Subgroups — #14577727

Order 2432.

992 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927271	C₂	1	2	yes	maximal, complemented
2	#11927271	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927269	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927265	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927261	C₂	1	2	yes	maximal, complemented
6	#11927232	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927230	C₂	1	2	yes	maximal, complemented
8	#11927228	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927226	C₂	1	2	yes	maximal, complemented
10	#11927209	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927207	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927207	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927153	C₂	1	2	yes	maximal, complemented
14	#11927152	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927151	C₂	1	2	yes	maximal, complemented
16	#11927100	C₂	1	2	yes	maximal, complemented
17	#11927098	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927077	C₂	1	2	yes	maximal
19	#11927072	C₂	1	1	yes	maximal, characteristic
20	#11927021	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927020	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
26	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
27	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₁₉×#126	C₂²	1	2	yes	—
29	C₁₉×#126	C₂²	1	2	yes	—
30	C₁₉×#125	C₂²	1	2	yes	—
31	C₁₉×#125	C₂²	1	2	yes	—
32	C₁₉×#125	C₂²	1	1	yes	characteristic
33	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₁₉×#117	C₂²	1	1	yes	characteristic
38	#10597392	C₂²	1	1	yes	characteristic
39	#10597392	C₂²	1	1	yes	characteristic
40	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
41	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
42	#10597390	C₂²	1	1	yes	characteristic
43	#10597390	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
46	#10597372	C₂²	1	1	yes	characteristic
47	#10597344	C₂²	1	1	yes	characteristic
48	#10597344	C₂²	1	2	yes	—
49	#10597344	C₂²	1	2	yes	—
50	#10597344	C₂²	1	2	yes	—
51	#10597343	C₂²	1	1	yes	characteristic
52	#10597343	C₂²	1	1	yes	characteristic
53	#10597342	C₂²	1	1	yes	characteristic
54	#10597342	C₂²	1	2	yes	—
55	#10597342	C₂²	1	2	yes	—
56	#10597342	C₂²	1	2	yes	—
57	#10597342	C₂²	1	2	yes	—
58	#10597342	C₂²	1	2	yes	—
59	#10597340	C₂²	1	1	yes	characteristic
60	#10597340	C₂²	1	2	yes	—
61	#10597339	C₂²	1	2	yes	—
62	#10597338	C₂²	1	2	yes	—
63	#10597338	C₂²	1	2	yes	—
64	#10597338	C₂²	1	2	yes	—
65	#10597338	C₂²	1	1	yes	characteristic
66	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
67	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
68	#10597336	C₂²	1	2	yes	—
69	#10597336	C₂²	1	1	yes	characteristic
70	#10597336	C₂²	1	2	yes	—
71	#10597335	C₂²	1	1	yes	characteristic
72	#10597335	C₂²	1	2	yes	—
73	#10597335	C₂²	1	2	yes	—
