Subgroups — #14578191

Order 2432.

1056 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927293	C₂	1	2	yes	maximal, complemented
2	#11927281	C₂	1	2	yes	maximal, complemented
3	#11927243	C₂	1	2	yes	maximal, complemented
4	#11927237	C₂	1	2	yes	maximal, complemented
5	#11927223	C₂	1	2	yes	maximal, complemented
6	#11927193	C₂	1	2	yes	maximal, complemented
7	#11927183	C₂	1	2	yes	maximal, complemented
8	#11927182	C₂	1	2	yes	maximal, complemented
9	#11927158	C₂	1	2	yes	maximal, complemented
10	#11927139	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927136	C₂	1	2	yes	maximal, complemented
12	#11927131	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927128	C₂	1	2	yes	maximal, complemented
14	#11927127	C₂	1	2	yes	maximal, complemented
15	#11927121	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927102	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10597322	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₁₉	C₂²	1	2	yes	complemented
21	C₂×#64543	C₂²	1	2	yes	complemented
22	C₂×D₄×D₁₉	C₂²	1	2	yes	—
23	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#124	C₂²	1	2	yes	complemented
26	C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#121	C₂²	1	2	yes	complemented
29	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
30	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	#10597393	C₂²	1	2	yes	—
34	#10597392	C₂²	1	2	yes	complemented
35	#10597392	C₂²	1	2	yes	complemented
36	#10597390	C₂²	1	2	yes	complemented
37	#10597385	C₂²	1	2	yes	—
38	#10597385	C₂²	1	2	yes	—
39	#10597385	C₂²	1	2	yes	—
40	#10597385	C₂²	1	2	yes	complemented
41	#10597385	C₂²	1	2	yes	complemented
42	#10597385	C₂²	1	2	yes	complemented
43	#10597385	C₂²	1	2	yes	complemented
44	#10597385	C₂²	1	2	yes	complemented
45	#10597383	C₂²	1	2	yes	—
46	#10597383	C₂²	1	2	yes	—
47	#10597383	C₂²	1	2	yes	complemented
48	#10597383	C₂²	1	2	yes	complemented
49	#10597381	C₂²	1	2	yes	complemented
50	#10597381	C₂²	1	2	yes	complemented
51	#10597381	C₂²	1	2	yes	complemented
52	#10597381	C₂²	1	2	yes	complemented
53	D₄×Dic₁₉	C₂²	1	2	yes	complemented
54	D₄×Dic₁₉	C₂²	1	2	yes	complemented
55	#10597376	C₂²	1	1	yes	characteristic
56	#10597376	C₂²	1	2	yes	—
57	#10597375	C₂²	1	2	yes	—
58	#10597375	C₂²	1	2	yes	complemented
59	#10597375	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
63	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
64	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
65	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
66	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
67	#10597370	C₂²	1	1	yes	characteristic, complemented
