Subgroups — #14577989

Order 2432.

1060 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	1	yes	maximal, characteristic, complemented
2	#11927290	C₂	1	2	yes	maximal, complemented
3	#11927286	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927260	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927256	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927221	C₂	1	2	yes	maximal, complemented
7	#11927218	C₂	1	2	yes	maximal, complemented
8	#11927217	C₂	1	2	yes	maximal, complemented
9	#11927186	C₂	1	2	yes	maximal, complemented
10	#11927182	C₂	1	2	yes	maximal, complemented
11	#11927168	C₂	1	2	yes	maximal, complemented
12	#11927164	C₂	1	2	yes	maximal, complemented
13	#11927134	C₂	1	2	yes	maximal, complemented
14	#11927128	C₂	1	2	yes	maximal, complemented
15	#11927118	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927105	C₂	1	2	yes	maximal, complemented
17	#11927071	C₂	1	2	yes	maximal, complemented
18	C₂×#10597393	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
23	C₂×#64541	C₂²	1	1	yes	characteristic
24	C₂²×D₇₆	C₂²	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#123	C₂²	1	2	yes	complemented
30	C₁₉×#123	C₂²	1	2	yes	complemented
31	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
34	#10597393	C₂²	1	1	yes	characteristic
35	#10597393	C₂²	1	1	yes	characteristic
36	#10597393	C₂²	1	2	yes	complemented
37	#10597393	C₂²	1	2	yes	complemented
38	#10597393	C₂²	1	1	yes	characteristic, complemented
39	#10597393	C₂²	1	1	yes	characteristic, complemented
40	#10597393	C₂²	1	1	yes	characteristic, complemented
41	#10597393	C₂²	1	1	yes	characteristic, complemented
42	#10597393	C₂²	1	2	yes	complemented
43	#10597392	C₂²	1	2	yes	complemented
44	#10597392	C₂²	1	2	yes	complemented
45	#10597392	C₂²	1	2	yes	complemented
46	#10597390	C₂²	1	1	yes	characteristic, complemented
47	#10597390	C₂²	1	1	yes	characteristic, complemented
48	#10597385	C₂²	1	2	yes	—
49	#10597385	C₂²	1	2	yes	complemented
50	#10597383	C₂²	1	2	yes	—
51	#10597383	C₂²	1	2	yes	complemented
52	D₄×Dic₁₉	C₂²	1	2	yes	complemented
53	#10597376	C₂²	1	2	yes	complemented
54	#10597375	C₂²	1	2	yes	complemented
55	#10597375	C₂²	1	2	yes	complemented
56	#10597375	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
58	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
59	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
60	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
61	#10597372	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
63	#10597344	C₂²	1	2	yes	complemented
64	#10597344	C₂²	1	2	yes	complemented
65	#10597344	C₂²	1	2	yes	complemented
66	#10597344	C₂²	1	2	yes	complemented
67	#10597343	C₂²	1	2	yes	complemented
68	#10597342	C₂²	1	2	yes	complemented
69	#10597342	C₂²	1	2	yes	complemented
70	#10597341	C₂²	1	2	yes	—
71	#10597341	C₂²	1	2	yes	complemented
72	#10597341	C₂²	1	2	yes	complemented
73	#10597340	C₂²	1	2	yes	—
74	#10597340	C₂²	1	2	yes	complemented
75	#10597340	C₂²	1	2	yes	complemented
76	#10597340	C₂²	1	2	yes	complemented
77	#10597340	C₂²	1	2	yes	complemented
78	#10597339	C₂²	1	2	yes	complemented
79	#10597338	C₂²	1	2	yes	complemented
80	#10597338	C₂²	1	2	yes	complemented
81	#10597335	C₂²	1	2	yes	complemented
82	#10597333	C₂²	1	2	yes	complemented
83	#10597332	C₂²	1	2	yes	complemented
84	#10597331	C₂²	1	2	yes	complemented
85	#10597331	C₂²	1	2	yes	complemented
86	#10597331	C₂²	1	2	yes	complemented
87	#10597330	C₂²	1	2	yes	—
88	#10597330	C₂²	1	2	yes	complemented