74	#10597335	C₂²	1	2	yes	—
75	#10597335	C₂²	1	2	yes	—
76	#10597335	C₂²	1	2	yes	—
77	#10597335	C₂²	1	2	yes	—
78	#10597335	C₂²	1	2	yes	—
79	#10597334	C₂²	1	1	yes	characteristic
80	#10597334	C₂²	1	2	yes	—
81	#10597334	C₂²	1	2	yes	—
82	#10597334	C₂²	1	2	yes	—
83	#10597334	C₂²	1	2	yes	—
84	#10597333	C₂²	1	2	yes	—
85	#10597333	C₂²	1	2	yes	—
86	#10597333	C₂²	1	2	yes	—
87	#10597333	C₂²	1	2	yes	—
88	#10597333	C₂²	1	2	yes	—
89	#10597333	C₂²	1	1	yes	characteristic
90	#10597333	C₂²	1	1	yes	characteristic
91	#10597333	C₂²	1	2	yes	—
92	#10597333	C₂²	1	2	yes	—
93	#10597331	C₂²	1	1	yes	characteristic
94	#10597331	C₂²	1	2	yes	—
95	#10597330	C₂²	1	1	yes	characteristic
96	#10597329	C₂²	1	1	yes	characteristic
97	#10597329	C₂²	1	2	yes	—
98	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
99	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
100	#10597325	C₂²	1	1	yes	characteristic
101	#10597325	C₂²	1	2	yes	—
102	#10597325	C₂²	1	2	yes	—
103	#10597324	C₂²	1	2	yes	—
104	#10597324	C₂²	1	2	yes	—
105	#10597323	C₂²	1	2	yes	—
106	#10597323	C₂²	1	2	yes	—
107	#10597322	C₂²	1	2	yes	—
108	C₄×D₇₆	C₂²	1	1	yes	characteristic
109	#10597318	C₂²	1	1	yes	characteristic
110	#10597318	C₂²	1	2	yes	—
111	#10597318	C₂²	1	2	yes	—
112	C₄²×D₁₉	C₂²	1	1	yes	characteristic
113	C₄²×D₁₉	C₂²	1	2	yes	—
114	#10597316	C₂²	1	2	yes	—
115	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
116	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
117	C₄×Dic₃₈	C₂²	1	2	yes	—
118	C₄×Dic₃₈	C₂²	1	2	yes	—
119	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
120	C₄×Dic₃₈	C₂²	1	2	yes	—
121	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
128	C₂²×Dic₁₉	C₂³	1	2	yes	—
129	Q₈×D₁₉	—	2	4	no	—
130	Q₈×D₁₉	—	2	4	no	—
131	C₂×D₇₆	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₉	C₂³	1	2	yes	—
135	C₂×C₄×D₁₉	C₂³	1	2	yes	—
136	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₉	C₂³	1	2	yes	—
139	C₂×Dic₃₈	—	2	4	no	—
140	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
141	C₂×Dic₃₈	C₂³	1	2	yes	—
142	C₂×Dic₃₈	C₂³	1	2	yes	—
143	C₂×Dic₃₈	C₂³	1	2	yes	—
144	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
145	C₂×Dic₃₈	C₂³	1	2	yes	—
146	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
152	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
154	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
155	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
161	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₄²×C₁₉	C₂³	1	1	yes	characteristic
164	C₄²×C₁₉	C₂³	1	1	yes	characteristic
165	C₄²×C₁₉	C₂³	1	2	yes	—
166	C₄²×C₁₉	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
169	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
170	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
173	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
174	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₁₉	C₂³	1	2	yes	—
