Subgroups — #16769447

Order 3328.

2038 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129605	C₂	1	2	yes	maximal, complemented
2	#13127986	C₂	1	2	yes	maximal, complemented
3	#13127985	C₂	1	2	yes	maximal, complemented
4	#13127979	C₂	1	4	yes	maximal, complemented
5	#13127978	C₂	1	4	yes	maximal, complemented
6	#13127974	C₂	1	2	yes	maximal, complemented
7	#13127973	C₂	1	2	yes	maximal, complemented
8	#13127970	C₂	1	2	yes	maximal, complemented
9	#13127969	C₂	1	4	yes	maximal, complemented
10	C₂×#11718565	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#508	C₂	1	4	yes	maximal, complemented
12	C₂×#11718562	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719648	—	2	2	no	—
15	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
16	#11719527	—	2	2	no	—
17	#11719476	C₂²	1	4	yes	complemented
18	#11719475	—	2	4	no	—
19	#11719474	C₂²	1	4	yes	complemented
20	#11719473	—	2	4	no	—
21	D₁₃×#135	C₂²	1	8	yes	complemented
22	#11719471	C₂²	1	4	yes	complemented
23	#11719467	—	2	4	no	—
24	#11719462	C₂²	1	4	yes	complemented
25	C₂×#88158	C₂²	1	2	yes	complemented
26	C₂×#88155	C₂²	1	1	yes	characteristic
27	C₁₃×#508	C₂²	1	2	yes	complemented
28	C₁₃×#508	C₂²	1	2	yes	complemented
29	C₁₃×#508	C₂²	1	2	yes	complemented
30	C₁₃×#508	C₂²	1	2	yes	complemented
31	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
33	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
35	#11718856	C₂²	1	4	yes	complemented
36	#11718855	C₂²	1	8	yes	complemented
37	#11718854	C₂²	1	4	yes	complemented
38	#11718840	C₂²	1	4	yes	complemented
39	#11718808	C₂²	1	4	yes	complemented
40	C₂×#88052	C₂²	1	1	yes	characteristic, complemented
41	#11718580	C₂²	1	4	yes	complemented
42	#11718579	C₂²	1	8	yes	complemented
43	D₁₃×Q₃₂	C₂²	1	4	yes	complemented
44	#11718577	C₂²	1	8	yes	complemented
45	#11718576	C₂²	1	8	yes	complemented
46	#11718575	C₂²	1	8	yes	complemented
47	D₁₃×SD₃₂	C₂²	1	8	yes	complemented
48	#11718573	C₂²	1	4	yes	complemented
49	#11718572	C₂²	1	8	yes	complemented
50	D₁₃×D₁₆	C₂²	1	4	yes	complemented
51	C₂×Dic₁₀₄	C₂²	1	1	yes	characteristic, complemented
52	#11718565	C₂²	1	2	yes	complemented
53	#11718565	C₂²	1	2	yes	complemented
54	#11718565	C₂²	1	2	yes	complemented
55	#11718565	C₂²	1	2	yes	complemented
56	C₂×#88040	C₂²	1	2	yes	complemented
57	C₂×D₂₀₈	C₂²	1	1	yes	characteristic, complemented
58	#11718562	C₂²	1	2	yes	complemented
59	#11718562	C₂²	1	2	yes	complemented
60	#11718562	C₂²	1	2	yes	complemented
61	#11718562	C₂²	1	2	yes	complemented
62	C₂×#88038	C₂²	1	2	yes	complemented
63	C₂×C₁₆×D₁₃	C₂²	1	2	yes	complemented
64	C₂×C₁₃×#41	—	2	2	no	—
65	#88257	—	2	4	no	—
66	#88257	—	4	2	no	—
67	#88256	—	2	4	no	—
68	#88256	—	4	2	no	—
69	#41×D₁₃	—	2	8	no	—
