Subgroups — #15869834

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718557	C₂	1	1	yes	maximal, characteristic
2	C₄×#88163	C₂	1	2	yes	maximal
3	C₂×#11718377	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123261	C₂	1	1	yes	maximal, characteristic
5	#13115749	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115617	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115492	C₂	1	2	yes	maximal, complemented
8	#13115350	C₂	1	2	yes	maximal
9	#13114892	C₂	1	1	yes	maximal, characteristic
10	C₄×#88064	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88163	C₂²	1	2	yes	—
13	C₂²×Dic₅₂	C₂²	1	1	yes	characteristic
14	C₂×#88155	C₂²	1	1	yes	characteristic
15	C₂×#88155	C₂²	1	1	yes	characteristic
16	C₄×#6127	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₂₆	C₂²	1	2	yes	—
18	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
21	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
22	C₂×#88064	C₂²	1	2	yes	—
23	C₂×#88064	C₂²	1	2	yes	—
24	#11718794	C₂²	1	2	yes	—
25	#11718782	C₂²	1	2	yes	—
26	#11718781	C₂²	1	2	yes	—
27	C₂×#88057	C₂²	1	1	yes	characteristic
28	C₂×#88056	C₂²	1	2	yes	—
29	#11718762	C₂²	1	1	yes	characteristic
30	#11718762	C₂²	1	1	yes	characteristic
31	C₄×#6099	C₂²	1	1	yes	characteristic
32	#11718557	C₄	1	8	yes	complemented
33	#11718377	—	2	2	no	—
34	#11718377	—	2	1	no	—
35	#11718377	—	2	1	no	—
36	#11718377	—	2	1	no	—
37	#11718377	—	2	1	no	—
38	#11718371	—	2	2	no	—
39	#11718369	—	2	1	no	—
40	#11718369	—	2	1	no	—
41	#11718368	—	2	1	no	—
42	D₁₃×#97	—	2	1	no	—
43	C₄×Dic₅₂	—	2	2	no	—
44	C₄×#6095	—	2	2	no	—
45	C₁₃×#341	C₂²	1	2	yes	—
46	#11718146	C₂²	1	2	yes	—
47	#11718146	C₂²	1	2	yes	—
48	C₂×#6127	C₂³	1	1	yes	characteristic
49	C₂²×Dic₂₆	C₂³	1	2	yes	—
50	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₃	—	2	2	no	—
56	#88180	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
58	C₂×#6101	—	2	2	no	—
59	C₂×C₄×Dic₁₃	—	2	2	no	—
60	C₂×#6099	C₂³	1	1	yes	characteristic
61	C₂×#6099	C₂³	1	1	yes	characteristic
62	#88163	—	2	4	no	—
63	#88163	C₂×C₄	1	8	yes	—
64	C₂×Dic₅₂	—	2	2	no	—
65	C₂×Dic₅₂	—	2	1	no	—
66	C₂×Dic₅₂	—	2	1	no	—
67	C₂×Dic₅₂	—	2	2	no	—
68	C₂×Dic₅₂	C₂×C₄	1	4	yes	complemented
69	C₂×#6095	—	2	2	no	—
70	#88155	—	2	2	no	—
71	#88155	—	2	2	no	—
72	#88155	—	2	2	no	—
73	#88155	C₂×C₄	1	4	yes	—
74	C₂×#6094	—	2	1	no	—
75	C₂×#6094	—	2	1	no	—
76	C₂×C₈×D₁₃	—	2	1	no	—
77	C₂×C₈×D₁₃	—	2	1	no	—
78	C₄×D₅₂	D₄	1	2	yes	—
79	#88126	—	2	1	no	—
80	C₄²×D₁₃	—	2	1	no	—
81	C₄×Dic₂₆	—	2	2	no	—
82	C₄×Dic₂₆	—	2	2	no	—
83	C₄×Dic₂₆	—	2	2	no	—
84	C₄×Dic₂₆	—	2	2	no	—
85	C₄×Dic₂₆	D₄	1	2	yes	—
86	C₁₃×#108	—	2	2	no	—
87	C₁₃×#108	C₂×C₄	1	4	yes	complemented
