154	C₂²×Dic₁₉	—	4	1	no	—
155	M₁₆×C₁₉	—	2	2	no	—
156	M₁₆×C₁₉	—	2	2	no	—
157	M₁₆×C₁₉	—	2	2	no	—
158	M₁₆×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	—	2	2	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	C₂²⋊C₄	1	4	yes	—
169	C₂²⋊Dic₁₉	—	2	2	no	—
170	C₂²⋊Dic₁₉	—	2	2	no	—
171	C₂²⋊Dic₁₉	—	2	2	no	—
172	C₂²⋊Dic₁₉	—	4	1	no	—
173	C₄⋊Dic₁₉	—	2	2	no	—
174	C₄⋊Dic₁₉	—	2	2	no	—
175	C₄⋊Dic₁₉	—	4	1	no	—
176	C₄⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
177	C₄×Dic₁₉	—	2	2	no	—
178	C₄×Dic₁₉	—	2	2	no	—
179	C₄×Dic₁₉	—	2	2	no	—
180	C₄×Dic₁₉	—	4	1	no	—
181	#64520	—	2	2	no	—
182	#64520	—	2	2	no	—
183	#64520	—	2	2	no	—
184	#64520	—	2	2	no	—
185	#64520	—	2	2	no	—
186	#64520	—	4	1	no	—
187	#64520	—	4	1	no	—
188	#64520	C₂²⋊C₄	1	4	yes	—
189	C₂×C₁₉⋊C₈	—	2	2	no	—
190	C₂×C₁₉⋊C₈	—	2	2	no	—
191	C₂×C₁₉⋊C₈	—	2	2	no	—
192	C₂×C₁₉⋊C₈	—	2	2	no	—
193	C₂×C₁₉⋊C₈	—	4	1	no	—
194	C₂×C₁₉⋊C₈	—	4	1	no	—
195	#10956	—	19	1	no	maximal, Sylow
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	4	2	no	—
198	C₂³×C₁₉	—	4	4	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	#117	1	1	yes	characteristic
202	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
203	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
204	C₂³×C₁₉	#121	1	1	yes	characteristic
205	C₂³×C₁₉	#123	1	1	yes	characteristic
206	C₂³×C₁₉	#124	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×C₄²	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#123	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	#127	1	1	yes	characteristic
255	C₂×Dic₁₉	—	2	4	no	—
256	C₂×Dic₁₉	—	4	2	no	—
257	C₂×Dic₁₉	—	8	2	no	—
258	C₂×Dic₁₉	—	8	2	no	—
259	C₈×C₁₉	—	2	4	no	—
260	C₈×C₁₉	—	4	2	no	—
261	C₁₉⋊C₈	—	2	4	no	—
262	C₁₉⋊C₈	—	4	2	no	—
263	C₂×#421	—	19	1	no	—
264	#2896	—	19	1	no	—
265	C₂×#408	D₁₉	1	1	yes	characteristic
266	#2873	—	19	1	no	—
267	C₂×#344	—	19	1	no	—
268	C₂×#341	—	19	1	no	—
269	#1735	—	19	1	no	—
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	2	2	no	—
272	C₂²×C₁₉	—	2	2	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	—	4	4	no	—
278	C₂²×C₁₉	—	4	2	no	—
279	C₂²×C₁₉	—	8	2	no	—
280	C₂²×C₁₉	—	8	2	no	—
281	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₁₉	#386	1	1	yes	characteristic
283	C₂²×C₁₉	#388	1	1	yes	characteristic
284	C₂²×C₁₉	#388	1	1	yes	characteristic
285	C₂²×C₁₉	#388	1	1	yes	characteristic
286	C₂²×C₁₉	#388	1	1	yes	characteristic
287	C₂²×C₁₉	#390	1	1	yes	characteristic
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
290	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
291	C₄×C₁₉	#386	1	1	yes	characteristic
292	C₄×C₁₉	#386	1	1	yes	characteristic
293	C₄×C₁₉	#388	1	1	yes	characteristic
294	C₄×C₁₉	#388	1	1	yes	characteristic
295	C₄×C₁₉	#390	1	1	yes	characteristic
296	C₄×C₁₉	#390	1	1	yes	characteristic
297	Dic₁₉	—	4	4	no	—
298	Dic₁₉	—	8	2	no	—
299	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
300	C₂²×M₁₆	—	19	1	no	—
301	C₂²×M₁₆	—	19	1	no	—
302	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
303	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
304	C₂×#117	—	19	1	no	—
305	C₂×#117	—	19	1	no	—
306	#421	—	19	4	no	—
307	#421	—	38	2	no	—
308	C₂×#104	—	38	2	no	—
309	#419	—	19	2	no	—
310	#418	—	19	2	no	—
311	#417	—	38	2	no	—
312	#416	—	38	2	no	—
313	#408	—	2	2	no	—
314	#408	Dic₁₉	1	4	yes	complemented
315	C₂×C₂²⋊C₈	—	2	2	no	—
316	#405	—	38	2	no	—