70	#41×D₁₃	—	4	4	no	—
71	#88254	—	2	4	no	—
72	#88251	—	2	4	no	—
73	#88251	—	4	4	no	—
74	C₂×#6127	—	2	2	no	—
75	C₂×#6127	—	4	4	no	—
76	C₂×#6127	D₄	1	1	yes	characteristic
77	C₁₃×#135	—	2	2	no	—
78	C₁₃×#135	—	2	2	no	—
79	C₁₃×#135	C₂³	1	4	yes	—
80	C₁₃×#135	C₂³	1	4	yes	—
81	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
82	C₂×C₁₃×SD₁₆	—	2	2	no	—
83	C₂×C₁₃×D₈	C₂³	1	2	yes	—
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	#88205	—	2	4	no	—
86	#88204	—	2	8	no	—
87	#88203	—	2	4	no	—
88	#88196	—	2	4	no	—
89	#88186	—	2	4	no	—
90	C₂×#6099	D₄	1	1	yes	characteristic
91	#88173	C₂³	1	8	yes	—
92	#88172	—	2	8	no	—
93	Q₁₆×D₁₃	C₂³	1	8	yes	—
94	#88170	—	2	8	no	—
95	#88169	—	2	8	no	—
96	#88168	—	2	8	no	—
97	SD₁₆×D₁₃	—	2	8	no	—
98	#88166	C₂³	1	8	yes	—
99	#88165	—	2	8	no	—
100	D₈×D₁₃	C₂³	1	8	yes	—
101	C₂×Dic₅₂	C₂³	1	2	yes	—
102	#88158	—	2	2	no	—
103	#88158	—	2	2	no	—
104	#88158	C₂³	1	4	yes	—
105	#88158	C₂³	1	4	yes	—
106	C₂×D₁₀₄	C₂³	1	2	yes	—
107	C₂×#6095	—	2	2	no	—
108	#88155	D₄	1	2	yes	—
109	#88155	D₄	1	2	yes	—
110	#88155	C₂³	1	2	yes	—
111	#88155	C₂³	1	2	yes	—
112	C₂×#6094	D₄	1	2	yes	—
113	C₂×C₈×D₁₃	C₂³	1	2	yes	—
114	C₁₃×Q₃₂	C₂³	1	2	yes	—
115	C₁₃×Q₃₂	C₂³	1	2	yes	—
116	C₁₃×SD₃₂	C₂³	1	4	yes	—
117	C₁₃×SD₃₂	C₂³	1	4	yes	—
118	C₁₃×D₁₆	C₂³	1	2	yes	—
119	C₁₃×D₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
126	#88069	C₂³	1	8	yes	—
127	#88068	C₂³	1	8	yes	—
128	#88067	C₂³	1	8	yes	—
129	#88066	C₂³	1	8	yes	—
130	#88052	C₂³	1	2	yes	—
131	#88052	C₂³	1	2	yes	—
132	C₂×#6090	C₂³	1	2	yes	—
133	Dic₁₀₄	C₂³	1	2	yes	—
134	Dic₁₀₄	C₂³	1	2	yes	—
135	#88040	C₂³	1	4	yes	—
136	#88040	C₂³	1	4	yes	—
137	D₂₀₈	C₂³	1	2	yes	—
138	D₂₀₈	C₂³	1	2	yes	—
139	#88038	C₂³	1	4	yes	—
140	#88038	C₂³	1	4	yes	—
141	C₁₆×D₁₃	C₂³	1	4	yes	—
142	C₁₆×D₁₃	C₂³	1	4	yes	—
143	#62635	—	13	1	no	maximal, Sylow
144	C₁₃×#41	—	2	4	no	—
145	C₁₃×#41	—	2	4	no	—
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	4	2	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂²×C₄×C₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₂²⋊D₁₃	—	4	2	no	—
154	C₂×C₂²⋊D₁₃	—	4	8	no	—
155	C₂×C₂²⋊D₁₃	D₈	1	2	yes	—
156	#6131	—	2	8	no	—
157	#6131	—	4	4	no	—
158	Q₈×D₁₃	—	2	8	no	—
159	Q₈×D₁₃	—	4	4	no	—
160	#6129	—	2	8	no	—
161	#6129	—	4	8	no	—
162	#6129	—	4	8	no	—
163	#6129	—	4	4	no	—
164	D₄×D₁₃	—	2	8	no	—
165	D₄×D₁₃	—	4	8	no	—
166	D₄×D₁₃	—	4	8	no	—
167	D₄×D₁₃	—	4	4	no	—
168	#6127	—	2	4	no	—
169	#6127	—	2	4	no	—
170	#6127	—	4	2	no	—
171	#6127	—	4	2	no	—
172	#6127	—	4	8	no	—
173	#6127	—	4	4	no	—
174	#6127	—	4	8	no	—
175	#6127	—	4	4	no	—
176	#6127	D₈	1	2	yes	—
177	#6127	D₈	1	2	yes	—
178	#6127	C₂×D₄	1	2	yes	—
179	#6127	C₂×D₄	1	2	yes	—
180	C₂×D₅₂	—	2	2	no	—
181	C₂×D₅₂	—	4	4	no	—
182	C₂×D₅₂	D₈	1	1	yes	characteristic