89	#10597330	C₂²	1	2	yes	complemented
90	#10597329	C₂²	1	2	yes	complemented
91	#10597328	C₂²	1	2	yes	—
92	#10597328	C₂²	1	2	yes	—
93	#10597328	C₂²	1	2	yes	complemented
94	#10597328	C₂²	1	2	yes	complemented
95	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
96	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
97	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
98	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
99	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
100	#10597325	C₂²	1	2	yes	complemented
101	#10597324	C₂²	1	2	yes	complemented
102	#10597323	C₂²	1	2	yes	complemented
103	#10597322	C₂²	1	2	yes	complemented
104	#10597321	C₂²	1	2	yes	complemented
105	C₄×D₇₆	C₂²	1	2	yes	complemented
106	#10597318	C₂²	1	2	yes	complemented
107	C₂³×D₁₉	C₂³	1	2	yes	—
108	C₂³×D₁₉	C₂³	1	2	yes	—
109	#41×C₁₉	—	4	2	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
113	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₁₉	C₂³	1	2	yes	—
117	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂²×Dic₁₉	C₂³	1	2	yes	—
128	C₂²×Dic₁₉	C₂³	1	2	yes	—
129	D₄×D₁₉	—	4	4	no	—
130	#64541	—	4	2	no	—
131	C₂×D₇₆	—	4	2	no	—
132	C₂×D₇₆	C₂³	1	2	yes	—
133	C₂×D₇₆	C₂³	1	1	yes	characteristic
134	C₂×D₇₆	C₂³	1	2	yes	—
135	C₂×D₇₆	C₂³	1	1	yes	characteristic
136	C₂×D₇₆	C₂³	1	1	yes	characteristic
137	C₂×D₇₆	C₂³	1	2	yes	—
138	C₂×D₇₆	C₂³	1	2	yes	—
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×C₄×D₁₉	C₂³	1	2	yes	—
143	C₂×C₄×D₁₉	C₂³	1	2	yes	—
144	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
145	C₂×Dic₃₈	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
147	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₄²×C₁₉	C₂³	1	1	yes	characteristic
157	C₄²×C₁₉	C₂³	1	1	yes	characteristic
158	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
161	(C₂×D₁₉)⋊C₄	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	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
181	C₄⋊Dic₁₉	C₂³	1	2	yes	—
182	C₄⋊Dic₁₉	C₂³	1	2	yes	—
183	C₄⋊Dic₁₉	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	C₄×Dic₁₉	C₂³	1	2	yes	—
193	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₉	C₂³	1	2	yes	—
198	C₄×Dic₁₉	C₂³	1	2	yes	—
199	C₂³×C₁₉	C₂⁴	1	2	yes	—
200	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
201	C₂²×D₁₉	—	2	4	no	—
202	C₂²×D₁₉	—	4	2	no	—
203	C₂²×D₁₉	—	4	2	no	—
204	C₂²×D₁₉	—	4	2	no	—
205	C₂²×D₁₉	—	4	2	no	—
206	C₂²×D₁₉	—	4	2	no	—
207	C₂²×D₁₉	C₂⁴	1	2	yes	—
208	C₂²×D₁₉	C₂⁴	1	2	yes	—
209	C₂²×D₁₉	C₂⁴	1	2	yes	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	4	1	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	D₄×C₁₉	—	2	4	no	—
216	D₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
225	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
226	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
227	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂²⋊D₁₉	—	2	4	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	—	4	2	no	—
236	C₂×Dic₁₉	—	4	2	no	—
237	C₂×Dic₁₉	C₂⁴	1	2	yes	—
238	C₂×Dic₁₉	C₂⁴	1	2	yes	—
239	C₂×Dic₁₉	C₂⁴	1	2	yes	—
240	C₂×Dic₁₉	C₂⁴	1	2	yes	—
241	C₂×Dic₁₉	C₂⁴	1	2	yes	—
242	D₇₆	—	4	1	no	—
243	D₇₆	—	4	2	no	—
244	D₇₆	—	4	1	no	—
245	D₇₆	—	4	2	no	—
246	D₇₆	—	4	2	no	—
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	C₄×D₁₉	—	4	2	no	—
253	C₄×D₁₉	—	4	2	no	—
254	Dic₃₈	—	4	2	no	—
255	Dic₃₈	—	4	1	no	—
256	#3545	—	19	1	no	maximal, Sylow
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	H(5,𝔽₂)	1	2	yes	—