68	#10597370	C₂²	1	2	yes	complemented
69	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
70	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
71	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
73	#10597344	C₂²	1	2	yes	complemented
74	#10597344	C₂²	1	2	yes	complemented
75	#10597342	C₂²	1	2	yes	complemented
76	#10597342	C₂²	1	2	yes	complemented
77	#10597340	C₂²	1	2	yes	—
78	#10597340	C₂²	1	2	yes	—
79	#10597335	C₂²	1	2	yes	complemented
80	#10597335	C₂²	1	2	yes	complemented
81	#10597332	C₂²	1	2	yes	complemented
82	#10597331	C₂²	1	2	yes	—
83	#10597331	C₂²	1	2	yes	complemented
84	#10597330	C₂²	1	2	yes	—
85	#10597330	C₂²	1	2	yes	complemented
86	#10597329	C₂²	1	2	yes	—
87	#10597329	C₂²	1	2	yes	complemented
88	#10597328	C₂²	1	2	yes	—
89	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
90	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
92	#10597325	C₂²	1	2	yes	complemented
93	#10597325	C₂²	1	2	yes	complemented
94	#10597324	C₂²	1	2	yes	complemented
95	#10597324	C₂²	1	2	yes	complemented
96	#10597323	C₂²	1	2	yes	complemented
97	#10597322	C₂²	1	2	yes	complemented
98	#10597322	C₂²	1	2	yes	complemented
99	#10597322	C₂²	1	2	yes	complemented
100	#10597322	C₂²	1	2	yes	complemented
101	#10597322	C₂²	1	2	yes	complemented
102	#10597321	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
104	#10597318	C₂²	1	2	yes	complemented
105	#10597316	C₂²	1	1	yes	characteristic, complemented
106	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₉	C₂³	1	1	yes	characteristic
108	C₂³×D₁₉	C₂³	1	2	yes	—
109	#41×C₁₉	—	4	4	no	—
110	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
111	C₂×D₄×C₁₉	C₂³	1	2	yes	—
112	C₂×D₄×C₁₉	C₂³	1	2	yes	—
113	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₁₉	C₂³	1	2	yes	—
115	C₂×D₄×C₁₉	C₂³	1	2	yes	—
116	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
129	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
130	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
131	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
132	C₂²×Dic₁₉	C₂³	1	2	yes	—
133	C₂²×Dic₁₉	C₂³	1	2	yes	—
134	C₂²×Dic₁₉	C₂³	1	2	yes	—
135	#64543	—	4	4	no	—
136	D₄×D₁₉	—	4	4	no	—
137	C₂×D₇₆	C₂³	1	2	yes	—
138	C₂×D₇₆	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₉	C₂³	1	2	yes	—
141	C₂×C₄×D₁₉	C₂³	1	2	yes	—
142	C₂×Dic₃₈	C₂³	1	2	yes	—
143	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
147	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
151	C₄²×C₁₉	C₂³	1	1	yes	characteristic
152	C₄²×C₁₉	C₂³	1	1	yes	characteristic
153	C₄²×C₁₉	C₂³	1	1	yes	characteristic
154	C₄²×C₁₉	C₂³	1	1	yes	characteristic