183	C₂×C₄×D₁₃	—	4	2	no	—
184	C₂×C₄×D₁₃	—	4	8	no	—
185	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
186	C₂×Dic₂₆	—	2	2	no	—
187	C₂×Dic₂₆	—	4	4	no	—
188	C₂×Dic₂₆	D₈	1	1	yes	characteristic
189	C₁₃×Q₁₆	—	2	2	no	—
190	C₁₃×Q₁₆	C₂⁴	1	4	yes	—
191	C₁₃×SD₁₆	—	2	4	no	—
192	C₁₃×SD₁₆	—	2	4	no	—
193	C₁₃×D₈	—	2	2	no	—
194	C₁₃×D₈	C₂⁴	1	4	yes	—
195	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
201	#6107	—	2	8	no	—
202	#6106	—	2	8	no	—
203	#6105	—	2	8	no	—
204	#6104	—	2	8	no	—
205	#6099	C₂×D₄	1	2	yes	—
206	#6099	C₂×D₄	1	2	yes	—
207	C₂×#1055	C₂×D₄	1	2	yes	—
208	Dic₅₂	—	2	2	no	—
209	Dic₅₂	C₂⁴	1	4	yes	—
210	D₁₀₄	—	2	2	no	—
211	D₁₀₄	C₂⁴	1	4	yes	—
212	#6095	—	2	4	no	—
213	#6095	—	2	4	no	—
214	#6094	C₂×D₄	1	4	yes	—
215	#6094	C₂×D₄	1	4	yes	—
216	C₈×D₁₃	C₂×D₄	1	4	yes	—
217	C₈×D₁₃	C₂⁴	1	4	yes	—
218	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
219	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
220	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
221	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
222	#6090	C₂⁴	1	4	yes	—
223	#3584	—	13	2	no	—
224	#3417	—	13	2	no	—
225	#3417	—	13	2	no	—
226	#3416	—	13	4	no	—
227	#3416	—	13	4	no	—
228	#3415	—	13	2	no	—
229	#3415	—	13	2	no	—
230	#3414	—	13	4	no	—
231	#3414	—	13	2	no	—
232	C₂×#508	—	13	4	no	—
233	C₂×#508	—	13	1	no	—
234	C₂×#508	D₁₃	1	1	yes	characteristic, complemented
235	C₂×#504	—	13	1	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
238	C₂²×D₁₃	—	4	2	no	—
239	C₂²×D₁₃	—	4	8	no	—
240	C₂²×D₁₃	C₂×D₈	1	2	yes	—
241	Q₈×C₁₃	—	2	4	no	—
242	Q₈×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	4	4	no	—
245	D₄×C₁₃	—	4	4	no	—
246	D₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	4	no	—
249	C₂×C₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂²⋊D₁₃	—	4	4	no	—
257	C₂²⋊D₁₃	—	4	4	no	—
258	C₂²⋊D₁₃	—	4	8	no	—
259	C₂²⋊D₁₃	—	4	8	no	—
260	C₂²⋊D₁₃	C₂×D₈	1	4	yes	—
261	C₂²⋊D₁₃	C₂×D₈	1	4	yes	—
262	C₂×Dic₁₃	—	4	2	no	—
263	C₂×Dic₁₃	—	4	8	no	—
264	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
265	D₅₂	—	2	4	no	—
266	D₅₂	—	4	8	no	—
267	D₅₂	—	4	2	no	—
268	D₅₂	C₂×D₈	1	2	yes	—
269	D₅₂	C₂×D₈	1	2	yes	—
270	C₄×D₁₃	—	4	8	no	—
271	C₄×D₁₃	—	4	4	no	—
272	C₄×D₁₃	—	4	4	no	—
273	C₄×D₁₃	—	4	8	no	—
274	C₄×D₁₃	C₂×D₈	1	4	yes	—
275	C₄×D₁₃	C₂²×D₄	1	4	yes	—
276	Dic₂₆	—	2	4	no	—
277	Dic₂₆	—	4	2	no	—
278	Dic₂₆	—	4	8	no	—
279	Dic₂₆	C₂×D₈	1	2	yes	—
280	Dic₂₆	C₂×D₈	1	2	yes	—
281	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
285	#1055	C₂²×D₄	1	4	yes	—
286	#585	—	26	2	no	—
287	#578	—	13	4	no	—
288	#578	—	13	4	no	—
289	#577	—	26	4	no	—
290	#577	—	26	4	no	—
291	#576	—	13	4	no	—
292	#576	—	13	4	no	—
293	#575	—	26	4	no	—
294	#575	—	26	2	no	—
