Subgroups — #15846830

Order 3328.

716 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125264	C₂	1	1	yes	maximal, characteristic, complemented
2	#13124987	C₂	1	2	yes	maximal, complemented
3	#13114206	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114201	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114196	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114191	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114184	C₂	1	2	yes	maximal, complemented
8	#13114177	C₂	1	2	yes	maximal, complemented
9	#13113599	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113539	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88158	—	2	1	no	—
14	C₂×#88158	—	2	1	no	—
15	#11719182	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₈×D₄×C₁₃	—	2	1	no	—
19	C₈×D₄×C₁₃	—	2	1	no	—
20	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#431	—	2	1	no	—
23	C₁₃×#431	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃	—	2	1	no	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	#11718899	—	2	2	no	—
27	#11718688	C₂²	1	2	yes	—
28	#11718687	—	2	2	no	—
29	#11718681	C₂²	1	2	yes	—
30	#11718676	C₂²	1	2	yes	—
31	#11718675	—	2	2	no	—
32	#11718668	C₂²	1	2	yes	—
33	#11718664	—	2	2	no	—
34	#11718587	C₂²	1	2	yes	—
35	#11718360	C₂²	1	1	yes	characteristic
36	#11718357	—	2	1	no	—
37	#11718357	—	2	1	no	—
38	#11718356	C₂²	1	1	yes	characteristic
39	#11718354	C₂²	1	2	yes	—
40	#11718077	C₂²	1	2	yes	—
41	#11718077	C₂²	1	2	yes	—
42	#11718074	C₂²	1	2	yes	—
43	#11718074	C₂²	1	2	yes	—
44	#11718050	C₂²	1	1	yes	characteristic
45	#11718050	C₂²	1	1	yes	characteristic
46	#11718049	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂×#6127	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₂²×C₈×C₁₃	—	2	1	no	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
58	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×#6106	—	2	2	no	—
64	C₂×#6104	—	2	2	no	—
65	#88184	—	2	2	no	—
66	#88184	—	2	2	no	—
67	C₂×Dic₅₂	—	2	1	no	—
68	C₂×Dic₅₂	—	2	1	no	—
69	#88158	—	4	4	no	—
70	#88158	—	4	4	no	—
71	C₂×D₁₀₄	—	2	1	no	—
72	C₂×D₁₀₄	—	2	1	no	—
73	C₂×#6095	—	2	2	no	—
74	C₂×#6095	—	2	2	no	—
75	#88129	—	2	2	no	—
76	#88128	C₂³	1	2	yes	—
77	C₄×D₅₂	—	2	2	no	—
78	C₄×D₅₂	—	2	2	no	—
79	#88123	C₂³	1	2	yes	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₂²⋊C₈	—	2	1	no	—
85	C₁₃×C₂²⋊C₈	—	2	1	no	—
86	C₁₃×C₂²⋊C₈	—	2	1	no	—
87	C₄×C₈×C₁₃	—	2	1	no	—
88	C₄×C₈×C₁₃	—	2	1	no	—
89	C₄×C₈×C₁₃	—	2	1	no	—
90	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	#88075	—	2	2	no	—
95	#88072	—	2	2	no	—
96	C₂²⋊#1055	—	2	2	no	—
97	#88049	—	2	2	no	—
98	#88049	—	2	2	no	—
99	#88048	—	2	2	no	—
100	#88047	—	2	2	no	—
101	C₄⋊#1055	C₂³	1	2	yes	—
102	C₄⋊#1055	C₂³	1	2	yes	—
103	#88043	—	2	2	no	—
104	#19269	—	13	1	no	maximal, Sylow
105	C₁₃×#41	—	2	2	no	—
106	C₁₃×#41	—	2	2	no	—
107	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₂×C₂²⋊D₁₃	—	4	2	no	—
117	#6127	—	4	4	no	—
118	#6127	—	4	4	no	—
119	C₂×D₅₂	—	2	2	no	—
120	C₂×D₅₂	—	2	2	no	—
121	C₂×D₅₂	—	2	2	no	—
122	C₂×C₄×D₁₃	—	4	2	no	—
123	C₂×Dic₂₆	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	4	2	no	—
129	C₂×C₈×C₁₃	—	4	2	no	—
130	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
138	C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₃	#41	1	1	yes	characteristic
147	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
148	#6106	—	4	4	no	—
149	#6104	—	4	4	no	—
150	#6103	—	4	2	no	—
151	#6103	—	4	2	no	—
152	C₄⋊Dic₁₃	—	2	2	no	—
153	C₄⋊Dic₁₃	—	2	2	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	2	no	—
156	Dic₅₂	—	4	2	no	—
157	Dic₅₂	—	4	2	no	—
158	D₁₀₄	—	4	2	no	—
159	D₁₀₄	—	4	2	no	—
160	#6095	—	4	4	no	—
161	#6095	—	4	4	no	—
162	#3147	—	13	1	no	—
163	#3115	—	13	2	no	—
164	C₈×#41	D₁₃	1	1	yes	characteristic, complemented
165	#1670	—	13	1	no	—
166	#1669	—	13	1	no	—