262	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
263	C₂×D₁₉	—	2	2	no	—
264	C₂×D₁₉	—	2	2	no	—
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	—	2	2	no	—
272	C₂×D₁₉	—	8	4	no	—
273	C₂×D₁₉	—	8	4	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	2	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	C₄×C₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	2	no	—
283	Dic₁₉	—	2	2	no	—
284	Dic₁₉	—	2	2	no	—
285	Dic₁₉	—	2	2	no	—
286	Dic₁₉	—	2	2	no	—
287	Dic₁₉	—	2	2	no	—
288	#563	—	19	1	no	—
289	#562	—	19	2	no	—
290	H(3,𝔽₄)	—	19	1	no	—
291	#555	—	19	1	no	—
292	#555	—	19	1	no	—
293	#551	—	19	2	no	—
294	#551	—	19	2	no	—
295	#551	—	19	2	no	—
296	#546	—	19	2	no	—
297	#546	—	19	2	no	—
298	#542	—	19	2	no	—
299	#542	—	19	2	no	—
300	#538	—	19	2	no	—
301	#538	—	19	2	no	—
302	#536	—	19	1	no	—
303	#536	D₁₉	1	1	yes	characteristic, complemented
304	#534	—	19	2	no	—
305	#529	—	19	2	no	—
306	C₂×#124	—	19	1	no	—
307	C₂×C₁₉	—	2	2	no	—
308	C₂×C₁₉	—	4	2	no	—
309	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₁₉	#585	1	2	yes	—
311	D₁₉	—	4	2	no	—
312	D₁₉	—	4	2	no	—
313	D₁₉	—	4	2	no	—
314	C₂×#41	—	19	1	no	—
315	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
316	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
317	C₂²×D₄	—	19	2	no	—
318	C₂²×D₄	—	19	1	no	—
319	C₄⋊Q₈	—	19	1	no	—
320	C₄⋊Q₈	—	19	1	no	—
321	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
322	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
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	#124	—	19	1	no	—
331	#124	—	19	1	no	—
332	#124	—	19	2	no	—
333	#124	—	19	2	no	—
334	#124	—	19	1	no	—
335	#124	—	19	1	no	—
336	#124	—	19	1	no	—
337	#124	—	19	1	no	—
338	#124	—	19	2	no	—
339	#124	—	19	2	no	—
340	#124	—	19	2	no	—
341	#124	—	19	2	no	—
342	#124	—	19	2	no	—
343	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
344	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
345	#123	—	19	2	no	—
346	#123	—	19	2	no	—
347	#123	—	19	2	no	—
348	#123	—	19	2	no	—
349	#123	—	19	2	no	—
350	#123	—	19	2	no	—
351	#123	—	19	2	no	—
352	#123	—	19	2	no	—
353	#123	—	19	2	no	—
354	#123	—	19	2	no	—
355	#123	C₂×D₁₉	1	2	yes	complemented
356	#123	C₂×D₁₉	1	2	yes	complemented
357	C₂²⋊Q₈	—	19	2	no	—
358	C₂²⋊Q₈	—	19	2	no	—
359	C₂²⋊Q₈	—	19	2	no	—
360	C₂²⋊Q₈	—	19	2	no	—
361	C₂²⋊Q₈	—	19	2	no	—
362	C₂²⋊Q₈	—	19	2	no	—
363	C₂²⋊Q₈	—	19	2	no	—
364	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
365	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
366	#121	—	19	2	no	—
367	#121	—	19	2	no	—
368	#121	—	19	2	no	—
369	#121	—	19	2	no	—
370	#121	—	19	2	no	—
371	#121	—	19	2	no	—
372	#121	—	19	2	no	—
373	#121	—	19	2	no	—
374	#121	—	19	2	no	—
375	#120	—	19	2	no	—
376	#120	—	19	2	no	—
377	#120	—	19	2	no	—
378	#120	—	19	2	no	—
379	#120	—	19	2	no	—
380	#120	—	19	2	no	—
381	C₄×Q₈	—	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	2	no	—
386	C₄×D₄	—	19	2	no	—
387	C₄×D₄	—	19	2	no	—
388	C₄×D₄	—	19	2	no	—
389	#117	—	19	1	no	—
390	#117	—	19	2	no	—
391	#117	—	19	2	no	—
392	#117	—	19	2	no	—
393	#117	—	19	2	no	—
394	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
395	C₂×C₂²⋊C₄	—	19	2	no	—
396	C₂×C₂²⋊C₄	—	19	2	no	—
397	C₂×C₂²⋊C₄	—	19	2	no	—
398	C₂×C₂²⋊C₄	—	19	2	no	—
399	C₂×C₂²⋊C₄	—	19	2	no	—
400	C₂×C₄²	—	19	1	no	—
401	C₁₉	#3545	1	1	yes	characteristic, complemented, Sylow
402	C₂⁴	—	19	2	no	—
403	C₂⁴	—	19	2	no	—
404	#41	—	4	2	no	—
405	#41	—	76	2	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	19	2	no	—