183	C₄⋊Dic₁₉	C₂³	1	2	yes	—
184	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₁₉	C₂³	1	2	yes	—
186	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₁₉	C₂³	1	2	yes	—
188	C₄⋊Dic₁₉	C₂³	1	2	yes	—
189	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
190	Dic₁₉⋊C₄	C₂³	1	2	yes	—
191	Dic₁₉⋊C₄	C₂³	1	2	yes	—
192	Dic₁₉⋊C₄	C₂³	1	2	yes	—
193	Dic₁₉⋊C₄	C₂³	1	2	yes	—
194	Dic₁₉⋊C₄	C₂³	1	2	yes	—
195	Dic₁₉⋊C₄	C₂³	1	2	yes	—
196	Dic₁₉⋊C₄	C₂³	1	2	yes	—
197	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
198	Dic₁₉⋊C₄	C₂³	1	2	yes	—
199	Dic₁₉⋊C₄	C₂³	1	2	yes	—
200	Dic₁₉⋊C₄	C₂³	1	2	yes	—
201	Dic₁₉⋊C₄	C₂³	1	2	yes	—
202	Dic₁₉⋊C₄	C₂³	1	2	yes	—
203	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₁₉⋊C₄	C₂³	1	2	yes	—
207	Dic₁₉⋊C₄	C₂³	1	2	yes	—
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
211	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
212	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
213	C₄×Dic₁₉	C₂³	1	2	yes	—
214	C₄×Dic₁₉	C₂³	1	2	yes	—
215	C₄×Dic₁₉	C₂³	1	2	yes	—
216	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₉	C₂³	1	2	yes	—
219	C₄×Dic₁₉	C₂³	1	2	yes	—
220	C₄×Dic₁₉	C₂³	1	2	yes	—
221	C₄×Dic₁₉	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	2	yes	—
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
228	Q₈×C₁₉	—	2	2	no	—
229	Q₈×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
236	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₁₉	—	2	2	no	—
242	C₂²⋊D₁₉	—	2	2	no	—
243	C₂×Dic₁₉	—	2	4	no	—
244	C₂×Dic₁₉	C₂⁴	1	2	yes	—
245	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₉	C₂⁴	1	2	yes	—
248	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₉	C₂⁴	1	2	yes	—
250	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₉	C₂⁴	1	2	yes	—
253	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
254	D₇₆	—	2	2	no	—
255	C₄×D₁₉	—	2	2	no	—
256	C₄×D₁₉	—	2	4	no	—
257	C₄×D₁₉	—	2	2	no	—
258	C₄×D₁₉	—	2	2	no	—
259	C₄×D₁₉	—	2	4	no	—
260	C₄×D₁₉	—	2	4	no	—
261	C₄×D₁₉	—	2	2	no	—
262	Dic₃₈	—	2	2	no	—
263	Dic₃₈	—	2	4	no	—
264	Dic₃₈	—	2	4	no	—
265	Dic₃₈	—	2	4	no	—
266	Dic₃₈	—	2	2	no	—
267	Dic₃₈	—	2	4	no	—
268	Dic₃₈	#41	1	4	yes	—
269	#3523	—	19	1	no	maximal, Sylow
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
274	C₂×D₁₉	—	2	1	no	—
275	C₂×D₁₉	—	2	1	no	—
276	C₂×D₁₉	—	2	1	no	—
277	C₂×D₁₉	—	2	1	no	—
278	C₂×D₁₉	—	2	1	no	—
279	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	2	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	2	no	—
285	C₄×C₁₉	—	2	1	no	—
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	C₂×#41	1	2	yes	—
290	Dic₁₉	—	2	1	no	—
291	Dic₁₉	—	2	1	no	—
292	Dic₁₉	—	2	2	no	—
293	Dic₁₉	—	2	1	no	—
294	Dic₁₉	—	2	2	no	—
295	Dic₁₉	—	2	2	no	—
296	Dic₁₉	—	2	1	no	—
297	Dic₁₉	—	2	1	no	—
298	Dic₁₉	C₂×#41	1	4	yes	—
299	Dic₁₉	2₋¹⁺⁴	1	2	yes	—
300	#557	—	19	1	no	—
301	#557	—	19	1	no	—
