Subgroups — #14577667

Order 2432.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927259	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927251	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927242	C₂	1	2	yes	maximal, complemented
4	#11927240	C₂	1	2	yes	maximal, complemented
5	#11927215	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927190	C₂	1	2	yes	maximal, complemented
7	#11927184	C₂	1	4	yes	maximal, complemented
8	D₄×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₂²⋊D₁₉	C₂	1	2	yes	maximal, complemented
10	#11927145	C₂	1	2	yes	maximal, complemented
11	#11927127	C₂	1	4	yes	maximal, complemented
12	#11927094	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927078	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927055	C₂	1	2	yes	maximal, complemented
15	C₂×#10597376	C₂	1	2	yes	maximal, complemented
16	#11927016	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
21	C₂×D₄×D₁₉	C₂²	1	2	yes	—
22	C₂×#64541	C₂²	1	2	yes	complemented
23	C₂×#64541	C₂²	1	2	yes	complemented
24	C₂²×D₇₆	C₂²	1	2	yes	complemented
25	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
28	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
30	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
33	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	#10597399	C₂²	1	4	yes	complemented
35	#10597386	C₂²	1	2	yes	complemented
36	#10597385	C₂²	1	4	yes	complemented
37	#10597384	C₂²	1	2	yes	complemented
38	#10597383	C₂²	1	4	yes	complemented
39	D₄×Dic₁₉	C₂²	1	2	yes	—
40	#10597376	C₂²	1	1	yes	characteristic
41	#10597376	C₂²	1	2	yes	complemented
42	#10597376	C₂²	1	2	yes	complemented
43	#10597376	C₂²	1	2	yes	complemented
44	#10597376	C₂²	1	4	yes	complemented
45	#10597376	C₂²	1	4	yes	complemented
46	#10597376	C₂²	1	2	yes	complemented
47	#10597376	C₂²	1	2	yes	complemented
48	#10597375	C₂²	1	4	yes	complemented
49	#10597375	C₂²	1	2	yes	complemented
50	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
51	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
52	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
53	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	complemented
54	#10597372	C₂²	1	2	yes	complemented
55	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
56	#10597370	C₂²	1	1	yes	characteristic, complemented
57	#10597370	C₂²	1	2	yes	complemented
58	#10597344	C₂²	1	4	yes	complemented
59	#10597341	C₂²	1	2	yes	complemented
60	#10597340	C₂²	1	4	yes	complemented
61	#10597339	C₂²	1	2	yes	complemented
62	#10597338	C₂²	1	2	yes	complemented
63	#10597336	C₂²	1	2	yes	complemented
64	#10597331	C₂²	1	4	yes	complemented
65	#10597330	C₂²	1	4	yes	complemented
66	#10597330	C₂²	1	4	yes	complemented
67	#10597329	C₂²	1	4	yes	complemented
68	#10597328	C₂²	1	4	yes	complemented
69	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
70	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	complemented
71	#10597324	C₂²	1	4	yes	complemented
72	#10597322	C₂²	1	2	yes	complemented
73	#10597321	C₂²	1	1	yes	characteristic, complemented
74	#10597321	C₂²	1	2	yes	complemented
75	#10597320	C₂²	1	1	yes	characteristic, complemented
76	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₇₆	C₂²	1	2	yes	complemented
78	C₄×D₇₆	C₂²	1	2	yes	complemented
79	#10597318	C₂²	1	2	yes	complemented
