Subgroups — #15846824

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	#13124981	C₂	1	2	yes	maximal, complemented
2	C₈×#6127	C₂	1	1	yes	maximal, characteristic, complemented
3	#13114203	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114198	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114193	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114188	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114181	C₂	1	2	yes	maximal, complemented
8	#13114174	C₂	1	2	yes	maximal, complemented
9	#13113599	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113541	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	—	2	1	no	—
13	C₂×C₁₃×#135	—	2	1	no	—
14	C₁₃×#532	C₂²	1	2	yes	—
15	C₄×#6127	C₂²	1	1	yes	characteristic
16	C₁₃×#495	—	2	1	no	—
17	C₁₃×#495	—	2	1	no	—
18	C₁₃×#494	C₂²	1	1	yes	characteristic
19	C₁₃×#493	C₂²	1	1	yes	characteristic
20	C₁₃×#492	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₃	—	2	1	no	—
23	C₈×C₂²⋊D₁₃	—	2	1	no	—
24	#11718755	C₂²	1	2	yes	—
25	#11718748	C₂²	1	2	yes	—
26	#11718736	C₂²	1	2	yes	—
27	#11718733	C₂²	1	2	yes	—
28	#11718698	—	2	2	no	—
29	#11718696	—	2	2	no	—
30	#11718679	—	2	2	no	—
31	#11718675	—	2	2	no	—
32	#11718587	C₂²	1	2	yes	—
33	#11718586	C₂²	1	1	yes	characteristic
34	C₈×D₅₂	C₂²	1	1	yes	characteristic
35	C₈×D₅₂	C₂²	1	1	yes	characteristic
36	#11718346	—	2	1	no	—
37	C₄×C₈×D₁₃	—	2	1	no	—
38	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
39	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
40	#11718139	C₂²	1	2	yes	—
41	#11718139	C₂²	1	2	yes	—
42	#11718136	C₂²	1	2	yes	—
43	#11718136	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	—	2	2	no	—
48	C₂×#6127	D₄	1	1	yes	characteristic
49	C₁₃×#135	—	4	4	no	—
50	C₁₃×#135	—	4	4	no	—
51	C₂×C₁₃×Q₁₆	—	2	1	no	—
52	C₂×C₁₃×Q₁₆	—	2	1	no	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₃×#127	C₂³	1	2	yes	—
61	C₁₃×#124	—	2	2	no	—
62	C₁₃×#121	—	2	2	no	—
63	C₁₃×#121	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×#6105	—	2	2	no	—
68	C₂×#6104	—	2	2	no	—
69	C₄×C₂²⋊D₁₃	—	2	1	no	—
70	C₄×C₂²⋊D₁₃	—	2	1	no	—
71	#88180	D₄	1	1	yes	characteristic
72	C₂×C₈×D₁₃	—	2	1	no	—
73	C₂×C₈×D₁₃	—	2	1	no	—
74	C₄×D₅₂	D₄	1	1	yes	characteristic
75	C₄×D₅₂	C₂³	1	1	yes	characteristic
76	#88126	—	2	1	no	—
77	C₄²×D₁₃	—	2	1	no	—
78	C₄×Dic₂₆	D₄	1	1	yes	characteristic
79	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	#88072	—	2	2	no	—
85	#88072	—	2	2	no	—
86	C₂²⋊#1055	—	2	2	no	—
87	C₂²⋊#1055	—	2	1	no	—
88	#88060	—	2	1	no	—
89	#88060	—	2	1	no	—
90	#88054	—	2	1	no	—
91	#88054	—	2	1	no	—
92	C₈×Dic₁₃	—	2	1	no	—
93	C₈×Dic₁₃	—	2	1	no	—
94	#88050	—	2	2	no	—
95	#88049	—	2	2	no	—
96	#88048	—	2	2	no	—
97	#88047	—	2	2	no	—
98	C₄⋊#1055	C₂³	1	2	yes	—
99	C₄⋊#1055	C₂³	1	2	yes	—
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	C₄⋊#1055	C₂³	1	1	yes	characteristic
102	#88043	—	2	2	no	—
103	C₄×#1055	—	2	1	no	—
104	#19269	—	13	1	no	maximal, Sylow
105	C₁₃×#41	—	4	4	no	—
106	C₁₃×#41	—	4	4	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	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	—	2	1	no	—
117	#6127	—	2	2	no	—
118	#6127	—	2	2	no	—
119	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	—	2	1	no	—
121	C₂×C₄×D₁₃	—	2	1	no	—
122	C₂×C₄×D₁₃	—	2	1	no	—
123	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
124	C₁₃×Q₁₆	—	4	2	no	—
125	C₁₃×Q₁₆	—	4	2	no	—
126	C₁₃×SD₁₆	—	4	4	no	—
127	C₁₃×SD₁₆	—	4	4	no	—
128	C₁₃×D₈	—	4	2	no	—
129	C₁₃×D₈	—	4	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₁₃×C₂²⋊C₄	—	4	2	no	—
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	#41	1	1	yes	characteristic
143	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₂²⋊Dic₁₃	—	2	1	no	—
145	#6105	—	4	4	no	—
