Subgroups — #14578280

Order 2432.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927295	C₂	1	2	yes	maximal, complemented
2	#11927289	C₂	1	2	yes	maximal, complemented
3	#11927272	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927264	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927261	C₂	1	2	yes	maximal, complemented
6	#11927259	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927254	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927240	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927240	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927234	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927234	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927230	C₂	1	2	yes	maximal, complemented
13	#11927172	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927172	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927165	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927165	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927162	C₂	1	2	yes	maximal, complemented
18	#11927158	C₂	1	2	yes	maximal, complemented
19	#11927153	C₂	1	2	yes	maximal, complemented
20	#11927137	C₂	1	2	yes	maximal, complemented
21	#11927101	C₂	1	1	yes	maximal, characteristic, complemented
22	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₉×#126	C₂²	1	1	yes	characteristic
25	C₁₉×#126	C₂²	1	1	yes	characteristic
26	C₁₉×#125	C₂²	1	1	yes	characteristic
27	C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#123	C₂²	1	1	yes	characteristic
29	C₁₉×#123	C₂²	1	1	yes	characteristic
30	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₉×#121	C₂²	1	1	yes	characteristic
32	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×#117	C₂²	1	1	yes	characteristic
37	C₁₉×#117	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
39	#10597392	C₂²	1	2	yes	—
40	#10597390	C₂²	1	2	yes	—
41	#10597385	C₂²	1	2	yes	—
42	#10597385	C₂²	1	2	yes	—
43	#10597384	C₂²	1	2	yes	—
44	#10597382	C₂²	1	2	yes	—
45	#10597381	C₂²	1	2	yes	—
46	#10597381	C₂²	1	2	yes	—
47	#10597376	C₂²	1	1	yes	characteristic
48	#10597376	C₂²	1	1	yes	characteristic
49	#10597376	C₂²	1	1	yes	characteristic
50	#10597375	C₂²	1	2	yes	—
51	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
52	#10597372	C₂²	1	1	yes	characteristic
53	#10597372	C₂²	1	1	yes	characteristic
54	#10597372	C₂²	1	1	yes	characteristic
55	#10597372	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
58	#10597370	C₂²	1	1	yes	characteristic
59	#10597370	C₂²	1	2	yes	—
60	#10597370	C₂²	1	2	yes	—
61	#10597370	C₂²	1	1	yes	characteristic
62	#10597370	C₂²	1	1	yes	characteristic
63	#10597344	C₂²	1	2	yes	—
64	#10597344	C₂²	1	2	yes	—
65	#10597344	C₂²	1	2	yes	—
66	#10597344	C₂²	1	2	yes	—
67	#10597342	C₂²	1	2	yes	—
68	#10597342	C₂²	1	2	yes	—
69	#10597342	C₂²	1	2	yes	—
70	#10597342	C₂²	1	2	yes	—
71	#10597338	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
73	#10597336	C₂²	1	2	yes	—
74	#10597336	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	2	yes	—
80	#10597334	C₂²	1	2	yes	—
81	#10597333	C₂²	1	2	yes	—
82	#10597333	C₂²	1	2	yes	—
83	#10597331	C₂²	1	2	yes	—
84	#10597331	C₂²	1	2	yes	—
85	#10597331	C₂²	1	2	yes	—
86	#10597331	C₂²	1	2	yes	—