80	#10597316	C₂²	1	1	yes	characteristic, complemented
81	#10597315	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
83	C₂⁴×C₁₉	C₂³	1	2	yes	—
84	C₂³×D₁₉	C₂³	1	4	yes	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	C₂³	1	2	yes	—
87	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	—	4	4	no	—
90	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₁₉	—	4	8	no	—
99	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
100	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
105	C₂²×Dic₁₉	C₂³	1	4	yes	—
106	D₄×D₁₉	—	2	8	no	—
107	#64541	—	4	4	no	—
108	#64541	—	4	4	no	—
109	C₂×D₇₆	—	4	4	no	—
110	C₂×D₇₆	C₂³	1	1	yes	characteristic
111	C₂×D₇₆	C₂³	1	2	yes	—
112	C₂×D₇₆	C₂³	1	2	yes	—
113	C₂×D₇₆	C₂³	1	4	yes	—
114	C₂×D₇₆	C₂³	1	2	yes	—
115	C₂×C₄×D₁₉	C₂³	1	2	yes	—
116	C₂×C₄×D₁₉	C₂³	1	4	yes	—
117	C₂×C₄×D₁₉	C₂³	1	4	yes	—
118	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
119	C₂×Dic₃₈	C₂³	1	2	yes	—
120	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
126	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
127	C₄²×C₁₉	C₂³	1	1	yes	characteristic
128	C₄²×C₁₉	C₂³	1	1	yes	characteristic
129	C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₄²×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
132	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
133	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
134	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
135	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
136	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
137	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
138	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
139	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
140	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
141	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
142	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
143	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₁₉	C₂³	1	2	yes	—
145	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₉	C₂³	1	4	yes	—
147	C₄⋊Dic₁₉	C₂³	1	2	yes	—
148	Dic₁₉⋊C₄	C₂³	1	2	yes	—
149	Dic₁₉⋊C₄	C₂³	1	2	yes	—
150	Dic₁₉⋊C₄	C₂³	1	2	yes	—
151	Dic₁₉⋊C₄	C₂³	1	2	yes	—
152	Dic₁₉⋊C₄	C₂³	1	4	yes	—
153	C₄×Dic₁₉	C₂³	1	2	yes	—
154	C₄×Dic₁₉	C₂³	1	4	yes	—
155	C₂³×C₁₉	—	2	4	no	—
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	C₂⁴	1	2	yes	—
159	C₂³×C₁₉	C₂⁴	1	2	yes	—
160	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₂²×D₁₉	—	2	8	no	—
162	C₂²×D₁₉	—	4	4	no	—
163	C₂²×D₁₉	—	4	4	no	—
164	C₂²×D₁₉	C₂⁴	1	2	yes	—
165	C₂²×D₁₉	C₂⁴	1	4	yes	—
166	D₄×C₁₉	—	2	4	no	—
167	D₄×C₁₉	—	2	2	no	—
168	D₄×C₁₉	#41	1	4	yes	complemented
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
178	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
179	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
185	C₂²⋊D₁₉	—	2	8	no	—
186	C₂²⋊D₁₉	—	2	8	no	—
187	C₂²⋊D₁₉	—	2	4	no	—
188	C₂²⋊D₁₉	—	4	4	no	—
189	C₂²⋊D₁₉	—	4	4	no	—
190	C₂²⋊D₁₉	—	4	4	no	—
191	C₂×Dic₁₉	—	4	4	no	—
192	C₂×Dic₁₉	C₂⁴	1	2	yes	—
193	C₂×Dic₁₉	C₂⁴	1	2	yes	—
194	C₂×Dic₁₉	C₂⁴	1	2	yes	—
195	C₂×Dic₁₉	C₂⁴	1	4	yes	—
196	D₇₆	—	2	4	no	—
197	D₇₆	—	2	2	no	—
198	D₇₆	—	2	4	no	—
199	D₇₆	—	4	4	no	—
200	D₇₆	—	4	2	no	—
201	C₄×D₁₉	—	2	4	no	—
202	C₄×D₁₉	—	4	4	no	—
203	C₄×D₁₉	—	4	4	no	—
204	Dic₃₈	—	2	2	no	—
205	Dic₃₈	—	4	2	no	—
206	#3519	—	19	1	no	maximal, Sylow