167	#1668	—	13	1	no	—
168	#1667	—	13	1	no	—
169	#1666	—	13	2	no	—
170	#1665	—	13	2	no	—
171	#1568	—	13	1	no	—
172	#1553	—	13	2	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	#121	1	1	yes	characteristic
175	C₂²×D₁₃	—	4	2	no	—
176	Q₈×C₁₃	—	2	1	no	—
177	Q₈×C₁₃	#135	1	2	yes	complemented
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	—	2	1	no	—
180	D₄×C₁₃	#135	1	2	yes	complemented
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂²⋊D₁₃	—	8	4	no	—
200	C₂×Dic₁₃	—	4	2	no	—
201	D₅₂	—	4	2	no	—
202	D₅₂	—	4	2	no	—
203	D₅₂	—	4	2	no	—
204	D₅₂	—	4	2	no	—
205	D₅₂	—	8	2	no	—
206	C₄×D₁₃	—	8	4	no	—
207	Dic₂₆	—	4	2	no	—
208	Dic₂₆	—	4	2	no	—
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	—	4	1	no	—
212	C₈×C₁₃	—	4	1	no	—
213	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
214	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
215	#1055	—	4	2	no	—
216	#1055	—	4	2	no	—
217	C₂×#135	—	26	1	no	—
218	C₂×#135	—	26	1	no	—
219	#532	—	13	2	no	—
220	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
221	#495	—	26	1	no	—
222	#495	—	26	1	no	—
223	#494	—	13	1	no	—
224	#493	—	13	1	no	—
225	#492	—	13	2	no	—
226	#482	—	26	2	no	—
227	#475	—	13	2	no	—
228	#474	—	13	2	no	—
229	#460	—	13	2	no	—
230	#459	—	13	2	no	—
231	#449	—	26	2	no	—
232	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
233	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
234	#442	—	26	2	no	—
235	#440	—	26	2	no	—
236	C₈×D₄	—	2	1	no	—
237	C₈×D₄	—	2	1	no	—
238	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
239	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
240	#432	—	13	2	no	—
241	#431	—	2	1	no	—
242	#431	C₂×D₁₃	1	1	yes	characteristic
243	C₂×C₄×C₈	—	2	1	no	—
244	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
245	#335	—	13	1	no	—
246	#335	—	13	1	no	—
247	#334	—	13	2	no	—
248	#332	—	13	2	no	—
249	#332	—	13	2	no	—
250	#331	—	13	2	no	—
251	#331	—	13	2	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	4	1	no	—
258	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
259	C₂×D₁₃	—	8	2	no	—
260	C₂×D₁₃	—	8	2	no	—
261	C₂×D₁₃	—	8	2	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	4	1	no	—
268	C₄×C₁₃	—	4	1	no	—
269	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
270	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
271	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	Dic₁₃	—	8	2	no	—
274	C₂×#41	—	26	2	no	—
275	C₂×#41	D₅₂	1	1	yes	characteristic
276	#135	—	52	4	no	—
277	#135	—	52	4	no	—
278	C₂×Q₁₆	—	26	1	no	—
279	C₂×Q₁₆	—	26	1	no	—
280	C₂×SD₁₆	—	26	2	no	—
281	C₂×SD₁₆	—	26	2	no	—
282	C₂×SD₁₆	—	26	2	no	—
283	C₂×D₈	—	26	2	no	—
284	C₂×D₈	—	26	1	no	—
285	C₂×D₈	—	26	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
290	C₄⋊Q₈	—	13	2	no	—
291	#127	—	13	2	no	—
292	#124	—	26	2	no	—
293	#121	—	26	2	no	—
294	#121	—	26	2	no	—
295	C₄×Q₈	D₅₂	1	1	yes	characteristic
296	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	26	2	no	—
300	C₄×D₄	—	26	2	no	—
301	C₄×D₄	D₅₂	1	1	yes	characteristic
302	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
303	#117	—	2	1	no	—
304	#117	D₅₂	1	1	yes	characteristic
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
307	#107	—	26	2	no	—
308	#106	—	26	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	13	2	no	—
312	C₄⋊C₈	—	13	2	no	—
313	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
314	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
315	#103	—	26	2	no	—
316	#102	—	26	2	no	—
317	#102	—	26	2	no	—
318	#102	—	26	2	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	26	2	no	—
323	#97	—	26	2	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	2	1	no	—
327	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
328	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
330	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
