Subgroups — #15834121

Order 3328.

638 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	#13124896	C₂	1	1	yes	maximal, characteristic
2	#13123968	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123902	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113718	C₂	1	2	yes	maximal, complemented
5	#13113711	C₂	1	2	yes	maximal, complemented
6	#13113703	C₂	1	2	yes	maximal, complemented
7	#13113633	C₂	1	2	yes	maximal, complemented
8	#13113624	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113288	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113119	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	#11719182	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	#11718899	C₄	1	2	yes	—
17	#11718688	C₄	1	1	yes	characteristic
18	C₄×#6106	C₂²	1	2	yes	—
19	Q₈×#1055	C₂²	1	2	yes	—
20	#11718682	C₄	1	1	yes	characteristic
21	#11718676	C₄	1	1	yes	characteristic
22	C₄×#6104	C₂²	1	2	yes	—
23	#11718673	—	2	2	no	—
24	#11718673	C₂²	1	2	yes	—
25	#11718669	C₄	1	1	yes	characteristic
26	#11718664	C₄	1	2	yes	—
27	#11718586	—	2	1	no	—
28	#11718586	C₂²	1	1	yes	characteristic
29	#11718586	C₂²	1	1	yes	characteristic
30	#11718585	—	2	1	no	—
31	#11718585	C₂²	1	1	yes	characteristic
32	#11718499	C₂²	1	2	yes	—
33	#11718495	C₂²	1	2	yes	—
34	#11718388	—	2	2	no	—
35	#11718349	—	2	1	no	—
36	C₈×D₅₂	—	2	1	no	—
37	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
41	#11718072	C₂²	1	2	yes	—
42	#11718071	C₂²	1	2	yes	—
43	#11718051	C₂²	1	2	yes	—
44	#11718051	C₂²	1	2	yes	—
45	#11718047	C₂²	1	2	yes	—
46	C₈×#1055	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
48	C₂×#6127	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×D₄×C₁₃	—	2	1	no	—
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#117	—	2	1	no	—
57	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	—	2	1	no	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×#6106	C₂×C₄	1	2	yes	—
61	C₂×#6104	C₂×C₄	1	2	yes	—
62	#88184	—	2	1	no	—
63	#88184	C₂×C₄	1	2	yes	—
64	C₂×#6099	—	2	1	no	—
65	C₂×#6099	—	2	2	no	—
66	C₂×#6094	—	2	2	no	—
67	C₂×C₈×D₁₃	—	2	2	no	—
68	#88129	—	2	1	no	—
69	#88128	C₂×C₄	1	1	yes	characteristic
70	C₄×D₅₂	—	2	1	no	—
71	C₄×D₅₂	C₂³	1	2	yes	—
72	#88123	C₂×C₄	1	1	yes	characteristic
73	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₁₃×C₂²⋊C₈	—	2	1	no	—
76	C₄×C₈×C₁₃	—	2	1	no	—
77	C₄×C₈×C₁₃	—	2	1	no	—
78	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	#88075	C₂×C₄	1	2	yes	—
81	#88072	C₂×C₄	1	2	yes	—
82	C₂²⋊#1055	—	2	2	no	—
83	C₂²⋊#1055	C₂×C₄	1	2	yes	—
84	C₂²⋊#1055	D₄	1	2	yes	—
85	#88060	—	2	2	no	—
86	#88060	—	2	2	no	—
87	#88049	C₂×C₄	1	2	yes	—
88	#88049	C₂×C₄	1	2	yes	—
89	#88048	C₂×C₄	1	2	yes	—
90	#88047	C₂×C₄	1	2	yes	—
91	C₄⋊#1055	—	2	1	no	—
92	C₄⋊#1055	—	2	2	no	—
93	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
94	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#1055	D₄	1	1	yes	characteristic
96	C₄⋊#1055	D₄	1	1	yes	characteristic
97	C₄⋊#1055	C₂³	1	2	yes	—
98	C₄×#1055	—	2	2	no	—
99	C₄×#1055	C₂³	1	2	yes	—
100	C₄×#1055	C₂³	1	2	yes	—
101	#18018	—	13	1	no	maximal, Sylow
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	4	1	no	—
104	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	C₂²×C₄	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	2	no	—
114	#6127	—	8	1	no	—
115	#6127	—	8	1	no	—
116	C₂×D₅₂	—	2	1	no	—
117	C₂×D₅₂	—	2	1	no	—
118	C₂×D₅₂	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₁₃	—	2	2	no	—
120	C₂×Dic₂₆	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	4	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
130	C₁₃×C₂²⋊C₄	—	2	1	no	—
131	C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	#41	1	1	yes	characteristic
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	#6106	—	2	4	no	—
141	#6104	—	4	2	no	—
142	#6103	—	2	2	no	—
143	#6103	—	2	2	no	—
144	C₄⋊Dic₁₃	—	2	1	no	—