88	C₁₃×#97	—	2	2	no	—
89	C₁₃×#97	D₄	1	1	yes	characteristic
90	C₁₃×#97	D₄	1	1	yes	characteristic
91	C₁₃×#97	D₄	1	1	yes	characteristic
92	C₁₃×#97	D₄	1	1	yes	characteristic
93	C₄×C₈×C₁₃	—	2	2	no	—
94	#88064	—	2	4	no	—
95	#88064	C₂×C₄	1	8	yes	complemented
96	#88061	—	2	2	no	—
97	#88058	—	2	2	no	—
98	#88057	—	2	1	no	—
99	#88057	—	2	1	no	—
100	#88057	—	2	2	no	—
101	#88056	—	2	2	no	—
102	#88056	—	2	2	no	—
103	#88056	—	2	2	no	—
104	#88056	—	2	2	no	—
105	#88056	—	2	2	no	—
106	#88055	—	2	1	no	—
107	#88055	—	2	1	no	—
108	C₈×Dic₁₃	—	2	1	no	—
109	C₈×Dic₁₃	—	2	1	no	—
110	#88043	—	2	1	no	—
111	C₄×#1055	—	2	1	no	—
112	#21556	—	13	1	no	maximal, Sylow
113	C₂²×C₄×C₁₃	#41	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₃	—	2	1	no	—
116	C₂²×Dic₁₃	—	2	2	no	—
117	C₂²×Dic₁₃	—	2	2	no	—
118	#6127	—	2	1	no	—
119	#6127	—	2	1	no	—
120	#6127	C₂²×C₄	1	2	yes	—
121	#6127	#41	1	2	yes	—
122	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₁₃	—	2	1	no	—
124	C₂×C₄×D₁₃	—	2	2	no	—
125	C₂×Dic₂₆	—	2	2	no	—
126	C₂×Dic₂₆	—	2	2	no	—
127	C₂×Dic₂₆	—	2	2	no	—
128	C₂×Dic₂₆	—	2	2	no	—
129	C₂×Dic₂₆	—	2	2	no	—
130	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
131	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
132	C₁₃×M₁₆	—	2	2	no	—
133	C₁₃×M₁₆	—	2	2	no	—
134	C₁₃×M₁₆	—	2	2	no	—
135	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	#41	1	2	yes	—
146	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₃	C₂×D₄	1	2	yes	—
149	C₂²⋊Dic₁₃	—	2	1	no	—
150	#6103	—	2	2	no	—
151	C₄⋊Dic₁₃	—	2	2	no	—
152	C₄⋊Dic₁₃	—	2	2	no	—
153	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
154	#6101	—	2	2	no	—
155	#6101	—	4	2	no	—
156	#6101	—	4	2	no	—
157	C₄×Dic₁₃	—	2	2	no	—
158	C₄×Dic₁₃	—	2	1	no	—
159	C₄×Dic₁₃	—	4	2	no	—
160	C₄×Dic₁₃	—	4	2	no	—
161	#6099	—	2	1	no	—
162	#6099	—	2	1	no	—
163	#6099	C₂²×C₄	1	2	yes	—
164	#6099	#41	1	2	yes	—
165	C₂×#1055	—	2	1	no	—
166	C₂×#1055	—	2	1	no	—
167	Dic₅₂	—	2	8	no	—
168	Dic₅₂	—	2	4	no	—
169	Dic₅₂	—	2	4	no	—
170	#6095	—	2	8	no	—
171	#6094	—	2	4	no	—
172	#6094	—	2	4	no	—
173	C₈×D₁₃	—	2	4	no	—
174	C₈×D₁₃	—	2	4	no	—
175	C₂×#473	—	13	1	no	—
176	C₄×#137	—	13	2	no	—
177	C₂×#441	—	13	1	no	—
178	#2875	—	13	1	no	—
179	#1979	—	13	1	no	—
180	#1951	—	13	1	no	—
181	#1930	—	13	2	no	—
182	#1908	—	13	2	no	—
183	#1815	—	13	1	no	—
184	#1778	D₁₃	1	1	yes	characteristic, complemented
185	C₄×#101	—	13	2	no	—
186	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂²×D₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	#121	1	2	yes	—
190	C₂×C₄×C₁₃	#121	1	2	yes	—
191	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂²⋊D₁₃	—	2	2	no	—
198	C₂²⋊D₁₃	—	2	2	no	—