408	C₂×Q₈	—	19	1	no	—
409	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
410	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
412	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
413	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
414	C₂×D₄	—	19	2	no	—
415	C₂×D₄	—	19	2	no	—
416	C₂×D₄	—	19	2	no	—
417	C₂×D₄	—	19	2	no	—
418	C₂×D₄	—	19	2	no	—
419	C₂×D₄	—	19	2	no	—
420	C₂×D₄	—	19	2	no	—
421	C₂×D₄	—	19	1	no	—
422	C₂×D₄	—	19	1	no	—
423	C₂×D₄	—	19	2	no	—
424	C₂×D₄	—	19	2	no	—
425	C₂×D₄	—	19	1	no	—
426	C₂×D₄	—	76	2	no	—
427	C₂×D₄	—	76	4	no	—
428	C₂×D₄	C₂²×D₁₉	1	2	yes	—
429	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
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	—	19	2	no	—
435	C₂²×C₄	—	19	2	no	—
436	C₂²×C₄	—	19	2	no	—
437	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
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	C₂²×D₁₉	1	2	yes	—
453	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
454	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
455	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
456	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
457	C₂²⋊C₄	—	19	2	no	—
458	C₂²⋊C₄	—	19	2	no	—
459	C₂²⋊C₄	—	19	2	no	—
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	C₂²×D₁₉	1	2	yes	—
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	1	no	—
486	C₄²	—	19	2	no	—
487	C₄²	—	19	1	no	—
488	C₄²	—	19	1	no	—
489	C₄²	—	19	2	no	—
490	C₄²	—	19	2	no	—
491	C₄²	—	19	1	no	—
492	C₄²	C₂²×D₁₉	1	1	yes	characteristic
493	C₄²	C₂²×D₁₉	1	1	yes	characteristic
494	C₂³	—	19	2	no	—
495	C₂³	—	19	2	no	—
496	C₂³	—	19	2	no	—
497	C₂³	—	38	4	no	—
498	C₂³	—	76	2	no	—
499	C₂³	—	76	2	no	—
500	C₂³	—	76	2	no	—
501	C₂³	—	76	2	no	—
502	C₂³	—	76	2	no	—
503	C₂³	C₂³×D₁₉	1	2	yes	—
504	C₂³	C₂³×D₁₉	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	76	1	no	—
511	Q₈	—	76	2	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	1	no	—
514	D₄	—	38	4	no	—
515	D₄	—	76	1	no	—
516	D₄	—	76	2	no	—
517	D₄	—	76	1	no	—
518	D₄	—	76	2	no	—
519	D₄	—	76	1	no	—
520	D₄	—	76	2	no	—
521	D₄	—	76	2	no	—
522	D₄	—	76	2	no	—
523	D₄	—	76	2	no	—
524	D₄	—	76	2	no	—
525	D₄	—	76	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	19	2	no	—
531	C₂×C₄	—	19	2	no	—
532	C₂×C₄	—	19	2	no	—
533	C₂×C₄	—	19	2	no	—
534	C₂×C₄	—	19	2	no	—
535	C₂×C₄	—	76	2	no	—
536	C₂×C₄	—	76	2	no	—
537	C₂×C₄	—	76	2	no	—
538	C₂×C₄	—	76	2	no	—
539	C₂×C₄	—	76	2	no	—
540	C₂×C₄	—	76	2	no	—
541	C₂×C₄	—	76	2	no	—
542	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₁₉	1	2	yes	—
546	C₂×C₄	C₂³×D₁₉	1	2	yes	—
547	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₁₉	1	2	yes	—
549	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	38	2	no	—
556	C₂²	—	38	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	—	38	2	no	—
564	C₂²	—	152	4	no	—
565	C₂²	—	152	4	no	—
566	C₂²	#10597430	1	2	yes	—
567	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	38	2	no	—
578	C₄	—	38	2	no	—
579	C₄	—	38	2	no	—
580	C₄	—	38	2	no	—
581	C₄	—	38	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	76	2	no	—
585	C₂	—	76	2	no	—
586	C₂	—	76	2	no	—
587	C₂	C₂×#10597430	1	1	yes	characteristic
588	C₂	#11927381	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#536	C₂
hypercenter	#536	D₁₉
hypocenter	C₁₉	#3545
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #11927293	C₂	semidirect
2. #11927290	C₂	semidirect
3. #11927286	C₂	semidirect
4. #11927260	C₂	semidirect
5. #11927256	C₂	semidirect
