Subgroups — #15869852

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124552	C₂	1	1	yes	maximal, characteristic
2	#13123737	C₂	1	2	yes	maximal, complemented
3	C₄×#88155	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115735	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115624	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115502	C₂	1	2	yes	maximal, complemented
7	#13115340	C₂	1	2	yes	maximal, complemented
8	#13114891	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114715	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114636	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	2	yes	—
14	#11719527	C₂²	1	2	yes	—
15	C₂×#88155	C₂²	1	1	yes	characteristic
16	C₂×#88155	C₂²	1	1	yes	characteristic
17	C₄×#6127	C₂²	1	1	yes	characteristic
18	C₁₃×#443	—	2	1	no	—
19	C₁₃×#443	—	2	1	no	—
20	C₁₃×#443	—	2	1	no	—
21	C₁₃×#443	—	2	1	no	—
22	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#104	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	#11718901	C₂²	1	2	yes	—
26	#11718898	C₂²	1	2	yes	—
27	#11718897	C₂²	1	2	yes	—
28	#11718853	C₄	1	2	yes	complemented
29	#11718838	C₄	1	4	yes	complemented
30	#11718821	C₄	1	2	yes	complemented
31	#11718806	—	2	4	no	—
32	#11718805	—	2	4	no	—
33	#11718800	C₂²	1	2	yes	—
34	#11718785	C₂²	1	2	yes	—
35	C₂×#88059	C₂²	1	1	yes	characteristic
36	#11718767	C₂²	1	1	yes	characteristic
37	#11718762	C₂²	1	1	yes	characteristic
38	#11718762	C₂²	1	2	yes	—
39	#11718762	C₂²	1	1	yes	characteristic
40	C₄×#6099	C₂²	1	1	yes	characteristic
41	#11718350	—	2	1	no	—
42	#11718350	—	2	1	no	—
43	C₄×#6094	—	2	1	no	—
44	C₄×C₈×D₁₃	—	2	1	no	—
45	#11718148	C₂²	1	2	yes	—
46	#11718148	C₂²	1	2	yes	—
47	#11718115	C₂²	1	2	yes	—
48	C₂×C₁₃×#41	C₂³	1	2	yes	—
49	C₂×#6127	C₂³	1	1	yes	characteristic
50	C₁₃×#135	—	2	1	no	—
51	C₁₃×#135	—	2	1	no	—
52	C₁₃×#135	—	2	1	no	—
53	C₁₃×#135	—	2	1	no	—
54	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
56	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
57	C₁₃×#131	—	2	2	no	—
58	C₁₃×#131	—	2	2	no	—
59	C₁₃×#131	—	2	2	no	—
60	C₁₃×#131	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃	—	2	2	no	—
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	#88205	—	2	2	no	—
68	#88204	—	2	4	no	—
69	#88203	—	2	2	no	—
70	#88196	C₂×C₄	1	4	yes	—
71	#88186	C₂×C₄	1	4	yes	—
72	C₄×C₂²⋊D₁₃	—	2	2	no	—
73	#88180	C₂³	1	2	yes	—
74	#88180	C₂³	1	1	yes	characteristic
75	C₂×#6099	C₂³	1	1	yes	characteristic
76	C₂×#6099	C₂³	1	2	yes	—
77	C₂×#6099	C₂³	1	1	yes	characteristic
78	#88155	—	2	1	no	—
79	#88155	—	2	1	no	—
80	#88155	—	2	1	no	—
81	#88155	—	2	1	no	—
82	#88155	C₂×C₄	1	2	yes	—
83	#88155	C₂×C₄	1	2	yes	—
84	#88155	D₄	1	2	yes	—
85	#88155	D₄	1	2	yes	—
86	C₂×#6094	—	2	1	no	—
87	C₂×#6094	—	2	1	no	—
88	C₂×C₈×D₁₃	—	2	1	no	—
89	C₂×C₈×D₁₃	—	2	1	no	—
90	C₄×D₅₂	—	2	1	no	—
91	#88126	—	2	1	no	—
92	C₄²×D₁₃	—	2	1	no	—
93	C₄×Dic₂₆	—	2	1	no	—
94	C₁₃×#108	—	2	1	no	—
95	C₁₃×#108	—	2	1	no	—
96	C₁₃×#104	—	2	2	no	—
97	C₁₃×#104	—	2	2	no	—
98	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
102	#88077	—	2	4	no	—
