Subgroups — #15834673

Order 3328.

722 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125411	C₂	1	1	yes	maximal, characteristic
2	#13123580	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123579	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113718	C₂	1	2	yes	maximal, complemented
5	#13113668	C₂	1	2	yes	maximal, complemented
6	#13113662	C₂	1	2	yes	maximal, complemented
7	#13113628	C₂	1	2	yes	maximal, complemented
8	C₂×#11718071	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113236	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₂×#88202	—	2	1	no	—
14	C₂×#88155	—	2	1	no	—
15	#11719182	C₂²	1	1	yes	characteristic
16	C₁₃×#431	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	#11718895	—	2	1	no	—
19	#11718771	—	2	1	no	—
20	#11718749	C₄	1	1	yes	characteristic
21	#11718739	C₄	1	1	yes	characteristic
22	#11718734	C₄	1	1	yes	characteristic
23	#11718731	C₄	1	1	yes	characteristic
24	#11718699	C₄	1	2	yes	—
25	#11718699	C₄	1	2	yes	—
26	C₄×#6104	C₂²	1	2	yes	—
27	C₄×#6104	C₂²	1	2	yes	—
28	#11718673	C₂²	1	2	yes	—
29	#11718672	—	2	2	no	—
30	D₄×#1055	C₂²	1	2	yes	—
31	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
32	C₄×#6099	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	#11718499	C₂²	1	2	yes	—
35	#11718497	—	2	2	no	—
36	#11718495	C₂²	1	2	yes	—
37	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
38	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
39	#11718071	C₂²	1	1	yes	characteristic
40	#11718071	C₂²	1	1	yes	characteristic
41	#11718071	C₂²	1	1	yes	characteristic
42	#11718071	C₂²	1	1	yes	characteristic
43	#11718051	C₂²	1	2	yes	—
44	#11718051	C₂²	1	2	yes	—
45	#11718046	C₂²	1	2	yes	—
46	C₈×#1055	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×#6127	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
52	C₁₃×#124	—	2	1	no	—
53	C₁₃×#121	—	2	1	no	—
54	C₁₃×#121	C₂×C₄	1	2	yes	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	#88202	—	4	4	no	—
59	C₂×#6104	C₂×C₄	1	2	yes	—
60	C₂×#6104	C₂×C₄	1	2	yes	—
61	#88184	—	2	1	no	—
62	#88184	C₂×C₄	1	2	yes	—
63	C₂×#6099	—	2	2	no	—
64	C₂×#6099	D₄	1	1	yes	characteristic
65	C₂×#6099	D₄	1	1	yes	characteristic
66	C₂²×#1055	—	2	1	no	—
67	C₂²×#1055	—	2	2	no	—
68	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
69	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
70	#88155	—	4	4	no	—
71	C₂×#6094	—	2	2	no	—
72	C₂×C₈×D₁₃	—	2	2	no	—
73	#88129	—	2	1	no	—
74	#88128	C₂×C₄	1	1	yes	characteristic
75	C₄×D₅₂	—	2	1	no	—
76	C₄×D₅₂	C₂³	1	2	yes	—
77	#88123	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₂²⋊C₈	—	2	1	no	—
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	#88072	C₂×C₄	1	2	yes	—
85	#88072	C₂×C₄	1	2	yes	—
86	C₂²⋊#1055	—	2	2	no	—
87	C₂²⋊#1055	—	2	2	no	—
88	#88060	—	2	2	no	—
89	#88060	—	2	2	no	—
90	#88049	C₂×C₄	1	2	yes	—
91	#88049	C₂×C₄	1	2	yes	—
92	#88047	C₂×C₄	1	2	yes	—
93	#88047	C₂×C₄	1	2	yes	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	C₂³	1	1	yes	characteristic
96	C₄⋊#1055	C₂³	1	1	yes	characteristic
97	#88043	D₄	1	2	yes	—
98	C₄×#1055	C₂×C₄	1	1	yes	characteristic
