Subgroups — #16743556

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128637	C₂	1	2	yes	maximal, complemented
2	#13127796	C₂	1	4	yes	maximal, complemented
3	#13127737	C₂	1	4	yes	maximal, complemented
4	#13127704	C₂	1	2	yes	maximal, complemented
5	#13127704	C₂	1	4	yes	maximal, complemented
6	Q₈×D₁₀₄	C₂	1	2	yes	maximal, complemented
7	#13125375	C₂	1	2	yes	maximal, complemented
8	#13125350	C₂	1	1	yes	maximal, characteristic, complemented
9	#13124668	C₂	1	4	yes	maximal, complemented
10	#13124635	C₂	1	2	yes	maximal, complemented
11	#13123689	C₂	1	2	yes	maximal
12	C₂×C₄×D₁₀₄	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#533	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₄	C₂²	1	1	yes	characteristic
16	#11719435	—	2	2	no	—
17	#11719432	—	2	2	no	—
18	#11719395	—	2	4	no	—
19	#11719339	—	2	4	no	—
20	D₁₃×C₂²⋊Q₈	—	2	4	no	—
21	#11719284	C₂²	1	4	yes	complemented
22	#11719284	C₂²	1	8	yes	complemented
23	Q₈×D₅₂	C₂²	1	4	yes	complemented
24	#11719226	C₂²	1	4	yes	—
25	#11719224	C₂²	1	4	yes	—
26	C₂×C₄×D₅₂	C₂²	1	2	yes	—
27	#11719175	C₂²	1	2	yes	—
28	C₁₃×#446	C₂²	1	2	yes	complemented
29	C₁₃×#446	C₂²	1	2	yes	complemented
30	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
31	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
32	C₁₃×#424	C₂²	1	2	yes	—
33	C₁₃×#423	C₂²	1	1	yes	characteristic
34	C₁₃×#405	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	#11718792	C₂²	1	4	yes	—
37	#11718782	C₂²	1	4	yes	—
38	C₂×#88061	C₂²	1	2	yes	—
39	#11718767	C₂²	1	2	yes	—
40	#11718767	C₂²	1	2	yes	—
41	C₂×#88058	C₂²	1	1	yes	characteristic
42	#11718508	C₂²	1	8	yes	complemented
43	#11718508	C₂²	1	8	yes	complemented
44	#11718508	C₂²	1	8	yes	complemented
45	#11718507	C₂²	1	4	yes	complemented
46	#11718507	C₂²	1	8	yes	complemented
47	#11718503	C₂²	1	4	yes	complemented
48	#11718503	C₂²	1	8	yes	complemented
49	#11718372	C₂²	1	8	yes	—
50	#11718363	C₂²	1	8	yes	complemented
51	C₄×D₁₀₄	C₂²	1	2	yes	—
52	C₄×D₁₀₄	C₂²	1	2	yes	—
53	C₄×D₁₀₄	C₂²	1	2	yes	—
54	C₄×D₁₀₄	C₂²	1	2	yes	—
55	C₄×D₁₀₄	C₂²	1	4	yes	—
56	C₄×D₁₀₄	C₂²	1	4	yes	—
57	#11718344	C₂²	1	2	yes	complemented
58	#11718344	C₂²	1	4	yes	complemented
59	#11718344	C₂²	1	2	yes	complemented
60	#11718343	C₂²	1	1	yes	characteristic, complemented
61	#11718343	C₂²	1	4	yes	complemented
62	#11718343	C₂²	1	1	yes	characteristic, complemented
63	#11718341	C₂²	1	2	yes	complemented
64	C₂×Q₈×D₁₃	—	2	4	no	—
65	C₂²×D₅₂	C₂³	1	2	yes	—
66	C₂²×C₄×D₁₃	—	2	2	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
72	C₁₃×#125	D₄	1	2	yes	—
73	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
74	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