295	C₂×#135	—	13	8	no	—
296	C₂×#135	—	13	2	no	—
297	C₂×#135	C₂×D₁₃	1	2	yes	complemented
298	C₂×#131	—	13	1	no	—
299	#510	—	13	4	no	—
300	#510	—	13	4	no	—
301	#510	—	13	8	no	—
302	#510	—	13	8	no	—
303	#509	—	13	4	no	—
304	#509	—	13	4	no	—
305	#509	—	13	8	no	—
306	#509	—	13	8	no	—
307	#508	—	13	8	no	—
308	#508	—	13	4	no	—
309	#508	—	13	8	no	—
310	#508	—	13	4	no	—
311	#508	—	13	2	no	—
312	#508	—	13	2	no	—
313	#508	—	13	2	no	—
314	#508	—	13	2	no	—
315	#508	C₂×D₁₃	1	2	yes	complemented
316	#508	C₂×D₁₃	1	2	yes	complemented
317	#508	C₂×D₁₃	1	2	yes	complemented
318	#508	C₂×D₁₃	1	2	yes	complemented
319	C₂×Q₃₂	—	13	4	no	—
320	C₂×Q₃₂	—	13	1	no	—
321	C₂×Q₃₂	C₂×D₁₃	1	1	yes	characteristic, complemented
322	C₂×SD₃₂	—	13	8	no	—
323	C₂×SD₃₂	—	13	2	no	—
324	C₂×SD₃₂	C₂×D₁₃	1	2	yes	complemented
325	C₂×D₁₆	—	13	4	no	—
326	C₂×D₁₆	—	13	1	no	—
327	C₂×D₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
328	#504	—	13	2	no	—
329	#504	—	13	2	no	—
330	#504	—	13	2	no	—
331	#504	—	13	2	no	—
332	C₂×M₃₂	—	13	1	no	—
333	C₂×M₃₂	—	13	2	no	—
334	C₂²×C₁₆	—	13	2	no	—
335	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	16	2	no	—
339	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
340	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
341	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
342	C₂×D₁₃	—	4	2	no	—
343	C₂×D₁₃	—	4	4	no	—
344	C₂×D₁₃	—	16	8	no	—
345	C₂×D₁₃	—	16	2	no	—
346	C₂×D₁₃	C₂²×D₈	1	4	yes	—
347	C₄×C₁₃	—	4	4	no	—
348	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
349	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
350	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
351	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
352	Dic₁₃	—	4	4	no	—
353	Dic₁₃	C₂²×D₈	1	4	yes	—
354	2₋¹⁺⁴	—	26	4	no	—
355	2₋¹⁺⁴	—	26	4	no	—
356	2₋¹⁺⁴	—	52	2	no	—
357	H(5,𝔽₂)	—	26	4	no	—
358	H(5,𝔽₂)	—	26	4	no	—
359	H(5,𝔽₂)	—	52	4	no	—
360	H(5,𝔽₂)	—	52	2	no	—
361	C₂×#41	—	2	2	no	—
362	C₂×#41	—	13	1	no	—
363	C₂×#41	—	26	8	no	—
364	C₂×#41	—	26	2	no	—
365	C₂×#41	—	52	4	no	—
366	C₂×#41	—	52	4	no	—
367	#137	—	26	8	no	—
368	#137	—	26	8	no	—
369	#137	—	26	4	no	—
370	#137	—	26	4	no	—
371	AGL(1,ℤ/8)	—	26	8	no	—
372	AGL(1,ℤ/8)	—	26	8	no	—
373	AGL(1,ℤ/8)	—	26	4	no	—
374	AGL(1,ℤ/8)	—	26	4	no	—
375	#135	—	2	2	no	—
376	#135	—	2	2	no	—
377	#135	—	13	8	no	—
378	#135	—	13	8	no	—
379	#135	—	13	4	no	—
380	#135	—	13	4	no	—
381	#135	—	26	8	no	—
382	#135	—	26	8	no	—
383	#135	—	26	2	no	—
384	#135	—	26	2	no	—
385	#135	C₂²×D₁₃	1	4	yes	—
386	#135	C₂²×D₁₃	1	4	yes	—
387	C₂×Q₁₆	—	13	8	no	—
388	C₂×Q₁₆	—	13	2	no	—
389	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×SD₁₆	—	26	8	no	—
392	C₂×SD₁₆	—	26	2	no	—
393	C₂×D₈	—	13	8	no	—
394	C₂×D₈	—	13	2	no	—