155	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
162	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
176	C₄⋊Dic₁₉	C₂³	1	2	yes	—
177	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
178	C₄⋊Dic₁₉	C₂³	1	2	yes	—
179	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
180	Dic₁₉⋊C₄	C₂³	1	2	yes	—
181	Dic₁₉⋊C₄	C₂³	1	2	yes	—
182	Dic₁₉⋊C₄	C₂³	1	2	yes	—
183	Dic₁₉⋊C₄	C₂³	1	2	yes	—
184	Dic₁₉⋊C₄	C₂³	1	2	yes	—
185	Dic₁₉⋊C₄	C₂³	1	2	yes	—
186	Dic₁₉⋊C₄	C₂³	1	2	yes	—
187	Dic₁₉⋊C₄	C₂³	1	2	yes	—
188	Dic₁₉⋊C₄	C₂³	1	2	yes	—
189	Dic₁₉⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₁₉	C₂³	1	2	yes	—
195	C₄×Dic₁₉	C₂³	1	2	yes	—
196	C₄×Dic₁₉	C₂³	1	2	yes	—
197	C₂³×C₁₉	C₂⁴	1	2	yes	—
198	C₂³×C₁₉	C₂⁴	1	2	yes	—
199	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
200	C₂²×D₁₉	—	2	2	no	—
201	C₂²×D₁₉	—	4	2	no	—
202	C₂²×D₁₉	—	4	2	no	—
203	C₂²×D₁₉	—	4	2	no	—
204	C₂²×D₁₉	—	4	1	no	—
205	C₂²×D₁₉	—	4	1	no	—
206	C₂²×D₁₉	C₂⁴	1	2	yes	—
207	C₂²×D₁₉	C₂⁴	1	2	yes	—
208	Q₈×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	2	4	no	—
210	D₄×C₁₉	—	2	4	no	—
211	D₄×C₁₉	—	4	2	no	—
212	D₄×C₁₉	—	4	1	no	—
213	D₄×C₁₉	—	4	1	no	—
214	D₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
222	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
223	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
228	C₂²⋊D₁₉	—	2	4	no	—
229	C₂²⋊D₁₉	—	4	2	no	—
230	C₂²⋊D₁₉	—	4	2	no	—
231	C₂²⋊D₁₉	—	4	2	no	—
232	C₂²⋊D₁₉	—	4	2	no	—
233	C₂²⋊D₁₉	—	4	2	no	—
234	C₂²⋊D₁₉	—	4	2	no	—
235	C₂×Dic₁₉	—	2	2	no	—
236	C₂×Dic₁₉	—	4	2	no	—
237	C₂×Dic₁₉	—	4	2	no	—
238	C₂×Dic₁₉	—	4	2	no	—
239	C₂×Dic₁₉	—	4	1	no	—
240	C₂×Dic₁₉	—	4	1	no	—
241	C₂×Dic₁₉	C₂⁴	1	2	yes	—
242	C₂×Dic₁₉	C₂⁴	1	2	yes	—
243	C₂×Dic₁₉	C₂⁴	1	2	yes	—
244	C₂×Dic₁₉	C₂⁴	1	2	yes	—
245	C₂×Dic₁₉	C₂⁴	1	2	yes	—
246	C₂×Dic₁₉	C₂⁴	1	2	yes	—
247	D₇₆	—	4	1	no	—
248	D₇₆	—	4	2	no	—
249	C₄×D₁₉	—	4	2	no	—
250	C₄×D₁₉	—	4	2	no	—
251	C₄×D₁₉	—	4	2	no	—
252	Dic₃₈	—	4	1	no	—
253	Dic₃₈	—	4	2	no	—
254	#3560	—	19	1	no	maximal, Sylow
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	2	no	—
258	C₂²×C₁₉	—	2	2	no	—
259	C₂²×C₁₉	—	2	2	no	—
260	C₂²×C₁₉	—	2	2	no	—
261	C₂²×C₁₉	—	2	2	no	—
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
264	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
265	C₂×D₁₉	—	2	2	no	—
266	C₂×D₁₉	—	2	2	no	—
267	C₂×D₁₉	—	2	2	no	—
268	C₂×D₁₉	—	2	2	no	—
269	C₂×D₁₉	—	2	2	no	—
270	C₂×D₁₉	—	2	2	no	—
271	C₂×D₁₉	—	8	2	no	—
272	C₂×D₁₉	—	8	4	no	—
273	C₄×C₁₉	—	2	2	no	—
274	C₄×C₁₉	—	2	2	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	Dic₁₉	—	2	2	no	—
282	Dic₁₉	—	2	2	no	—
283	Dic₁₉	—	2	2	no	—
284	Dic₁₉	—	2	2	no	—
285	Dic₁₉	—	2	2	no	—