75	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
76	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
77	C₁₃×#117	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	#88200	—	2	4	no	—
80	#88200	—	2	8	no	—
81	C₂×#6103	—	2	2	no	—
82	#88180	C₂³	1	4	yes	—
83	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
84	#88178	—	2	2	no	—
85	#88178	—	2	2	no	—
86	C₂×D₁₀₄	Q₈	1	8	yes	complemented
87	C₂×D₁₀₄	C₂³	1	2	yes	—
88	C₂×D₁₀₄	C₂³	1	2	yes	—
89	#88151	—	2	4	no	—
90	#88151	—	2	8	no	—
91	#88150	—	2	8	no	—
92	#88150	—	2	8	no	—
93	#88150	—	2	8	no	—
94	#88147	—	2	4	no	—
95	#88147	—	2	4	no	—
96	C₄⋊C₄×D₁₃	—	2	4	no	—
97	C₄⋊C₄×D₁₃	—	2	8	no	—
98	#88144	—	2	4	no	—
99	#88142	—	2	4	no	—
100	C₂²⋊C₄×D₁₃	—	2	8	no	—
101	#88132	—	2	8	no	—
102	C₄×D₅₂	—	2	2	no	—
103	C₄×D₅₂	—	2	2	no	—
104	C₄×D₅₂	C₂³	1	4	yes	—
105	C₄×D₅₂	C₂³	1	4	yes	—
106	C₄×D₅₂	C₂³	1	8	yes	—
107	C₄×D₅₂	C₂³	1	8	yes	—
108	#88124	C₂³	1	4	yes	—
109	#88124	C₂³	1	8	yes	—
110	#88123	C₂³	1	2	yes	—
111	#88123	C₂³	1	2	yes	—
112	#88123	C₂³	1	8	yes	—
113	C₄×Dic₂₆	—	2	2	no	—
114	C₄×Dic₂₆	—	2	2	no	—
115	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
119	C₁₃×#97	C₂³	1	4	yes	—
120	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	#88061	C₂³	1	4	yes	—
126	#88061	C₂³	1	8	yes	—
127	#88061	C₂³	1	8	yes	—
128	#88061	C₂³	1	4	yes	—
129	#88058	C₂³	1	2	yes	—
130	#88058	C₂³	1	8	yes	—
131	#88058	C₂³	1	2	yes	—
132	#88058	C₂³	1	2	yes	—
133	#88058	C₂³	1	2	yes	—
134	#88058	C₂³	1	2	yes	—
135	#88058	C₂³	1	2	yes	—
136	#88057	C₂³	1	4	yes	—
137	#88057	C₂³	1	8	yes	—
138	#88057	C₂³	1	4	yes	—
139	#61370	—	13	1	no	maximal, Sylow
140	C₂³×D₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²×Dic₁₃	—	2	2	no	—
147	Q₈×D₁₃	—	8	8	no	—
148	C₂×D₅₂	—	2	2	no	—
149	C₂×D₅₂	—	2	4	no	—
150	C₂×D₅₂	C₂×Q₈	1	8	yes	complemented
151	C₂×D₅₂	C₂⁴	1	4	yes	—
152	C₂×C₄×D₁₃	—	2	4	no	—
153	C₂×C₄×D₁₃	—	2	4	no	—
154	C₂×C₄×D₁₃	—	2	8	no	—
155	C₂×C₄×D₁₃	—	2	8	no	—
156	C₂×C₄×D₁₃	—	8	4	no	—
157	C₂×Dic₂₆	—	2	2	no	—
158	C₂×Dic₂₆	—	2	2	no	—
159	C₂×Dic₂₆	—	2	8	no	—
160	C₁₃×M₁₆	—	2	4	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
163	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
166	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
174	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₄²×C₁₃	C₂⁴	1	4	yes	—
180	C₂²⋊Dic₁₃	—	2	4	no	—
181	#6103	—	2	4	no	—
182	#6103	—	2	4	no	—
183	#6103	—	2	8	no	—
184	#6103	—	2	8	no	—
185	C₄⋊Dic₁₃	—	2	2	no	—
186	C₄⋊Dic₁₃	—	2	2	no	—
187	C₄⋊Dic₁₃	—	2	8	no	—
188	C₄⋊Dic₁₃	—	2	2	no	—
189	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
190	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
191	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
192	#6101	—	2	4	no	—