99	C₄×#1055	C₂×C₄	1	1	yes	characteristic
100	C₄×#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	C₂³	1	1	yes	characteristic
102	C₄×#1055	C₂³	1	2	yes	—
103	#18066	—	13	1	no	maximal, Sylow
104	C₁₃×#41	—	4	2	no	—
105	C₁₃×#41	—	4	2	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₃	—	2	2	no	—
116	#6127	—	4	2	no	—
117	#6127	—	4	2	no	—
118	C₂×D₅₂	—	2	1	no	—
119	C₂×D₅₂	—	2	1	no	—
120	C₂×D₅₂	C₂²×C₄	1	2	yes	—
121	C₂×C₄×D₁₃	—	2	2	no	—
122	C₂×Dic₂₆	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	4	2	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	#41	1	1	yes	characteristic
134	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
135	#6104	—	2	4	no	—
136	#6104	—	4	2	no	—
137	#6103	—	2	2	no	—
138	#6103	—	2	2	no	—
139	C₄⋊Dic₁₃	—	2	1	no	—
140	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
141	#6099	—	2	2	no	—
142	#6099	—	4	4	no	—
143	#6099	D₈	1	4	yes	complemented
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	—	2	1	no	—
147	C₂×#1055	—	4	1	no	—
148	C₂×#1055	—	4	2	no	—
149	C₂×#1055	—	4	4	no	—
150	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
151	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
152	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
153	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
154	C₂×#1055	C₂×D₄	1	2	yes	—
155	C₂×#1055	C₂×D₄	1	2	yes	—
156	#6094	—	4	4	no	—
157	C₈×D₁₃	—	4	4	no	—
158	#3169	—	13	1	no	—
159	#2935	—	13	1	no	—
160	#2935	—	13	1	no	—
161	#1589	—	13	2	no	—
162	#1581	—	13	2	no	—
163	#1581	—	13	2	no	—
164	C₈×D₈	—	13	2	no	—
165	C₂×#335	—	13	1	no	—
166	#1480	—	13	1	no	—
167	#1480	D₁₃	1	1	yes	characteristic, complemented
168	C₈×M₁₆	—	13	1	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂²×D₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	—	2	2	no	—
175	D₄×C₁₃	—	4	4	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	8	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
188	C₂×C₄×C₁₃	#135	1	2	yes	—
189	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₂²⋊D₁₃	—	4	4	no	—
193	C₂×Dic₁₃	—	2	2	no	—
194	D₅₂	—	2	2	no	—
195	D₅₂	—	2	2	no	—
196	D₅₂	—	4	2	no	—
197	D₅₂	—	8	1	no	—
198	C₄×D₁₃	—	4	2	no	—
199	C₄×D₁₃	—	4	2	no	—
200	Dic₂₆	—	4	2	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₈×C₁₃	—	4	1	no	—
203	C₈×C₁₃	—	4	1	no	—
204	#1055	—	2	1	no	—
205	#1055	—	2	1	no	—
206	#1055	—	2	1	no	—
207	#1055	—	2	2	no	—
208	#1055	—	4	1	no	—
209	#1055	—	4	1	no	—
210	#1055	#131	1	2	yes	complemented
211	#1055	C₂×D₈	1	4	yes	—
212	C₂×#131	—	26	1	no	—
213	C₂×#131	—	26	1	no	—
214	#532	—	13	1	no	—
215	#532	C₂×D₁₃	1	1	yes	characteristic
216	#500	—	13	1	no	—
217	#493	—	13	1	no	—
218	#486	—	13	1	no	—
219	#486	—	13	1	no	—
220	#466	—	13	2	no	—
221	#466	—	13	2	no	—
222	C₄×D₈	—	13	2	no	—
223	C₄×D₈	—	13	2	no	—
224	#436	—	13	2	no	—
225	#436	—	13	2	no	—
226	#435	—	26	2	no	—
227	#435	—	26	2	no	—
228	C₈×D₄	—	13	2	no	—
229	C₈×D₄	—	13	2	no	—
230	#431	C₂×D₁₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	—	13	1	no	—
232	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
233	#408	—	26	1	no	—
234	#408	—	26	1	no	—