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	4	8	no	—
215	C₂²×C₁₉	C₂×#41	1	4	yes	—
216	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
217	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
218	C₂×D₁₉	—	2	2	no	—
219	C₂×D₁₉	—	2	4	no	—
220	C₂×D₁₉	—	2	4	no	—
221	C₂×D₁₉	—	2	4	no	—
222	C₂×D₁₉	—	2	2	no	—
223	C₂×D₁₉	—	2	2	no	—
224	C₂×D₁₉	—	8	8	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	2	2	no	—
229	C₄×C₁₉	—	2	2	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	C₂×#41	1	2	yes	—
232	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
233	Dic₁₉	—	2	2	no	—
234	Dic₁₉	—	2	2	no	—
235	Dic₁₉	—	2	4	no	—
236	Dic₁₉	—	2	2	no	—
237	#555	—	19	1	no	—
238	#554	—	19	1	no	—
239	#553	—	19	2	no	—
240	#553	—	19	2	no	—
241	#550	—	19	1	no	—
242	#546	—	19	2	no	—
243	#546	—	19	4	no	—
244	D₄²	—	19	2	no	—
245	D₄²	—	19	1	no	—
246	#540	—	19	2	no	—
247	#538	—	19	4	no	—
248	#532	—	19	1	no	—
249	#529	—	19	1	no	—
250	#525	—	19	2	no	—
251	C₂×#121	—	19	2	no	—
252	#518	—	19	2	no	—
253	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic, complemented
254	C₂×C₁₉	—	2	4	no	—
255	C₂×C₁₉	—	2	2	no	—
256	C₂×C₁₉	—	4	2	no	—
257	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
258	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	D₁₉	—	4	4	no	—
261	D₁₉	—	4	2	no	—
262	C₂×#41	—	19	2	no	—
263	C₂×#41	—	19	2	no	—
264	C₂²×D₄	—	19	4	no	—
265	C₂²×D₄	—	19	2	no	—
266	C₂²×D₄	—	19	2	no	—
267	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
268	C₂³×C₄	C₂×D₁₉	1	2	yes	complemented
269	C₄⋊Q₈	—	19	1	no	—
270	#127	—	19	2	no	—
271	#127	—	19	1	no	—
272	#126	—	19	4	no	—
273	#126	—	19	2	no	—
274	#125	—	19	2	no	—
275	#125	—	19	1	no	—
276	#124	—	19	4	no	—
277	#124	—	19	1	no	—
278	#124	—	19	2	no	—
279	#123	—	19	4	no	—
280	#123	—	19	2	no	—
281	#123	—	19	4	no	—
282	#123	—	19	4	no	—
283	C₂²⋊Q₈	—	19	1	no	—
284	C₂²⋊Q₈	—	19	2	no	—
285	C₂²⋊Q₈	—	19	4	no	—
286	#121	—	19	2	no	—
287	#121	—	19	4	no	—
288	#121	—	19	1	no	—
289	#121	—	19	2	no	—
290	#121	—	19	4	no	—
291	#121	—	19	4	no	—
292	#121	—	19	2	no	—
293	#121	—	19	2	no	—
294	#121	—	19	2	no	—
295	#121	—	19	2	no	—
296	#121	—	19	2	no	—
297	#121	—	19	4	no	—
298	#121	—	19	4	no	—
299	#120	—	19	4	no	—
300	#120	—	19	4	no	—
301	#120	—	19	4	no	—
302	C₄×Q₈	—	19	1	no	—
303	C₄×D₄	—	19	2	no	—
304	C₄×D₄	—	19	4	no	—
305	C₄×D₄	—	19	4	no	—
306	C₄×D₄	—	19	2	no	—
307	C₄×D₄	—	19	2	no	—
308	C₄×D₄	—	19	4	no	—
309	C₄×D₄	—	19	2	no	—
310	C₄×D₄	—	19	1	no	—
311	C₄×D₄	—	19	2	no	—
312	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
313	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
314	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
315	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
316	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
317	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
318	#117	—	19	2	no	—
319	#117	—	19	2	no	—
320	#117	—	19	2	no	—
321	C₂×C₄⋊C₄	—	19	2	no	—
322	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
323	C₂×C₂²⋊C₄	—	19	4	no	—
324	C₂×C₂²⋊C₄	—	19	4	no	—
325	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	complemented
326	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
327	C₁₉	#3519	1	1	yes	characteristic, complemented, Sylow
328	C₂⁴	—	19	4	no	—
329	C₂⁴	C₂²×D₁₉	1	2	yes	—
330	#41	—	76	4	no	—
331	#41	—	76	4	no	—
332	C₂×Q₈	—	19	1	no	—