103	#88076	C₂×C₄	1	4	yes	complemented
104	#88074	—	2	4	no	—
105	#88073	C₂×C₄	1	4	yes	complemented
106	#88065	—	2	4	no	—
107	#88062	—	2	4	no	—
108	#88059	C₂×C₄	1	2	yes	complemented
109	#88059	C₂×C₄	1	2	yes	complemented
110	#88058	—	2	1	no	—
111	#88057	—	2	1	no	—
112	#88055	—	2	2	no	—
113	#88055	—	2	1	no	—
114	#88055	—	2	1	no	—
115	C₈×Dic₁₃	—	2	2	no	—
116	C₈×Dic₁₃	—	2	1	no	—
117	C₈×Dic₁₃	—	2	1	no	—
118	#88043	—	2	1	no	—
119	C₄×#1055	—	2	1	no	—
120	#21558	—	13	1	no	maximal, Sylow
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₃	—	2	1	no	—
132	#6127	—	2	1	no	—
133	#6127	—	2	1	no	—
134	#6127	C₂²×C₄	1	2	yes	—
135	#6127	C₂×D₄	1	2	yes	—
136	C₂×D₅₂	#41	1	1	yes	characteristic
137	C₂×C₄×D₁₃	—	2	1	no	—
138	C₂×C₄×D₁₃	—	2	2	no	—
139	C₂×Dic₂₆	#41	1	1	yes	characteristic
140	C₁₃×Q₁₆	—	2	1	no	—
141	C₁₃×Q₁₆	—	2	1	no	—
142	C₁₃×SD₁₆	—	2	2	no	—
143	C₁₃×SD₁₆	—	2	2	no	—
144	C₁₃×D₈	—	2	1	no	—
145	C₁₃×D₈	—	2	1	no	—
146	C₁₃×M₁₆	—	2	2	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	4	2	no	—
149	C₁₃×M₁₆	—	4	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	4	2	no	—
152	C₂×C₈×C₁₃	—	4	2	no	—
153	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
162	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
163	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
164	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²⋊Dic₁₃	—	2	2	no	—
169	C₂²⋊Dic₁₃	#41	1	2	yes	—
170	#6107	—	2	4	no	—
171	#6106	—	2	4	no	—
172	#6105	—	2	4	no	—
173	#6104	—	2	4	no	—
174	#6103	—	2	2	no	—
175	C₄⋊Dic₁₃	—	2	1	no	—
176	C₄⋊Dic₁₃	—	2	2	no	—
177	#6101	—	2	2	no	—
178	C₄×Dic₁₃	—	2	2	no	—
179	C₄×Dic₁₃	—	2	1	no	—
180	C₄×Dic₁₃	—	2	2	no	—
181	#6099	—	2	1	no	—
182	#6099	—	2	1	no	—
183	#6099	—	2	2	no	—
184	#6099	C₂²×C₄	1	2	yes	—
185	#6099	C₂²×C₄	1	4	yes	—
186	#6099	C₂×D₄	1	2	yes	—
187	C₂×#1055	—	2	1	no	—
188	C₂×#1055	—	2	1	no	—
189	C₂×#1055	—	2	2	no	—
190	#6094	—	2	2	no	—
191	#6094	—	2	2	no	—
192	#6094	—	2	2	no	—
193	#6094	—	2	2	no	—
194	C₈×D₁₃	—	2	2	no	—
195	C₈×D₁₃	—	2	2	no	—
196	C₈×D₁₃	—	2	2	no	—
197	C₈×D₁₃	—	2	2	no	—
198	#3067	—	13	1	no	—
199	#2955	—	13	2	no	—
200	C₂×#443	D₁₃	1	1	yes	characteristic, complemented
201	C₄×#131	—	13	1	no	—
202	#1976	—	13	1	no	—
203	#1953	—	13	1	no	—
204	#1932	—	13	2	no	—
205	#1906	—	13	2	no	—
206	#1814	—	13	1	no	—
207	#1772	—	13	1	no	—
208	#1757	—	13	2	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂²×D₁₃	—	2	1	no	—
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	2	2	no	—
216	D₄×C₁₃	—	4	2	no	—
217	D₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂²⋊D₁₃	—	2	2	no	—
231	C₂²⋊D₁₃	—	2	2	no	—
232	C₂×Dic₁₃	—	2	1	no	—
233	C₂×Dic₁₃	—	2	2	no	—
234	C₂×Dic₁₃	—	4	2	no	—
235	D₅₂	—	2	1	no	—
236	D₅₂	C₄×D₄	1	2	yes	—
237	C₄×D₁₃	—	2	2	no	—
238	C₄×D₁₃	—	2	2	no	—
239	C₄×D₁₃	—	4	4	no	—
240	Dic₂₆	—	2	1	no	—
241	Dic₂₆	C₄×D₄	1	2	yes	—
242	C₈×C₁₃	—	4	2	no	—
243	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
244	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
245	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