302	#557	—	19	2	no	—
303	#556	—	19	2	no	—
304	#556	—	19	1	no	—
305	#552	—	19	2	no	—
306	#552	—	19	2	no	—
307	#552	—	19	1	no	—
308	#552	—	19	1	no	—
309	D₄×Q₈	—	19	1	no	—
310	D₄×Q₈	—	19	1	no	—
311	D₄×Q₈	—	19	1	no	—
312	#541	—	19	2	no	—
313	#541	—	19	2	no	—
314	#541	—	19	1	no	—
315	#541	D₁₉	1	1	yes	characteristic, complemented
316	#533	—	19	2	no	—
317	#533	—	19	1	no	—
318	#529	—	19	2	no	—
319	#529	—	19	1	no	—
320	#519	—	19	1	no	—
321	#519	—	19	1	no	—
322	C₂×C₄×Q₈	—	19	1	no	—
323	C₂×C₁₉	—	4	1	no	—
324	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
325	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
327	D₁₉	—	2	2	no	—
328	D₁₉	—	4	1	no	—
329	C₂²×Q₈	—	19	1	no	—
330	C₂²×Q₈	—	19	1	no	—
331	C₂²×Q₈	—	19	1	no	—
332	C₄⋊Q₈	—	19	1	no	—
333	C₄⋊Q₈	—	19	1	no	—
334	C₄⋊Q₈	—	19	2	no	—
335	C₄⋊Q₈	—	19	2	no	—
336	C₄⋊Q₈	—	19	1	no	—
337	C₄⋊Q₈	—	19	2	no	—
338	C₄⋊Q₈	—	19	2	no	—
339	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
340	#126	—	19	1	no	—
341	#126	—	19	2	no	—
342	#126	—	19	2	no	—
343	#126	—	19	2	no	—
344	#126	—	19	1	no	—
345	#126	—	19	2	no	—
346	#126	—	19	2	no	—
347	#126	—	19	2	no	—
348	#126	C₂×D₁₉	1	2	yes	—
349	#126	C₂×D₁₉	1	2	yes	—
350	#125	—	19	2	no	—
351	#125	—	19	1	no	—
352	#125	—	19	2	no	—
353	#125	—	19	2	no	—
354	#125	—	19	2	no	—
355	#125	—	19	2	no	—
356	#125	—	19	2	no	—
357	#125	—	19	2	no	—
358	#125	—	19	2	no	—
359	#125	—	19	2	no	—
360	#125	—	19	1	no	—
361	#125	—	19	2	no	—
362	#125	C₂×D₁₉	1	2	yes	—
363	#125	C₂×D₁₉	1	2	yes	—
364	#125	C₂×D₁₉	1	1	yes	characteristic
365	#124	—	19	2	no	—
366	#124	—	19	1	no	—
367	#123	—	19	2	no	—
368	#123	—	19	1	no	—
369	#123	—	19	2	no	—
370	#123	—	19	1	no	—
371	C₂²⋊Q₈	—	19	1	no	—
372	C₂²⋊Q₈	—	19	1	no	—
373	C₂²⋊Q₈	—	19	2	no	—
374	C₂²⋊Q₈	—	19	1	no	—
375	C₂²⋊Q₈	—	19	2	no	—
376	C₂²⋊Q₈	—	19	2	no	—
377	C₂²⋊Q₈	—	19	1	no	—
378	C₂²⋊Q₈	—	19	2	no	—
379	C₂²⋊Q₈	—	19	1	no	—
380	C₂²⋊Q₈	—	19	2	no	—
381	C₂²⋊Q₈	—	19	2	no	—
382	C₂²⋊Q₈	—	19	2	no	—
383	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
384	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
385	#121	—	19	1	no	—
386	C₄×Q₈	—	19	1	no	—
387	C₄×Q₈	—	19	1	no	—
388	C₄×Q₈	—	19	1	no	—
389	C₄×Q₈	—	19	2	no	—
390	C₄×Q₈	—	19	2	no	—
391	C₄×Q₈	—	19	2	no	—
392	C₄×Q₈	—	19	1	no	—
393	C₄×Q₈	—	19	2	no	—
394	C₄×Q₈	—	19	2	no	—
395	C₄×Q₈	—	19	2	no	—
396	C₄×Q₈	—	19	2	no	—
397	C₄×Q₈	—	19	1	no	—
398	C₄×Q₈	—	19	2	no	—
399	C₄×Q₈	—	19	1	no	—
400	C₄×Q₈	—	19	1	no	—
401	C₄×Q₈	—	19	1	no	—
402	C₄×Q₈	—	19	2	no	—
403	C₄×Q₈	—	19	1	no	—
404	C₄×Q₈	—	19	2	no	—
405	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
406	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
407	C₄×D₄	—	19	1	no	—
408	C₄×D₄	—	19	1	no	—
409	C₄×D₄	—	19	2	no	—
410	C₄×D₄	—	19	2	no	—
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	—	19	1	no	—
413	#117	—	19	1	no	—
414	#117	—	19	2	no	—
415	#117	—	19	1	no	—