333	C₂×Q₈	—	19	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	19	4	no	—
336	C₂×D₄	—	19	4	no	—
337	C₂×D₄	—	19	2	no	—
338	C₂×D₄	—	19	4	no	—
339	C₂×D₄	—	19	4	no	—
340	C₂×D₄	—	19	4	no	—
341	C₂×D₄	—	19	2	no	—
342	C₂×D₄	—	19	1	no	—
343	C₂×D₄	—	19	2	no	—
344	C₂×D₄	—	19	2	no	—
345	C₂×D₄	—	19	4	no	—
346	C₂×D₄	—	38	8	no	—
347	C₂×D₄	—	76	4	no	—
348	C₂×D₄	—	76	8	no	—
349	C₂×D₄	C₂²×D₁₉	1	2	yes	—
350	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
351	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	19	4	no	—
354	C₂²×C₄	—	19	2	no	—
355	C₂²×C₄	—	19	4	no	—
356	C₂²×C₄	—	19	4	no	—
357	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
361	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
362	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
363	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
364	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
365	C₄⋊C₄	—	19	2	no	—
366	C₄⋊C₄	—	19	2	no	—
367	C₄⋊C₄	—	19	2	no	—
368	C₄⋊C₄	—	19	4	no	—
369	C₄⋊C₄	—	19	2	no	—
370	C₄⋊C₄	—	19	1	no	—
371	C₄⋊C₄	—	19	2	no	—
372	C₄⋊C₄	—	19	4	no	—
373	C₄⋊C₄	—	19	1	no	—
374	C₄⋊C₄	—	19	2	no	—
375	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
376	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
378	C₂²⋊C₄	—	19	4	no	—
379	C₂²⋊C₄	—	19	4	no	—
380	C₂²⋊C₄	—	19	2	no	—
381	C₂²⋊C₄	—	19	2	no	—
382	C₂²⋊C₄	—	19	4	no	—
383	C₂²⋊C₄	—	19	2	no	—
384	C₂²⋊C₄	—	19	4	no	—
385	C₂²⋊C₄	—	19	4	no	—
386	C₂²⋊C₄	—	19	2	no	—
387	C₂²⋊C₄	—	19	2	no	—
388	C₂²⋊C₄	—	19	4	no	—
389	C₂²⋊C₄	—	19	4	no	—
390	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
391	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
392	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
394	C₄²	—	19	4	no	—
395	C₄²	—	19	2	no	—
396	C₄²	C₂²×D₁₉	1	1	yes	characteristic
397	C₄²	C₂²×D₁₉	1	1	yes	characteristic
398	C₄²	C₂²×D₁₉	1	1	yes	characteristic
399	C₄²	C₂²×D₁₉	1	1	yes	characteristic
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	19	2	no	—
404	C₂³	—	19	4	no	—
405	C₂³	—	38	8	no	—
406	C₂³	—	76	4	no	—
407	C₂³	—	76	4	no	—
408	C₂³	C₂³×D₁₉	1	2	yes	—
409	C₂³	C₂³×D₁₉	1	2	yes	—
410	C₂³	C₂³×D₁₉	1	1	yes	characteristic
411	Q₈	—	38	2	no	—
412	Q₈	—	76	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	—	38	8	no	—
416	D₄	—	38	4	no	—
417	D₄	—	38	8	no	—
418	D₄	—	38	4	no	—
419	D₄	—	38	2	no	—
420	D₄	—	38	4	no	—
421	D₄	—	76	4	no	—
422	D₄	—	76	2	no	—
423	D₄	—	76	4	no	—
424	D₄	—	76	4	no	—
425	D₄	—	76	4	no	—
426	D₄	#64541	1	4	yes	complemented
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	19	2	no	—
436	C₂×C₄	—	19	2	no	—
437	C₂×C₄	—	19	4	no	—
438	C₂×C₄	—	19	2	no	—
439	C₂×C₄	—	38	4	no	—
440	C₂×C₄	—	76	4	no	—
441	C₂×C₄	—	76	4	no	—
442	C₂×C₄	—	76	4	no	—
443	C₂×C₄	C₂³×D₁₉	1	2	yes	—
444	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
448	C₂×C₄	C₂³×D₁₉	1	2	yes	—
449	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	38	2	no	—
460	C₂²	—	38	4	no	—
461	C₂²	—	38	4	no	—
462	C₂²	—	38	2	no	—
463	C₂²	—	38	4	no	—
464	C₂²	—	38	2	no	—
465	C₂²	—	152	8	no	—
466	C₂²	C₂×#64541	1	4	yes	—
467	C₂²	#10597435	1	2	yes	—
468	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	38	2	no	—
476	C₄	—	38	2	no	—
477	C₄	—	38	2	no	—
478	C₄	—	38	4	no	—
479	C₄	C₂×#64541	1	2	yes	—
480	C₄	#10597430	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	4	no	—
483	C₂	—	4	2	no	—
