Subgroups — #16739160

Order 3328.

2620 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129610	C₂	1	2	yes	maximal, complemented
2	#13129605	C₂	1	2	yes	maximal, complemented
3	#13126641	C₂	1	2	yes	maximal, complemented
4	#13126636	C₂	1	2	yes	maximal, complemented
5	#13126630	C₂	1	4	yes	maximal, complemented
6	#13126624	C₂	1	4	yes	maximal, complemented
7	#13126623	C₂	1	4	yes	maximal, complemented
8	#13125264	C₂	1	1	yes	maximal, characteristic, complemented
9	#13124557	C₂	1	2	yes	maximal, complemented
10	#13124556	C₂	1	2	yes	maximal, complemented
11	#13124187	C₂	1	4	yes	maximal, complemented
12	C₂×#11718361	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719648	C₂²	1	4	yes	complemented
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
17	#11719527	C₂²	1	4	yes	complemented
18	#11719476	C₂²	1	4	yes	complemented
19	#11719475	C₂²	1	8	yes	complemented
20	#11719474	C₂²	1	4	yes	complemented
21	#11719473	—	2	4	no	—
22	D₁₃×#135	—	2	4	no	—
23	#11719471	—	2	2	no	—
24	#11719467	—	2	4	no	—
25	#11719462	—	2	2	no	—
26	#11719458	—	2	2	no	—
27	#11719458	C₂²	1	4	yes	complemented
28	#11719457	—	2	2	no	—
29	#11719457	C₂²	1	4	yes	complemented
30	#11719456	—	2	4	no	—
31	#11719456	C₂²	1	8	yes	complemented
32	#11719453	—	2	4	no	—
33	#11719453	C₂²	1	4	yes	complemented
34	C₂×#88158	—	2	4	no	—
35	C₂×#88158	C₂²	1	1	yes	characteristic
36	C₂×#88158	C₂²	1	2	yes	complemented
37	C₂×#88158	C₂²	1	2	yes	complemented
38	C₂×#88155	C₂²	1	2	yes	complemented
39	#11719182	C₂²	1	2	yes	complemented
40	C₁₃×#443	C₂²	1	2	yes	complemented
41	C₁₃×#443	C₂²	1	2	yes	complemented
42	C₁₃×#443	C₂²	1	2	yes	complemented
43	C₁₃×#443	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
46	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	#11718804	C₂²	1	4	yes	complemented
48	#11718803	C₂²	1	4	yes	complemented
49	#11718802	C₂²	1	8	yes	complemented
50	#11718793	C₂²	1	4	yes	complemented
51	C₂×#88059	C₂²	1	1	yes	characteristic, complemented
52	C₂×#88045	C₂²	1	2	yes	complemented
53	#11718559	C₂²	1	8	yes	complemented
54	#11718558	C₂²	1	4	yes	complemented
55	#11718557	C₂²	1	4	yes	complemented
56	#11718488	C₂²	1	8	yes	complemented
57	#11718487	C₂²	1	8	yes	complemented
58	#11718486	C₂²	1	8	yes	complemented
59	#11718483	C₂²	1	8	yes	complemented
60	#11718361	C₂²	1	2	yes	complemented
61	#11718361	C₂²	1	2	yes	complemented
62	#11718361	C₂²	1	2	yes	complemented
63	#11718361	C₂²	1	2	yes	complemented
64	#11718360	C₂²	1	1	yes	characteristic, complemented
65	#11718357	C₂²	1	2	yes	complemented
66	#11718357	C₂²	1	2	yes	complemented
67	#11718356	C₂²	1	1	yes	characteristic, complemented
68	#11718354	C₂²	1	2	yes	complemented
69	C₂×C₁₃×#41	C₂³	1	2	yes	—
70	#88257	—	2	4	no	—
71	#88257	C₂³	1	8	yes	—
72	#88256	—	2	4	no	—
73	#88256	C₂³	1	8	yes	—
74	#41×D₁₃	—	2	8	no	—
75	#41×D₁₃	—	4	4	no	—
76	#88254	—	2	4	no	—