193	#6101	—	2	4	no	—
194	#6101	—	2	8	no	—
195	#6101	—	2	8	no	—
196	C₄×Dic₁₃	—	2	4	no	—
197	D₁₀₄	C₂×Q₈	1	8	yes	complemented
198	D₁₀₄	C₂×Q₈	1	8	yes	complemented
199	#3501	—	13	2	no	—
200	#3389	—	13	4	no	—
201	#3384	—	13	4	no	—
202	#3380	—	13	2	no	—
203	#3380	—	13	4	no	—
204	Q₈×D₈	—	13	2	no	—
205	#3164	—	13	2	no	—
206	#3160	—	13	1	no	—
207	#3081	—	13	4	no	—
208	#3077	—	13	2	no	—
209	#2960	D₁₃	1	1	yes	characteristic, complemented
210	#2948	—	13	2	no	—
211	C₂×C₄×D₈	—	13	1	no	—
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂²×D₁₃	—	2	4	no	—
214	C₂²×D₁₃	—	2	8	no	—
215	C₂²×D₁₃	—	8	2	no	—
216	C₂²×D₁₃	—	8	2	no	—
217	Q₈×C₁₃	—	2	4	no	—
218	Q₈×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
229	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₂×Dic₁₃	—	2	4	no	—
232	C₂×Dic₁₃	—	2	4	no	—
233	C₂×Dic₁₃	—	2	4	no	—
234	C₂×Dic₁₃	—	8	2	no	—
235	D₅₂	—	2	8	no	—
236	D₅₂	—	2	4	no	—
237	D₅₂	C₂²×Q₈	1	8	yes	—
238	C₄×D₁₃	—	4	8	no	—
239	C₄×D₁₃	—	8	8	no	—
240	C₄×D₁₃	—	8	4	no	—
241	C₄×D₁₃	—	8	8	no	—
242	Dic₂₆	—	4	4	no	—
243	Dic₂₆	—	8	2	no	—
244	Dic₂₆	—	8	8	no	—
245	C₈×C₁₃	—	2	1	no	—
246	C₈×C₁₃	—	2	1	no	—
247	C₈×C₁₃	—	2	4	no	—
248	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
249	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
250	C₂²×D₈	—	13	1	no	—
251	#554	—	13	4	no	—
252	#554	—	13	8	no	—
253	#554	—	26	2	no	—
254	#554	—	26	4	no	—
255	D₄×Q₈	—	13	4	no	—
256	D₄×Q₈	—	26	2	no	—
257	#544	—	13	4	no	—
258	#543	—	26	4	no	—
259	#533	—	13	2	no	—
260	#533	C₂×D₁₃	1	1	yes	characteristic
261	C₂×C₂²⋊Q₈	—	26	4	no	—
262	#518	—	13	4	no	—
263	C₂×C₄×D₄	—	13	2	no	—
264	#501	—	13	8	no	—
265	#500	—	13	1	no	—
266	#500	—	13	4	no	—
267	#500	—	13	1	no	—
268	#499	—	13	2	no	—
269	#499	—	13	4	no	—
270	#499	—	13	2	no	—
271	#498	—	13	2	no	—
272	#478	—	13	8	no	—
273	#478	—	13	8	no	—
274	#478	—	13	8	no	—
275	#476	—	13	4	no	—
276	#476	—	13	8	no	—
277	#474	—	13	4	no	—
278	#474	—	13	8	no	—
279	#446	C₂×D₁₃	1	2	yes	complemented
280	#446	C₂×D₁₃	1	2	yes	complemented
281	C₈×Q₈	C₂×D₁₃	1	2	yes	complemented
282	C₈×Q₈	C₂×D₁₃	1	2	yes	complemented
283	#442	—	13	8	no	—
284	C₄×D₈	—	13	2	no	—
285	C₄×D₈	—	13	4	no	—
286	C₄×D₈	—	13	2	no	—
287	C₄×D₈	—	13	4	no	—
288	C₄×D₈	—	13	2	no	—
289	C₄×D₈	—	13	2	no	—
290	#428	—	13	4	no	—
291	#427	—	13	2	no	—
292	#427	—	13	2	no	—
293	C₂×#107	—	13	1	no	—
294	#424	C₂×D₁₃	1	2	yes	—
295	#423	C₂×D₁₃	1	1	yes	characteristic
296	#418	—	13	4	no	—
297	C₂×#102	—	13	2	no	—
298	#405	C₂×D₁₃	1	2	yes	—
299	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
303	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
304	C₂×D₁₃	—	2	8	no	—
305	C₂×D₁₃	—	4	4	no	—
306	C₂×D₁₃	—	4	4	no	—
307	C₂×D₁₃	—	8	8	no	—