6. #11927221	C₂	semidirect
7. #11927218	C₂	semidirect
8. #11927217	C₂	semidirect
9. #11927186	C₂	semidirect
10. #11927182	C₂	semidirect
11. #11927168	C₂	semidirect
12. #11927164	C₂	semidirect
13. #11927134	C₂	semidirect
14. #11927128	C₂	semidirect
15. #11927118	C₂	semidirect
16. #11927105	C₂	semidirect
17. #11927071	C₂	semidirect
18. C₂×#10597393	C₂	semidirect
19. C₁₉×#536	C₂	semidirect
21. C₂²×Q₈×C₁₉	C₂²	semidirect
22. C₂×D₄×D₁₉	C₂²	semidirect
25. C₁₉×C₄⋊Q₈	C₂²	semidirect
26. C₁₉×C₄⋊Q₈	C₂²	semidirect
27. C₁₉×#124	C₂²	semidirect
28. C₁₉×#124	C₂²	semidirect
29. C₁₉×#123	C₂²	semidirect
30. C₁₉×#123	C₂²	semidirect
31. C₁₉×C₂²⋊Q₈	C₂²	semidirect
32. C₁₉×C₂²⋊Q₈	C₂²	semidirect
33. C₁₉×#117	C₂²	semidirect
36. #10597393	C₂²	semidirect
37. #10597393	C₂²	semidirect
38. #10597393	C₂²	semidirect
39. #10597393	C₂²	semidirect
40. #10597393	C₂²	semidirect
41. #10597393	C₂²	semidirect
42. #10597393	C₂²	semidirect
43. #10597392	C₂²	semidirect
44. #10597392	C₂²	semidirect
45. #10597392	C₂²	semidirect
46. #10597390	C₂²	semidirect
47. #10597390	C₂²	semidirect
49. #10597385	C₂²	semidirect
51. #10597383	C₂²	semidirect
52. D₄×Dic₁₉	C₂²	semidirect
53. #10597376	C₂²	semidirect
54. #10597375	C₂²	semidirect
55. #10597375	C₂²	semidirect
56. #10597375	C₂²	semidirect
57. C₄×C₂²⋊D₁₉	C₂²	semidirect
58. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
59. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
60. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
61. #10597372	C₂²	semidirect
62. C₂×C₄×Dic₁₉	C₂²	semidirect
63. #10597344	C₂²	semidirect
64. #10597344	C₂²	semidirect
65. #10597344	C₂²	semidirect
66. #10597344	C₂²	semidirect
67. #10597343	C₂²	semidirect
68. #10597342	C₂²	semidirect
69. #10597342	C₂²	semidirect
71. #10597341	C₂²	semidirect
72. #10597341	C₂²	semidirect
74. #10597340	C₂²	semidirect
75. #10597340	C₂²	semidirect
76. #10597340	C₂²	semidirect
77. #10597340	C₂²	semidirect
78. #10597339	C₂²	semidirect
79. #10597338	C₂²	semidirect
80. #10597338	C₂²	semidirect
81. #10597335	C₂²	semidirect
82. #10597333	C₂²	semidirect
83. #10597332	C₂²	semidirect
84. #10597331	C₂²	semidirect
85. #10597331	C₂²	semidirect
86. #10597331	C₂²	semidirect
88. #10597330	C₂²	semidirect
89. #10597330	C₂²	semidirect
90. #10597329	C₂²	semidirect
93. #10597328	C₂²	semidirect
94. #10597328	C₂²	semidirect
95. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
96. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
97. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
98. C₂²⋊C₄×D₁₉	C₂²	semidirect
99. C₂²⋊C₄×D₁₉	C₂²	semidirect
100. #10597325	C₂²	semidirect
101. #10597324	C₂²	semidirect
102. #10597323	C₂²	semidirect
103. #10597322	C₂²	semidirect
104. #10597321	C₂²	semidirect
105. C₄×D₇₆	C₂²	semidirect
106. #10597318	C₂²	semidirect
303. #536	D₁₉	semidirect
316. C₂²×Q₈	C₂×D₁₉	semidirect
321. C₄⋊Q₈	C₂×D₁₉	semidirect
322. C₄⋊Q₈	C₂×D₁₉	semidirect
343. #124	C₂×D₁₉	semidirect
344. #124	C₂×D₁₉	semidirect
355. #123	C₂×D₁₉	semidirect
356. #123	C₂×D₁₉	semidirect
364. C₂²⋊Q₈	C₂×D₁₉	semidirect
365. C₂²⋊Q₈	C₂×D₁₉	semidirect
394. #117	C₂×D₁₉	semidirect
401. C₁₉	#3545	semidirect

Maximal subgroups

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

subgroup	index
#11927293	2
#11927290	2
#11927286	2
#11927260	2
#11927256	2
#11927221	2
#11927218	2
#11927217	2
#11927186	2
#11927182	2
#11927168	2
#11927164	2
#11927134	2
#11927128	2
#11927118	2
#11927105	2
#11927071	2
C₂×#10597393	2
C₁₉×#536	2
#3545	19