Subgroups — #15869191

Order 3328.

1140 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718688	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718687	C₂	1	2	yes	maximal, complemented
3	C₄×#88128	C₂	1	1	yes	maximal, characteristic
4	#13115763	C₂	1	1	yes	maximal, characteristic
5	#13115594	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115456	C₂	1	2	yes	maximal, complemented
7	#13115191	C₂	1	2	yes	maximal, complemented
8	#13114841	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114689	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114664	C₂	1	2	yes	maximal, complemented
11	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×#6106	C₂²	1	2	yes	—
16	C₂×#88128	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₅₂	—	2	1	no	—
18	C₂×C₄×D₅₂	—	2	1	no	—
19	C₂×C₄×D₅₂	C₂²	1	2	yes	—
20	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
21	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
22	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄³×C₁₃	—	2	1	no	—
27	C₄³×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×#88075	C₂²	1	2	yes	—
29	#11718688	C₄	1	8	yes	complemented
30	#11718687	—	2	8	no	—
31	C₂×#88049	C₂²	1	2	yes	—
32	C₂×#88049	C₂²	1	2	yes	—
33	C₂×#88049	C₂²	1	2	yes	—
34	C₂×#88047	C₂²	1	2	yes	—
35	#11718600	—	2	1	no	—
36	#11718600	—	2	1	no	—
37	#11718600	C₂²	1	2	yes	—
38	#11718596	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
41	C₂×#88043	C₂²	1	2	yes	—
42	#11718121	C₂²	1	2	yes	—
43	#11718121	C₂²	1	2	yes	—
44	#11718116	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×D₅₂	—	2	1	no	—
47	C₂²×D₅₂	—	2	1	no	—
48	C₂²×D₅₂	C₂³	1	2	yes	—
49	C₂²×C₄×D₁₃	—	2	2	no	—
50	C₄×Q₈×C₁₃	—	2	2	no	—
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×Q₈×C₁₃	—	2	2	no	—
54	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
55	C₄×Q₈×C₁₃	D₄	1	4	yes	complemented
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	—	2	1	no	—
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×#6106	—	2	4	no	—
76	C₂×#6106	—	2	4	no	—
77	C₂×#6106	C₂×C₄	1	8	yes	complemented
78	C₂×#6103	—	2	2	no	—
79	C₂×#6103	—	2	2	no	—
80	C₂×#6103	—	2	2	no	—
81	C₂×C₄⋊Dic₁₃	—	2	1	no	—
82	C₂×C₄⋊Dic₁₃	—	2	1	no	—
83	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
84	C₂²×#1055	C₂³	1	2	yes	—
85	C₂²×#1055	C₂³	1	2	yes	—
86	#88128	—	2	2	no	—
87	#88128	C₂×C₄	1	4	yes	—
88	C₄×D₅₂	—	2	4	no	—
89	C₄×D₅₂	—	2	4	no	—
90	C₄×D₅₂	—	4	4	no	—
91	C₄×D₅₂	—	4	4	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	1	no	—
94	C₁₃×#95	—	2	1	no	—
95	#88075	—	2	4	no	—
96	#88049	—	2	4	no	—
97	#88049	—	2	4	no	—
98	#88049	C₂×C₄	1	8	yes	complemented
99	#88047	—	2	4	no	—
100	C₄⋊#1055	—	2	2	no	—
101	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
102	#88043	—	2	4	no	—
103	#21505	—	13	1	no	maximal, Sylow
104	C₂³×D₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×Q₈×C₁₃	#41	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₂²×Dic₁₃	—	2	2	no	—
123	C₂×D₅₂	—	2	2	no	—
124	C₂×D₅₂	—	2	2	no	—
125	C₂×D₅₂	—	2	2	no	—
126	C₂×D₅₂	—	2	2	no	—
127	C₂×D₅₂	—	2	4	no	—
128	C₂×D₅₂	—	2	4	no	—
129	C₂×D₅₂	—	2	2	no	—
130	C₂×D₅₂	—	4	2	no	—
131	C₂×D₅₂	—	4	2	no	—
132	C₂×D₅₂	—	4	2	no	—
133	C₂×D₅₂	—	4	2	no	—
134	C₂×D₅₂	C₂²×C₄	1	4	yes	—
135	C₂×C₄×D₁₃	—	4	4	no	—
136	C₂×C₄×D₁₃	—	4	4	no	—