395	C₂×D₈	C₂²×D₁₃	1	2	yes	—
396	#131	—	13	2	no	—
397	#131	—	13	2	no	—
398	#131	—	13	2	no	—
399	#131	—	13	2	no	—
400	C₂×M₁₆	—	13	1	no	—
401	C₂×M₁₆	—	13	2	no	—
402	C₂²×C₈	—	13	2	no	—
403	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
404	Q₃₂	—	13	8	no	—
405	Q₃₂	—	13	2	no	—
406	Q₃₂	—	13	2	no	—
407	Q₃₂	C₂²×D₁₃	1	2	yes	—
408	Q₃₂	C₂²×D₁₃	1	2	yes	—
409	SD₃₂	—	13	8	no	—
410	SD₃₂	—	13	8	no	—
411	SD₃₂	—	13	4	no	—
412	SD₃₂	—	13	4	no	—
413	SD₃₂	C₂²×D₁₃	1	4	yes	—
414	SD₃₂	C₂²×D₁₃	1	4	yes	—
415	D₁₆	—	13	8	no	—
416	D₁₆	—	13	2	no	—
417	D₁₆	—	13	2	no	—
418	D₁₆	C₂²×D₁₃	1	2	yes	—
419	D₁₆	C₂²×D₁₃	1	2	yes	—
420	M₃₂	—	13	2	no	—
421	M₃₂	—	13	2	no	—
422	M₃₂	—	13	4	no	—
423	M₃₂	—	13	4	no	—
424	C₂×C₁₆	—	13	2	no	—
425	C₂×C₁₆	—	13	4	no	—
426	C₂×C₁₆	—	13	4	no	—
427	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
428	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
429	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
430	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
431	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
432	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
433	C₂×C₁₃	—	2	1	no	—
434	C₂×C₁₃	—	2	1	no	—
435	C₂×C₁₃	—	2	1	no	—
436	C₂×C₁₃	—	8	4	no	—
437	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
438	D₁₃	—	2	4	no	—
439	D₁₃	—	8	4	no	—
440	#41	—	2	4	no	—
441	#41	—	2	4	no	—
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	13	2	no	—
445	#41	—	13	2	no	—
446	#41	—	13	2	no	—
447	#41	—	13	2	no	—
448	#41	—	26	8	no	—
449	#41	—	26	8	no	—
450	#41	—	26	4	no	—
451	#41	—	26	4	no	—
452	#41	—	52	8	no	—
453	#41	—	52	8	no	—
454	#41	—	52	4	no	—
455	#41	—	52	4	no	—
456	#41	—	52	8	no	—
457	#41	—	52	8	no	—
458	#41	—	52	4	no	—
459	#41	—	52	4	no	—
460	#41	—	52	2	no	—
461	#41	—	52	2	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	13	1	no	—
464	C₂×Q₈	—	26	8	no	—
465	C₂×Q₈	—	26	2	no	—
466	C₂×Q₈	—	52	4	no	—
467	C₂×Q₈	—	52	4	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	4	2	no	—
470	C₂×D₄	—	13	2	no	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	26	8	no	—
473	C₂×D₄	—	26	2	no	—
474	C₂×D₄	—	52	4	no	—
475	C₂×D₄	—	52	8	no	—
476	C₂×D₄	—	52	4	no	—
477	C₂×D₄	—	52	8	no	—
478	C₂×D₄	—	52	8	no	—
479	C₂×D₄	—	52	2	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	13	2	no	—
482	C₂²×C₄	—	52	8	no	—
483	C₂²×C₄	—	52	2	no	—
484	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
485	Q₁₆	—	2	2	no	—
486	Q₁₆	—	13	4	no	—
487	Q₁₆	—	26	8	no	—
488	Q₁₆	—	26	2	no	—
489	Q₁₆	C₂³×D₁₃	1	4	yes	—
490	SD₁₆	—	2	4	no	—
491	SD₁₆	—	2	4	no	—
492	SD₁₆	—	26	8	no	—
493	SD₁₆	—	26	8	no	—
494	SD₁₆	—	26	4	no	—
495	SD₁₆	—	26	4	no	—
496	D₈	—	2	2	no	—
497	D₈	—	13	4	no	—
498	D₈	—	26	8	no	—
499	D₈	—	26	2	no	—
500	D₈	C₂³×D₁₃	1	4	yes	—