77	#88251	—	2	4	no	—
78	#88251	—	4	4	no	—
79	C₂×#6127	—	2	8	no	—
80	C₂×#6127	C₂³	1	2	yes	—
81	C₂×#6127	C₂³	1	4	yes	—
82	C₁₃×#135	D₄	1	2	yes	complemented
83	C₁₃×#135	D₄	1	2	yes	complemented
84	C₁₃×#135	C₂³	1	2	yes	—
85	C₁₃×#135	C₂³	1	2	yes	—
86	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic, complemented
87	C₂×C₁₃×SD₁₆	D₄	1	2	yes	complemented
88	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic, complemented
89	C₁₃×#131	—	2	2	no	—
90	C₁₃×#131	—	2	2	no	—
91	C₁₃×#131	C₂³	1	4	yes	—
92	C₁₃×#131	C₂³	1	4	yes	—
93	C₂×C₁₃×M₁₆	—	2	2	no	—
94	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
95	C₂²×C₈×C₁₃	—	2	2	no	—
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	#88205	C₂³	1	8	yes	—
100	#88204	—	2	8	no	—
101	#88203	C₂³	1	8	yes	—
102	#88196	—	2	4	no	—
103	#88186	—	2	4	no	—
104	#88184	—	4	2	no	—
105	C₂×#6099	C₂³	1	2	yes	—
106	#88173	—	2	4	no	—
107	#88172	—	2	8	no	—
108	Q₁₆×D₁₃	—	2	4	no	—
109	#88170	—	2	8	no	—
110	#88169	—	2	8	no	—
111	#88168	—	2	8	no	—
112	SD₁₆×D₁₃	—	2	8	no	—
113	#88166	—	2	4	no	—
114	#88165	—	2	8	no	—
115	D₈×D₁₃	—	2	4	no	—
116	#88163	—	2	4	no	—
117	#88163	—	2	8	no	—
118	#88163	—	2	8	no	—
119	#88163	C₂³	1	8	yes	—
120	#88162	—	2	4	no	—
121	#88162	—	2	8	no	—
122	#88162	—	2	8	no	—
123	#88162	C₂³	1	8	yes	—
124	C₂×Dic₅₂	—	2	4	no	—
125	C₂×Dic₅₂	D₄	1	1	yes	characteristic, complemented
126	C₂×Dic₅₂	C₂³	1	2	yes	—
127	C₂×Dic₅₂	C₂³	1	2	yes	—
128	#88158	—	2	8	no	—
129	#88158	—	2	2	no	—
130	#88158	—	2	2	no	—
131	#88158	—	2	2	no	—
132	#88158	—	2	2	no	—
133	#88158	—	2	2	no	—
134	#88158	—	2	2	no	—
135	#88158	—	2	2	no	—
136	#88158	—	2	2	no	—
137	#88158	—	2	4	no	—
138	#88158	—	2	4	no	—
139	#88158	—	2	8	no	—
140	#88158	D₄	1	2	yes	complemented
141	#88158	D₄	1	2	yes	complemented
142	#88158	C₂³	1	2	yes	—
143	#88158	C₂³	1	2	yes	—
144	C₂×D₁₀₄	—	2	4	no	—
145	C₂×D₁₀₄	D₄	1	1	yes	characteristic, complemented
146	C₂×D₁₀₄	C₂³	1	2	yes	—
147	C₂×D₁₀₄	C₂³	1	2	yes	—
148	C₂×#6095	—	2	8	no	—
149	C₂×#6095	D₄	1	2	yes	complemented
150	C₂×#6095	C₂³	1	4	yes	—
151	C₂×#6095	C₂³	1	4	yes	—
152	#88155	—	2	2	no	—
153	#88155	—	2	2	no	—
154	#88155	C₂³	1	4	yes	—
155	#88155	C₂³	1	4	yes	—
156	C₂×#6094	—	2	2	no	—
157	C₂×C₈×D₁₃	—	2	2	no	—
158	#88129	C₂³	1	4	yes	—
159	#88128	C₂³	1	2	yes	—
160	C₄×D₅₂	—	4	2	no	—
161	#88123	C₂³	1	2	yes	—
162	C₁₃×#108	C₂³	1	2	yes	—
163	C₁₃×#108	C₂³	1	2	yes	—
164	C₁₃×#104	C₂³	1	4	yes	—
165	C₁₃×#104	C₂³	1	4	yes	—
166	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
170	#88064	C₂³	1	8	yes	—
171	#88063	C₂³	1	8	yes	—
172	#88059	C₂³	1	2	yes	—
173	#88059	C₂³	1	2	yes	—
174	#88045	C₂³	1	4	yes	—
175	#88045	C₂³	1	4	yes	—
176	#61105	—	13	1	no	maximal, Sylow
177	C₁₃×#41	—	2	2	no	—
178	C₁₃×#41	—	2	2	no	—
179	C₁₃×#41	C₂×D₄	1	4	yes	—
180	C₁₃×#41	C₂⁴	1	4	yes	—
181	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
182	C₂×D₄×C₁₃	—	2	2	no	—