416	#117	—	19	2	no	—
417	#117	—	19	2	no	—
418	#117	—	19	2	no	—
419	#117	—	19	2	no	—
420	#117	—	19	1	no	—
421	#117	—	19	2	no	—
422	#117	—	19	2	no	—
423	#117	C₂×D₁₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	—	19	2	no	—
425	C₂×C₄⋊C₄	—	19	1	no	—
426	C₂×C₄²	—	19	2	no	—
427	C₂×C₄²	—	19	1	no	—
428	C₁₉	#3523	1	1	yes	characteristic, complemented, Sylow
429	C₂×Q₈	—	19	1	no	—
430	C₂×Q₈	—	19	2	no	—
431	C₂×Q₈	—	19	1	no	—
432	C₂×Q₈	—	19	2	no	—
433	C₂×Q₈	—	19	2	no	—
434	C₂×Q₈	—	19	2	no	—
435	C₂×Q₈	—	19	1	no	—
436	C₂×Q₈	—	38	4	no	—
437	C₂×Q₈	—	38	4	no	—
438	C₂×Q₈	—	38	4	no	—
439	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
440	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
441	C₂×D₄	—	19	1	no	—
442	C₂×D₄	—	19	1	no	—
443	C₂×D₄	—	19	1	no	—
444	C₂²×C₄	—	19	2	no	—
445	C₂²×C₄	—	19	1	no	—
446	C₂²×C₄	—	19	2	no	—
447	C₂²×C₄	—	19	1	no	—
448	C₂²×C₄	—	19	2	no	—
449	C₂²×C₄	—	19	1	no	—
450	C₂²×C₄	—	19	2	no	—
451	C₂²×C₄	—	19	1	no	—
452	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
453	C₄⋊C₄	—	19	2	no	—
454	C₄⋊C₄	—	19	2	no	—
455	C₄⋊C₄	—	19	2	no	—
456	C₄⋊C₄	—	19	2	no	—
457	C₄⋊C₄	—	19	2	no	—
458	C₄⋊C₄	—	19	2	no	—
459	C₄⋊C₄	—	19	1	no	—
460	C₄⋊C₄	—	19	2	no	—
461	C₄⋊C₄	—	19	1	no	—
462	C₄⋊C₄	—	19	2	no	—
463	C₄⋊C₄	—	19	2	no	—
464	C₄⋊C₄	—	19	1	no	—
465	C₄⋊C₄	—	19	2	no	—
466	C₄⋊C₄	—	19	1	no	—
467	C₄⋊C₄	—	19	2	no	—
468	C₄⋊C₄	—	19	1	no	—
469	C₄⋊C₄	—	19	2	no	—
470	C₄⋊C₄	—	19	2	no	—
471	C₄⋊C₄	—	19	2	no	—
472	C₄⋊C₄	—	19	2	no	—
473	C₄⋊C₄	—	19	1	no	—
474	C₄⋊C₄	—	19	1	no	—
475	C₄⋊C₄	—	19	2	no	—
476	C₄⋊C₄	—	19	1	no	—
477	C₄⋊C₄	—	19	2	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	1	no	—
481	C₄⋊C₄	—	19	2	no	—
482	C₄⋊C₄	—	19	1	no	—
483	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
485	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
487	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
488	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
489	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
493	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
494	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
495	C₂²⋊C₄	—	19	2	no	—
496	C₂²⋊C₄	—	19	1	no	—
497	C₂²⋊C₄	—	19	1	no	—
498	C₂²⋊C₄	—	19	1	no	—
499	C₂²⋊C₄	—	19	2	no	—
500	C₂²⋊C₄	—	19	1	no	—
501	C₂²⋊C₄	—	19	1	no	—
502	C₂²⋊C₄	—	19	2	no	—
503	C₂²⋊C₄	—	19	2	no	—
504	C₂²⋊C₄	—	19	1	no	—
505	C₂²⋊C₄	—	19	1	no	—
506	C₂²⋊C₄	—	19	2	no	—
507	C₂²⋊C₄	—	19	2	no	—
508	C₂²⋊C₄	—	19	1	no	—
509	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
510	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
513	C₄²	—	19	2	no	—
514	C₄²	—	19	2	no	—
515	C₄²	—	19	1	no	—
516	C₄²	—	19	2	no	—
517	C₄²	—	19	1	no	—
518	C₄²	—	19	1	no	—
519	C₄²	—	19	2	no	—
520	C₄²	—	19	2	no	—
521	C₄²	—	19	2	no	—
522	C₄²	—	19	2	no	—
523	C₄²	—	19	2	no	—
524	C₄²	—	19	2	no	—
525	C₄²	—	19	2	no	—
526	C₄²	—	19	1	no	—
527	C₄²	C₂²×D₁₉	1	1	yes	characteristic