137	C₂×C₄×D₁₃	—	4	4	no	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
145	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
146	C₁₃×C₄⋊C₄	#41	1	2	yes	—
147	C₄²×C₁₃	—	2	4	no	—
148	C₄²×C₁₃	—	2	4	no	—
149	C₄²×C₁₃	—	2	4	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	2	1	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	4	1	no	—
156	C₄²×C₁₃	—	4	2	no	—
157	C₄²×C₁₃	—	4	2	no	—
158	C₄²×C₁₃	—	4	2	no	—
159	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
160	C₄²×C₁₃	C₂×D₄	1	2	yes	—
161	C₄²×C₁₃	#41	1	2	yes	—
162	C₄²×C₁₃	#41	1	2	yes	—
163	#6106	—	2	16	no	—
164	#6103	—	4	4	no	—
165	#6103	—	4	4	no	—
166	#6103	—	4	4	no	—
167	C₄⋊Dic₁₃	—	2	2	no	—
168	C₄⋊Dic₁₃	—	2	2	no	—
169	C₄⋊Dic₁₃	—	4	2	no	—
170	C₄⋊Dic₁₃	—	4	2	no	—
171	C₂×#1055	—	2	2	no	—
172	C₂×#1055	—	2	2	no	—
173	C₂×#1055	—	2	2	no	—
174	C₂×#1055	—	2	2	no	—
175	C₂×#1055	—	2	2	no	—
176	C₂×#1055	C₂²×C₄	1	4	yes	—
177	C₂×#460	—	13	1	no	—
178	C₂×#440	—	13	2	no	—
179	C₄×#127	—	13	1	no	—
180	C₄²×Q₈	D₁₃	1	1	yes	characteristic, complemented
181	#1982	—	13	1	no	—
182	#1947	—	13	1	no	—
183	#1925	—	13	2	no	—
184	#1880	—	13	2	no	—
185	#1803	—	13	1	no	—
186	#1767	—	13	1	no	—
187	#1762	—	13	2	no	—
188	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂²×D₁₃	—	2	4	no	—
190	C₂²×D₁₃	—	4	2	no	—
191	C₂²×D₁₃	—	4	2	no	—
192	C₂²×D₁₃	—	4	2	no	—
193	C₂²×D₁₃	—	4	2	no	—
194	C₂²×D₁₃	—	4	2	no	—
195	C₂²×D₁₃	—	4	2	no	—
196	Q₈×C₁₃	—	2	2	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	2	2	no	—
199	Q₈×C₁₃	C₄×D₄	1	4	yes	complemented
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₁₃	#121	1	2	yes	—
226	C₂×C₄×C₁₃	#121	1	2	yes	—
227	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₁₃	#137	1	2	yes	—
230	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₂×Dic₁₃	—	4	2	no	—
237	C₂×Dic₁₃	—	4	2	no	—
238	C₂×Dic₁₃	—	4	2	no	—
239	D₅₂	—	2	4	no	—
240	D₅₂	—	2	4	no	—
241	D₅₂	—	4	8	no	—
242	D₅₂	—	4	2	no	—
243	D₅₂	—	4	2	no	—
244	D₅₂	—	4	8	no	—
245	C₄×D₁₃	—	8	8	no	—
246	#1055	—	2	4	no	—
247	#1055	—	4	2	no	—
248	C₂²×SD₁₆	—	13	2	no	—
249	C₂×#127	—	13	1	no	—
250	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
253	C₂×C₄×D₄	—	13	2	no	—
254	C₂×C₄×D₄	—	26	1	no	—
255	C₂×C₄×D₄	—	26	1	no	—
256	#460	—	13	8	no	—
257	#440	—	26	8	no	—
258	C₂×#107	—	13	2	no	—
259	C₂×C₄⋊C₈	—	13	1	no	—
260	C₂×C₄⋊C₈	—	13	1	no	—
261	C₂×#103	—	13	2	no	—
262	C₂×#102	—	13	2	no	—
263	C₂×#102	—	13	2	no	—
264	C₂×#102	—	13	2	no	—
265	C₂×#97	—	13	2	no	—
266	#390	—	13	2	no	—
267	#390	—	26	1	no	—
268	#390	—	26	1	no	—
269	#384	—	13	1	no	—
270	C₄×C₄⋊C₄	—	2	1	no	—
271	C₄×C₄⋊C₄	—	2	1	no	—
272	C₄×C₄⋊C₄	—	2	1	no	—
273	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
275	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
276	C₄³	—	2	1	no	—
277	C₄³	C₂×D₁₃	1	1	yes	characteristic
278	#340	—	13	2	no	—
279	#340	—	13	2	no	—
280	#336	—	13	2	no	—
281	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
283	C₂²×C₁₃	#525	1	1	yes	characteristic
284	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
287	C₂²×C₁₃	#575	1	1	yes	characteristic
288	C₂×D₁₃	—	4	4	no	—
289	C₂×D₁₃	—	4	4	no	—
290	C₂×D₁₃	—	4	4	no	—
291	C₂×D₁₃	—	8	2	no	—
292	C₂×D₁₃	—	8	2	no	—
293	C₂×D₁₃	—	8	2	no	—
294	C₂×D₁₃	—	8	2	no	—
295	C₄×C₁₃	—	2	2	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	2	4	no	—