183	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₃	—	2	2	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂×C₂²⋊D₁₃	—	2	2	no	—
188	C₂×C₂²⋊D₁₃	—	2	4	no	—
189	C₂×C₂²⋊D₁₃	—	4	8	no	—
190	#6131	—	2	8	no	—
191	#6131	—	4	4	no	—
192	Q₈×D₁₃	—	2	8	no	—
193	Q₈×D₁₃	—	4	4	no	—
194	#6129	—	2	8	no	—
195	#6129	—	4	4	no	—
196	#6129	—	4	8	no	—
197	#6129	—	4	8	no	—
198	D₄×D₁₃	—	2	8	no	—
199	D₄×D₁₃	—	4	4	no	—
200	D₄×D₁₃	—	4	8	no	—
201	D₄×D₁₃	—	4	8	no	—
202	#6127	—	2	2	no	—
203	#6127	—	2	2	no	—
204	#6127	—	2	4	no	—
205	#6127	—	2	4	no	—
206	#6127	—	2	4	no	—
207	#6127	—	2	4	no	—
208	#6127	—	2	8	no	—
209	#6127	—	2	8	no	—
210	#6127	—	4	8	no	—
211	#6127	—	4	8	no	—
212	#6127	C₂×D₄	1	4	yes	—
213	#6127	C₂⁴	1	4	yes	—
214	C₂×D₅₂	—	2	8	no	—
215	C₂×D₅₂	—	4	2	no	—
216	C₂×D₅₂	C₂×D₄	1	2	yes	—
217	C₂×D₅₂	C₂⁴	1	4	yes	—
218	C₂×C₄×D₁₃	—	2	2	no	—
219	C₂×C₄×D₁₃	—	2	4	no	—
220	C₂×C₄×D₁₃	—	4	8	no	—
221	C₂×Dic₂₆	—	2	8	no	—
222	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
223	C₂×Dic₂₆	C₂⁴	1	4	yes	—
224	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
225	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
226	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
227	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
228	C₁₃×D₈	C₂×D₄	1	2	yes	—
229	C₁₃×D₈	C₂×D₄	1	2	yes	—
230	C₁₃×M₁₆	—	2	2	no	—
231	C₁₃×M₁₆	—	2	4	no	—
232	C₁₃×M₁₆	—	2	4	no	—
233	C₁₃×M₁₆	C₂⁴	1	4	yes	—
234	C₂×C₈×C₁₃	—	2	2	no	—
235	C₂×C₈×C₁₃	—	2	4	no	—
236	C₂×C₈×C₁₃	—	2	4	no	—
237	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₄²×C₁₃	—	2	1	no	—
250	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
252	#6107	—	2	8	no	—
253	#6106	—	2	8	no	—
254	#6105	—	2	8	no	—
255	#6104	—	2	8	no	—
256	#6103	—	4	4	no	—
257	C₄⋊Dic₁₃	—	4	2	no	—
258	#6099	—	2	2	no	—
259	#6099	C₂⁴	1	4	yes	—
260	C₂×#1055	—	2	2	no	—
261	Dic₅₂	—	2	8	no	—
262	Dic₅₂	—	2	2	no	—
263	Dic₅₂	—	2	2	no	—
264	Dic₅₂	—	2	2	no	—
265	Dic₅₂	—	2	2	no	—
266	Dic₅₂	C₂×D₄	1	2	yes	—
267	Dic₅₂	C₂×D₄	1	2	yes	—
268	D₁₀₄	—	2	8	no	—
269	D₁₀₄	—	2	2	no	—
270	D₁₀₄	—	2	2	no	—
271	D₁₀₄	—	2	2	no	—
272	D₁₀₄	—	2	2	no	—
273	D₁₀₄	C₂×D₄	1	2	yes	—
274	D₁₀₄	C₂×D₄	1	2	yes	—
275	#6095	—	2	8	no	—
276	#6095	—	2	8	no	—
277	#6095	—	2	4	no	—
278	#6095	—	2	4	no	—
279	#6095	—	2	4	no	—
280	#6095	—	2	4	no	—
281	#6095	C₂×D₄	1	4	yes	—
282	#6095	C₂×D₄	1	4	yes	—
283	#6094	—	2	4	no	—
284	#6094	—	2	4	no	—
285	C₈×D₁₃	—	2	4	no	—
286	C₈×D₁₃	—	2	4	no	—
287	#3584	—	13	2	no	—
288	#3584	—	13	2	no	—
289	#3293	—	13	2	no	—
290	#3292	—	13	2	no	—
291	#3291	—	13	4	no	—
292	#3290	—	13	4	no	—
293	#3290	—	13	4	no	—
294	#3147	—	13	1	no	—
295	#3067	—	13	2	no	—
296	#3067	—	13	2	no	—
297	#3018	—	13	4	no	—
298	C₂×#443	—	13	1	no	—
299	C₂×#443	D₁₃	1	1	yes	characteristic, complemented
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
302	C₂²×D₁₃	—	2	2	no	—
303	C₂²×D₁₃	—	2	4	no	—
304	C₂²×D₁₃	—	4	8	no	—
305	Q₈×C₁₃	—	2	2	no	—