246	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
247	C₈×C₁₃	#121	1	1	yes	characteristic
248	C₈×C₁₃	#121	1	1	yes	characteristic
249	C₈×C₁₃	#121	1	1	yes	characteristic
250	C₈×C₁₃	#121	1	1	yes	characteristic
251	#1055	—	2	2	no	—
252	#1055	—	2	4	no	—
253	#1055	—	2	2	no	—
254	#575	—	13	2	no	—
255	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
256	C₂×#131	—	13	1	no	—
257	C₂×#131	—	13	1	no	—
258	C₂×#131	C₂×D₁₃	1	2	yes	—
259	C₄×#41	—	13	1	no	—
260	#473	—	13	2	no	—
261	#472	—	13	2	no	—
262	#471	—	13	4	no	—
263	#444	—	26	4	no	—
264	#443	—	2	1	no	—
265	#443	—	2	1	no	—
266	#443	—	2	1	no	—
267	#443	—	2	1	no	—
268	#443	—	26	4	no	—
269	#430	—	13	2	no	—
270	C₂×#108	—	13	1	no	—
271	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
272	#427	—	13	1	no	—
273	#421	—	13	2	no	—
274	#421	—	13	2	no	—
275	C₂×#104	C₂×D₁₃	1	2	yes	—
276	#413	—	13	2	no	—
277	#410	—	13	2	no	—
278	#405	—	13	1	no	—
279	#405	—	13	1	no	—
280	#405	—	13	2	no	—
281	#405	—	26	1	no	—
282	#405	—	26	1	no	—
283	C₄×M₁₆	—	13	1	no	—
284	C₄×M₁₆	—	26	1	no	—
285	C₂×C₄×C₈	—	26	1	no	—
286	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
287	#344	—	13	2	no	—
288	#344	—	13	2	no	—
289	#339	—	13	2	no	—
290	C₂²×C₁₃	—	4	1	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	8	2	no	—
293	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
294	C₂²×C₁₃	#525	1	1	yes	characteristic
295	C₂²×C₁₃	#532	1	1	yes	characteristic
296	C₂×D₁₃	—	2	2	no	—
297	C₂×D₁₃	—	4	2	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	4	1	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
302	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
303	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
304	C₄×C₁₃	#529	1	1	yes	characteristic
305	Dic₁₃	—	2	2	no	—
306	Dic₁₃	—	4	2	no	—
307	Dic₁₃	—	8	2	no	—
308	C₂×#41	—	13	1	no	—
309	C₂×#41	C₂²×D₁₃	1	2	yes	—
310	#137	—	13	4	no	—
311	#137	—	26	2	no	—
312	AGL(1,ℤ/8)	—	13	4	no	—
313	AGL(1,ℤ/8)	—	26	2	no	—
314	#135	—	2	1	no	—
315	#135	—	2	1	no	—
316	#135	—	2	1	no	—
317	#135	—	2	1	no	—
318	#135	—	26	4	no	—
319	C₂×Q₁₆	C₄×D₁₃	1	1	yes	characteristic, complemented
320	C₂×SD₁₆	C₄×D₁₃	1	2	yes	complemented
321	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic, complemented
322	#131	—	2	2	no	—
323	#131	—	2	2	no	—
324	#131	—	2	2	no	—
325	#131	—	2	2	no	—
326	#131	—	13	2	no	—
327	#131	—	13	2	no	—
328	#131	—	13	2	no	—
329	#131	—	13	2	no	—
330	#131	—	26	1	no	—
331	#131	—	26	1	no	—
332	#131	—	26	1	no	—
333	#131	—	26	1	no	—
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	—	13	1	no	—
336	C₂×M₁₆	—	13	1	no	—
337	C₂×M₁₆	—	13	2	no	—
338	C₂×M₁₆	—	26	1	no	—
339	C₂×M₁₆	—	26	1	no	—
340	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
341	C₂²×C₈	—	2	2	no	—
342	C₂²×C₈	—	26	1	no	—
343	C₂²×C₈	—	26	1	no	—
344	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
346	C₄×Q₈	—	26	1	no	—
347	C₄×D₄	—	26	1	no	—
348	C₄×D₄	—	26	2	no	—
349	#117	—	13	1	no	—
350	#117	—	13	2	no	—
351	#117	—	26	1	no	—
352	C₂×C₄²	—	26	1	no	—
353	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
354	#108	—	2	1	no	—