286	Dic₁₉	—	2	2	no	—
287	#563	—	19	2	no	—
288	#560	—	19	2	no	—
289	#553	—	19	2	no	—
290	#553	—	19	2	no	—
291	#551	—	19	2	no	—
292	#547	—	19	2	no	—
293	#546	—	19	2	no	—
294	#546	—	19	2	no	—
295	#542	—	19	2	no	—
296	#539	—	19	1	no	—
297	#539	—	19	2	no	—
298	#538	—	19	2	no	—
299	#538	—	19	1	no	—
300	#538	—	19	2	no	—
301	#537	—	19	1	no	—
302	#534	—	19	1	no	—
303	#532	D₁₉	1	1	yes	characteristic, complemented
304	#529	—	19	1	no	—
305	C₂×#126	—	19	1	no	—
306	C₂×C₁₉	—	2	2	no	—
307	C₂×C₁₉	—	4	2	no	—
308	C₂×C₁₉	—	4	2	no	—
309	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₁₉	#585	1	1	yes	characteristic
311	C₂×C₁₉	#585	1	1	yes	characteristic
312	D₁₉	—	4	2	no	—
313	D₁₉	—	4	2	no	—
314	C₂×#41	—	19	2	no	—
315	C₂×#41	C₂×D₁₉	1	2	yes	complemented
316	C₂²×D₄	—	19	2	no	—
317	C₄⋊Q₈	—	19	2	no	—
318	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
319	#127	C₂×D₁₉	1	1	yes	characteristic, complemented
320	#126	—	19	2	no	—
321	#126	—	19	2	no	—
322	#126	—	19	2	no	—
323	#126	—	19	2	no	—
324	#126	—	19	2	no	—
325	#126	—	19	2	no	—
326	#126	—	19	2	no	—
327	#126	—	19	2	no	—
328	#126	—	19	2	no	—
329	#125	—	19	2	no	—
330	#125	—	19	2	no	—
331	#125	—	19	1	no	—
332	#124	—	19	2	no	—
333	#124	—	19	2	no	—
334	#124	—	19	2	no	—
335	#124	—	19	1	no	—
336	#124	C₂×D₁₉	1	2	yes	complemented
337	#123	—	19	2	no	—
338	#123	—	19	2	no	—
339	#123	—	19	2	no	—
340	#123	—	19	2	no	—
341	#123	—	19	2	no	—
342	#123	—	19	2	no	—
343	#123	—	19	2	no	—
344	#123	—	19	2	no	—
345	#123	—	19	2	no	—
346	#123	—	19	2	no	—
347	#123	—	19	2	no	—
348	#123	—	19	2	no	—
349	C₂²⋊Q₈	—	19	2	no	—
350	C₂²⋊Q₈	—	19	2	no	—
351	C₂²⋊Q₈	—	19	1	no	—
352	C₂²⋊Q₈	—	19	2	no	—
353	C₂²⋊Q₈	—	19	2	no	—
354	C₂²⋊Q₈	—	19	2	no	—
355	C₂²⋊Q₈	—	19	2	no	—
356	C₂²⋊Q₈	—	19	2	no	—
357	#121	—	19	2	no	—
358	#121	—	19	2	no	—
359	#121	—	19	2	no	—
360	#121	—	19	2	no	—
361	#121	—	19	2	no	—
362	#121	—	19	2	no	—
363	#121	—	19	2	no	—
364	#121	—	19	2	no	—
365	#121	—	19	1	no	—
366	#121	—	19	2	no	—
367	#121	—	19	2	no	—
368	#121	—	19	2	no	—
369	#121	C₂×D₁₉	1	1	yes	characteristic
370	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
371	#121	C₂×D₁₉	1	2	yes	complemented
372	#120	—	19	2	no	—
373	#120	—	19	2	no	—
374	#120	—	19	2	no	—
375	#120	—	19	2	no	—
376	#120	—	19	2	no	—
377	C₄×Q₈	—	19	1	no	—
378	C₄×D₄	—	19	2	no	—
379	C₄×D₄	—	19	2	no	—
380	C₄×D₄	—	19	2	no	—
381	C₄×D₄	—	19	2	no	—
382	C₄×D₄	—	19	2	no	—
383	C₄×D₄	—	19	2	no	—
384	C₄×D₄	—	19	2	no	—
385	C₄×D₄	—	19	1	no	—
386	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
387	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
388	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