306	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
307	D₄×C₁₃	—	2	4	no	—
308	D₄×C₁₃	—	2	4	no	—
309	D₄×C₁₃	—	2	2	no	—
310	D₄×C₁₃	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	4	no	—
314	C₂×C₄×C₁₃	—	2	4	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	4	2	no	—
317	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
323	C₂²⋊D₁₃	—	2	4	no	—
324	C₂²⋊D₁₃	—	2	4	no	—
325	C₂²⋊D₁₃	—	4	8	no	—
326	C₂²⋊D₁₃	—	4	8	no	—
327	C₂²⋊D₁₃	—	4	4	no	—
328	C₂²⋊D₁₃	—	4	4	no	—
329	C₂×Dic₁₃	—	2	2	no	—
330	C₂×Dic₁₃	—	2	4	no	—
331	C₂×Dic₁₃	—	4	8	no	—
332	D₅₂	—	2	2	no	—
333	D₅₂	—	2	4	no	—
334	D₅₂	—	2	4	no	—
335	D₅₂	—	4	8	no	—
336	D₅₂	—	8	4	no	—
337	D₅₂	C₂²×D₄	1	4	yes	—
338	C₄×D₁₃	—	2	4	no	—
339	C₄×D₁₃	—	2	4	no	—
340	C₄×D₁₃	—	4	8	no	—
341	C₄×D₁₃	—	4	8	no	—
342	C₄×D₁₃	—	4	4	no	—
343	C₄×D₁₃	—	4	4	no	—
344	Dic₂₆	—	2	2	no	—
345	Dic₂₆	—	2	4	no	—
346	Dic₂₆	—	2	4	no	—
347	Dic₂₆	—	4	8	no	—
348	Dic₂₆	C₂²×D₄	1	4	yes	—
349	C₈×C₁₃	—	2	4	no	—
350	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
353	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	#1055	—	2	4	no	—
359	#585	—	13	4	no	—
360	#578	—	13	4	no	—
361	#578	—	13	4	no	—
362	#578	—	26	2	no	—
363	#578	—	26	2	no	—
364	#577	—	13	8	no	—
365	#577	—	13	8	no	—
366	#577	—	26	4	no	—
367	#577	—	26	4	no	—
368	#576	—	13	4	no	—
369	#576	—	13	4	no	—
370	#576	—	26	2	no	—
371	#576	—	26	2	no	—
372	#575	—	13	4	no	—
373	#575	—	13	4	no	—
374	#575	—	26	4	no	—
375	#575	—	26	4	no	—
376	C₂×#135	—	13	1	no	—
377	C₂×#135	—	13	2	no	—
378	C₂×#135	—	13	2	no	—
379	C₂×#135	—	26	4	no	—
380	C₂×#135	—	26	4	no	—
381	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
382	C₂×#131	—	13	2	no	—
383	C₂×#131	C₂×D₁₃	1	2	yes	complemented
384	#532	—	13	2	no	—
385	#495	—	13	2	no	—
386	#495	—	13	2	no	—
387	#494	—	13	1	no	—
388	#493	—	13	1	no	—
389	#492	—	13	2	no	—
390	#473	—	13	4	no	—
391	#473	—	13	4	no	—
392	#472	—	13	4	no	—
393	#472	—	13	4	no	—
394	#471	—	13	8	no	—
395	#471	—	13	8	no	—
396	#456	—	13	8	no	—
397	#455	—	13	8	no	—
398	#454	—	13	8	no	—
399	#453	—	13	8	no	—
400	#443	—	13	2	no	—
401	#443	—	13	2	no	—
402	#443	—	13	2	no	—
403	#443	—	13	2	no	—
404	#443	C₂×D₁₃	1	2	yes	complemented
405	#443	C₂×D₁₃	1	2	yes	complemented
406	#443	C₂×D₁₃	1	2	yes	complemented
407	#443	C₂×D₁₃	1	2	yes	complemented
408	C₂×#108	—	13	1	no	—
409	C₂×#108	C₂×D₁₃	1	1	yes	characteristic, complemented
410	C₂×#104	—	13	2	no	—
411	C₂×#104	C₂×D₁₃	1	2	yes	complemented
412	#413	—	13	4	no	—
413	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
414	C₂²×C₁₃	—	2	4	no	—
415	C₂²×C₁₃	—	4	1	no	—
416	C₂²×C₁₃	—	8	2	no	—
417	C₂²×C₁₃	D₄²	1	1	yes	characteristic
418	C₂²×C₁₃	D₄²	1	1	yes	characteristic
419	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂×D₁₃	—	2	4	no	—
421	C₂×D₁₃	—	4	4	no	—
422	C₂×D₁₃	—	8	2	no	—
423	C₂×D₁₃	—	8	4	no	—
424	C₂×D₁₃	—	16	8	no	—
425	C₄×C₁₃	—	2	2	no	—
426	C₄×C₁₃	—	2	4	no	—
