Subgroups — #15845387

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124890	C₂	1	2	yes	maximal, complemented
2	C₈×#6127	C₂	1	1	yes	maximal, characteristic, complemented
3	#13114249	C₂	1	2	yes	maximal, complemented
4	#13114242	C₂	1	2	yes	maximal, complemented
5	#13114237	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114232	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114193	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114188	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113584	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113498	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	C₂²	1	2	yes	—
13	C₄×#6127	C₂²	1	1	yes	characteristic
14	C₁₃×#500	C₂²	1	1	yes	characteristic
15	C₁₃×#493	C₂²	1	1	yes	characteristic
16	C₁₃×#486	C₂²	1	2	yes	—
17	C₁₃×#466	—	2	1	no	—
18	C₁₃×#466	—	2	1	no	—
19	C₄×C₁₃×D₈	—	2	1	no	—
20	C₄×C₁₃×D₈	—	2	1	no	—
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	#11718752	C₂²	1	2	yes	—
25	#11718745	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	C₄×#6105	—	2	2	no	—
31	C₄×#6104	—	2	2	no	—
32	#11718586	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	#11718138	C₂²	1	2	yes	—
41	#11718138	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	C₂×C₁₃×D₈	—	2	1	no	—
50	C₂×C₁₃×D₈	—	2	1	no	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₁₃×#127	C₂³	1	2	yes	—
55	C₁₃×#124	—	2	2	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₁₃×#121	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×#6105	—	2	2	no	—
62	C₂×#6104	—	2	2	no	—
63	C₄×C₂²⋊D₁₃	—	2	1	no	—
64	C₄×C₂²⋊D₁₃	—	2	1	no	—
65	#88180	D₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	—	2	1	no	—
67	C₂×C₈×D₁₃	—	2	1	no	—
68	C₄×D₅₂	D₄	1	1	yes	characteristic
69	C₄×D₅₂	C₂³	1	1	yes	characteristic
70	#88126	—	2	1	no	—
71	C₄²×D₁₃	—	2	1	no	—
72	C₄×Dic₂₆	D₄	1	1	yes	characteristic
73	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#107	—	2	1	no	—
76	C₁₃×#102	—	2	2	no	—
77	C₁₃×#102	—	2	2	no	—
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	#88072	—	2	2	no	—
83	#88072	—	2	2	no	—
84	C₂²⋊#1055	—	2	2	no	—
85	C₂²⋊#1055	—	2	1	no	—
86	#88060	—	2	1	no	—
87	#88060	—	2	1	no	—
88	#88054	—	2	1	no	—
89	#88054	—	2	1	no	—
90	C₈×Dic₁₃	—	2	1	no	—
91	C₈×Dic₁₃	—	2	1	no	—
92	#88050	—	2	2	no	—
93	#88049	—	2	2	no	—
94	#88048	—	2	2	no	—
95	#88047	—	2	2	no	—
96	C₄⋊#1055	C₂³	1	2	yes	—
97	C₄⋊#1055	C₂³	1	2	yes	—
98	C₄⋊#1055	C₂³	1	1	yes	characteristic
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	C₄×#1055	—	2	2	no	—
101	C₄×#1055	—	2	1	no	—
102	#19128	—	13	1	no	maximal, Sylow
103	C₁₃×#41	—	8	4	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₁₃	—	2	1	no	—
114	#6127	—	2	2	no	—
115	#6127	—	2	2	no	—
116	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	—	2	1	no	—
118	C₂×C₄×D₁₃	—	2	1	no	—
119	C₂×C₄×D₁₃	—	2	1	no	—
120	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
121	C₁₃×D₈	—	4	2	no	—
122	C₁₃×D₈	—	4	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	4	1	no	—
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	#41	1	1	yes	characteristic
136	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂²⋊Dic₁₃	—	2	1	no	—
138	#6105	—	4	4	no	—
139	#6104	—	4	4	no	—
140	#6103	—	2	1	no	—
141	#6103	—	2	1	no	—
142	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
143	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
144	#6101	—	2	1	no	—
145	#6101	—	2	1	no	—
146	C₄×Dic₁₃	—	2	1	no	—
147	C₄×Dic₁₃	—	2	1	no	—
148	C₄×Dic₁₃	—	2	1	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	2	1	no	—
152	C₂×#1055	—	2	1	no	—
153	C₈×D₁₃	—	4	2	no	—
154	C₈×D₁₃	—	4	2	no	—
155	#3169	D₁₃	1	1	yes	characteristic, complemented
156	#3106	—	13	2	no	—
157	C₈×#41	—	13	1	no	—
158	#1678	—	13	2	no	—