199	C₂×Dic₁₃	—	2	1	no	—
200	C₂×Dic₁₃	—	2	4	no	—
201	C₂×Dic₁₃	—	2	2	no	—
202	C₂×Dic₁₃	—	4	2	no	—
203	C₂×Dic₁₃	—	4	2	no	—
204	C₂×Dic₁₃	—	4	2	no	—
205	C₂×Dic₁₃	—	8	2	no	—
206	D₅₂	—	2	1	no	—
207	D₅₂	C₄×D₄	1	2	yes	—
208	C₄×D₁₃	—	2	2	no	—
209	C₄×D₁₃	—	2	2	no	—
210	C₄×D₁₃	—	8	2	no	—
211	Dic₂₆	—	2	1	no	—
212	Dic₂₆	—	2	4	no	—
213	Dic₂₆	—	2	4	no	—
214	Dic₂₆	—	4	2	no	—
215	Dic₂₆	—	4	2	no	—
216	Dic₂₆	C₄×D₄	1	2	yes	—
217	C₈×C₁₃	—	2	4	no	—
218	C₈×C₁₃	—	2	1	no	—
219	C₈×C₁₃	—	2	1	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₈×C₁₃	C₄×D₄	1	2	yes	—
222	C₈×C₁₃	C₄×D₄	1	2	yes	—
223	#1055	—	2	2	no	—
224	#1055	—	2	2	no	—
225	C₂×#137	—	13	2	no	—
226	C₂²×Q₁₆	—	13	1	no	—
227	C₂×#131	—	13	1	no	—
228	C₂×#131	—	13	1	no	—
229	C₄×#41	—	13	1	no	—
230	C₂×C₄×Q₈	—	13	2	no	—
231	#473	—	13	8	no	—
232	#441	—	26	2	no	—
233	#441	—	26	1	no	—
234	#441	—	26	1	no	—
235	#441	—	26	1	no	—
236	#441	—	26	1	no	—
237	#440	—	26	2	no	—
238	C₄×Q₁₆	—	26	2	no	—
239	C₄×SD₁₆	—	26	2	no	—
240	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
241	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
242	#428	—	13	2	no	—
243	C₂×#106	—	13	1	no	—
244	#419	—	13	2	no	—
245	#417	—	13	2	no	—
246	C₂×#103	—	13	2	no	—
247	C₂×#101	—	13	2	no	—
248	C₂×#101	—	13	2	no	—
249	#405	—	13	1	no	—
250	#405	—	13	1	no	—
251	#405	—	26	1	no	—
252	#405	—	26	1	no	—
253	C₄×M₁₆	—	13	1	no	—
254	C₄×M₁₆	—	26	1	no	—
255	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
256	C₂×#97	—	26	1	no	—
257	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
258	#343	—	13	2	no	—
259	#343	—	13	2	no	—
260	#341	C₂×D₁₃	1	2	yes	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
264	C₂²×C₁₃	#529	1	1	yes	characteristic
265	C₂×D₁₃	—	2	2	no	—
266	C₂×D₁₃	—	4	2	no	—
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
271	C₄×C₁₃	#525	1	1	yes	characteristic
272	C₄×C₁₃	#532	1	1	yes	characteristic
273	Dic₁₃	—	2	2	no	—
274	Dic₁₃	—	4	4	no	—
275	Dic₁₃	—	4	2	no	—
276	Dic₁₃	—	8	2	no	—
277	C₂×#41	—	13	1	no	—
278	C₂²×Q₈	—	13	2	no	—
279	#137	—	13	8	no	—
280	#137	—	26	4	no	—
281	C₂×Q₁₆	—	13	4	no	—
282	C₂×Q₁₆	—	26	2	no	—
283	C₂×Q₁₆	—	26	1	no	—
284	C₂×Q₁₆	—	26	1	no	—
285	C₂×Q₁₆	—	26	2	no	—
286	C₂×SD₁₆	—	26	2	no	—
287	#131	—	13	4	no	—
288	#131	—	26	2	no	—
289	#131	—	26	2	no	—
290	#131	—	26	2	no	—
291	C₂×M₁₆	—	13	1	no	—
292	C₂×M₁₆	—	13	1	no	—
293	C₂×M₁₆	—	26	1	no	—
294	C₂×M₁₆	—	26	1	no	—
295	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
296	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
297	C₂²×C₈	—	26	1	no	—
298	C₂²×C₈	—	26	1	no	—
299	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
301	C₄×Q₈	—	13	2	no	—
302	C₄×Q₈	—	26	2	no	—