427	C₄×C₁₃	—	4	1	no	—
428	C₄×C₁₃	D₄²	1	1	yes	characteristic
429	C₄×C₁₃	D₄²	1	1	yes	characteristic
430	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
431	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
432	Dic₁₃	—	2	4	no	—
433	Dic₁₃	—	4	4	no	—
434	2₋¹⁺⁴	—	13	8	no	—
435	2₋¹⁺⁴	—	26	4	no	—
436	2₋¹⁺⁴	—	26	4	no	—
437	H(5,𝔽₂)	—	13	8	no	—
438	H(5,𝔽₂)	—	26	4	no	—
439	H(5,𝔽₂)	—	26	4	no	—
440	H(5,𝔽₂)	—	52	4	no	—
441	C₂×#41	—	13	2	no	—
442	C₂×#41	—	13	4	no	—
443	C₂×#41	—	26	8	no	—
444	C₂×#41	—	26	8	no	—
445	C₂×#41	—	52	4	no	—
446	C₂×#41	C₂²×D₁₃	1	2	yes	—
447	#137	—	13	8	no	—
448	#137	—	13	8	no	—
449	#137	—	26	8	no	—
450	#137	—	26	8	no	—
451	#137	—	26	4	no	—
452	#137	—	26	4	no	—
453	#137	—	26	8	no	—
454	#137	—	26	8	no	—
455	AGL(1,ℤ/8)	—	13	8	no	—
456	AGL(1,ℤ/8)	—	13	8	no	—
457	AGL(1,ℤ/8)	—	26	8	no	—
458	AGL(1,ℤ/8)	—	26	8	no	—
459	AGL(1,ℤ/8)	—	26	4	no	—
460	AGL(1,ℤ/8)	—	26	4	no	—
461	AGL(1,ℤ/8)	—	26	8	no	—
462	AGL(1,ℤ/8)	—	26	8	no	—
463	#135	—	13	2	no	—
464	#135	—	13	2	no	—
465	#135	—	13	2	no	—
466	#135	—	13	2	no	—
467	#135	—	26	4	no	—
468	#135	—	26	8	no	—
469	#135	—	26	4	no	—
470	#135	—	26	8	no	—
471	#135	—	26	8	no	—
472	#135	—	26	4	no	—
473	#135	—	26	8	no	—
474	#135	—	26	4	no	—
475	#135	—	26	2	no	—
476	#135	—	26	2	no	—
477	#135	—	26	2	no	—
478	#135	—	26	2	no	—
479	#135	—	26	2	no	—
480	#135	—	26	2	no	—
481	#135	—	26	2	no	—
482	#135	—	26	2	no	—
483	#135	D₅₂	1	2	yes	complemented
484	#135	D₅₂	1	2	yes	complemented
485	#135	C₂²×D₁₃	1	2	yes	—
486	#135	C₂²×D₁₃	1	2	yes	—
487	C₂×Q₁₆	—	13	1	no	—
488	C₂×Q₁₆	—	13	2	no	—
489	C₂×Q₁₆	—	13	2	no	—
490	C₂×Q₁₆	—	26	4	no	—
491	C₂×Q₁₆	—	26	4	no	—
492	C₂×Q₁₆	D₅₂	1	1	yes	characteristic, complemented
493	C₂×SD₁₆	—	13	2	no	—
494	C₂×SD₁₆	—	13	4	no	—
495	C₂×SD₁₆	—	13	4	no	—
496	C₂×SD₁₆	—	26	8	no	—
497	C₂×SD₁₆	—	26	8	no	—
498	C₂×SD₁₆	D₅₂	1	2	yes	complemented
499	C₂×D₈	—	13	1	no	—
500	C₂×D₈	—	13	2	no	—
501	C₂×D₈	—	13	2	no	—
502	C₂×D₈	—	26	4	no	—
503	C₂×D₈	—	26	4	no	—
504	C₂×D₈	D₅₂	1	1	yes	characteristic, complemented
505	#131	—	2	2	no	—
506	#131	—	2	2	no	—
507	#131	—	13	4	no	—
508	#131	—	13	4	no	—
509	#131	—	26	2	no	—
510	#131	—	26	2	no	—
511	#131	C₂²×D₁₃	1	4	yes	—
512	#131	C₂²×D₁₃	1	4	yes	—
513	C₂×M₁₆	—	2	2	no	—
514	C₂×M₁₆	—	13	2	no	—
515	C₂×M₁₆	—	26	2	no	—
516	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
517	C₂²×C₈	—	2	2	no	—
518	C₂²×C₈	—	26	2	no	—
519	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
520	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
521	C₄⋊Q₈	—	13	2	no	—
522	#127	—	13	2	no	—
523	#124	—	13	4	no	—
524	#121	—	52	2	no	—
525	C₄×D₄	—	52	2	no	—
526	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
527	#108	—	13	2	no	—
528	#108	—	13	2	no	—
529	#108	C₂²×D₁₃	1	2	yes	—
530	#108	C₂²×D₁₃	1	2	yes	—
531	#104	—	13	4	no	—
532	#104	—	13	4	no	—
533	#104	C₂²×D₁₃	1	4	yes	—
534	#104	C₂²×D₁₃	1	4	yes	—