389	#117	—	19	2	no	—
390	#117	—	19	2	no	—
391	C₂×C₄⋊C₄	—	19	1	no	—
392	C₂×C₄⋊C₄	—	19	1	no	—
393	C₂×C₄⋊C₄	—	19	1	no	—
394	C₂×C₄⋊C₄	—	19	2	no	—
395	C₂×C₂²⋊C₄	—	19	1	no	—
396	C₂×C₂²⋊C₄	—	19	1	no	—
397	C₂×C₂²⋊C₄	—	19	1	no	—
398	C₂×C₂²⋊C₄	—	19	2	no	—
399	C₂×C₂²⋊C₄	—	19	2	no	—
400	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
401	C₁₉	#3560	1	1	yes	characteristic, complemented, Sylow
402	C₂⁴	—	19	1	no	—
403	C₂⁴	—	19	2	no	—
404	#41	—	4	4	no	—
405	#41	—	76	4	no	—
406	C₂×Q₈	—	19	1	no	—
407	C₂×Q₈	—	19	2	no	—
408	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
409	C₂×D₄	—	19	2	no	—
410	C₂×D₄	—	19	2	no	—
411	C₂×D₄	—	19	2	no	—
412	C₂×D₄	—	19	2	no	—
413	C₂×D₄	—	19	2	no	—
414	C₂×D₄	—	19	2	no	—
415	C₂×D₄	—	19	2	no	—
416	C₂×D₄	—	19	1	no	—
417	C₂×D₄	—	19	2	no	—
418	C₂×D₄	—	76	4	no	—
419	C₂×D₄	C₂²×D₁₉	1	2	yes	—
420	C₂×D₄	C₂²×D₁₉	1	2	yes	—
421	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
422	C₂×D₄	C₂²×D₁₉	1	2	yes	—
423	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
424	C₂×D₄	C₂²×D₁₉	1	2	yes	—
425	C₂²×C₄	—	19	1	no	—
426	C₂²×C₄	—	19	1	no	—
427	C₂²×C₄	—	19	1	no	—
428	C₂²×C₄	—	19	2	no	—
429	C₂²×C₄	—	19	2	no	—
430	C₂²×C₄	—	19	2	no	—
431	C₂²×C₄	—	19	2	no	—
432	C₂²×C₄	—	19	2	no	—
433	C₂²×C₄	—	19	2	no	—
434	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
435	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
438	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
439	C₄⋊C₄	—	19	2	no	—
440	C₄⋊C₄	—	19	2	no	—
441	C₄⋊C₄	—	19	2	no	—
442	C₄⋊C₄	—	19	2	no	—
443	C₄⋊C₄	—	19	2	no	—
444	C₄⋊C₄	—	19	2	no	—
445	C₄⋊C₄	—	19	2	no	—
446	C₄⋊C₄	—	19	2	no	—
447	C₄⋊C₄	—	19	2	no	—
448	C₄⋊C₄	—	19	2	no	—
449	C₄⋊C₄	—	19	2	no	—
450	C₄⋊C₄	—	19	2	no	—
451	C₄⋊C₄	—	19	2	no	—
452	C₄⋊C₄	—	19	2	no	—
453	C₄⋊C₄	—	19	2	no	—
454	C₄⋊C₄	—	19	2	no	—
455	C₄⋊C₄	—	19	1	no	—
456	C₄⋊C₄	—	19	1	no	—
457	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
459	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
460	C₂²⋊C₄	—	19	2	no	—
461	C₂²⋊C₄	—	19	2	no	—
462	C₂²⋊C₄	—	19	2	no	—
463	C₂²⋊C₄	—	19	2	no	—
464	C₂²⋊C₄	—	19	2	no	—
465	C₂²⋊C₄	—	19	2	no	—
466	C₂²⋊C₄	—	19	2	no	—
467	C₂²⋊C₄	—	19	2	no	—
468	C₂²⋊C₄	—	19	2	no	—
469	C₂²⋊C₄	—	19	2	no	—
470	C₂²⋊C₄	—	19	2	no	—
471	C₂²⋊C₄	—	19	2	no	—
472	C₂²⋊C₄	—	19	2	no	—
473	C₂²⋊C₄	—	19	2	no	—
474	C₂²⋊C₄	—	19	2	no	—
475	C₂²⋊C₄	—	19	2	no	—
476	C₂²⋊C₄	—	19	2	no	—
477	C₂²⋊C₄	—	19	2	no	—
478	C₂²⋊C₄	—	19	2	no	—
479	C₂²⋊C₄	—	19	2	no	—
480	C₂²⋊C₄	—	19	2	no	—
481	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
485	C₄²	—	19	2	no	—
486	C₄²	—	19	2	no	—
487	C₄²	—	19	2	no	—
488	C₄²	C₂²×D₁₉	1	1	yes	characteristic
