Subgroups — #15832489

Order 3328.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#6127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#88204	C₂	1	1	yes	maximal, characteristic
3	#13113712	C₂	1	2	yes	maximal, complemented
4	#13113705	C₂	1	2	yes	maximal, complemented
5	#13113698	C₂	1	2	yes	maximal, complemented
6	#13113691	C₂	1	2	yes	maximal, complemented
7	#13113582	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113218	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11718046	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88204	C₄	1	1	yes	characteristic
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	C₁₃×#446	C₂²	1	2	yes	—
16	C₁₃×#436	C₂²	1	2	yes	—
17	C₁₃×#435	—	2	2	no	—
18	C₁₃×#431	—	2	1	no	—
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×M₁₆	—	2	1	no	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	#11718894	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₃	—	2	2	no	—
24	C₄×#6107	C₄	1	1	yes	characteristic
25	C₄×#6107	C₂²	1	1	yes	characteristic
26	C₄×#6106	C₄	1	1	yes	characteristic
27	C₄×#6106	C₂²	1	1	yes	characteristic
28	C₄×#6105	C₄	1	1	yes	characteristic
29	C₄×#6105	C₂²	1	1	yes	characteristic
30	C₄×#6104	C₄	1	1	yes	characteristic
31	C₄×#6104	C₂²	1	1	yes	characteristic
32	#11718663	C₄	1	1	yes	characteristic
33	#11718659	C₄	1	1	yes	characteristic
34	#11718586	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	C₈×D₅₂	C₂²	1	2	yes	—
38	#11718346	—	2	1	no	—
39	C₄×C₈×D₁₃	—	2	1	no	—
40	C₈×Dic₂₆	C₂²	1	2	yes	—
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	D₄⋊#1055	C₂²	1	2	yes	—
43	#11718076	C₂²	1	2	yes	—
44	#11718075	C₂²	1	2	yes	—
45	#11718072	C₂²	1	2	yes	—
46	#11718071	C₂²	1	2	yes	—
47	#11718046	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×#6127	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂²×C₈×C₁₃	D₄	1	2	yes	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	#88204	—	2	4	no	—
64	C₂×#6107	C₂×C₄	1	1	yes	characteristic
65	C₂×#6106	C₂×C₄	1	1	yes	characteristic
66	C₂×#6105	C₂×C₄	1	1	yes	characteristic
67	C₂×#6104	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₃	—	2	1	no	—
69	C₄×C₂²⋊D₁₃	—	2	1	no	—
70	#88180	C₂×C₄	1	1	yes	characteristic
71	C₂²×#1055	—	2	1	no	—
72	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
73	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₁₃	—	2	2	no	—
75	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
76	C₄×D₅₂	C₂³	1	1	yes	characteristic
77	#88126	—	2	1	no	—
78	C₄²×D₁₃	—	2	1	no	—
79	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
83	C₁₃×C₂²⋊C₈	—	2	1	no	—
84	C₁₃×C₂²⋊C₈	—	2	2	no	—
85	C₁₃×#97	—	2	2	no	—
86	C₄×C₈×C₁₃	—	2	1	no	—
87	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	2	yes	—
90	#88075	C₂×C₄	1	1	yes	characteristic
91	#88075	C₂×C₄	1	1	yes	characteristic
92	#88072	C₂×C₄	1	1	yes	characteristic
93	#88072	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊#1055	—	2	1	no	—
95	#88060	—	2	2	no	—
96	#88054	—	2	2	no	—
97	C₈×Dic₁₃	—	2	2	no	—
98	#88050	C₂×C₄	1	1	yes	characteristic
99	#88050	C₂×C₄	1	1	yes	characteristic
100	#88049	C₂×C₄	1	1	yes	characteristic
101	#88049	C₂×C₄	1	1	yes	characteristic
102	#88048	C₂×C₄	1	1	yes	characteristic
103	#88048	C₂×C₄	1	1	yes	characteristic
104	#88047	C₂×C₄	1	1	yes	characteristic
105	#88047	C₂×C₄	1	1	yes	characteristic
106	C₄⋊#1055	C₂³	1	2	yes	—
107	C₄×#1055	—	2	1	no	—
108	C₄×#1055	—	2	1	no	—