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	—	2	4	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	4	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	D₄×Q₈	1	2	yes	—
314	C₄×C₁₃	#576	1	2	yes	—
315	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
316	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	Dic₁₃	—	4	4	no	—
318	Dic₁₃	—	4	4	no	—
319	Dic₁₃	—	4	4	no	—
320	C₂²×Q₈	—	26	4	no	—
321	C₂²×D₄	—	13	2	no	—
322	C₂³×C₄	—	26	2	no	—
323	C₂×D₈	—	13	8	no	—
324	C₂×D₈	—	13	2	no	—
325	C₂×D₈	—	13	2	no	—
326	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
327	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
328	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
329	C₄⋊Q₈	—	13	2	no	—
330	C₄⋊Q₈	—	13	2	no	—
331	C₄⋊Q₈	—	13	8	no	—
332	C₄⋊Q₈	—	26	4	no	—
333	C₄⋊Q₈	D₅₂	1	1	yes	characteristic
334	C₄⋊Q₈	D₅₂	1	1	yes	characteristic
335	#125	—	13	4	no	—
336	#125	—	13	8	no	—
337	#125	—	26	4	no	—
338	#125	D₅₂	1	2	yes	—
339	C₂²⋊Q₈	—	26	4	no	—
340	C₂²⋊Q₈	—	26	8	no	—
341	C₂²⋊Q₈	—	26	2	no	—
342	C₂²⋊Q₈	—	26	2	no	—
343	C₂²⋊Q₈	—	26	4	no	—
344	C₂²⋊Q₈	—	26	8	no	—
345	C₂²⋊Q₈	—	26	8	no	—
346	C₂²⋊Q₈	—	26	8	no	—
347	C₂²⋊Q₈	—	26	8	no	—
348	C₂²⋊Q₈	—	26	8	no	—
349	C₂²⋊Q₈	D₅₂	1	2	yes	—
350	C₂²⋊Q₈	D₅₂	1	2	yes	—
351	C₄×Q₈	—	26	2	no	—
352	C₄×Q₈	—	26	2	no	—
353	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
354	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
355	C₄×D₄	—	13	4	no	—
356	C₄×D₄	—	13	4	no	—
357	C₄×D₄	—	13	8	no	—
358	C₄×D₄	—	13	8	no	—
359	C₄×D₄	—	26	4	no	—
360	C₄×D₄	—	26	4	no	—
361	C₄×D₄	—	26	2	no	—
362	C₄×D₄	—	26	2	no	—
363	#117	—	13	4	no	—
364	#117	C₂²×D₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	—	13	2	no	—
366	C₂×C₄⋊C₄	—	26	8	no	—
367	C₂×C₄⋊C₄	—	26	4	no	—
368	C₂×C₂²⋊C₄	—	26	2	no	—
369	C₂×C₂²⋊C₄	—	26	8	no	—
370	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
371	#107	—	13	2	no	—
372	#107	—	13	2	no	—
373	#107	—	13	2	no	—
374	#107	—	13	2	no	—
375	#107	—	13	2	no	—
376	#107	—	13	2	no	—
377	#107	—	13	8	no	—
378	#106	—	13	4	no	—
379	#106	—	13	4	no	—
380	#106	—	13	8	no	—
381	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
382	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
383	C₄⋊C₈	C₂²×D₁₃	1	4	yes	—
384	C₄⋊C₈	C₂²×D₁₃	1	4	yes	—
385	#102	—	13	4	no	—
386	#102	—	13	4	no	—
387	#102	—	13	8	no	—
388	#102	—	13	8	no	—
389	#97	C₂²×D₁₃	1	4	yes	—
390	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
391	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
392	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
393	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
394	C₄×C₈	C₂²×D₁₃	1	4	yes	—
395	C₂×C₁₃	—	2	2	no	—
396	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