489	C₄²	C₂²×D₁₉	1	1	yes	characteristic
490	C₄²	C₂²×D₁₉	1	1	yes	characteristic
491	C₄²	C₂²×D₁₉	1	1	yes	characteristic
492	C₂³	—	19	2	no	—
493	C₂³	—	19	2	no	—
494	C₂³	—	38	2	no	—
495	C₂³	—	76	2	no	—
496	C₂³	—	76	1	no	—
497	C₂³	—	76	1	no	—
498	C₂³	—	76	2	no	—
499	C₂³	—	76	2	no	—
500	C₂³	C₂³×D₁₉	1	2	yes	—
501	C₂³	C₂³×D₁₉	1	2	yes	—
502	C₂³	C₂³×D₁₉	1	1	yes	characteristic
503	Q₈	—	4	2	no	—
504	Q₈	—	76	2	no	—
505	Q₈	—	76	1	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	4	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	38	4	no	—
513	D₄	—	76	2	no	—
514	D₄	—	76	1	no	—
515	D₄	—	76	2	no	—
516	D₄	—	76	2	no	—
517	D₄	—	76	2	no	—
518	D₄	—	76	2	no	—
519	D₄	—	76	2	no	—
520	D₄	—	76	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	19	2	no	—
527	C₂×C₄	—	19	2	no	—
528	C₂×C₄	—	19	2	no	—
529	C₂×C₄	—	19	2	no	—
530	C₂×C₄	—	19	2	no	—
531	C₂×C₄	—	19	2	no	—
532	C₂×C₄	—	38	2	no	—
533	C₂×C₄	—	76	2	no	—
534	C₂×C₄	—	76	2	no	—
535	C₂×C₄	—	76	2	no	—
536	C₂×C₄	—	76	2	no	—
537	C₂×C₄	—	76	1	no	—
538	C₂×C₄	—	76	1	no	—
539	C₂×C₄	—	76	2	no	—
540	C₂×C₄	—	76	2	no	—
541	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
542	C₂×C₄	C₂³×D₁₉	1	2	yes	—
543	C₂×C₄	C₂³×D₁₉	1	2	yes	—
544	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	38	2	no	—
558	C₂²	—	38	2	no	—
559	C₂²	—	38	2	no	—
560	C₂²	—	38	2	no	—
561	C₂²	—	38	2	no	—
562	C₂²	—	38	2	no	—
563	C₂²	—	152	2	no	—
564	C₂²	—	152	4	no	—
565	C₂²	#10597430	1	2	yes	—
566	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	38	2	no	—
576	C₄	—	38	2	no	—
577	C₄	—	38	2	no	—
578	C₄	—	38	2	no	—
579	C₄	—	38	2	no	—
580	C₄	—	38	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	76	2	no	—
585	C₂	—	76	2	no	—
586	C₂	C₂×#10597430	1	1	yes	characteristic
587	C₂	#11927380	1	1	yes	characteristic
588	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#532	C₂
hypercenter	#532	D₁₉
hypocenter	C₁₉	#3560
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #11927293	C₂	semidirect
2. #11927281	C₂	semidirect
3. #11927243	C₂	semidirect
4. #11927237	C₂	semidirect
5. #11927223	C₂	semidirect
6. #11927193	C₂	semidirect
7. #11927183	C₂	semidirect
8. #11927182	C₂	semidirect
9. #11927158	C₂	semidirect
10. #11927139	C₂	semidirect
11. #11927136	C₂	semidirect
12. #11927131	C₂	semidirect
13. #11927128	C₂	semidirect
14. #11927127	C₂	semidirect
15. #11927121	C₂	semidirect
16. #11927102	C₂	semidirect
17. #11927078	C₂	semidirect
18. C₂×#10597322	C₂	semidirect
19. C₁₉×#532	C₂	semidirect
20. C₂×#41×C₁₉	C₂²	semidirect
21. C₂×#64543	C₂²	semidirect
23. C₁₉×C₄⋊Q₈	C₂²	semidirect
24. C₁₉×#127	C₂²	semidirect
25. C₁₉×#124	C₂²	semidirect