109	C₄×#1055	C₂×C₄	1	1	yes	characteristic
110	C₄×#1055	C₂×C₄	1	1	yes	characteristic
111	C₄×#1055	C₂³	1	2	yes	—
112	C₄×#1055	C₂³	1	1	yes	characteristic
113	C₄×#1055	C₂³	1	1	yes	characteristic
114	#17868	—	13	1	no	maximal, Sylow
115	C₁₃×#41	—	2	2	no	—
116	C₁₃×#41	—	2	2	no	—
117	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₂×C₂²⋊D₁₃	—	2	1	no	—
127	#6127	—	2	2	no	—
128	#6127	M₁₆	1	4	yes	complemented
129	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₁₃	—	2	1	no	—
131	C₂×C₄×D₁₃	—	2	1	no	—
132	C₂×C₄×D₁₃	—	2	1	no	—
133	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
134	C₁₃×M₁₆	—	4	4	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	4	2	no	—
137	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	#41	1	1	yes	characteristic
152	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²⋊Dic₁₃	—	2	1	no	—
154	#6107	—	2	2	no	—
155	#6106	—	2	2	no	—
156	#6105	—	2	2	no	—
157	#6104	—	2	2	no	—
158	#6103	—	2	1	no	—
159	#6103	—	2	1	no	—
160	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
162	#6101	—	2	1	no	—
163	#6101	—	2	1	no	—
164	C₄×Dic₁₃	—	2	1	no	—
165	C₄×Dic₁₃	—	2	1	no	—
166	C₄×Dic₁₃	—	2	1	no	—
167	C₂×#1055	—	2	4	no	—
168	C₂×#1055	—	2	2	no	—
169	C₂×#1055	—	2	2	no	—
170	C₂×#1055	—	2	2	no	—
171	C₂×#1055	—	2	2	no	—
172	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
173	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
174	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
175	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
176	C₈×D₁₃	—	4	4	no	—
177	#2965	D₁₃	1	1	yes	characteristic, complemented
178	C₈×#41	—	13	1	no	—
179	C₄×#135	—	13	1	no	—
180	#1588	—	13	2	no	—
181	#1587	—	13	2	no	—
182	#1586	—	13	2	no	—
183	#1585	—	13	2	no	—
184	#1564	—	13	1	no	—
185	#1476	—	13	1	no	—
186	#1476	—	13	1	no	—
187	C₂×#322	—	13	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
190	C₂²×D₁₃	—	2	1	no	—
191	Q₈×C₁₃	—	2	1	no	—
192	Q₈×C₁₃	—	2	1	no	—
193	D₄×C₁₃	—	2	1	no	—
194	D₄×C₁₃	—	2	1	no	—
195	D₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
208	C₂×C₄×C₁₃	#131	1	2	yes	—
209	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂²⋊D₁₃	—	2	4	no	—
213	C₂×Dic₁₃	—	2	1	no	—
214	C₂×Dic₁₃	—	2	1	no	—
215	C₂×Dic₁₃	—	2	1	no	—
216	D₅₂	—	2	1	no	—
217	D₅₂	C₂×M₁₆	1	2	yes	—
218	C₄×D₁₃	—	2	4	no	—
219	C₄×D₁₃	—	4	2	no	—
220	C₄×D₁₃	—	4	2	no	—
221	Dic₂₆	—	2	1	no	—
222	Dic₂₆	C₂×M₁₆	1	2	yes	—
223	C₈×C₁₃	—	2	2	no	—
224	C₈×C₁₃	—	2	2	no	—
225	C₈×C₁₃	—	4	2	no	—
226	#1055	—	2	4	no	—
227	#1055	—	2	1	no	—
228	#1055	—	2	1	no	—
229	#1055	—	2	1	no	—
230	#1055	—	2	1	no	—
231	#1055	—	4	2	no	—
232	C₂×#135	—	13	1	no	—
233	C₄×#41	—	13	1	no	—
234	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
235	#446	C₂×D₁₃	1	2	yes	—
236	C₈×Q₈	—	13	2	no	—
237	C₄×Q₁₆	—	13	1	no	—
238	C₄×Q₁₆	—	13	1	no	—
239	C₄×SD₁₆	—	13	1	no	—
240	C₄×SD₁₆	—	13	1	no	—
241	C₄×SD₁₆	—	13	1	no	—
242	C₄×SD₁₆	—	13	1	no	—
243	C₄×D₈	—	13	1	no	—
244	C₄×D₈	—	13	1	no	—
245	#436	C₂×D₁₃	1	2	yes	—
246	#435	—	2	2	no	—
247	C₈×D₄	—	13	2	no	—
248	C₈×D₄	—	26	2	no	—
249	#431	—	2	1	no	—
250	#431	—	13	1	no	—
251	#431	—	26	1	no	—
252	#431	C₂×D₁₃	1	1	yes	characteristic
253	#427	—	13	1	no	—
254	#416	—	13	1	no	—
255	#416	—	13	1	no	—
256	C₄×M₁₆	—	2	1	no	—
257	C₂×C₄×C₈	—	13	1	no	—
258	C₂×C₄×C₈	—	13	1	no	—
259	C₂×C₄×C₈	—	26	1	no	—
260	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
261	#335	—	13	2	no	—
262	#334	—	13	2	no	—
263	Q₈⋊C₈	—	13	2	no	—