235	C₄×M₁₆	—	13	1	no	—
236	C₂×C₄×C₈	—	13	1	no	—
237	#335	—	13	1	no	—
238	#335	—	13	1	no	—
239	#335	—	13	1	no	—
240	#335	—	13	1	no	—
241	D₄⋊C₈	—	13	2	no	—
242	D₄⋊C₈	—	13	2	no	—
243	D₄⋊C₈	C₂×D₁₃	1	2	yes	—
244	D₄⋊C₈	C₂×D₁₃	1	2	yes	—
245	#322	—	13	2	no	—
246	C₈²	—	13	2	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	1	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	4	2	no	—
251	C₂²×C₁₃	—	4	2	no	—
252	C₂²×C₁₃	C₄×D₈	1	2	yes	—
253	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂×D₁₃	—	4	2	no	—
255	C₂×D₁₃	—	4	2	no	—
256	C₂×D₁₃	—	4	2	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	C₄×D₈	1	2	yes	—
262	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
263	C₄×C₁₃	#568	1	1	yes	characteristic
264	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
265	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
266	Dic₁₃	—	4	2	no	—
267	C₂×#41	—	2	1	no	—
268	C₂×#41	—	26	1	no	—
269	C₂×D₈	—	13	2	no	—
270	C₂×D₈	—	13	2	no	—
271	#131	—	52	4	no	—
272	#131	—	52	4	no	—
273	C₂×M₁₆	—	13	1	no	—
274	C₂×M₁₆	—	13	1	no	—
275	C₂×M₁₆	—	26	2	no	—
276	C₂×M₁₆	—	26	2	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	1	no	—
280	C₂²×C₈	—	26	2	no	—
281	C₂²×C₈	—	26	2	no	—
282	C₂²×C₈	—	26	1	no	—
283	C₄⋊Q₈	—	13	1	no	—
284	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
285	#127	—	13	1	no	—
286	#127	C₄×D₁₃	1	1	yes	characteristic
287	#124	—	2	1	no	—
288	#124	—	26	1	no	—
289	#121	—	2	1	no	—
290	#121	—	13	2	no	—
291	#121	—	26	1	no	—
292	#121	C₄×D₁₃	1	2	yes	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	13	2	no	—
295	C₄×D₄	—	26	1	no	—
296	C₄×D₄	C₂²×D₁₃	1	2	yes	—
297	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
298	#107	—	13	2	no	—
299	#107	—	13	2	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	13	1	no	—
303	C₄⋊C₈	—	13	1	no	—
304	C₄⋊C₈	—	26	1	no	—
305	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
307	#102	—	13	2	no	—
308	#102	—	13	2	no	—
309	#102	—	13	2	no	—
310	#102	—	13	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	26	2	no	—
313	C₂²⋊C₈	—	26	2	no	—
314	C₂²⋊C₈	—	26	2	no	—
315	C₂²⋊C₈	—	26	2	no	—
316	#97	—	13	2	no	—
317	C₄×C₈	—	13	1	no	—
318	C₄×C₈	—	13	1	no	—
319	C₄×C₈	—	13	1	no	—
320	C₄×C₈	—	13	2	no	—
321	C₄×C₈	—	13	1	no	—
322	C₄×C₈	C₂²×D₁₃	1	2	yes	—
323	C₂×C₁₃	—	2	2	no	—
324	C₂×C₁₃	—	8	2	no	—
325	C₂×C₁₃	#2935	1	1	yes	characteristic
326	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
327	C₂×C₁₃	#2957	1	1	yes	characteristic
328	D₁₃	—	8	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	52	2	no	—
332	#41	—	52	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	26	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	13	2	no	—
339	C₂×D₄	—	26	2	no	—
340	C₂×D₄	—	26	1	no	—
341	C₂×D₄	—	26	1	no	—
342	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	26	2	no	—
345	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
347	C₂²×C₄	#6129	1	1	yes	characteristic
348	D₈	—	26	4	no	—
349	D₈	—	52	2	no	—
350	M₁₆	—	13	4	no	—
351	M₁₆	—	26	2	no	—
352	M₁₆	—	52	4	no	—
353	M₁₆	—	52	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	13	1	no	—