303	C₄×Q₈	—	26	2	no	—
304	C₄×Q₈	—	26	2	no	—
305	C₄×Q₈	—	26	2	no	—
306	C₄×D₄	—	13	2	no	—
307	C₄×D₄	—	26	2	no	—
308	#117	—	13	1	no	—
309	#117	—	26	1	no	—
310	C₂×C₄⋊C₄	—	13	2	no	—
311	C₂×C₄⋊C₄	—	26	2	no	—
312	C₂×C₄²	—	26	1	no	—
313	C₂×C₄²	—	26	2	no	—
314	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
315	#108	—	2	2	no	—
316	#108	C₄×D₁₃	1	4	yes	complemented
317	#107	—	26	2	no	—
318	#106	—	26	2	no	—
319	#106	—	26	1	no	—
320	#106	—	26	1	no	—
321	#103	—	26	2	no	—
322	#103	—	26	2	no	—
323	#103	—	26	2	no	—
324	#103	—	26	2	no	—
325	#103	—	26	2	no	—
326	#102	—	26	2	no	—
327	#101	—	13	8	no	—
328	#101	—	26	4	no	—
329	#97	—	2	2	no	—
330	#97	—	26	1	no	—
331	#97	—	26	1	no	—
332	#97	—	26	1	no	—
333	#97	D₅₂	1	1	yes	characteristic
334	#97	D₅₂	1	1	yes	characteristic
335	#97	D₅₂	1	1	yes	characteristic
336	#97	D₅₂	1	1	yes	characteristic
337	C₄×C₈	—	2	2	no	—
338	C₄×C₈	—	26	1	no	—
339	C₄×C₈	—	26	1	no	—
340	C₄×C₈	—	26	1	no	—
341	C₂×C₁₃	—	2	1	no	—
342	C₂×C₁₃	—	2	1	no	—
343	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
344	C₂×C₁₃	#3069	1	2	yes	—
345	D₁₃	—	4	2	no	—
346	#41	—	13	2	no	—
347	#41	—	13	2	no	—
348	#41	—	26	1	no	—
349	#41	—	26	1	no	—
350	C₂×Q₈	—	13	4	no	—
351	C₂×Q₈	—	13	1	no	—
352	C₂×Q₈	—	26	2	no	—
353	C₂×Q₈	—	26	2	no	—
354	C₂×Q₈	—	26	2	no	—
355	C₂×Q₈	—	26	2	no	—
356	C₂×Q₈	—	26	2	no	—
357	C₂×D₄	—	13	1	no	—
358	C₂×D₄	—	26	1	no	—
359	C₂²×C₄	—	26	1	no	—
360	C₂²×C₄	—	26	2	no	—
361	C₂²×C₄	—	26	2	no	—
362	C₂²×C₄	—	26	2	no	—
363	C₂²×C₄	#6131	1	2	yes	—
364	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
365	Q₁₆	—	26	8	no	—
366	Q₁₆	—	26	4	no	—
367	Q₁₆	—	26	4	no	—
368	SD₁₆	—	26	8	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	13	2	no	—
373	M₁₆	—	13	2	no	—
374	M₁₆	—	26	4	no	—
375	M₁₆	—	26	1	no	—
376	M₁₆	—	26	1	no	—
377	M₁₆	—	26	4	no	—
378	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	26	4	no	—
384	C₂×C₈	—	26	1	no	—
385	C₂×C₈	—	26	1	no	—
386	C₂×C₈	—	26	4	no	—
387	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
388	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
389	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
390	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
391	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
392	C₂×C₈	#6127	1	2	yes	—
393	C₄⋊C₄	—	13	2	no	—
394	C₄⋊C₄	—	26	2	no	—
395	C₄⋊C₄	—	26	2	no	—
396	C₄⋊C₄	—	26	2	no	—
397	C₄⋊C₄	—	52	2	no	—
398	C₄⋊C₄	—	52	2	no	—
399	C₂²⋊C₄	—	26	1	no	—
400	C₂²⋊C₄	—	26	2	no	—
401	C₄²	—	26	2	no	—
402	C₄²	—	26	1	no	—
403	C₄²	—	52	2	no	—
404	C₄²	—	52	2	no	—
405	C₄²	C₂×D₅₂	1	1	yes	characteristic
406	C₄²	C₂×D₅₂	1	1	yes	characteristic
407	C₄²	D₄×D₁₃	1	2	yes	—