397	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
398	C₂×C₁₃	#3584	1	1	yes	characteristic
399	D₁₃	—	4	8	no	—
400	C₂⁴	—	26	2	no	—
401	C₂×Q₈	—	26	2	no	—
402	C₂×Q₈	—	26	2	no	—
403	C₂×Q₈	—	26	8	no	—
404	C₂×Q₈	—	104	8	no	—
405	C₂×Q₈	C₂×D₅₂	1	2	yes	—
406	C₂×Q₈	C₂×D₅₂	1	2	yes	—
407	C₂×D₄	—	13	8	no	—
408	C₂×D₄	—	13	4	no	—
409	C₂×D₄	—	26	2	no	—
410	C₂×D₄	—	26	4	no	—
411	C₂²×C₄	—	26	2	no	—
412	C₂²×C₄	—	26	4	no	—
413	C₂²×C₄	—	26	8	no	—
414	C₂²×C₄	—	26	8	no	—
415	C₂²×C₄	—	26	4	no	—
416	C₂²×C₄	—	104	4	no	—
417	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
419	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
420	D₈	—	13	8	no	—
421	D₈	—	13	8	no	—
422	M₁₆	—	2	4	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	Q₈×D₁₃	1	4	yes	complemented
425	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
426	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
427	C₂×C₈	C₂³×D₁₃	1	4	yes	—
428	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
429	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
430	C₄⋊C₄	—	13	4	no	—
431	C₄⋊C₄	—	13	4	no	—
432	C₄⋊C₄	—	13	4	no	—
433	C₄⋊C₄	—	26	2	no	—
434	C₄⋊C₄	—	26	4	no	—
435	C₄⋊C₄	—	26	2	no	—
436	C₄⋊C₄	—	26	8	no	—
437	C₄⋊C₄	—	26	8	no	—
438	C₄⋊C₄	—	26	8	no	—
439	C₄⋊C₄	—	26	4	no	—
440	C₄⋊C₄	—	26	2	no	—
441	C₄⋊C₄	C₂×D₅₂	1	4	yes	—
442	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
443	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
444	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
445	C₄⋊C₄	C₂×D₅₂	1	4	yes	—
446	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
447	C₂²⋊C₄	—	26	4	no	—
448	C₂²⋊C₄	—	26	8	no	—
449	C₂²⋊C₄	—	26	8	no	—
450	C₂²⋊C₄	—	26	4	no	—
451	C₂²⋊C₄	—	26	4	no	—
452	C₂²⋊C₄	C₂×D₅₂	1	4	yes	—
453	C₄²	—	26	4	no	—
454	C₄²	C₂×D₅₂	1	1	yes	characteristic
455	C₄²	C₂×D₅₂	1	1	yes	characteristic
456	C₄²	C₂³×D₁₃	1	1	yes	characteristic
457	C₄²	C₂³×D₁₃	1	1	yes	characteristic
458	C₄²	C₂³×D₁₃	1	4	yes	—
459	C₁₃	#61370	1	1	yes	characteristic, complemented, Sylow
460	C₂³	—	26	4	no	—
461	C₂³	—	26	8	no	—
462	C₂³	—	104	2	no	—
463	C₂³	—	104	2	no	—
464	C₂³	C₂²×D₅₂	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	52	4	no	—
468	Q₈	—	104	2	no	—
469	Q₈	—	104	8	no	—
470	D₄	—	13	8	no	—
471	D₄	—	26	8	no	—
472	D₄	—	26	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	26	4	no	—
476	C₂×C₄	—	26	4	no	—
477	C₂×C₄	—	26	4	no	—
478	C₂×C₄	—	52	8	no	—
479	C₂×C₄	—	104	8	no	—
480	C₂×C₄	—	104	4	no	—
481	C₂×C₄	—	104	8	no	—
482	C₂×C₄	—	104	2	no	—
483	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₅₂	1	4	yes	—
487	C₂×C₄	C₂²×D₅₂	1	4	yes	—
488	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