264	Q₈⋊C₈	—	13	2	no	—
265	D₄⋊C₈	—	13	2	no	—
266	D₄⋊C₈	—	13	2	no	—
267	#322	—	13	2	no	—
268	#322	—	13	2	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	4	1	no	—
272	C₂²×C₁₃	—	4	1	no	—
273	C₂²×C₁₃	—	4	1	no	—
274	C₂²×C₁₃	#435	1	2	yes	—
275	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂×D₁₃	—	2	2	no	—
277	C₂×D₁₃	—	4	1	no	—
278	C₂×D₁₃	—	4	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	4	1	no	—
283	C₄×C₁₃	—	4	1	no	—
284	C₄×C₁₃	#435	1	2	yes	—
285	C₄×C₁₃	#443	1	2	yes	—
286	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
287	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
288	C₄×C₁₃	#575	1	2	yes	—
289	Dic₁₃	—	2	2	no	—
290	Dic₁₃	—	4	1	no	—
291	Dic₁₃	—	4	1	no	—
292	C₂×#41	—	13	1	no	—
293	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
294	#135	—	26	4	no	—
295	C₂×Q₁₆	—	13	1	no	—
296	C₂×SD₁₆	—	13	1	no	—
297	C₂×SD₁₆	—	13	1	no	—
298	C₂×D₈	—	13	1	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂²×C₈	—	13	1	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	26	1	no	—
303	C₂²×C₈	—	26	2	no	—
304	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
305	C₄×Q₈	—	13	1	no	—
306	C₄×Q₈	—	13	1	no	—
307	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
308	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	13	1	no	—
312	C₄×D₄	—	13	1	no	—
313	C₄×D₄	—	26	1	no	—
314	C₄×D₄	—	26	1	no	—
315	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
316	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
317	#117	—	2	1	no	—
318	#117	—	13	1	no	—
319	#117	—	26	1	no	—
320	#117	C₄×D₁₃	1	1	yes	characteristic
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	26	1	no	—
323	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
324	#107	—	13	1	no	—
325	#107	—	13	1	no	—
326	#106	—	13	1	no	—
327	#106	—	13	1	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	13	2	no	—
330	C₄⋊C₈	—	26	2	no	—
331	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
332	#103	—	13	1	no	—
333	#103	—	13	1	no	—
334	#103	—	13	1	no	—
335	#103	—	13	1	no	—
336	#102	—	13	1	no	—
337	#102	—	13	1	no	—
338	#102	—	13	1	no	—
339	#102	—	13	1	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	2	no	—
342	C₂²⋊C₈	—	26	1	no	—
343	C₂²⋊C₈	—	26	2	no	—
344	#97	—	2	2	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	—	13	1	no	—
347	C₄×C₈	—	13	1	no	—
348	C₄×C₈	—	13	1	no	—
349	C₄×C₈	—	13	1	no	—
350	C₄×C₈	—	13	2	no	—
351	C₄×C₈	—	26	2	no	—
352	C₄×C₈	—	26	1	no	—
353	C₄×C₈	—	26	1	no	—
354	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
355	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₁₃	1	2	yes	—
357	C₂×C₁₃	—	2	2	no	—
358	C₂×C₁₃	—	8	1	no	—
359	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
360	C₂×C₁₃	#2943	1	1	yes	characteristic
361	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
362	D₁₃	—	4	2	no	—
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	13	4	no	—
366	#41	—	26	2	no	—
367	C₂×Q₈	—	13	1	no	—
368	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	13	1	no	—
371	C₂×D₄	—	26	1	no	—
372	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	26	1	no	—
377	C₂²×C₄	—	26	1	no	—
378	C₂²×C₄	—	26	1	no	—
379	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
380	C₂²×C₄	#6127	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
382	Q₁₆	—	26	2	no	—
383	SD₁₆	—	26	2	no	—
384	SD₁₆	—	26	2	no	—
385	D₈	—	26	2	no	—
386	M₁₆	—	4	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	2	no	—