145	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
146	#6099	—	8	2	no	—
147	#6099	—	8	1	no	—
148	C₂×#1055	—	2	2	no	—
149	C₂×#1055	C₂²×C₄	1	2	yes	—
150	C₂×#1055	C₂²×C₄	1	2	yes	—
151	C₂×#1055	C₂×D₄	1	2	yes	—
152	C₂×#1055	C₂×D₄	1	2	yes	—
153	#6094	—	8	2	no	—
154	C₈×D₁₃	—	8	2	no	—
155	#3106	—	13	1	no	—
156	#2991	—	13	1	no	—
157	#2979	—	13	1	no	—
158	#1589	—	13	2	no	—
159	#1588	—	13	2	no	—
160	#1586	—	13	2	no	—
161	C₈×SD₁₆	—	13	2	no	—
162	#1574	—	13	1	no	—
163	#1492	—	13	1	no	—
164	#1476	D₁₃	1	1	yes	characteristic, complemented
165	#1450	—	13	1	no	—
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₁₃	—	2	2	no	—
169	Q₈×C₁₃	—	2	1	no	—
170	Q₈×C₁₃	#131	1	2	yes	—
171	D₄×C₁₃	—	2	1	no	—
172	D₄×C₁₃	—	2	1	no	—
173	D₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	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	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
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	—	8	2	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	—	8	1	no	—
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	4	1	no	—
204	C₈×C₁₃	—	4	1	no	—
205	#1055	—	2	2	no	—
206	#1055	—	2	2	no	—
207	#1055	—	2	2	no	—
208	#1055	—	2	2	no	—
209	#1055	—	4	2	no	—
210	#532	—	13	1	no	—
211	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
212	#482	—	13	2	no	—
213	#477	—	13	1	no	—
214	#476	—	13	1	no	—
215	#460	—	13	1	no	—
216	#459	—	13	1	no	—
217	#449	—	13	2	no	—
218	C₈×Q₈	—	13	2	no	—
219	C₄×SD₁₆	—	13	2	no	—
220	C₄×D₈	—	13	2	no	—
221	#436	—	13	2	no	—
222	#436	—	13	2	no	—
223	#436	—	26	1	no	—
224	#436	—	26	2	no	—
225	C₈×D₄	—	13	2	no	—
226	C₈×D₄	—	26	1	no	—
227	#431	—	13	1	no	—
228	#431	—	13	1	no	—
229	#431	—	26	1	no	—
230	#431	C₂×D₁₃	1	1	yes	characteristic
231	#423	—	13	1	no	—
232	#423	—	26	1	no	—
233	#408	—	26	2	no	—
234	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
235	#335	—	13	2	no	—
236	#334	—	13	2	no	—
237	Q₈⋊C₈	C₂×D₁₃	1	1	yes	characteristic
238	Q₈⋊C₈	C₂×D₁₃	1	1	yes	characteristic
239	D₄⋊C₈	—	13	2	no	—
240	D₄⋊C₈	—	13	2	no	—
241	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
242	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
243	#322	—	13	2	no	—
244	C₈²	—	13	2	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	4	1	no	—
249	C₂²×C₁₃	—	4	1	no	—
250	C₂²×C₁₃	—	4	1	no	—
251	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂×D₁₃	—	4	2	no	—
253	C₂×D₁₃	—	4	2	no	—
254	C₂×D₁₃	—	4	2	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	4	1	no	—
260	C₄×C₁₃	—	4	1	no	—
261	C₄×C₁₃	#443	1	2	yes	—
262	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
263	C₄×C₁₃	#568	1	1	yes	characteristic
264	C₄×C₁₃	#576	1	1	yes	characteristic
265	C₄×C₁₃	#577	1	1	yes	characteristic
266	Dic₁₃	—	4	2	no	—
267	C₂×#41	—	26	1	no	—
268	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
269	C₂×SD₁₆	—	13	2	no	—
270	C₂×D₈	—	13	2	no	—
271	C₂×M₁₆	—	26	2	no	—
272	C₂×M₁₆	—	26	2	no	—
273	C₂×M₁₆	—	26	1	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₂²×C₈	—	26	2	no	—
276	C₄⋊Q₈	—	13	1	no	—
277	#127	—	13	1	no	—
278	#124	—	26	1	no	—
279	#121	—	13	2	no	—
280	#121	—	26	1	no	—
281	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
282	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	13	2	no	—
286	C₄×D₄	—	26	1	no	—
287	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
288	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
289	#117	—	2	1	no	—
290	#117	C₄×D₁₃	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
293	#107	—	13	2	no	—
294	#106	—	13	2	no	—
295	C₄⋊C₈	—	13	1	no	—
296	C₄⋊C₈	—	13	1	no	—
297	C₄⋊C₈	—	13	1	no	—
298	C₄⋊C₈	—	13	1	no	—
299	C₄⋊C₈	—	13	2	no	—
300	C₄⋊C₈	—	26	2	no	—
301	C₄⋊C₈	—	26	1	no	—
302	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
303	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
304	#103	—	13	2	no	—
305	#102	—	13	2	no	—