408	C₁₃	#21556	1	1	yes	characteristic, complemented, Sylow
409	C₂³	—	26	1	no	—
410	C₂³	C₂×#6131	1	1	yes	characteristic
411	Q₈	—	13	2	no	—
412	Q₈	—	26	1	no	—
413	Q₈	—	26	4	no	—
414	Q₈	—	26	4	no	—
415	Q₈	—	52	2	no	—
416	Q₈	—	52	2	no	—
417	D₄	—	13	2	no	—
418	D₄	—	26	2	no	—
419	D₄	—	26	2	no	—
420	D₄	—	26	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	26	1	no	—
423	C₂×C₄	—	26	2	no	—
424	C₂×C₄	—	26	2	no	—
425	C₂×C₄	—	26	2	no	—
426	C₂×C₄	—	26	4	no	—
427	C₂×C₄	—	52	2	no	—
428	C₂×C₄	—	52	2	no	—
429	C₂×C₄	—	52	2	no	—
430	C₂×C₄	—	104	2	no	—
431	C₂×C₄	—	104	2	no	—
432	C₂×C₄	#88149	1	2	yes	—
433	C₂×C₄	#88149	1	2	yes	—
434	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
436	C₂×C₄	C₂×#6127	1	1	yes	characteristic
437	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
438	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
439	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
440	C₈	—	2	1	no	—
441	C₈	—	2	1	no	—
442	C₈	—	2	4	no	—
443	C₈	—	4	2	no	—
444	C₈	—	26	2	no	—
445	C₈	—	26	2	no	—
446	C₈	C₄×D₅₂	1	2	yes	—
447	C₈	C₄×D₅₂	1	2	yes	—
448	C₂²	—	2	2	no	—
449	C₂²	—	26	2	no	—
450	C₂²	—	52	2	no	—
451	C₂²	C₂×#88149	1	1	yes	characteristic
452	C₂²	C₄×#6131	1	1	yes	characteristic
453	C₂²	#11719285	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	26	2	no	—
457	C₄	—	52	4	no	—
458	C₄	—	52	2	no	—
459	C₄	—	104	2	no	—
460	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
461	C₄	#11719229	1	1	yes	characteristic
462	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
463	C₄	#11719253	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	52	2	no	—
467	C₂	C₄×#88149	1	1	yes	characteristic
468	C₂	#13124574	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#88149
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1778	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂×#6127	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1778	D₁₃
hypocenter	C₁₃	#21556
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1778

Complements

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

N	H ≅ G/N	type
3. C₂×#11718377	C₂	semidirect
5. #13115749	C₂	semidirect
6. #13115617	C₂	semidirect
7. #13115492	C₂	semidirect
10. C₄×#88064	C₂	semidirect
11. C₁₃×#1778	C₂	semidirect
32. #11718557	C₄	semidirect
68. C₂×Dic₅₂	C₂×C₄	semidirect
87. C₁₃×#108	C₂×C₄	semidirect
95. #88064	C₂×C₄	semidirect
184. #1778	D₁₃	semidirect
316. #108	C₄×D₁₃	semidirect
408. C₁₃	#21556	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718557	2
C₄×#88163	2
C₂×#11718377	2
#13123261	2
#13115749	2
#13115617	2
#13115492	2
#13115350	2
#13114892	2
C₄×#88064	2
C₁₃×#1778	2
#21556	13