Subgroups — #15869366

Order 3328.

922 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124285	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718485	C₂	1	2	yes	maximal, complemented
3	#13123548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#88161	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115487	C₂	1	2	yes	maximal, complemented
7	#13115160	C₂	1	2	yes	maximal, complemented
8	#13114857	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114674	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₂×#88204	C₂²	1	2	yes	—
14	C₂×#88202	C₂²	1	2	yes	—
15	C₂×#88161	C₂²	1	1	yes	characteristic
16	C₂×#88161	C₂²	1	1	yes	characteristic
17	C₄×#6127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#104	C₂²	1	2	yes	—
19	C₂×C₁₃×#104	C₂²	1	2	yes	—
20	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	#11718895	C₂²	1	2	yes	—
23	#11718894	C₂²	1	2	yes	—
24	C₂×#88062	C₂²	1	2	yes	—
25	#11718783	C₂²	1	1	yes	characteristic
26	#11718783	C₂²	1	1	yes	characteristic
27	#11718751	C₄	1	1	yes	characteristic, complemented
28	#11718744	C₄	1	1	yes	characteristic, complemented
29	#11718736	C₄	1	1	yes	characteristic, complemented
30	#11718733	C₄	1	1	yes	characteristic, complemented
31	#11718718	C₄	1	2	yes	complemented
32	#11718715	C₄	1	2	yes	complemented
33	#11718673	—	2	1	no	—
34	#11718673	—	2	1	no	—
35	D₄×#1055	—	2	1	no	—
36	D₄×#1055	—	2	1	no	—
37	C₂×#88045	C₂²	1	2	yes	—
38	#11718585	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	C₂×C₄×#1055	C₂²	1	2	yes	—
41	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
42	#11718485	—	2	8	no	—
43	#11718369	—	2	1	no	—
44	#11718369	—	2	1	no	—
45	C₄×#6094	—	2	1	no	—
46	C₄×C₈×D₁₃	—	2	1	no	—
47	#11718150	C₂²	1	2	yes	—
48	#11718116	C₂²	1	2	yes	—
49	#11718115	C₂²	1	2	yes	—
50	C₂×C₁₃×#41	C₂³	1	2	yes	—
51	C₂×#6127	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
56	C₁₃×#124	C₂×C₄	1	2	yes	—
57	C₁₃×#121	—	2	1	no	—
58	C₁₃×#121	—	2	1	no	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	#88204	—	2	4	no	—
65	#88204	—	2	4	no	—
66	#88202	—	2	4	no	—
67	#88202	—	2	4	no	—
68	C₂×#6107	C₂×C₄	1	2	yes	—
69	C₂×#6106	C₂×C₄	1	2	yes	—
70	C₂×#6105	C₂×C₄	1	2	yes	—
71	C₂×#6104	C₂×C₄	1	2	yes	—
72	C₄×C₂²⋊D₁₃	—	2	1	no	—
73	C₄×C₂²⋊D₁₃	—	2	1	no	—
74	#88180	C₂³	1	1	yes	characteristic
75	C₂×#6099	—	2	2	no	—
76	C₂×#6099	C₂³	1	2	yes	—
77	C₂²×#1055	—	2	2	no	—
78	C₂²×#1055	C₂³	1	2	yes	—
79	C₂²×#1055	C₂³	1	1	yes	characteristic
80	C₂²×#1055	C₂³	1	1	yes	characteristic
81	#88161	—	2	2	no	—
82	#88161	—	2	2	no	—
83	#88161	—	2	2	no	—
84	#88161	D₄	1	4	yes	complemented
85	C₂×#6094	—	2	1	no	—
86	C₂×#6094	—	2	1	no	—
87	C₂×C₈×D₁₃	—	2	1	no	—
88	C₂×C₈×D₁₃	—	2	1	no	—
89	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
90	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
91	#88126	—	2	1	no	—
92	C₄²×D₁₃	—	2	1	no	—
93	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
94	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#104	—	2	4	no	—
96	C₁₃×#104	—	2	4	no	—
97	C₁₃×#97	—	2	1	no	—
98	C₄×C₈×C₁₃	—	2	1	no	—
99	C₁₃×#95	—	2	1	no	—
100	#88075	C₂×C₄	1	2	yes	—
101	#88075	C₂×C₄	1	2	yes	—
102	#88072	C₂×C₄	1	2	yes	—
103	#88072	C₂×C₄	1	2	yes	—
104	C₂²⋊#1055	—	2	2	no	—
105	C₂²⋊#1055	—	2	2	no	—
106	#88062	—	2	4	no	—
107	#88055	—	2	1	no	—
108	#88055	—	2	1	no	—
109	C₈×Dic₁₃	—	2	1	no	—
110	C₈×Dic₁₃	—	2	1	no	—
111	#88045	—	2	4	no	—
112	C₄⋊#1055	—	2	1	no	—
113	C₄⋊#1055	—	2	1	no	—
114	C₄⋊#1055	C₂×C₄	1	2	yes	—
115	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
116	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