331	C₂×C₁₃	—	4	1	no	—
332	C₂×C₁₃	—	4	2	no	—
333	C₂×C₁₃	#3038	1	1	yes	characteristic
334	C₂×C₁₃	#3050	1	1	yes	characteristic
335	C₂×C₁₃	#3067	1	1	yes	characteristic
336	D₁₃	—	16	2	no	—
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	52	4	no	—
340	#41	—	52	4	no	—
341	C₂×Q₈	—	26	2	no	—
342	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	26	2	no	—
345	C₂×D₄	—	26	2	no	—
346	C₂×D₄	—	26	2	no	—
347	C₂×D₄	—	52	2	no	—
348	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	52	2	no	—
353	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
354	C₂²×C₄	#6127	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
356	Q₁₆	—	52	2	no	—
357	Q₁₆	—	52	2	no	—
358	SD₁₆	—	52	4	no	—
359	SD₁₆	—	52	4	no	—
360	SD₁₆	—	52	4	no	—
361	D₈	—	52	2	no	—
362	D₈	—	52	4	no	—
363	D₈	—	52	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	26	2	no	—
371	C₂×C₈	—	26	2	no	—
372	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
373	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
374	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
375	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	26	2	no	—
379	C₄⋊C₄	—	26	2	no	—
380	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
381	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	52	2	no	—
386	C₂²⋊C₄	—	52	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×D₅₂	1	1	yes	characteristic
391	C₄²	#6127	1	1	yes	characteristic
392	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
393	C₄²	C₂³×D₁₃	1	1	yes	characteristic
394	C₁₃	#19269	1	1	yes	characteristic, complemented, Sylow
395	C₂³	—	2	1	no	—
396	C₂³	—	52	2	no	—
397	C₂³	#88184	1	1	yes	characteristic
398	Q₈	—	2	1	no	—
399	Q₈	—	52	2	no	—
400	Q₈	—	52	2	no	—
401	Q₈	#88158	1	2	yes	complemented
402	D₄	—	2	4	no	—
403	D₄	—	2	1	no	—
404	D₄	—	52	2	no	—
405	D₄	—	52	2	no	—
406	D₄	—	52	2	no	—
407	D₄	—	52	2	no	—
408	D₄	—	104	2	no	—
409	D₄	—	104	4	no	—
410	D₄	#88158	1	2	yes	complemented
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	52	2	no	—
424	C₂×C₄	—	104	4	no	—
425	C₂×C₄	#88184	1	1	yes	characteristic
426	C₂×C₄	#88184	1	1	yes	characteristic
427	C₂×C₄	#88184	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
429	C₂×C₄	C₂×#6127	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	52	2	no	—
436	C₈	—	52	2	no	—
437	C₈	#88203	1	2	yes	—
438	C₈	#88203	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	104	2	no	—
446	C₂²	—	104	2	no	—
447	C₂²	—	104	2	no	—
448	C₂²	C₂×#88184	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	104	2	no	—
457	C₄	C₂×#88158	1	1	yes	characteristic
458	C₄	C₂×#88158	1	1	yes	characteristic
459	C₄	C₂×#88203	1	1	yes	characteristic
460	C₄	C₂×#88203	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	4	2	no	—
463	C₂	—	208	2	no	—
464	C₂	#13124316	1	1	yes	characteristic
465	C₂	#13124417	1	1	yes	characteristic
466	C₂	#13124556	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88184
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×#41	C₂
socle	C₂²×C₁₃	C₂×#121
hypercenter	C₈×#41	D₁₃
hypocenter	C₁₃	#19269
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #13125264	C₂	semidirect
2. #13124987	C₂	semidirect
3. #13114206	C₂	semidirect
4. #13114201	C₂	semidirect
5. #13114196	C₂	semidirect
6. #13114191	C₂	semidirect
7. #13114184	C₂	semidirect
8. #13114177	C₂	semidirect
9. #13113599	C₂	semidirect
10. #13113539	C₂	semidirect
11. C₈×C₁₃×#41	C₂	semidirect
164. C₈×#41	D₁₃	semidirect
177. Q₈×C₁₃	#135	semidirect
180. D₄×C₁₃	#135	semidirect
394. C₁₃	#19269	semidirect
401. Q₈	#88158	semidirect
410. D₄	#88158	semidirect

Maximal subgroups

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

subgroup	index
#13125264	2
#13124987	2
#13114206	2
#13114201	2
#13114196	2
#13114191	2
#13114184	2
#13114177	2
#13113599	2
#13113539	2
C₈×C₁₃×#41	2
#19269	13