317	#405	—	38	2	no	—
318	C₄×M₁₆	—	38	2	no	—
319	#344	—	38	2	no	—
320	#341	—	38	2	no	—
321	#340	—	38	2	no	—
322	C₂×C₁₉	—	2	1	no	—
323	C₂×C₁₉	—	2	1	no	—
324	C₂×C₁₉	—	2	1	no	—
325	C₂×C₁₉	—	2	1	no	—
326	C₂×C₁₉	—	2	1	no	—
327	C₂×C₁₉	—	2	1	no	—
328	C₂×C₁₉	—	8	2	no	—
329	C₂×C₁₉	#1437	1	1	yes	characteristic
330	C₂×C₁₉	#1881	1	2	yes	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	1	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	C₄×D₁₉	1	2	yes	—
342	C₂×#41	C₂×Dic₁₉	1	2	yes	—
343	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	19	2	no	—
353	C₂×M₁₆	—	19	2	no	—
354	C₂×M₁₆	—	19	2	no	—
355	C₂×M₁₆	—	19	2	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	C₂×M₁₆	—	38	1	no	—
364	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
365	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
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	—	38	1	no	—
373	C₂²×C₈	—	38	1	no	—
374	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
375	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
376	#117	—	19	2	no	—
377	#117	—	19	2	no	—
378	#117	—	19	2	no	—
379	#117	—	38	1	no	—
380	#117	—	38	1	no	—
381	#117	—	38	1	no	—
382	#117	—	38	1	no	—
383	#117	—	38	1	no	—
384	C₂×C₄⋊C₄	—	19	2	no	—
385	C₂×C₄⋊C₄	—	38	1	no	—
386	C₂×C₂²⋊C₄	—	38	1	no	—
387	C₂×C₂²⋊C₄	—	38	1	no	—
388	C₂×C₄²	—	38	1	no	—
389	C₂×C₄²	—	38	1	no	—
390	#104	—	38	8	no	—
391	#103	—	38	4	no	—
392	#102	—	38	4	no	—
393	C₂²⋊C₈	—	2	8	no	—
394	#97	—	38	4	no	—
395	C₄×C₈	—	38	4	no	—
396	C₁₉	#10956	1	1	yes	characteristic, complemented, Sylow
397	C₂⁴	—	2	1	no	—
398	C₂⁴	#64541	1	1	yes	characteristic
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	4	1	no	—
408	#41	—	4	1	no	—
409	#41	—	4	1	no	—
410	#41	—	4	1	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	—	4	1	no	—
414	#41	—	4	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	38	2	no	—
441	C₂²×C₄	—	76	1	no	—
442	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
444	C₂²×C₄	#64541	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	D₄×D₁₉	1	1	yes	characteristic
448	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
449	C₂²×C₄	#64543	1	1	yes	characteristic
450	C₂²×C₄	#64543	1	1	yes	characteristic
451	C₂²×C₄	#64543	1	1	yes	characteristic
452	C₂²×C₄	#64543	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	19	4	no	—
461	M₁₆	—	38	2	no	—
462	M₁₆	—	38	2	no	—
463	M₁₆	—	38	2	no	—
464	M₁₆	—	38	2	no	—
465	M₁₆	—	38	2	no	—
466	M₁₆	—	76	1	no	—
467	M₁₆	—	76	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	4	1	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	38	2	no	—
478	C₂×C₈	—	38	2	no	—
479	C₂×C₈	—	38	2	no	—
480	C₂×C₈	—	38	2	no	—
481	C₂×C₈	—	76	1	no	—
482	C₂×C₈	—	76	1	no	—
483	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
484	C₄⋊C₄	—	19	4	no	—
485	C₄⋊C₄	—	38	2	no	—
486	C₄⋊C₄	—	38	2	no	—
487	C₄⋊C₄	—	76	1	no	—
488	C₂²⋊C₄	—	38	2	no	—
489	C₂²⋊C₄	—	38	2	no	—
490	C₂²⋊C₄	—	38	2	no	—
491	C₂²⋊C₄	—	76	1	no	—
492	C₄²	—	38	2	no	—
493	C₄²	—	38	2	no	—
494	C₄²	—	38	2	no	—
495	C₄²	—	76	1	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	#10597325	1	1	yes	characteristic
502	C₂³	#10597329	1	1	yes	characteristic
503	C₂³	#10597330	1	1	yes	characteristic
504	C₂³	#10597331	1	1	yes	characteristic
505	C₂³	#10597372	1	1	yes	characteristic
506	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
507	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