535	#101	—	13	8	no	—
536	#100	—	13	8	no	—
537	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
538	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
539	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
540	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
541	C₂×C₁₃	—	2	1	no	—
542	C₂×C₁₃	—	2	1	no	—
543	C₂×C₁₃	—	2	1	no	—
544	C₂×C₁₃	—	4	4	no	—
545	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
546	D₁₃	—	4	4	no	—
547	D₁₃	—	8	4	no	—
548	#41	—	2	2	no	—
549	#41	—	2	2	no	—
550	#41	—	13	4	no	—
551	#41	—	13	4	no	—
552	#41	—	26	8	no	—
553	#41	—	26	8	no	—
554	#41	—	26	2	no	—
555	#41	—	26	2	no	—
556	#41	—	26	8	no	—
557	#41	—	26	8	no	—
558	#41	—	26	4	no	—
559	#41	—	26	4	no	—
560	#41	—	26	4	no	—
561	#41	—	26	4	no	—
562	#41	—	52	8	no	—
563	#41	—	52	8	no	—
564	#41	—	52	8	no	—
565	#41	—	52	8	no	—
566	#41	—	52	4	no	—
567	#41	—	52	4	no	—
568	#41	C₂×D₅₂	1	4	yes	—
569	#41	C₂³×D₁₃	1	4	yes	—
570	C₂×Q₈	—	13	2	no	—
571	C₂×Q₈	—	13	4	no	—
572	C₂×Q₈	—	26	8	no	—
573	C₂×Q₈	—	26	8	no	—
574	C₂×Q₈	—	52	4	no	—
575	C₂×Q₈	C₂×D₅₂	1	2	yes	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	13	2	no	—
578	C₂×D₄	—	13	4	no	—
579	C₂×D₄	—	26	8	no	—
580	C₂×D₄	—	26	2	no	—
581	C₂×D₄	—	26	8	no	—
582	C₂×D₄	—	26	4	no	—
583	C₂×D₄	—	52	2	no	—
584	C₂×D₄	—	52	8	no	—
585	C₂×D₄	—	52	4	no	—
586	C₂×D₄	—	52	8	no	—
587	C₂×D₄	—	52	8	no	—
588	C₂×D₄	C₂×D₅₂	1	2	yes	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	26	2	no	—
592	C₂²×C₄	—	26	4	no	—
593	C₂²×C₄	—	52	8	no	—
594	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
595	Q₁₆	—	13	2	no	—
596	Q₁₆	—	13	2	no	—
597	Q₁₆	—	26	8	no	—
598	Q₁₆	—	26	8	no	—
599	Q₁₆	—	26	2	no	—
600	Q₁₆	—	26	2	no	—
601	Q₁₆	—	26	2	no	—
602	Q₁₆	—	26	2	no	—
603	Q₁₆	C₂×D₅₂	1	2	yes	—
604	Q₁₆	C₂×D₅₂	1	2	yes	—
605	SD₁₆	—	13	4	no	—
606	SD₁₆	—	13	4	no	—
607	SD₁₆	—	26	8	no	—
608	SD₁₆	—	26	8	no	—
609	SD₁₆	—	26	8	no	—
610	SD₁₆	—	26	8	no	—
611	SD₁₆	—	26	4	no	—
612	SD₁₆	—	26	4	no	—
613	SD₁₆	—	26	4	no	—
614	SD₁₆	—	26	4	no	—
615	SD₁₆	C₂×D₅₂	1	4	yes	—
616	SD₁₆	C₂×D₅₂	1	4	yes	—
617	D₈	—	13	2	no	—
618	D₈	—	13	2	no	—
619	D₈	—	26	8	no	—
620	D₈	—	26	8	no	—
621	D₈	—	26	2	no	—
622	D₈	—	26	2	no	—
623	D₈	—	26	2	no	—
624	D₈	—	26	2	no	—
625	D₈	C₂×D₅₂	1	2	yes	—
626	D₈	C₂×D₅₂	1	2	yes	—
627	M₁₆	—	2	2	no	—
628	M₁₆	—	2	4	no	—
629	M₁₆	—	2	4	no	—
630	M₁₆	—	13	4	no	—
631	M₁₆	—	26	2	no	—
632	M₁₆	—	26	4	no	—
633	M₁₆	—	26	4	no	—
634	M₁₆	C₂³×D₁₃	1	4	yes	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	4	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	—	26	2	no	—
639	C₂×C₈	—	26	4	no	—
640	C₂×C₈	—	26	4	no	—
641	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
642	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
643	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
644	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
645	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