159	#1677	—	13	2	no	—
160	#1676	—	13	1	no	—
161	#1675	—	13	1	no	—
162	#1668	—	13	1	no	—
163	#1667	—	13	1	no	—
164	#1564	—	13	1	no	—
165	#1543	—	13	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	#121	1	1	yes	characteristic
168	C₂²×D₁₃	—	2	1	no	—
169	Q₈×C₁₃	—	8	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	8	2	no	—
175	D₄×C₁₃	—	8	4	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	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	2	no	—
182	C₂×C₄×C₁₃	—	8	4	no	—
183	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂²⋊D₁₃	—	2	4	no	—
190	C₂×Dic₁₃	—	2	1	no	—
191	C₂×Dic₁₃	—	2	1	no	—
192	C₂×Dic₁₃	—	2	1	no	—
193	D₅₂	—	2	1	no	—
194	D₅₂	#135	1	2	yes	—
195	C₄×D₁₃	—	2	4	no	—
196	C₄×D₁₃	—	4	1	no	—
197	C₄×D₁₃	—	4	1	no	—
198	C₄×D₁₃	—	4	2	no	—
199	Dic₂₆	—	2	1	no	—
200	Dic₂₆	#135	1	2	yes	—
201	C₈×C₁₃	—	2	1	no	—
202	C₈×C₁₃	—	2	1	no	—
203	C₈×C₁₃	—	2	1	no	—
204	C₈×C₁₃	#135	1	2	yes	—
205	#1055	—	4	1	no	—
206	#1055	—	4	2	no	—
207	#1055	—	4	2	no	—
208	#1055	—	4	1	no	—
209	#532	C₂×D₁₃	1	2	yes	—
210	C₄×#41	—	13	1	no	—
211	#500	C₂×D₁₃	1	1	yes	characteristic
212	#493	C₂×D₁₃	1	1	yes	characteristic
213	#486	C₂×D₁₃	1	2	yes	—
214	#482	—	26	2	no	—
215	#477	—	13	2	no	—
216	#476	—	13	2	no	—
217	#466	—	2	1	no	—
218	#466	—	2	1	no	—
219	#460	—	13	2	no	—
220	#459	—	13	2	no	—
221	#449	—	26	2	no	—
222	C₈×Q₈	—	13	1	no	—
223	C₈×Q₈	—	13	1	no	—
224	C₄×SD₁₆	—	26	2	no	—
225	C₄×D₈	—	2	1	no	—
226	C₄×D₈	—	2	1	no	—
227	C₄×D₈	—	26	2	no	—
228	C₈×D₄	—	13	1	no	—
229	C₈×D₄	—	13	1	no	—
230	C₈×D₄	—	26	1	no	—
231	C₈×D₄	—	26	1	no	—
232	#431	—	13	1	no	—
233	#431	—	13	2	no	—
234	#431	—	26	1	no	—
235	C₂×C₄×C₈	—	26	1	no	—
236	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
237	#335	—	13	1	no	—
238	#335	—	13	1	no	—
239	#334	—	13	2	no	—
240	#333	—	13	2	no	—
241	#333	—	13	2	no	—
242	#331	—	13	2	no	—
243	#331	—	13	2	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
251	C₂×D₁₃	—	2	2	no	—
252	C₂×D₁₃	—	4	1	no	—
253	C₂×D₁₃	—	4	1	no	—
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	8	2	no	—
258	C₄×C₁₃	#472	1	2	yes	—
259	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
260	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
261	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
262	C₄×C₁₃	#575	1	1	yes	characteristic
263	Dic₁₃	—	2	2	no	—
264	Dic₁₃	—	4	1	no	—
265	Dic₁₃	—	4	1	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	13	1	no	—
268	C₂×SD₁₆	—	26	2	no	—
269	C₂×D₈	—	2	1	no	—
270	C₂×D₈	—	2	1	no	—
271	C₂×D₈	—	26	2	no	—
272	C₂²×C₈	—	26	1	no	—
273	C₂²×C₈	—	26	1	no	—
274	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
276	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
277	#127	C₂²×D₁₃	1	2	yes	—
278	#124	—	2	2	no	—
279	#121	—	2	2	no	—
280	#121	—	2	2	no	—
281	C₄×Q₈	—	13	1	no	—
282	C₄×Q₈	—	13	1	no	—
283	C₄×D₄	—	2	2	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	13	1	no	—
286	C₄×D₄	—	13	1	no	—
287	C₄×D₄	—	26	1	no	—
288	C₄×D₄	—	26	1	no	—
289	#117	—	13	1	no	—
290	#117	—	26	1	no	—
291	C₂×C₄²	—	26	1	no	—
292	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
293	#107	—	2	1	no	—
294	#107	—	2	1	no	—
295	#107	—	26	2	no	—
296	#106	—	26	2	no	—
297	C₄⋊C₈	—	13	1	no	—
298	C₄⋊C₈	—	13	1	no	—
299	C₄⋊C₈	—	13	2	no	—
300	C₄⋊C₈	—	13	2	no	—
301	C₄⋊C₈	—	26	1	no	—
302	C₄⋊C₈	—	26	1	no	—
303	#103	—	26	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	26	2	no	—
307	#102	—	26	2	no	—
308	#102	—	26	2	no	—
309	C₂²⋊C₈	—	26	2	no	—
310	C₂²⋊C₈	—	26	1	no	—
311	C₂²⋊C₈	—	26	1	no	—
312	C₂²⋊C₈	—	26	1	no	—
313	C₄×C₈	—	26	1	no	—
314	C₄×C₈	—	26	1	no	—
315	C₄×C₈	—	26	2	no	—
316	C₄×C₈	—	26	1	no	—
317	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
318	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