87	#10597329	C₂²	1	2	yes	—
88	#10597329	C₂²	1	2	yes	—
89	#10597329	C₂²	1	2	yes	—
90	#10597329	C₂²	1	2	yes	—
91	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
93	#10597325	C₂²	1	2	yes	—
94	#10597325	C₂²	1	2	yes	—
95	#10597325	C₂²	1	2	yes	—
96	#10597325	C₂²	1	2	yes	—
97	#10597324	C₂²	1	2	yes	—
98	#10597324	C₂²	1	2	yes	—
99	#10597324	C₂²	1	2	yes	—
100	#10597324	C₂²	1	2	yes	—
101	#10597323	C₂²	1	2	yes	—
102	#10597323	C₂²	1	2	yes	—
103	#10597322	C₂²	1	2	yes	—
104	#10597321	C₂²	1	1	yes	characteristic
105	C₄×D₇₆	C₂²	1	1	yes	characteristic
106	C₄×D₇₆	C₂²	1	1	yes	characteristic
107	C₄×D₇₆	C₂²	1	1	yes	characteristic
108	#10597318	C₂²	1	2	yes	—
109	#10597316	C₂²	1	1	yes	characteristic
110	#10597316	C₂²	1	1	yes	characteristic
111	#10597316	C₂²	1	1	yes	characteristic
112	#10597316	C₂²	1	1	yes	characteristic
113	#10597316	C₂²	1	1	yes	characteristic
114	#10597315	C₂²	1	1	yes	characteristic
115	#10597315	C₂²	1	1	yes	characteristic
116	#10597315	C₂²	1	1	yes	characteristic
117	#10597315	C₂²	1	1	yes	characteristic
118	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
119	C₄×Dic₃₈	C₂²	1	2	yes	—
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×D₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
135	C₂²×Dic₁₉	C₂³	1	2	yes	—
136	C₂²×Dic₁₉	C₂³	1	2	yes	—
137	C₂×D₇₆	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₉	C₂³	1	2	yes	—
139	C₂×C₄×D₁₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₉	C₂³	1	2	yes	—
141	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
142	C₂×Dic₃₈	C₂³	1	2	yes	—
143	C₂×Dic₃₈	C₂³	1	2	yes	—
144	C₂×Dic₃₈	C₂³	1	2	yes	—
145	C₂×Dic₃₈	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₉	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	1	yes	characteristic
152	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
156	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
157	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
158	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
159	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
161	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
162	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
163	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
165	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₄²×C₁₉	C₂³	1	1	yes	characteristic
167	C₄²×C₁₉	C₂³	1	1	yes	characteristic
168	C₄²×C₁₉	C₂³	1	1	yes	characteristic
169	C₄²×C₁₉	C₂³	1	1	yes	characteristic
170	C₄²×C₁₉	C₂³	1	1	yes	characteristic
171	C₄²×C₁₉	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
179	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
187	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₉	C₂³	1	2	yes	—
191	C₄⋊Dic₁₉	C₂³	1	2	yes	—
192	C₄⋊Dic₁₉	C₂³	1	2	yes	—
193	C₄⋊Dic₁₉	C₂³	1	2	yes	—
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	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	2	yes	—
204	Dic₁₉⋊C₄	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	2	yes	—
215	C₄×Dic₁₉	C₂³	1	2	yes	—
216	C₄×Dic₁₉	C₂³	1	2	yes	—
217	C₄×Dic₁₉	C₂³	1	2	yes	—
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	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