501	M₁₆	—	13	2	no	—
502	M₁₆	—	13	2	no	—
503	M₁₆	—	13	4	no	—
504	M₁₆	—	13	4	no	—
505	C₂×C₈	—	13	2	no	—
506	C₂×C₈	—	13	4	no	—
507	C₂×C₈	—	13	4	no	—
508	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
509	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
510	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
511	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
512	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
513	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
514	C₁₆	—	13	4	no	—
515	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
516	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
517	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
518	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
519	C₁₃	#62635	1	1	yes	characteristic, complemented, Sylow
520	C₂³	—	4	2	no	—
521	C₂³	—	13	2	no	—
522	C₂³	—	52	8	no	—
523	C₂³	—	52	2	no	—
524	C₂³	D₈×D₁₃	1	1	yes	characteristic
525	Q₈	—	2	4	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	13	2	no	—
528	Q₈	—	13	2	no	—
529	Q₈	—	26	4	no	—
530	Q₈	—	52	8	no	—
531	Q₈	—	52	2	no	—
532	D₄	—	2	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	2	no	—
536	D₄	—	13	4	no	—
537	D₄	—	13	4	no	—
538	D₄	—	13	2	no	—
539	D₄	—	13	2	no	—
540	D₄	—	26	4	no	—
541	D₄	—	52	8	no	—
542	D₄	—	52	8	no	—
543	D₄	—	52	8	no	—
544	D₄	—	52	4	no	—
545	D₄	—	52	4	no	—
546	D₄	—	52	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	13	2	no	—
551	C₂×C₄	—	13	4	no	—
552	C₂×C₄	—	13	4	no	—
553	C₂×C₄	—	52	8	no	—
554	C₂×C₄	—	52	8	no	—
555	C₂×C₄	—	52	8	no	—
556	C₂×C₄	—	52	2	no	—
557	C₂×C₄	—	52	4	no	—
558	C₂×C₄	—	52	4	no	—
559	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
560	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
561	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
565	C₈	—	13	4	no	—
566	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
567	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
568	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
569	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
570	C₂²	—	4	1	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	13	4	no	—
573	C₂²	—	16	2	no	—
574	C₂²	—	52	2	no	—
575	C₂²	—	52	4	no	—
576	C₂²	—	208	2	no	—
577	C₂²	—	208	8	no	—
578	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
579	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
580	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
581	C₄	—	4	4	no	—
582	C₄	—	13	4	no	—
583	C₄	—	52	4	no	—
584	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
585	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
586	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
587	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	8	4	no	—