490	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
491	C₂×C₄	#88257	1	2	yes	—
492	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	4	no	—
496	C₈	C₂×Q₈×D₁₃	1	2	yes	—
497	C₈	C₂×Q₈×D₁₃	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	26	8	no	—
501	C₂²	—	52	4	no	—
502	C₂²	—	52	4	no	—
503	C₂²	—	104	8	no	—
504	C₂²	Q₈×D₅₂	1	2	yes	—
505	C₂²	C₂³×D₅₂	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	4	no	—
511	C₄	—	52	4	no	—
512	C₄	—	52	4	no	—
513	C₄	—	52	4	no	—
514	C₄	Q₈×D₅₂	1	2	yes	—
515	C₄	#11719457	1	2	yes	—
516	C₄	C₂²×Q₈×D₁₃	1	1	yes	characteristic
517	C₄	C₂×#88257	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	52	8	no	—
520	C₂	C₂×Q₈×D₅₂	1	1	yes	characteristic
521	C₂	C₂×#11719457	1	1	yes	characteristic
522	C₂	#13129610	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₅₂
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₁₃×#2960	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂²×D₁₀₄	C₂²
hypercenter	#2960	D₁₃
hypocenter	C₁₃	#61370
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #533 ◁ #2960

Complements

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

N	H ≅ G/N	type
1. #13128637	C₂	semidirect
2. #13127796	C₂	semidirect
3. #13127737	C₂	semidirect
4. #13127704	C₂	semidirect
5. #13127704	C₂	semidirect
6. Q₈×D₁₀₄	C₂	semidirect
7. #13125375	C₂	semidirect
8. #13125350	C₂	semidirect
9. #13124668	C₂	semidirect
10. #13124635	C₂	semidirect
13. C₁₃×#2960	C₂	semidirect
21. #11719284	C₂²	semidirect
22. #11719284	C₂²	semidirect
23. Q₈×D₅₂	C₂²	semidirect
28. C₁₃×#446	C₂²	semidirect
29. C₁₃×#446	C₂²	semidirect
30. C₈×Q₈×C₁₃	C₂²	semidirect
31. C₈×Q₈×C₁₃	C₂²	semidirect
42. #11718508	C₂²	semidirect
43. #11718508	C₂²	semidirect
44. #11718508	C₂²	semidirect
45. #11718507	C₂²	semidirect
46. #11718507	C₂²	semidirect
47. #11718503	C₂²	semidirect
48. #11718503	C₂²	semidirect
50. #11718363	C₂²	semidirect
57. #11718344	C₂²	semidirect
58. #11718344	C₂²	semidirect
59. #11718344	C₂²	semidirect
60. #11718343	C₂²	semidirect
61. #11718343	C₂²	semidirect
62. #11718343	C₂²	semidirect
63. #11718341	C₂²	semidirect
86. C₂×D₁₀₄	Q₈	semidirect
150. C₂×D₅₂	C₂×Q₈	semidirect
162. C₂×C₈×C₁₃	C₂×Q₈	semidirect
197. D₁₀₄	C₂×Q₈	semidirect
198. D₁₀₄	C₂×Q₈	semidirect
209. #2960	D₁₃	semidirect
279. #446	C₂×D₁₃	semidirect
280. #446	C₂×D₁₃	semidirect
281. C₈×Q₈	C₂×D₁₃	semidirect
282. C₈×Q₈	C₂×D₁₃	semidirect
424. C₂×C₈	Q₈×D₁₃	semidirect
459. C₁₃	#61370	semidirect

Maximal subgroups

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

subgroup	index
#13128637	2
#13127796	2
#13127737	2
#13127704	2
Q₈×D₁₀₄	2
#13125375	2
#13125350	2
#13124668	2
#13124635	2
#13123689	2
C₂×C₄×D₁₀₄	2
C₁₃×#2960	2
#61370	13