27. C₁₉×#121	C₂²	semidirect
28. C₁₉×#121	C₂²	semidirect
29. C₄×D₄×C₁₉	C₂²	semidirect
30. C₄×D₄×C₁₉	C₂²	semidirect
31. C₄×D₄×C₁₉	C₂²	semidirect
32. C₂×C₄²×C₁₉	C₂²	semidirect
34. #10597392	C₂²	semidirect
35. #10597392	C₂²	semidirect
36. #10597390	C₂²	semidirect
40. #10597385	C₂²	semidirect
41. #10597385	C₂²	semidirect
42. #10597385	C₂²	semidirect
43. #10597385	C₂²	semidirect
44. #10597385	C₂²	semidirect
47. #10597383	C₂²	semidirect
48. #10597383	C₂²	semidirect
49. #10597381	C₂²	semidirect
50. #10597381	C₂²	semidirect
51. #10597381	C₂²	semidirect
52. #10597381	C₂²	semidirect
53. D₄×Dic₁₉	C₂²	semidirect
54. D₄×Dic₁₉	C₂²	semidirect
58. #10597375	C₂²	semidirect
59. #10597375	C₂²	semidirect
60. C₄×C₂²⋊D₁₉	C₂²	semidirect
61. C₄×C₂²⋊D₁₉	C₂²	semidirect
62. C₄×C₂²⋊D₁₉	C₂²	semidirect
66. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
67. #10597370	C₂²	semidirect
68. #10597370	C₂²	semidirect
69. C₂×Dic₁₉⋊C₄	C₂²	semidirect
70. C₂×Dic₁₉⋊C₄	C₂²	semidirect
71. C₂×Dic₁₉⋊C₄	C₂²	semidirect
72. C₂×Dic₁₉⋊C₄	C₂²	semidirect
73. #10597344	C₂²	semidirect
74. #10597344	C₂²	semidirect
75. #10597342	C₂²	semidirect
76. #10597342	C₂²	semidirect
79. #10597335	C₂²	semidirect
80. #10597335	C₂²	semidirect
81. #10597332	C₂²	semidirect
83. #10597331	C₂²	semidirect
85. #10597330	C₂²	semidirect
87. #10597329	C₂²	semidirect
89. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
90. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
91. C₂²⋊C₄×D₁₉	C₂²	semidirect
92. #10597325	C₂²	semidirect
93. #10597325	C₂²	semidirect
94. #10597324	C₂²	semidirect
95. #10597324	C₂²	semidirect
96. #10597323	C₂²	semidirect
97. #10597322	C₂²	semidirect
98. #10597322	C₂²	semidirect
99. #10597322	C₂²	semidirect
100. #10597322	C₂²	semidirect
101. #10597322	C₂²	semidirect
102. #10597321	C₂²	semidirect
103. C₄×D₇₆	C₂²	semidirect
104. #10597318	C₂²	semidirect
105. #10597316	C₂²	semidirect
106. C₄×Dic₃₈	C₂²	semidirect
303. #532	D₁₉	semidirect
315. C₂×#41	C₂×D₁₉	semidirect
318. C₄⋊Q₈	C₂×D₁₉	semidirect
319. #127	C₂×D₁₉	semidirect
336. #124	C₂×D₁₉	semidirect
370. #121	C₂×D₁₉	semidirect
371. #121	C₂×D₁₉	semidirect
386. C₄×D₄	C₂×D₁₉	semidirect
387. C₄×D₄	C₂×D₁₉	semidirect
388. C₄×D₄	C₂×D₁₉	semidirect
400. C₂×C₄²	C₂×D₁₉	semidirect
401. C₁₉	#3560	semidirect

Maximal subgroups

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

subgroup	index
#11927293	2
#11927281	2
#11927243	2
#11927237	2
#11927223	2
#11927193	2
#11927183	2
#11927182	2
#11927158	2
#11927139	2
#11927136	2
#11927131	2
#11927128	2
#11927127	2
#11927121	2
#11927102	2
#11927078	2
C₂×#10597322	2
C₁₉×#532	2
#3560	19