592	C₂	—	26	4	no	—
593	C₂	—	104	4	no	—
594	C₂	C₂²×D₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₁₃
commutator, cosocle	C₈×C₁₃	C₂⁵
Frattini	C₈	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#508	C₂
socle	C₂×C₁₃	C₂³×D₈
hypercenter	C₂×#508	D₁₃
hypocenter	C₁₃	#62635
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#508

Complements

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

N	H ≅ G/N	type
1. #13129605	C₂	semidirect
2. #13127986	C₂	semidirect
3. #13127985	C₂	semidirect
4. #13127979	C₂	semidirect
5. #13127978	C₂	semidirect
6. #13127974	C₂	semidirect
7. #13127973	C₂	semidirect
8. #13127970	C₂	semidirect
9. #13127969	C₂	semidirect
10. C₂×#11718565	C₂	semidirect
11. D₁₃×#508	C₂	semidirect
12. C₂×#11718562	C₂	semidirect
13. C₂×C₁₃×#508	C₂	semidirect
15. C₂×C₁₃×#135	C₂²	semidirect
17. #11719476	C₂²	semidirect
19. #11719474	C₂²	semidirect
21. D₁₃×#135	C₂²	semidirect
22. #11719471	C₂²	semidirect
24. #11719462	C₂²	semidirect
25. C₂×#88158	C₂²	semidirect
27. C₁₃×#508	C₂²	semidirect
28. C₁₃×#508	C₂²	semidirect
29. C₁₃×#508	C₂²	semidirect
30. C₁₃×#508	C₂²	semidirect
31. C₂×C₁₃×Q₃₂	C₂²	semidirect
32. C₂×C₁₃×SD₃₂	C₂²	semidirect
33. C₂×C₁₃×D₁₆	C₂²	semidirect
34. C₂²×C₁₃×C₁₆	C₂²	semidirect
35. #11718856	C₂²	semidirect
36. #11718855	C₂²	semidirect
37. #11718854	C₂²	semidirect
38. #11718840	C₂²	semidirect
39. #11718808	C₂²	semidirect
40. C₂×#88052	C₂²	semidirect
41. #11718580	C₂²	semidirect
42. #11718579	C₂²	semidirect
43. D₁₃×Q₃₂	C₂²	semidirect
44. #11718577	C₂²	semidirect
45. #11718576	C₂²	semidirect
46. #11718575	C₂²	semidirect
47. D₁₃×SD₃₂	C₂²	semidirect
48. #11718573	C₂²	semidirect
49. #11718572	C₂²	semidirect
50. D₁₃×D₁₆	C₂²	semidirect
51. C₂×Dic₁₀₄	C₂²	semidirect
52. #11718565	C₂²	semidirect
53. #11718565	C₂²	semidirect
54. #11718565	C₂²	semidirect
55. #11718565	C₂²	semidirect
56. C₂×#88040	C₂²	semidirect
57. C₂×D₂₀₈	C₂²	semidirect
58. #11718562	C₂²	semidirect
59. #11718562	C₂²	semidirect
60. #11718562	C₂²	semidirect
61. #11718562	C₂²	semidirect
62. C₂×#88038	C₂²	semidirect
63. C₂×C₁₆×D₁₃	C₂²	semidirect
234. C₂×#508	D₁₃	semidirect
297. C₂×#135	C₂×D₁₃	semidirect
315. #508	C₂×D₁₃	semidirect
316. #508	C₂×D₁₃	semidirect
317. #508	C₂×D₁₃	semidirect
318. #508	C₂×D₁₃	semidirect
321. C₂×Q₃₂	C₂×D₁₃	semidirect
324. C₂×SD₃₂	C₂×D₁₃	semidirect
327. C₂×D₁₆	C₂×D₁₃	semidirect
335. C₂²×C₁₆	C₂×D₁₃	semidirect
519. C₁₃	#62635	semidirect

Maximal subgroups

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

subgroup	index
#13129605	2
#13127986	2
#13127985	2
#13127979	2
#13127978	2
#13127974	2
#13127973	2
#13127970	2
#13127969	2
C₂×#11718565	2
D₁₃×#508	2
C₂×#11718562	2
C₂×C₁₃×#508	2
#62635	13