484	C₂	—	76	2	no	—
485	C₂	—	76	4	no	—
486	C₂	C₂²×#64541	1	1	yes	characteristic
487	C₂	C₂×#10597430	1	1	yes	characteristic
488	C₂	C₂×#10597435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂×C₄×D₄×C₁₉	C₂
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#3519
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #11927259	C₂	semidirect
2. #11927251	C₂	semidirect
3. #11927242	C₂	semidirect
4. #11927240	C₂	semidirect
5. #11927215	C₂	semidirect
6. #11927190	C₂	semidirect
7. #11927184	C₂	semidirect
8. D₄×D₇₆	C₂	semidirect
9. D₄×C₂²⋊D₁₉	C₂	semidirect
10. #11927145	C₂	semidirect
11. #11927127	C₂	semidirect
12. #11927094	C₂	semidirect
13. #11927078	C₂	semidirect
14. #11927055	C₂	semidirect
15. C₂×#10597376	C₂	semidirect
16. #11927016	C₂	semidirect
17. C₂×C₄×D₄×C₁₉	C₂	semidirect
19. C₂³×C₄×C₁₉	C₂²	semidirect
20. C₂²×C₂²⋊D₁₉	C₂²	semidirect
22. C₂×#64541	C₂²	semidirect
23. C₂×#64541	C₂²	semidirect
24. C₂²×D₇₆	C₂²	semidirect
27. C₄×D₄×C₁₉	C₂²	semidirect
28. C₄×D₄×C₁₉	C₂²	semidirect
29. C₄×D₄×C₁₉	C₂²	semidirect
30. C₄×D₄×C₁₉	C₂²	semidirect
31. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
32. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
33. C₂×C₄²×C₁₉	C₂²	semidirect
34. #10597399	C₂²	semidirect
35. #10597386	C₂²	semidirect
36. #10597385	C₂²	semidirect
37. #10597384	C₂²	semidirect
38. #10597383	C₂²	semidirect
41. #10597376	C₂²	semidirect
42. #10597376	C₂²	semidirect
43. #10597376	C₂²	semidirect
44. #10597376	C₂²	semidirect
45. #10597376	C₂²	semidirect
46. #10597376	C₂²	semidirect
47. #10597376	C₂²	semidirect
48. #10597375	C₂²	semidirect
49. #10597375	C₂²	semidirect
50. C₄×C₂²⋊D₁₉	C₂²	semidirect
51. C₄×C₂²⋊D₁₉	C₂²	semidirect
52. C₄×C₂²⋊D₁₉	C₂²	semidirect
53. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
54. #10597372	C₂²	semidirect
55. C₂×C₄⋊Dic₁₉	C₂²	semidirect
56. #10597370	C₂²	semidirect
57. #10597370	C₂²	semidirect
58. #10597344	C₂²	semidirect
59. #10597341	C₂²	semidirect
60. #10597340	C₂²	semidirect
61. #10597339	C₂²	semidirect
62. #10597338	C₂²	semidirect
63. #10597336	C₂²	semidirect
64. #10597331	C₂²	semidirect
65. #10597330	C₂²	semidirect
66. #10597330	C₂²	semidirect
67. #10597329	C₂²	semidirect
68. #10597328	C₂²	semidirect
69. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
70. C₂²⋊C₄×D₁₉	C₂²	semidirect
71. #10597324	C₂²	semidirect
72. #10597322	C₂²	semidirect
73. #10597321	C₂²	semidirect
74. #10597321	C₂²	semidirect
75. #10597320	C₂²	semidirect
76. C₄×D₇₆	C₂²	semidirect
77. C₄×D₇₆	C₂²	semidirect
78. C₄×D₇₆	C₂²	semidirect
79. #10597318	C₂²	semidirect
80. #10597316	C₂²	semidirect
81. #10597315	C₂²	semidirect
82. C₄×Dic₃₈	C₂²	semidirect
168. D₄×C₁₉	#41	semidirect
253. C₂×C₄×D₄	D₁₉	semidirect
268. C₂³×C₄	C₂×D₁₉	semidirect
314. C₄×D₄	C₂×D₁₉	semidirect
315. C₄×D₄	C₂×D₁₉	semidirect
316. C₄×D₄	C₂×D₁₉	semidirect
317. C₄×D₄	C₂×D₁₉	semidirect
322. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
325. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
326. C₂×C₄²	C₂×D₁₉	semidirect
327. C₁₉	#3519	semidirect
426. D₄	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927259	2
#11927251	2
#11927242	2
#11927240	2
#11927215	2
#11927190	2
#11927184	2
D₄×D₇₆	2
D₄×C₂²⋊D₁₉	2
#11927145	2
#11927127	2
#11927094	2
#11927078	2
#11927055	2
C₂×#10597376	2
#11927016	2
C₂×C₄×D₄×C₁₉	2
#3519	19