528	C₄²	C₂²×D₁₉	1	2	yes	—
529	C₄²	C₂²×D₁₉	1	2	yes	—
530	C₄²	C₂²×D₁₉	1	1	yes	characteristic
531	C₂³	—	19	1	no	—
532	C₂³	—	19	1	no	—
533	C₂³	C₂³×D₁₉	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	19	4	no	—
537	Q₈	—	38	4	no	—
538	Q₈	—	38	4	no	—
539	Q₈	—	38	4	no	—
540	Q₈	—	38	4	no	—
541	Q₈	—	38	2	no	—
542	Q₈	—	38	2	no	—
543	D₄	—	38	2	no	—
544	D₄	—	38	2	no	—
545	D₄	—	38	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	19	1	no	—
548	C₂×C₄	—	19	2	no	—
549	C₂×C₄	—	19	2	no	—
550	C₂×C₄	—	19	2	no	—
551	C₂×C₄	—	19	1	no	—
552	C₂×C₄	—	19	1	no	—
553	C₂×C₄	—	19	1	no	—
554	C₂×C₄	—	19	1	no	—
555	C₂×C₄	—	19	1	no	—
556	C₂×C₄	—	19	2	no	—
557	C₂×C₄	—	38	4	no	—
558	C₂×C₄	—	38	4	no	—
559	C₂×C₄	—	38	2	no	—
560	C₂×C₄	—	38	2	no	—
561	C₂×C₄	—	38	4	no	—
562	C₂×C₄	—	38	4	no	—
563	C₂×C₄	—	38	2	no	—
564	C₂×C₄	—	38	2	no	—
565	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₁₉	1	2	yes	—
569	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₉	1	2	yes	—
572	C₂×C₄	C₂³×D₁₉	1	2	yes	—
573	C₂×C₄	C₂³×D₁₉	1	2	yes	—
574	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	19	2	no	—
579	C₂²	—	38	1	no	—
580	C₂²	—	38	1	no	—
581	C₂²	—	38	1	no	—
582	C₂²	—	38	1	no	—
583	C₂²	—	38	1	no	—
584	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	19	4	no	—
595	C₄	—	19	2	no	—
596	C₄	—	38	2	no	—
597	C₄	—	38	1	no	—
598	C₄	—	38	1	no	—
599	C₄	—	38	2	no	—
600	C₄	—	38	1	no	—
601	C₄	—	38	1	no	—
602	C₄	—	38	2	no	—
603	C₄	—	38	1	no	—
604	C₄	#41×D₁₉	1	2	yes	—
605	C₂	—	4	1	no	—
606	C₂	—	38	2	no	—
607	C₂	—	76	1	no	—
608	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
609	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
610	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#541	C₂
prime radical	#10597330	C₂²
hypercenter	#541	D₁₉
hypocenter	C₁₉	#3523
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #11927271	C₂	semidirect
2. #11927271	C₂	semidirect
3. #11927269	C₂	semidirect
4. #11927265	C₂	semidirect
5. #11927261	C₂	semidirect
6. #11927232	C₂	semidirect
7. #11927230	C₂	semidirect
8. #11927228	C₂	semidirect
9. #11927226	C₂	semidirect
10. #11927209	C₂	semidirect
11. #11927207	C₂	semidirect
12. #11927207	C₂	semidirect
13. #11927153	C₂	semidirect
14. #11927152	C₂	semidirect
15. #11927151	C₂	semidirect
16. #11927100	C₂	semidirect
17. #11927098	C₂	semidirect
20. #11927021	C₂	semidirect
21. #11927020	C₂	semidirect
22. C₄×Q₈×D₁₉	C₂	semidirect
23. C₁₉×#541	C₂	semidirect
315. #541	D₁₉	semidirect
428. C₁₉	#3523	semidirect

Maximal subgroups

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

subgroup	index
#11927271	2
#11927269	2
#11927265	2
#11927261	2
#11927232	2
#11927230	2
#11927228	2
#11927226	2
#11927209	2
#11927207	2
#11927153	2
#11927152	2
#11927151	2
#11927100	2
#11927098	2
#11927077	2
#11927072	2
#11927021	2
#11927020	2
C₄×Q₈×D₁₉	2
C₁₉×#541	2
#3523	19