389	C₂×C₈	—	13	1	no	—
390	C₂×C₈	—	13	1	no	—
391	C₂×C₈	—	13	1	no	—
392	C₂×C₈	—	13	1	no	—
393	C₂×C₈	—	26	4	no	—
394	C₂×C₈	—	26	2	no	—
395	C₂×C₈	—	26	2	no	—
396	C₂×C₈	—	26	2	no	—
397	C₂×C₈	—	26	2	no	—
398	C₂×C₈	—	52	4	no	—
399	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
400	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	13	1	no	—
404	C₄⋊C₄	—	13	1	no	—
405	C₄⋊C₄	—	26	1	no	—
406	C₄⋊C₄	—	26	1	no	—
407	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
408	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	26	1	no	—
413	C₂²⋊C₄	—	26	1	no	—
414	C₂²⋊C₄	—	26	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	26	1	no	—
419	C₄²	—	26	1	no	—
420	C₄²	—	26	1	no	—
421	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
422	C₄²	#6127	1	1	yes	characteristic
423	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
424	C₄²	C₂³×D₁₃	1	1	yes	characteristic
425	C₁₃	#17868	1	1	yes	characteristic, complemented, Sylow
426	C₂³	—	2	1	no	—
427	C₂³	—	26	1	no	—
428	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
429	Q₈	—	2	1	no	—
430	Q₈	—	2	1	no	—
431	Q₈	—	13	2	no	—
432	Q₈	—	26	1	no	—
433	D₄	—	2	1	no	—
434	D₄	—	2	1	no	—
435	D₄	—	4	2	no	—
436	D₄	—	13	2	no	—
437	D₄	—	26	4	no	—
438	D₄	—	26	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	26	1	no	—
448	C₂×C₄	—	26	4	no	—
449	C₂×C₄	—	26	1	no	—
450	C₂×C₄	—	26	1	no	—
451	C₂×C₄	—	52	2	no	—
452	C₂×C₄	—	52	2	no	—
453	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
454	C₂×C₄	#88161	1	2	yes	—
455	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
456	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
457	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂×#6127	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	26	4	no	—
465	C₈	—	26	1	no	—
466	C₈	—	26	1	no	—
467	C₈	—	26	1	no	—
468	C₈	—	26	1	no	—
469	C₈	—	52	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	26	2	no	—
476	C₂²	—	52	1	no	—
477	C₂²	—	52	1	no	—
478	C₂²	#11718788	1	2	yes	—
479	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	26	2	no	—
486	C₄	—	52	1	no	—
487	C₄	—	52	1	no	—
488	C₄	#11718788	1	2	yes	—
489	C₄	#11718805	1	2	yes	—
490	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
491	C₄	C₂×#88161	1	1	yes	characteristic
492	C₄	#11719527	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	8	1	no	—
495	C₂	—	52	2	no	—
496	C₂	C₂×#11718788	1	1	yes	characteristic
497	C₂	#13123634	1	1	yes	characteristic
498	C₂	C₂×#11718805	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2965	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88204	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2965	D₁₃
hypocenter	C₁₃	#17868
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #2965

Complements

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

N	H ≅ G/N	type
1. C₈×#6127	C₂	semidirect
3. #13113712	C₂	semidirect
4. #13113705	C₂	semidirect
5. #13113698	C₂	semidirect
6. #13113691	C₂	semidirect
7. #13113582	C₂	semidirect
8. #13113218	C₂	semidirect
9. #13113216	C₂	semidirect
10. C₂×#11718046	C₂	semidirect
11. C₁₃×#2965	C₂	semidirect
128. #6127	M₁₆	semidirect
177. #2965	D₁₃	semidirect
425. C₁₃	#17868	semidirect

Maximal subgroups

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

subgroup	index
C₈×#6127	2
C₄×#88204	2
#13113712	2
#13113705	2
#13113698	2
#13113691	2
#13113582	2
#13113218	2
#13113216	2
C₂×#11718046	2
C₁₃×#2965	2
#17868	13