646	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
647	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
648	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
649	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
650	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
651	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
652	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
653	C₄⋊C₄	—	52	2	no	—
654	C₂²⋊C₄	—	52	4	no	—
655	C₄²	—	2	1	no	—
656	C₄²	C₂³×D₁₃	1	1	yes	characteristic
657	C₄²	C₂³×D₁₃	1	1	yes	characteristic
658	C₁₃	#61105	1	1	yes	characteristic, complemented, Sylow
659	C₂³	—	2	2	no	—
660	C₂³	—	26	2	no	—
661	C₂³	—	26	4	no	—
662	C₂³	—	52	8	no	—
663	C₂³	#88256	1	1	yes	characteristic
664	Q₈	—	2	2	no	—
665	Q₈	—	13	4	no	—
666	Q₈	—	26	2	no	—
667	Q₈	—	26	4	no	—
668	Q₈	—	26	4	no	—
669	Q₈	—	52	8	no	—
670	Q₈	C₂²×D₅₂	1	4	yes	—
671	D₄	—	2	4	no	—
672	D₄	—	2	4	no	—
673	D₄	—	2	2	no	—
674	D₄	—	13	4	no	—
675	D₄	—	26	4	no	—
676	D₄	—	26	4	no	—
677	D₄	—	26	2	no	—
678	D₄	—	26	4	no	—
679	D₄	—	26	4	no	—
680	D₄	—	52	8	no	—
681	D₄	—	52	8	no	—
682	D₄	—	52	8	no	—
683	D₄	—	52	4	no	—
684	D₄	—	52	4	no	—
685	D₄	—	104	4	no	—
686	D₄	C₂²×D₅₂	1	4	yes	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	26	2	no	—
694	C₂×C₄	—	26	4	no	—
695	C₂×C₄	—	26	4	no	—
696	C₂×C₄	—	26	4	no	—
697	C₂×C₄	—	52	8	no	—
698	C₂×C₄	—	52	8	no	—
699	C₂×C₄	—	52	8	no	—
700	C₂×C₄	—	52	4	no	—
701	C₂×C₄	—	52	4	no	—
702	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
704	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
705	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
706	C₂×C₄	#88256	1	1	yes	characteristic
707	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
708	C₈	—	2	4	no	—
709	C₈	—	26	4	no	—
710	C₈	C₂²×D₅₂	1	1	yes	characteristic
711	C₈	C₂²×D₅₂	1	1	yes	characteristic
712	C₈	C₂²×D₅₂	1	1	yes	characteristic
713	C₈	C₂²×D₅₂	1	1	yes	characteristic
714	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
715	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
716	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
717	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
718	C₂²	—	2	4	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	8	2	no	—
721	C₂²	—	26	4	no	—
722	C₂²	—	52	4	no	—
723	C₂²	—	104	2	no	—
724	C₂²	—	104	4	no	—
725	C₂²	—	208	8	no	—
726	C₂²	D₄×D₅₂	1	1	yes	characteristic
727	C₂²	D₄×D₅₂	1	1	yes	characteristic
728	C₂²	C₂×#88256	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	4	1	no	—
732	C₄	—	26	4	no	—
733	C₄	—	52	4	no	—
734	C₄	D₄×D₅₂	1	1	yes	characteristic
735	C₄	D₄×D₅₂	1	1	yes	characteristic
736	C₄	C₂³×D₅₂	1	1	yes	characteristic
737	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
738	C₂	—	2	1	no	—
739	C₂	—	2	1	no	—
740	C₂	—	2	1	no	—
741	C₂	—	4	4	no	—
742	C₂	—	52	4	no	—
743	C₂	—	104	4	no	—