224	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
225	C₂²×D₁₉	C₂⁴	1	2	yes	—
226	Q₈×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₁₉	—	4	2	no	—
248	C₂²⋊D₁₉	—	4	2	no	—
249	C₂²⋊D₁₉	—	4	2	no	—
250	C₂×Dic₁₉	—	4	2	no	—
251	C₂×Dic₁₉	—	4	2	no	—
252	C₂×Dic₁₉	C₂⁴	1	2	yes	—
253	C₂×Dic₁₉	C₂⁴	1	2	yes	—
254	C₂×Dic₁₉	C₂⁴	1	2	yes	—
255	C₂×Dic₁₉	C₂⁴	1	2	yes	—
256	C₂×Dic₁₉	C₂⁴	1	2	yes	—
257	C₂×Dic₁₉	C₂⁴	1	2	yes	—
258	C₂×Dic₁₉	C₂⁴	1	2	yes	—
259	D₇₆	—	2	2	no	—
260	C₄×D₁₉	—	4	2	no	—
261	C₄×D₁₉	—	4	2	no	—
262	C₄×D₁₉	—	4	2	no	—
263	Dic₃₈	—	2	2	no	—
264	Dic₃₈	—	4	2	no	—
265	Dic₃₈	—	4	2	no	—
266	Dic₃₈	—	4	2	no	—
267	Dic₃₈	—	4	2	no	—
268	#3565	—	19	1	no	maximal, Sylow
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	1	no	—
275	C₂²×C₁₉	—	2	1	no	—
276	C₂²×C₁₉	—	2	1	no	—
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
279	C₂×D₁₉	—	2	2	no	—
280	C₂×D₁₉	—	2	2	no	—
281	C₂×D₁₉	—	2	2	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	1	no	—
285	C₄×C₁₉	—	2	1	no	—
286	C₄×C₁₉	—	2	1	no	—
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	2	1	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
294	Dic₁₉	—	2	2	no	—
295	Dic₁₉	—	2	2	no	—
296	Dic₁₉	—	2	2	no	—
297	Dic₁₉	—	2	2	no	—
298	Dic₁₉	—	2	2	no	—
299	Dic₁₉	—	2	2	no	—
300	Dic₁₉	—	2	2	no	—
301	#563	—	19	2	no	—
302	#562	—	19	2	no	—
303	#557	—	19	1	no	—
304	#556	—	19	2	no	—
305	#556	—	19	1	no	—
306	#555	—	19	1	no	—
307	#554	—	19	1	no	—
308	#553	—	19	1	no	—
309	#553	—	19	1	no	—
310	#552	—	19	2	no	—
311	#552	—	19	1	no	—
312	#552	—	19	1	no	—
313	#544	—	19	1	no	—
314	#544	—	19	1	no	—
315	#542	—	19	2	no	—
316	#542	—	19	2	no	—
317	#542	—	19	1	no	—
318	#542	—	19	1	no	—
319	#541	—	19	2	no	—
320	#539	—	19	2	no	—
321	#533	—	19	1	no	—
322	#529	—	19	1	no	—
323	#529	D₁₉	1	1	yes	characteristic, complemented
324	C₂×C₁₉	—	4	1	no	—
325	C₂×C₁₉	—	4	1	no	—
326	C₂×C₁₉	—	4	1	no	—
327	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
328	C₂×C₁₉	#585	1	1	yes	characteristic
329	C₂×C₁₉	#585	1	1	yes	characteristic
330	D₁₉	—	4	2	no	—
331	C₄⋊Q₈	—	19	2	no	—
332	C₄⋊Q₈	—	19	2	no	—
333	C₄⋊Q₈	—	19	2	no	—
334	C₄⋊Q₈	—	19	1	no	—
335	C₄⋊Q₈	—	19	1	no	—
336	C₄⋊Q₈	—	19	1	no	—
337	C₄⋊Q₈	—	19	1	no	—
338	#126	—	19	2	no	—
339	#126	—	19	2	no	—
340	#126	—	19	2	no	—
341	#126	—	19	2	no	—
342	#126	—	19	2	no	—
343	#126	—	19	2	no	—
344	#126	—	19	2	no	—
345	#126	—	19	2	no	—
346	#126	—	19	2	no	—
347	#126	C₂×D₁₉	1	1	yes	characteristic
348	#126	C₂×D₁₉	1	1	yes	characteristic
349	#125	—	19	2	no	—
350	#125	—	19	2	no	—
351	#125	—	19	2	no	—
352	#125	—	19	2	no	—
353	#125	—	19	2	no	—
354	#125	—	19	2	no	—
355	#125	—	19	1	no	—
356	#125	—	19	1	no	—
357	#125	—	19	1	no	—
358	#125	—	19	1	no	—
359	#125	—	19	1	no	—
360	#125	C₂×D₁₉	1	1	yes	characteristic
361	#124	—	19	2	no	—
362	#124	—	19	2	no	—
363	#124	—	19	2	no	—
364	#124	—	19	2	no	—
365	#124	—	19	2	no	—
366	#124	—	19	1	no	—
367	#124	C₂×D₁₉	1	1	yes	characteristic
368	#123	—	19	2	no	—
369	#123	—	19	2	no	—
370	#123	—	19	2	no	—
371	#123	—	19	2	no	—
372	#123	—	19	2	no	—
373	#123	—	19	2	no	—
374	#123	—	19	2	no	—
375	#123	C₂×D₁₉	1	1	yes	characteristic
376	#123	C₂×D₁₉	1	1	yes	characteristic
377	C₂²⋊Q₈	—	19	2	no	—
378	C₂²⋊Q₈	—	19	1	no	—
379	C₂²⋊Q₈	—	19	2	no	—