508	Q₈	—	2	2	no	—
509	Q₈	—	2	2	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	38	4	no	—
528	C₂×C₄	—	76	2	no	—
529	C₂×C₄	—	152	2	no	—
530	C₂×C₄	—	152	2	no	—
531	C₂×C₄	#10597323	1	1	yes	characteristic
532	C₂×C₄	#10597323	1	1	yes	characteristic
533	C₂×C₄	#10597325	1	1	yes	characteristic
534	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
535	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
536	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
537	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
538	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
539	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
540	C₂×C₄	#10597329	1	1	yes	characteristic
541	C₂×C₄	#10597330	1	1	yes	characteristic
542	C₂×C₄	#10597331	1	1	yes	characteristic
543	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
544	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
545	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
546	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
547	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
548	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
549	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
550	C₂×C₄	#10597381	1	1	yes	characteristic
551	C₂×C₄	#10597382	1	1	yes	characteristic
552	C₂×C₄	#10597383	1	1	yes	characteristic
553	C₂×C₄	#10597384	1	1	yes	characteristic
554	C₂×C₄	#10597384	1	1	yes	characteristic
555	C₂×C₄	#10597385	1	1	yes	characteristic
556	C₂×C₄	#10597385	1	1	yes	characteristic
557	C₂×C₄	#10597386	1	1	yes	characteristic
558	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
559	C₈	—	2	4	no	—
560	C₈	—	4	2	no	—
561	C₈	—	38	4	no	—
562	C₈	—	76	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	8	2	no	—
573	C₂²	—	8	2	no	—
574	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
575	C₂²	#11926420	1	1	yes	characteristic
576	C₂²	#11926432	1	1	yes	characteristic
577	C₂²	#11926437	1	1	yes	characteristic
578	C₂²	#11926437	1	1	yes	characteristic
579	C₂²	#11926438	1	1	yes	characteristic
580	C₂²	#11926444	1	1	yes	characteristic
581	C₄	—	4	2	no	—
582	C₄	—	76	4	no	—
583	C₄	—	152	2	no	—
584	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
585	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
586	C₄	#11926420	1	1	yes	characteristic
587	C₄	#11926424	1	1	yes	characteristic
588	C₄	#11926432	1	1	yes	characteristic
589	C₄	#11926438	1	1	yes	characteristic
590	C₄	#11926444	1	1	yes	characteristic
591	C₄	#11926447	1	1	yes	characteristic
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	8	2	no	—
599	C₂	#14561872	1	1	yes	characteristic
600	C₂	#14564000	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#408	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#408	D₁₉
hypocenter	C₁₉	#10956
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#408

Complements

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

N	H ≅ G/N	type
3. #14572053	C₂	semidirect
4. C₂×#11926315	C₂	semidirect
5. C₂×#11926309	C₂	semidirect
6. #14563352	C₂	semidirect
13. #11926561	C₄	semidirect
15. #11926553	C₄	semidirect
16. #11926549	C₄	semidirect
29. C₁₉×#408	C₄	semidirect
314. #408	Dic₁₉	semidirect
396. C₁₉	#10956	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926561	2
#14572154	2
#14572053	2
C₂×#11926315	2
C₂×#11926309	2
#14563352	2
C₂×C₁₉×#408	2
#10956	19