359	C₂×C₈	—	13	2	no	—
360	C₂×C₈	—	13	1	no	—
361	C₂×C₈	—	13	1	no	—
362	C₂×C₈	—	13	1	no	—
363	C₂×C₈	—	13	2	no	—
364	C₂×C₈	—	26	2	no	—
365	C₂×C₈	—	26	1	no	—
366	C₂×C₈	—	26	1	no	—
367	C₂×C₈	—	52	4	no	—
368	C₂×C₈	—	52	4	no	—
369	C₂×C₈	—	52	1	no	—
370	C₂×C₈	—	52	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	13	2	no	—
373	C₄⋊C₄	—	26	1	no	—
374	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	26	2	no	—
378	C₂²⋊C₄	—	26	2	no	—
379	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
380	C₄²	D₄×D₁₃	1	1	yes	characteristic
381	C₄²	#6129	1	1	yes	characteristic
382	C₄²	C₂³×D₁₃	1	1	yes	characteristic
383	C₁₃	#18066	1	1	yes	characteristic, complemented, Sylow
384	C₂³	—	2	2	no	—
385	C₂³	—	26	2	no	—
386	C₂³	#88135	1	1	yes	characteristic
387	Q₈	—	4	2	no	—
388	Q₈	—	52	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	1	no	—
394	D₄	—	26	2	no	—
395	D₄	—	26	2	no	—
396	D₄	—	52	4	no	—
397	D₄	—	52	2	no	—
398	D₄	—	104	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	—	52	2	no	—
407	C₂×C₄	—	52	2	no	—
408	C₂×C₄	#88135	1	1	yes	characteristic
409	C₂×C₄	#88135	1	1	yes	characteristic
410	C₂×C₄	#88135	1	1	yes	characteristic
411	C₂×C₄	D₈×D₁₃	1	2	yes	—
412	C₂×C₄	#88170	1	2	yes	—
413	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#6129	1	1	yes	characteristic
416	C₈	—	4	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	13	2	no	—
420	C₈	—	13	4	no	—
421	C₈	—	26	1	no	—
422	C₈	—	26	1	no	—
423	C₈	—	26	1	no	—
424	C₈	—	26	2	no	—
425	C₈	—	52	1	no	—
426	C₈	—	52	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	52	2	no	—
433	C₂²	—	52	2	no	—
434	C₂²	—	52	2	no	—
435	C₂²	#11718417	1	2	yes	—
436	C₂²	C₂×#88135	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	52	2	no	—
442	C₄	#11718417	1	2	yes	—
443	C₄	D₁₃×#131	1	1	yes	characteristic
444	C₄	#11719455	1	1	yes	characteristic
445	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
446	C₄	C₂×#88170	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	8	2	no	—
449	C₂	—	104	2	no	—
450	C₂	#13123576	1	1	yes	characteristic
451	C₂	C₂×#11718417	1	1	yes	characteristic
452	C₂	#13123749	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1480	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13125411	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1480	D₁₃
hypocenter	C₁₃	#18066
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1480

Complements

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

N	H ≅ G/N	type
2. #13123580	C₂	semidirect
3. #13123579	C₂	semidirect
4. #13113718	C₂	semidirect
5. #13113668	C₂	semidirect
6. #13113662	C₂	semidirect
7. #13113628	C₂	semidirect
8. C₂×#11718071	C₂	semidirect
9. #13113236	C₂	semidirect
10. #13113117	C₂	semidirect
11. C₁₃×#1480	C₂	semidirect
143. #6099	D₈	semidirect
167. #1480	D₁₃	semidirect
210. #1055	#131	semidirect
383. C₁₃	#18066	semidirect

Maximal subgroups

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

subgroup	index
#13125411	2
#13123580	2
#13123579	2
#13113718	2
#13113668	2
#13113662	2
#13113628	2
C₂×#11718071	2
#13113236	2
#13113117	2
C₁₃×#1480	2
#18066	13