300	C₄×C₁₃	—	4	1	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	#440	1	4	yes	complemented
305	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
306	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
307	C₄×C₁₃	#529	1	1	yes	characteristic
308	C₄×C₁₃	#532	1	1	yes	characteristic
309	Dic₁₃	—	8	2	no	—
310	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₂²×D₄	—	13	2	no	—
312	C₂²×D₄	—	26	1	no	—
313	C₂²×D₄	—	26	1	no	—
314	C₂³×C₄	—	26	2	no	—
315	C₂×SD₁₆	—	13	8	no	—
316	C₂×SD₁₆	—	26	4	no	—
317	C₂×SD₁₆	—	26	4	no	—
318	C₂²×C₈	—	13	2	no	—
319	C₂²×C₈	—	13	2	no	—
320	#127	—	13	4	no	—
321	#127	—	26	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	C₄×D₁₃	1	4	yes	complemented
327	C₄×Q₈	D₅₂	1	4	yes	complemented
328	C₄×D₄	—	26	4	no	—
329	C₄×D₄	—	26	4	no	—
330	C₄×D₄	—	52	4	no	—
331	C₄×D₄	—	52	4	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	13	2	no	—
336	C₂×C₄⋊C₄	—	26	1	no	—
337	C₂×C₄⋊C₄	—	26	1	no	—
338	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	26	2	no	—
342	C₂×C₂²⋊C₄	—	26	2	no	—
343	C₂×C₂²⋊C₄	—	26	2	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
351	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
352	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
353	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
354	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
357	#107	—	26	4	no	—
358	C₄⋊C₈	—	13	4	no	—
359	C₄⋊C₈	—	26	2	no	—
360	#103	—	26	4	no	—
361	#102	—	13	8	no	—
362	#102	—	26	4	no	—
363	#102	—	26	4	no	—
364	#97	—	26	4	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
369	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
370	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
371	C₂×C₁₃	#3037	1	1	yes	characteristic
372	C₂×C₁₃	#3038	1	1	yes	characteristic
373	C₂×C₁₃	#3112	1	1	yes	characteristic
374	C₂×C₁₃	#3115	1	1	yes	characteristic
375	D₁₃	—	8	4	no	—
376	C₂⁴	—	26	2	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
381	C₂×Q₈	C₂×D₅₂	1	2	yes	—
382	C₂×Q₈	#6127	1	2	yes	—
383	C₂×D₄	—	13	4	no	—
384	C₂×D₄	—	26	4	no	—
385	C₂×D₄	—	26	4	no	—
386	C₂×D₄	—	26	2	no	—
387	C₂×D₄	—	26	2	no	—
388	C₂×D₄	—	26	2	no	—
389	C₂×D₄	—	26	2	no	—
390	C₂×D₄	—	26	2	no	—
391	C₂×D₄	—	52	2	no	—
392	C₂×D₄	—	52	2	no	—
393	C₂×D₄	—	52	2	no	—
394	C₂×D₄	—	52	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	26	2	no	—
400	C₂²×C₄	—	52	4	no	—
401	C₂²×C₄	—	52	4	no	—
402	C₂²×C₄	—	52	4	no	—
403	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
410	SD₁₆	—	26	16	no	—
411	C₂×C₈	—	13	4	no	—
412	C₂×C₈	—	26	2	no	—
413	C₂×C₈	—	26	2	no	—
414	C₂×C₈	—	26	2	no	—
415	C₂×C₈	—	26	2	no	—
416	C₂×C₈	—	26	2	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	26	2	no	—
424	C₄⋊C₄	—	26	2	no	—
425	C₄⋊C₄	—	52	2	no	—
426	C₄⋊C₄	—	52	2	no	—
427	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
428	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
429	C₄⋊C₄	#6127	1	2	yes	—
430	C₂²⋊C₄	—	52	4	no	—
431	C₂²⋊C₄	—	52	4	no	—
432	C₂²⋊C₄	—	52	4	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	2	4	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	4	1	no	—
442	C₄²	—	4	2	no	—
443	C₄²	—	4	2	no	—
444	C₄²	—	4	2	no	—
445	C₄²	C₂×C₄×D₁₃	1	2	yes	—
446	C₄²	C₂×D₅₂	1	2	yes	—
447	C₄²	#6127	1	2	yes	—