146	#6104	—	4	4	no	—
147	#6103	—	2	1	no	—
148	#6103	—	2	1	no	—
149	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
151	#6101	—	2	1	no	—
152	#6101	—	2	1	no	—
153	C₄×Dic₁₃	—	2	1	no	—
154	C₄×Dic₁₃	—	2	1	no	—
155	C₄×Dic₁₃	—	2	1	no	—
156	C₂×#1055	—	2	2	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	—	2	1	no	—
159	C₂×#1055	—	2	1	no	—
160	C₈×D₁₃	—	4	2	no	—
161	C₈×D₁₃	—	4	2	no	—
162	#3147	D₁₃	1	1	yes	characteristic, complemented
163	#3115	—	13	2	no	—
164	C₈×#41	—	13	1	no	—
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	—	4	2	no	—
174	C₂³×C₁₃	#121	1	1	yes	characteristic
175	C₂²×D₁₃	—	2	1	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	8	2	no	—
183	D₄×C₁₃	—	8	4	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	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	8	4	no	—
191	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂²⋊D₁₃	—	2	4	no	—
198	C₂×Dic₁₃	—	2	1	no	—
199	C₂×Dic₁₃	—	2	1	no	—
200	C₂×Dic₁₃	—	2	1	no	—
201	D₅₂	—	2	1	no	—
202	D₅₂	#135	1	2	yes	complemented
203	C₄×D₁₃	—	2	4	no	—
204	C₄×D₁₃	—	4	2	no	—
205	C₄×D₁₃	—	4	1	no	—
206	C₄×D₁₃	—	4	1	no	—
207	Dic₂₆	—	2	1	no	—
208	Dic₂₆	#135	1	2	yes	complemented
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
212	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
213	#1055	—	4	2	no	—
214	#1055	—	4	2	no	—
215	#1055	—	4	1	no	—
216	#1055	—	4	1	no	—
217	C₂×#135	—	2	1	no	—
218	C₂×#135	—	2	1	no	—
219	#532	C₂×D₁₃	1	2	yes	—
220	C₄×#41	—	13	1	no	—
221	#495	—	2	1	no	—
222	#495	—	2	1	no	—
223	#494	C₂×D₁₃	1	1	yes	characteristic
224	#493	C₂×D₁₃	1	1	yes	characteristic
225	#492	C₂×D₁₃	1	2	yes	—
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	—	13	1	no	—
233	C₈×Q₈	—	13	1	no	—
234	#442	—	26	2	no	—
235	#440	—	26	2	no	—
236	C₈×D₄	—	13	1	no	—
237	C₈×D₄	—	13	1	no	—
238	C₈×D₄	—	26	1	no	—
239	C₈×D₄	—	26	1	no	—
240	#432	—	13	2	no	—
241	#431	—	13	1	no	—
242	#431	—	26	1	no	—
243	C₂×C₄×C₈	—	26	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	1	no	—
255	C₂²×C₁₃	—	8	2	no	—
256	C₂²×C₁₃	—	8	2	no	—
257	C₂²×C₁₃	—	8	2	no	—
258	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
259	C₂×D₁₃	—	2	2	no	—
260	C₂×D₁₃	—	4	1	no	—
261	C₂×D₁₃	—	4	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	8	2	no	—
267	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
268	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
269	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	Dic₁₃	—	2	2	no	—
272	Dic₁₃	—	4	1	no	—
273	Dic₁₃	—	4	1	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	13	1	no	—
276	#135	—	4	4	no	—
277	#135	—	4	4	no	—
278	C₂×Q₁₆	—	2	1	no	—
279	C₂×Q₁₆	—	2	1	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	26	2	no	—
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	—	2	1	no	—
285	C₂×D₈	—	26	2	no	—
286	C₂²×C₈	—	26	1	no	—
287	C₂²×C₈	—	26	1	no	—
288	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
290	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
291	#127	C₂²×D₁₃	1	2	yes	—
292	#124	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	C₄×Q₈	—	13	1	no	—
296	C₄×Q₈	—	13	1	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	13	1	no	—
300	C₄×D₄	—	13	1	no	—
301	C₄×D₄	—	26	1	no	—
302	C₄×D₄	—	26	1	no	—
303	#117	—	13	1	no	—
304	#117	—	26	1	no	—
305	C₂×C₄²	—	26	1	no	—
306	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
307	#107	—	26	2	no	—
308	#106	—	26	2	no	—
309	C₄⋊C₈	—	13	1	no	—
310	C₄⋊C₈	—	13	1	no	—
311	C₄⋊C₈	—	13	2	no	—
312	C₄⋊C₈	—	13	2	no	—
313	C₄⋊C₈	—	26	1	no	—
314	C₄⋊C₈	—	26	1	no	—
315	#103	—	26	2	no	—
316	#102	—	26	2	no	—
317	#102	—	26	2	no	—
318	#102	—	26	2	no	—
319	C₂²⋊C₈	—	26	2	no	—
320	C₂²⋊C₈	—	26	1	no	—
321	C₂²⋊C₈	—	26	1	no	—
322	C₂²⋊C₈	—	26	1	no	—