306	#102	—	13	2	no	—
307	#102	—	13	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	13	2	no	—
310	C₂²⋊C₈	—	13	2	no	—
311	C₂²⋊C₈	—	26	2	no	—
312	C₂²⋊C₈	—	26	2	no	—
313	C₂²⋊C₈	—	26	2	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	13	2	no	—
317	C₄×C₈	—	13	2	no	—
318	C₄×C₈	—	26	2	no	—
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	—	8	1	no	—
323	C₂×C₁₃	#2933	1	1	yes	characteristic
324	C₂×C₁₃	#2946	1	1	yes	characteristic
325	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
326	D₁₃	—	8	2	no	—
327	#41	—	2	2	no	—
328	#41	—	4	1	no	—
329	#41	—	104	1	no	—
330	#41	—	104	1	no	—
331	C₂×Q₈	—	26	1	no	—
332	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	13	2	no	—
335	C₂×D₄	—	26	2	no	—
336	C₂×D₄	—	26	1	no	—
337	C₂×D₄	—	26	1	no	—
338	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	26	2	no	—
343	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
344	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
345	C₂²×C₄	#6129	1	1	yes	characteristic
346	SD₁₆	—	26	4	no	—
347	D₈	—	52	2	no	—
348	M₁₆	—	104	2	no	—
349	M₁₆	—	104	2	no	—
350	M₁₆	—	104	1	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	13	2	no	—
357	C₂×C₈	—	13	2	no	—
358	C₂×C₈	—	13	2	no	—
359	C₂×C₈	—	13	2	no	—
360	C₂×C₈	—	26	2	no	—
361	C₂×C₈	—	104	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	13	2	no	—
365	C₄⋊C₄	—	26	1	no	—
366	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	26	2	no	—
372	C₂²⋊C₄	—	26	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
377	C₄²	D₄×D₁₃	1	1	yes	characteristic
378	C₄²	#6129	1	1	yes	characteristic
379	C₄²	C₂³×D₁₃	1	1	yes	characteristic
380	C₁₃	#18018	1	1	yes	characteristic, complemented, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	26	2	no	—
383	C₂³	#88135	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	104	1	no	—
386	Q₈	#88155	1	2	yes	—
387	D₄	—	2	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	4	2	no	—
390	D₄	—	26	2	no	—
391	D₄	—	26	2	no	—
392	D₄	—	52	2	no	—
393	D₄	—	104	1	no	—
394	D₄	—	104	2	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	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	52	2	no	—
409	C₂×C₄	—	52	2	no	—
410	C₂×C₄	#88135	1	1	yes	characteristic
411	C₂×C₄	#88135	1	1	yes	characteristic
412	C₂×C₄	#88135	1	1	yes	characteristic
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	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	26	2	no	—
421	C₈	—	26	2	no	—
422	C₈	—	26	2	no	—
423	C₈	—	26	2	no	—
424	C₈	—	52	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	52	2	no	—
432	C₂²	—	52	2	no	—
433	C₂²	—	52	2	no	—
434	C₂²	C₂×#88135	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	52	2	no	—
442	C₄	#11718485	1	2	yes	—
443	C₄	C₂×#88155	1	1	yes	characteristic
444	C₄	#11719450	1	1	yes	characteristic
445	C₄	#11719474	1	1	yes	characteristic
446	C₄	#11719475	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	—	104	2	no	—
450	C₂	#13123557	1	1	yes	characteristic
451	C₂	#13123671	1	1	yes	characteristic
452	C₂	C₂×#11718485	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×#1476	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124896	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1476	D₁₃
hypocenter	C₁₃	#18018
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
2. #13123968	C₂	semidirect
3. #13123902	C₂	semidirect
4. #13113718	C₂	semidirect
5. #13113711	C₂	semidirect
6. #13113703	C₂	semidirect
7. #13113633	C₂	semidirect
8. #13113624	C₂	semidirect
9. #13113288	C₂	semidirect
10. #13113119	C₂	semidirect
11. C₁₃×#1476	C₂	semidirect
164. #1476	D₁₃	semidirect
380. C₁₃	#18018	semidirect

Maximal subgroups

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

subgroup	index
#13124896	2
#13123968	2
#13123902	2
#13113718	2
#13113711	2
#13113703	2
#13113633	2
#13113624	2
#13113288	2
#13113119	2
C₁₃×#1476	2
#18018	13