355	#108	—	2	1	no	—
356	#108	—	13	2	no	—
357	#108	—	13	2	no	—
358	#108	—	26	4	no	—
359	#107	—	26	1	no	—
360	#106	—	26	1	no	—
361	#104	—	2	2	no	—
362	#104	—	2	2	no	—
363	#104	—	26	4	no	—
364	#104	—	26	4	no	—
365	#101	—	13	4	no	—
366	#100	—	13	4	no	—
367	#99	—	26	4	no	—
368	#97	—	26	2	no	—
369	#97	—	26	1	no	—
370	#97	—	26	1	no	—
371	#97	—	26	1	no	—
372	C₄×C₈	—	26	2	no	—
373	C₄×C₈	—	26	1	no	—
374	C₄×C₈	—	26	1	no	—
375	C₄×C₈	—	26	1	no	—
376	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
377	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
378	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
379	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
380	C₂×C₁₃	—	2	1	no	—
381	C₂×C₁₃	—	2	1	no	—
382	C₂×C₁₃	—	2	1	no	—
383	C₂×C₁₃	—	8	2	no	—
384	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
385	D₁₃	—	4	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	13	2	no	—
391	#41	—	13	2	no	—
392	#41	—	26	1	no	—
393	#41	—	26	1	no	—
394	C₂×Q₈	—	13	1	no	—
395	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	13	1	no	—
398	C₂×D₄	—	26	1	no	—
399	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	26	2	no	—
403	C₂²×C₄	—	26	1	no	—
404	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
405	Q₁₆	—	2	1	no	—
406	Q₁₆	—	2	1	no	—
407	Q₁₆	—	26	4	no	—
408	SD₁₆	—	2	2	no	—
409	SD₁₆	—	2	2	no	—
410	SD₁₆	—	26	4	no	—
411	SD₁₆	—	26	4	no	—
412	D₈	—	2	1	no	—
413	D₈	—	2	1	no	—
414	D₈	—	26	4	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	4	2	no	—
418	M₁₆	—	4	2	no	—
419	M₁₆	—	13	2	no	—
420	M₁₆	—	13	4	no	—
421	M₁₆	—	13	2	no	—
422	M₁₆	—	26	1	no	—
423	M₁₆	—	26	1	no	—
424	M₁₆	—	26	2	no	—
425	M₁₆	—	26	2	no	—
426	M₁₆	—	26	2	no	—
427	M₁₆	—	26	2	no	—
428	M₁₆	—	26	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	4	2	no	—
431	C₂×C₈	—	4	2	no	—
432	C₂×C₈	—	26	2	no	—
433	C₂×C₈	—	26	1	no	—
434	C₂×C₈	—	26	1	no	—
435	C₂×C₈	—	26	2	no	—
436	C₂×C₈	—	26	2	no	—
437	C₂×C₈	—	26	2	no	—
438	C₂×C₈	—	26	2	no	—
439	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
440	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
441	C₂×C₈	#6127	1	1	yes	characteristic
442	C₂×C₈	#6127	1	1	yes	characteristic
443	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
444	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
445	C₂×C₈	#6129	1	1	yes	characteristic
446	C₂×C₈	#6129	1	1	yes	characteristic
447	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
448	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
449	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
450	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
451	C₄⋊C₄	—	26	2	no	—
452	C₄⋊C₄	—	26	1	no	—
453	C₄⋊C₄	—	26	2	no	—
454	C₂²⋊C₄	—	13	2	no	—
455	C₂²⋊C₄	—	26	2	no	—
456	C₂²⋊C₄	—	26	2	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	26	2	no	—
459	C₄²	—	26	1	no	—
460	C₄²	—	26	2	no	—
461	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
462	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
463	C₁₃	#21558	1	1	yes	characteristic, complemented, Sylow
464	C₂³	—	2	2	no	—
465	C₂³	—	26	1	no	—