323	#97	—	26	2	no	—
324	C₄×C₈	—	26	1	no	—
325	C₄×C₈	—	26	1	no	—
326	C₄×C₈	—	26	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	—	16	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	—	4	2	no	—
337	#41	—	4	4	no	—
338	#41	—	4	4	no	—
339	#41	—	26	2	no	—
340	#41	—	26	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	13	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	13	1	no	—
348	C₂×D₄	—	26	1	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	26	1	no	—
351	C₂²×C₄	—	26	1	no	—
352	C₂²×C₄	—	26	1	no	—
353	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
354	C₂²×C₄	#6129	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
356	Q₁₆	—	4	2	no	—
357	Q₁₆	—	4	2	no	—
358	SD₁₆	—	4	4	no	—
359	SD₁₆	—	4	4	no	—
360	SD₁₆	—	52	4	no	—
361	D₈	—	4	2	no	—
362	D₈	—	4	2	no	—
363	D₈	—	52	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	26	2	no	—
367	C₂×C₈	—	26	2	no	—
368	C₂×C₈	—	26	1	no	—
369	C₂×C₈	—	26	1	no	—
370	C₂×C₈	—	52	2	no	—
371	C₂×C₈	—	52	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	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	13	1	no	—
379	C₄⋊C₄	—	13	1	no	—
380	C₄⋊C₄	—	26	1	no	—
381	C₄⋊C₄	—	26	1	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	26	1	no	—
385	C₂²⋊C₄	—	26	1	no	—
386	C₂²⋊C₄	—	26	1	no	—
387	C₄²	—	26	1	no	—
388	C₄²	—	26	1	no	—
389	C₄²	—	26	1	no	—
390	C₄²	D₄×D₁₃	1	1	yes	characteristic
391	C₄²	#6129	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	—	4	2	no	—
396	C₂³	—	26	1	no	—
397	C₂³	#88192	1	1	yes	characteristic
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	13	2	no	—
401	Q₈	—	26	1	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	4	no	—
408	D₄	—	13	2	no	—
409	D₄	—	26	4	no	—
410	D₄	—	26	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	—	26	4	no	—
419	C₂×C₄	—	26	1	no	—
420	C₂×C₄	—	26	1	no	—
421	C₂×C₄	—	26	1	no	—
422	C₂×C₄	—	52	2	no	—
423	C₂×C₄	—	52	1	no	—
424	C₂×C₄	—	52	1	no	—
425	C₂×C₄	#88192	1	1	yes	characteristic
426	C₂×C₄	#88192	1	1	yes	characteristic
427	C₂×C₄	#88192	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#6129	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	—	52	2	no	—
434	C₈	—	52	2	no	—
435	C₈	—	52	1	no	—
436	C₈	—	52	1	no	—
437	C₈	#88186	1	2	yes	—
438	C₈	#88186	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	26	2	no	—
446	C₂²	—	52	1	no	—
447	C₂²	—	52	1	no	—
448	C₂²	C₂×#88192	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	8	2	no	—
454	C₄	—	26	2	no	—
455	C₄	—	52	1	no	—
456	C₄	—	52	1	no	—
457	C₄	D₁₃×#135	1	1	yes	characteristic
458	C₄	D₁₃×#135	1	1	yes	characteristic
459	C₄	C₂×#88186	1	1	yes	characteristic
460	C₄	C₂×#88186	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	16	2	no	—
463	C₂	—	52	2	no	—
464	C₂	#13124312	1	1	yes	characteristic
465	C₂	#13124413	1	1	yes	characteristic
466	C₂	#13124552	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88192
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3147	C₂
socle	C₂²×C₁₃	C₂×#121
hypercenter	#3147	D₁₃
hypocenter	C₁₃	#19269
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #13124981	C₂	semidirect
2. C₈×#6127	C₂	semidirect
3. #13114203	C₂	semidirect
4. #13114198	C₂	semidirect
5. #13114193	C₂	semidirect
6. #13114188	C₂	semidirect
7. #13114181	C₂	semidirect
8. #13114174	C₂	semidirect
9. #13113599	C₂	semidirect
10. #13113541	C₂	semidirect
11. C₁₃×#3147	C₂	semidirect
162. #3147	D₁₃	semidirect
202. D₅₂	#135	semidirect
208. Dic₂₆	#135	semidirect
394. C₁₃	#19269	semidirect

Maximal subgroups

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

subgroup	index
#13124981	2
C₈×#6127	2
#13114203	2
#13114198	2
#13114193	2
#13114188	2
#13114181	2
#13114174	2
#13113599	2
#13113541	2
C₁₃×#3147	2
#19269	13