321	C₂×C₁₃	—	4	1	no	—
322	C₂×C₁₃	—	16	2	no	—
323	C₂×C₁₃	#3035	1	1	yes	characteristic
324	C₂×C₁₃	#3050	1	1	yes	characteristic
325	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
326	D₁₃	—	4	2	no	—
327	#41	—	8	4	no	—
328	#41	—	26	2	no	—
329	#41	—	26	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	13	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	13	1	no	—
337	C₂×D₄	—	26	1	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	26	1	no	—
340	C₂²×C₄	—	26	1	no	—
341	C₂²×C₄	—	26	1	no	—
342	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
343	C₂²×C₄	#6129	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
345	SD₁₆	—	52	4	no	—
346	D₈	—	4	2	no	—
347	D₈	—	4	2	no	—
348	D₈	—	52	4	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	26	2	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	26	1	no	—
354	C₂×C₈	—	26	1	no	—
355	C₂×C₈	—	52	2	no	—
356	C₂×C₈	—	52	2	no	—
357	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
358	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
360	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	13	1	no	—
364	C₄⋊C₄	—	13	1	no	—
365	C₄⋊C₄	—	26	1	no	—
366	C₄⋊C₄	—	26	1	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	26	1	no	—
370	C₂²⋊C₄	—	26	1	no	—
371	C₂²⋊C₄	—	26	1	no	—
372	C₄²	—	26	1	no	—
373	C₄²	—	26	1	no	—
374	C₄²	—	26	1	no	—
375	C₄²	D₄×D₁₃	1	1	yes	characteristic
376	C₄²	#6129	1	1	yes	characteristic
377	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
378	C₄²	C₂³×D₁₃	1	1	yes	characteristic
379	C₁₃	#19128	1	1	yes	characteristic, complemented, Sylow
380	C₂³	—	4	2	no	—
381	C₂³	—	26	1	no	—
382	C₂³	#88192	1	1	yes	characteristic
383	Q₈	—	8	2	no	—
384	Q₈	—	13	2	no	—
385	Q₈	—	26	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	4	no	—
392	D₄	—	13	2	no	—
393	D₄	—	26	4	no	—
394	D₄	—	26	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	—	26	4	no	—
403	C₂×C₄	—	26	1	no	—
404	C₂×C₄	—	26	1	no	—
405	C₂×C₄	—	26	1	no	—
406	C₂×C₄	—	52	1	no	—
407	C₂×C₄	—	52	1	no	—
408	C₂×C₄	—	52	2	no	—
409	C₂×C₄	#88192	1	1	yes	characteristic
410	C₂×C₄	#88192	1	1	yes	characteristic
411	C₂×C₄	#88192	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂×#6129	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	52	2	no	—
419	C₈	—	52	2	no	—
420	C₈	—	52	1	no	—
421	C₈	—	52	1	no	—
422	C₈	#88204	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	26	2	no	—
430	C₂²	—	52	1	no	—
431	C₂²	—	52	1	no	—
432	C₂²	C₂×#88192	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	26	2	no	—
438	C₄	—	52	1	no	—
439	C₄	—	52	1	no	—
440	C₄	#11718821	1	2	yes	—
441	C₄	D₁₃×#135	1	1	yes	characteristic
442	C₄	D₁₃×#135	1	1	yes	characteristic
443	C₄	C₂×#88204	1	1	yes	characteristic
444	C₄	#11719527	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	16	2	no	—
447	C₂	—	52	2	no	—
448	C₂	#13124285	1	1	yes	characteristic
449	C₂	#13124413	1	1	yes	characteristic
450	C₂	C₂×#11718821	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88192
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3169	C₂
socle	C₂²×C₁₃	C₂×#121
hypercenter	#3169	D₁₃
hypocenter	C₁₃	#19128
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #13124890	C₂	semidirect
2. C₈×#6127	C₂	semidirect
3. #13114249	C₂	semidirect
4. #13114242	C₂	semidirect
5. #13114237	C₂	semidirect
6. #13114232	C₂	semidirect
7. #13114193	C₂	semidirect
8. #13114188	C₂	semidirect
9. #13113584	C₂	semidirect
10. #13113498	C₂	semidirect
11. C₁₃×#3169	C₂	semidirect
155. #3169	D₁₃	semidirect
379. C₁₃	#19128	semidirect

Maximal subgroups

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

subgroup	index
#13124890	2
C₈×#6127	2
#13114249	2
#13114242	2
#13114237	2
#13114232	2
#13114193	2
#13114188	2
#13113584	2
#13113498	2
C₁₃×#3169	2
#19128	13