380	C₂²⋊Q₈	—	19	2	no	—
381	C₂²⋊Q₈	—	19	1	no	—
382	C₂²⋊Q₈	—	19	1	no	—
383	C₂²⋊Q₈	—	19	2	no	—
384	C₂²⋊Q₈	—	19	2	no	—
385	C₂²⋊Q₈	—	19	2	no	—
386	C₂²⋊Q₈	—	19	2	no	—
387	C₂²⋊Q₈	—	19	2	no	—
388	C₂²⋊Q₈	—	19	2	no	—
389	C₂²⋊Q₈	—	19	2	no	—
390	C₂²⋊Q₈	—	19	2	no	—
391	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
392	#121	—	19	2	no	—
393	#121	—	19	2	no	—
394	#121	—	19	2	no	—
395	#121	—	19	1	no	—
396	#121	—	19	1	no	—
397	#121	—	19	1	no	—
398	#121	C₂×D₁₉	1	1	yes	characteristic
399	C₄×Q₈	—	19	2	no	—
400	C₄×Q₈	—	19	2	no	—
401	C₄×Q₈	—	19	1	no	—
402	C₄×Q₈	—	19	2	no	—
403	C₄×Q₈	—	19	2	no	—
404	C₄×Q₈	—	19	1	no	—
405	C₄×Q₈	—	19	1	no	—
406	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
407	C₄×D₄	—	19	2	no	—
408	C₄×D₄	—	19	2	no	—
409	C₄×D₄	—	19	2	no	—
410	C₄×D₄	—	19	1	no	—
411	C₄×D₄	—	19	1	no	—
412	C₄×D₄	—	19	1	no	—
413	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
414	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
415	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
416	#117	—	19	1	no	—
417	#117	—	19	1	no	—
418	#117	—	19	1	no	—
419	#117	—	19	1	no	—
420	#117	—	19	2	no	—
421	#117	—	19	2	no	—
422	#117	—	19	2	no	—
423	#117	—	19	2	no	—
424	#117	C₂×D₁₉	1	1	yes	characteristic
425	#117	C₂×D₁₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	—	19	1	no	—
427	C₂×C₄⋊C₄	—	19	1	no	—
428	C₂×C₄⋊C₄	—	19	2	no	—
429	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
430	C₁₉	#3565	1	1	yes	characteristic, complemented, Sylow
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	2	no	—
436	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
437	C₂×D₄	—	19	2	no	—
438	C₂×D₄	—	19	2	no	—
439	C₂×D₄	—	19	2	no	—
440	C₂×D₄	—	19	1	no	—
441	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
442	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
443	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
444	C₂²×C₄	—	19	2	no	—
445	C₂²×C₄	—	19	2	no	—
446	C₂²×C₄	—	19	2	no	—
447	C₂²×C₄	—	19	2	no	—
448	C₂²×C₄	—	19	2	no	—
449	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	2	no	—
460	C₄⋊C₄	—	19	2	no	—
461	C₄⋊C₄	—	19	2	no	—
462	C₄⋊C₄	—	19	2	no	—
463	C₄⋊C₄	—	19	2	no	—
464	C₄⋊C₄	—	19	2	no	—
465	C₄⋊C₄	—	19	2	no	—
466	C₄⋊C₄	—	19	2	no	—
467	C₄⋊C₄	—	19	2	no	—
468	C₄⋊C₄	—	19	2	no	—
469	C₄⋊C₄	—	19	2	no	—
470	C₄⋊C₄	—	19	1	no	—
471	C₄⋊C₄	—	19	1	no	—
472	C₄⋊C₄	—	19	1	no	—
473	C₄⋊C₄	—	19	1	no	—
474	C₄⋊C₄	—	19	2	no	—
475	C₄⋊C₄	—	19	2	no	—
476	C₄⋊C₄	—	19	2	no	—
477	C₄⋊C₄	—	19	1	no	—
478	C₄⋊C₄	—	19	1	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	2	no	—
481	C₄⋊C₄	—	19	2	no	—
482	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
492	C₂²⋊C₄	—	19	2	no	—
493	C₂²⋊C₄	—	19	2	no	—
494	C₂²⋊C₄	—	19	2	no	—
495	C₂²⋊C₄	—	19	2	no	—
496	C₂²⋊C₄	—	19	2	no	—
497	C₂²⋊C₄	—	19	2	no	—
498	C₂²⋊C₄	—	19	2	no	—
499	C₂²⋊C₄	—	19	2	no	—
500	C₂²⋊C₄	—	19	2	no	—
501	C₂²⋊C₄	—	19	2	no	—
502	C₂²⋊C₄	—	19	2	no	—
503	C₂²⋊C₄	—	19	2	no	—
504	C₂²⋊C₄	—	19	2	no	—
505	C₂²⋊C₄	—	19	2	no	—
506	C₂²⋊C₄	—	19	2	no	—
507	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
508	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
509	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
510	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