744	C₂	C₂×D₄×D₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₅₂
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#443	C₂
socle	C₂×C₁₃	C₂×D₄²
hypercenter	C₂×#443	D₁₃
hypocenter	C₁₃	#61105
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. #13129610	C₂	semidirect
2. #13129605	C₂	semidirect
3. #13126641	C₂	semidirect
4. #13126636	C₂	semidirect
5. #13126630	C₂	semidirect
6. #13126624	C₂	semidirect
7. #13126623	C₂	semidirect
8. #13125264	C₂	semidirect
9. #13124557	C₂	semidirect
10. #13124556	C₂	semidirect
11. #13124187	C₂	semidirect
12. C₂×#11718361	C₂	semidirect
13. C₂×C₁₃×#443	C₂	semidirect
14. #11719648	C₂²	semidirect
16. C₂×C₁₃×#131	C₂²	semidirect
17. #11719527	C₂²	semidirect
18. #11719476	C₂²	semidirect
19. #11719475	C₂²	semidirect
20. #11719474	C₂²	semidirect
27. #11719458	C₂²	semidirect
29. #11719457	C₂²	semidirect
31. #11719456	C₂²	semidirect
33. #11719453	C₂²	semidirect
36. C₂×#88158	C₂²	semidirect
37. C₂×#88158	C₂²	semidirect
38. C₂×#88155	C₂²	semidirect
39. #11719182	C₂²	semidirect
40. C₁₃×#443	C₂²	semidirect
41. C₁₃×#443	C₂²	semidirect
42. C₁₃×#443	C₂²	semidirect
43. C₁₃×#443	C₂²	semidirect
44. C₂×C₁₃×#108	C₂²	semidirect
45. C₂×C₁₃×#104	C₂²	semidirect
46. C₂×C₄×C₈×C₁₃	C₂²	semidirect
47. #11718804	C₂²	semidirect
48. #11718803	C₂²	semidirect
49. #11718802	C₂²	semidirect
50. #11718793	C₂²	semidirect
51. C₂×#88059	C₂²	semidirect
52. C₂×#88045	C₂²	semidirect
53. #11718559	C₂²	semidirect
54. #11718558	C₂²	semidirect
55. #11718557	C₂²	semidirect
56. #11718488	C₂²	semidirect
57. #11718487	C₂²	semidirect
58. #11718486	C₂²	semidirect
59. #11718483	C₂²	semidirect
60. #11718361	C₂²	semidirect
61. #11718361	C₂²	semidirect
62. #11718361	C₂²	semidirect
63. #11718361	C₂²	semidirect
64. #11718360	C₂²	semidirect
65. #11718357	C₂²	semidirect
66. #11718357	C₂²	semidirect
67. #11718356	C₂²	semidirect
68. #11718354	C₂²	semidirect
82. C₁₃×#135	D₄	semidirect
83. C₁₃×#135	D₄	semidirect
86. C₂×C₁₃×Q₁₆	D₄	semidirect
87. C₂×C₁₃×SD₁₆	D₄	semidirect
88. C₂×C₁₃×D₈	D₄	semidirect
125. C₂×Dic₅₂	D₄	semidirect
140. #88158	D₄	semidirect
141. #88158	D₄	semidirect
145. C₂×D₁₀₄	D₄	semidirect
149. C₂×#6095	D₄	semidirect
299. C₂×#443	D₁₃	semidirect
383. C₂×#131	C₂×D₁₃	semidirect
404. #443	C₂×D₁₃	semidirect
405. #443	C₂×D₁₃	semidirect
406. #443	C₂×D₁₃	semidirect
407. #443	C₂×D₁₃	semidirect
409. C₂×#108	C₂×D₁₃	semidirect
411. C₂×#104	C₂×D₁₃	semidirect
413. C₂×C₄×C₈	C₂×D₁₃	semidirect
483. #135	D₅₂	semidirect
484. #135	D₅₂	semidirect
492. C₂×Q₁₆	D₅₂	semidirect
498. C₂×SD₁₆	D₅₂	semidirect
504. C₂×D₈	D₅₂	semidirect
658. C₁₃	#61105	semidirect

Maximal subgroups

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

subgroup	index
#13129610	2
#13129605	2
#13126641	2
#13126636	2
#13126630	2
#13126624	2
#13126623	2
#13125264	2
#13124557	2
#13124556	2
#13124187	2
C₂×#11718361	2
C₂×C₁₃×#443	2
#61105	13