448	C₄²	#6127	1	2	yes	—
449	C₁₃	#21505	1	1	yes	characteristic, complemented, Sylow
450	C₂³	—	26	4	no	—
451	C₂³	—	52	2	no	—
452	C₂³	—	52	2	no	—
453	C₂³	—	52	2	no	—
454	C₂³	—	52	2	no	—
455	C₂³	—	52	2	no	—
456	C₂³	—	52	2	no	—
457	C₂³	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	2	2	no	—
461	Q₈	C₄×D₅₂	1	4	yes	complemented
462	D₄	—	26	4	no	—
463	D₄	—	26	4	no	—
464	D₄	—	52	8	no	—
465	D₄	—	52	2	no	—
466	D₄	—	52	2	no	—
467	D₄	—	52	8	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	52	2	no	—
492	C₂×C₄	—	52	2	no	—
493	C₂×C₄	—	52	2	no	—
494	C₂×C₄	—	104	8	no	—
495	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
496	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
497	C₂×C₄	#88184	1	2	yes	—
498	C₂×C₄	#88184	1	2	yes	—
499	C₂×C₄	#88196	1	2	yes	—
500	C₂×C₄	#88203	1	2	yes	—
501	C₂×C₄	#88203	1	2	yes	—
502	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
504	C₂×C₄	C₂×#6127	1	1	yes	characteristic
505	C₂×C₄	C₂×#6127	1	1	yes	characteristic
506	C₂×C₄	C₂×#6127	1	1	yes	characteristic
507	C₂×C₄	C₂×#6127	1	1	yes	characteristic
508	C₈	—	26	4	no	—
509	C₈	—	52	2	no	—
510	C₂²	—	52	4	no	—
511	C₂²	—	52	4	no	—
512	C₂²	—	52	4	no	—
513	C₂²	—	104	2	no	—
514	C₂²	—	104	2	no	—
515	C₂²	—	104	2	no	—
516	C₂²	—	104	2	no	—
517	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
518	C₂²	C₂×#88184	1	1	yes	characteristic
519	C₂²	#11719496	1	1	yes	characteristic
520	C₂²	C₂×#88196	1	1	yes	characteristic
521	C₂²	C₂×#88203	1	1	yes	characteristic
522	C₂²	C₂×#88203	1	1	yes	characteristic
523	C₂²	#11719527	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	4	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	2	no	—
533	C₄	—	104	2	no	—
534	C₄	#11718687	1	4	yes	complemented
535	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
536	C₄	C₄×#6127	1	1	yes	characteristic
537	C₄	#11719182	1	1	yes	characteristic
538	C₄	#11719184	1	1	yes	characteristic
539	C₂	—	104	4	no	—
540	C₂	C₄×#88184	1	1	yes	characteristic
541	C₂	C₂×#11718687	1	1	yes	characteristic
542	C₂	C₄×#88203	1	1	yes	characteristic
543	C₂	#13124308	1	1	yes	characteristic
544	C₂	#13124316	1	1	yes	characteristic
545	C₂	#13124958	1	1	yes	characteristic
546	C₂	#13124987	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄²×Q₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂×#88128	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄²×Q₈	D₁₃
hypocenter	C₁₃	#21505
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11718687	C₂	semidirect
5. #13115594	C₂	semidirect
6. #13115456	C₂	semidirect
7. #13115191	C₂	semidirect
8. #13114841	C₂	semidirect
9. #13114689	C₂	semidirect
10. #13114664	C₂	semidirect
11. C₄²×Q₈×C₁₃	C₂	semidirect
29. #11718688	C₄	semidirect
54. C₄×Q₈×C₁₃	C₂×C₄	semidirect
55. C₄×Q₈×C₁₃	D₄	semidirect
77. C₂×#6106	C₂×C₄	semidirect
98. #88049	C₂×C₄	semidirect
101. C₄⋊#1055	C₂×C₄	semidirect
180. C₄²×Q₈	D₁₃	semidirect
199. Q₈×C₁₃	C₄×D₄	semidirect
304. C₄×C₁₃	#440	semidirect
326. C₄×Q₈	C₄×D₁₃	semidirect
327. C₄×Q₈	D₅₂	semidirect
449. C₁₃	#21505	semidirect
461. Q₈	C₄×D₅₂	semidirect
534. C₄	#11718687	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718688	2
C₂×#11718687	2
C₄×#88128	2
#13115763	2
#13115594	2
#13115456	2
#13115191	2
#13114841	2
#13114689	2
#13114664	2
C₄²×Q₈×C₁₃	2
#21505	13