512	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
513	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
515	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
516	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
517	C₄²	—	19	2	no	—
518	C₄²	—	19	2	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	C₂²×D₁₉	1	1	yes	characteristic
525	C₄²	C₂²×D₁₉	1	1	yes	characteristic
526	C₄²	C₂²×D₁₉	1	1	yes	characteristic
527	C₄²	C₂²×D₁₉	1	1	yes	characteristic
528	C₄²	C₂²×D₁₉	1	1	yes	characteristic
529	C₄²	C₂²×D₁₉	1	1	yes	characteristic
530	C₂³	—	19	2	no	—
531	C₂³	C₂³×D₁₉	1	1	yes	characteristic
532	C₂³	C₂³×D₁₉	1	1	yes	characteristic
533	C₂³	C₂³×D₁₉	1	1	yes	characteristic
534	Q₈	—	4	1	no	—
535	Q₈	—	38	2	no	—
536	Q₈	—	76	2	no	—
537	Q₈	—	76	2	no	—
538	Q₈	—	76	2	no	—
539	Q₈	—	76	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	38	2	no	—
544	D₄	—	76	2	no	—
545	D₄	—	76	2	no	—
546	D₄	—	76	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	19	2	no	—
553	C₂×C₄	—	19	2	no	—
554	C₂×C₄	—	19	2	no	—
555	C₂×C₄	—	19	2	no	—
556	C₂×C₄	—	19	2	no	—
557	C₂×C₄	—	19	2	no	—
558	C₂×C₄	—	19	2	no	—
559	C₂×C₄	—	76	2	no	—
560	C₂×C₄	—	76	2	no	—
561	C₂×C₄	—	76	2	no	—
562	C₂×C₄	—	76	2	no	—
563	C₂×C₄	—	76	2	no	—
564	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
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	1	yes	characteristic
569	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
574	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
575	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	38	2	no	—
586	C₂²	—	38	2	no	—
587	C₂²	—	38	2	no	—
588	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	38	2	no	—
601	C₄	—	38	2	no	—
602	C₄	—	38	2	no	—
603	C₄	—	38	2	no	—
604	C₄	—	38	2	no	—
605	C₄	—	38	2	no	—
606	C₄	—	38	2	no	—
607	C₄	#10597436	1	2	yes	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	76	2	no	—
612	C₂	C₂×#10597436	1	1	yes	characteristic
613	C₂	#11927380	1	1	yes	characteristic
614	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#529	C₂
hypercenter	#529	D₁₉
hypocenter	C₁₉	#3565
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #11927295	C₂	semidirect
2. #11927289	C₂	semidirect
3. #11927272	C₂	semidirect
4. #11927264	C₂	semidirect
5. #11927261	C₂	semidirect
6. #11927259	C₂	semidirect
7. #11927254	C₂	semidirect
8. #11927240	C₂	semidirect
9. #11927240	C₂	semidirect
10. #11927234	C₂	semidirect
11. #11927234	C₂	semidirect
12. #11927230	C₂	semidirect
13. #11927172	C₂	semidirect
14. #11927172	C₂	semidirect
15. #11927165	C₂	semidirect
16. #11927165	C₂	semidirect
17. #11927162	C₂	semidirect
18. #11927158	C₂	semidirect
19. #11927153	C₂	semidirect
20. #11927137	C₂	semidirect
21. #11927101	C₂	semidirect
22. #11927078	C₂	semidirect
23. C₁₉×#529	C₂	semidirect
323. #529	D₁₉	semidirect
430. C₁₉	#3565	semidirect

Maximal subgroups

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

subgroup	index
#11927295	2
#11927289	2
#11927272	2
#11927264	2
#11927261	2
#11927259	2
#11927254	2
#11927240	2
#11927234	2
#11927230	2
#11927172	2
#11927165	2
#11927162	2
#11927158	2
#11927153	2
#11927137	2
#11927101	2
#11927078	2
C₁₉×#529	2
#3565	19