466	C₂³	#41×D₁₃	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	13	2	no	—
470	Q₈	—	26	1	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	13	2	no	—
476	D₄	—	26	2	no	—
477	D₄	—	26	2	no	—
478	D₄	—	26	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	26	1	no	—
486	C₂×C₄	—	26	2	no	—
487	C₂×C₄	—	26	2	no	—
488	C₂×C₄	—	26	2	no	—
489	C₂×C₄	—	52	4	no	—
490	C₂×C₄	—	52	2	no	—
491	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂×#6127	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
494	C₂×C₄	C₂×#6129	1	1	yes	characteristic
495	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
496	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
497	C₈	—	4	2	no	—
498	C₈	—	26	2	no	—
499	C₈	—	26	4	no	—
500	C₈	—	26	2	no	—
501	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
502	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
503	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
504	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
505	C₈	#88192	1	1	yes	characteristic
506	C₈	#88192	1	1	yes	characteristic
507	C₈	#88192	1	1	yes	characteristic
508	C₈	#88192	1	1	yes	characteristic
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	26	2	no	—
513	C₂²	—	52	2	no	—
514	C₂²	C₄×#6129	1	1	yes	characteristic
515	C₂²	#11719253	1	1	yes	characteristic
516	C₂²	#11719533	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	26	2	no	—
521	C₄	—	52	2	no	—
522	C₄	—	104	2	no	—
523	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
524	C₄	#11719262	1	1	yes	characteristic
525	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
526	C₄	C₂×#88192	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	8	2	no	—
531	C₂	—	52	2	no	—
532	C₂	C₄×#88192	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#88192
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#443	C₂
socle	C₂×C₁₃	C₄×#121
prime radical	#13124552	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#443	D₁₃
hypocenter	C₁₃	#21558
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. #13123737	C₂	semidirect
3. C₄×#88155	C₂	semidirect
4. #13115735	C₂	semidirect
5. #13115624	C₂	semidirect
6. #13115502	C₂	semidirect
7. #13115340	C₂	semidirect
8. #13114891	C₂	semidirect
9. #13114715	C₂	semidirect
10. #13114636	C₂	semidirect
11. C₂×C₁₃×#443	C₂	semidirect
28. #11718853	C₄	semidirect
29. #11718838	C₄	semidirect
30. #11718821	C₄	semidirect
54. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
55. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
56. C₂×C₁₃×D₈	C₂×C₄	semidirect
103. #88076	C₂×C₄	semidirect
105. #88073	C₂×C₄	semidirect
108. #88059	C₂×C₄	semidirect
109. #88059	C₂×C₄	semidirect
200. C₂×#443	D₁₃	semidirect
319. C₂×Q₁₆	C₄×D₁₃	semidirect
320. C₂×SD₁₆	C₄×D₁₃	semidirect
321. C₂×D₈	C₄×D₁₃	semidirect
463. C₁₃	#21558	semidirect

Maximal subgroups

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

subgroup	index
#13124552	2
#13123737	2
C₄×#88155	2
#13115735	2
#13115624	2
#13115502	2
#13115340	2
#13114891	2
#13114715	2
#13114636	2
C₂×C₁₃×#443	2
#21558	13