117	C₄×#1055	—	2	4	no	—
118	C₄×#1055	D₄	1	1	yes	characteristic
119	C₄×#1055	D₄	1	1	yes	characteristic
120	C₄×#1055	D₄	1	1	yes	characteristic
121	C₄×#1055	D₄	1	1	yes	characteristic
122	#21517	—	13	1	no	maximal, Sylow
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	2	2	no	—
127	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃	—	2	1	no	—
138	#6127	—	2	1	no	—
139	#6127	—	2	1	no	—
140	#6127	C₂×D₄	1	2	yes	—
141	#6127	#41	1	2	yes	—
142	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄×D₁₃	—	2	1	no	—
144	C₂×C₄×D₁₃	—	2	1	no	—
145	C₂×C₄×D₁₃	—	2	1	no	—
146	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
147	C₁₃×M₁₆	—	2	1	no	—
148	C₁₃×M₁₆	—	2	1	no	—
149	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
150	C₁₃×M₁₆	#41	1	2	yes	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²⋊Dic₁₃	—	2	1	no	—
165	#6107	—	2	4	no	—
166	#6106	—	2	4	no	—
167	#6105	—	2	4	no	—
168	#6104	—	2	4	no	—
169	#6103	—	2	1	no	—
170	#6103	—	2	1	no	—
171	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
173	#6101	—	2	1	no	—
174	#6101	—	2	1	no	—
175	C₄×Dic₁₃	—	2	1	no	—
176	C₄×Dic₁₃	—	2	1	no	—
177	C₄×Dic₁₃	—	2	1	no	—
178	#6099	—	2	2	no	—
179	#6099	—	2	2	no	—
180	#6099	—	4	4	no	—
181	C₂×#1055	—	2	2	no	—
182	C₂×#1055	—	2	1	no	—
183	C₂×#1055	—	2	1	no	—
184	C₂×#1055	—	2	2	no	—
185	C₂×#1055	—	2	2	no	—
186	C₂×#1055	—	4	4	no	—
187	C₂×#1055	C₂²×C₄	1	2	yes	—
188	C₂×#1055	C₂²×C₄	1	2	yes	—
189	C₂×#1055	C₂×D₄	1	1	yes	characteristic
190	C₂×#1055	C₂×D₄	1	1	yes	characteristic
191	C₂×#1055	C₂×D₄	1	1	yes	characteristic
192	C₂×#1055	C₂×D₄	1	1	yes	characteristic
193	C₂×#1055	C₂×D₄	1	2	yes	—
194	C₂×#1055	#41	1	2	yes	—
195	#6094	—	2	4	no	—
196	#6094	—	2	4	no	—
197	C₈×D₁₃	—	2	4	no	—
198	C₈×D₁₃	—	2	4	no	—
199	#3035	—	13	1	no	—
200	C₂×#443	—	13	2	no	—
201	#2931	—	13	1	no	—
202	C₄×#131	—	13	1	no	—
203	#1980	D₁₃	1	1	yes	characteristic, complemented
204	#1950	—	13	1	no	—
205	#1929	—	13	2	no	—
206	#1876	—	13	2	no	—
207	#1806	—	13	1	no	—
208	C₈×C₄⋊C₄	—	13	1	no	—
209	#1764	—	13	2	no	—
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂²×D₁₃	—	2	1	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	2	2	no	—
216	D₄×C₁₃	—	2	2	no	—
217	D₄×C₁₃	—	4	2	no	—
218	D₄×C₁₃	—	4	2	no	—
219	D₄×C₁₃	—	4	2	no	—
220	D₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
239	C₂²⋊D₁₃	—	2	2	no	—
240	C₂²⋊D₁₃	—	2	2	no	—
241	C₂×Dic₁₃	—	2	1	no	—
242	C₂×Dic₁₃	—	2	1	no	—
243	C₂×Dic₁₃	—	2	1	no	—
244	D₅₂	—	2	1	no	—
245	D₅₂	C₄×D₄	1	2	yes	—
246	C₄×D₁₃	—	2	2	no	—
247	C₄×D₁₃	—	2	2	no	—
248	C₄×D₁₃	—	4	2	no	—
249	C₄×D₁₃	—	4	2	no	—
250	Dic₂₆	—	2	1	no	—
251	Dic₂₆	C₄×D₄	1	2	yes	—
252	C₈×C₁₃	—	2	2	no	—
253	C₈×C₁₃	—	2	2	no	—
254	#1055	—	2	2	no	—
255	#1055	—	2	2	no	—
256	#1055	—	2	1	no	—
257	#1055	—	2	1	no	—
258	#1055	—	4	2	no	—
259	#1055	#121	1	2	yes	—
260	#1055	#121	1	2	yes	—
261	C₂×#135	—	13	2	no	—
262	C₂×#131	—	13	2	no	—
263	C₂×#131	—	13	1	no	—
264	C₂×#131	—	13	1	no	—
265	#532	C₂×D₁₃	1	1	yes	characteristic
266	C₄×#41	—	13	1	no	—
267	#464	—	13	2	no	—
268	#463	—	13	2	no	—
269	#462	—	13	1	no	—
270	#461	—	13	1	no	—
271	#460	—	13	1	no	—
272	#459	—	13	1	no	—
273	#443	—	26	8	no	—
274	#436	—	26	1	no	—
275	#436	—	26	1	no	—
276	C₈×D₄	—	26	1	no	—
277	C₈×D₄	—	26	1	no	—
278	C₂×#108	—	13	2	no	—
279	#423	—	13	1	no	—
280	C₂×C₄⋊C₈	—	13	1	no	—
281	C₂×#104	—	13	2	no	—
282	C₂×#104	C₂×D₁₃	1	2	yes	—
283	C₂×#104	C₂×D₁₃	1	2	yes	—
284	#416	—	13	2	no	—
285	#408	—	13	2	no	—
286	#405	—	13	1	no	—
287	#405	—	13	1	no	—
288	#405	—	26	1	no	—
289	#405	—	26	1	no	—
290	C₄×M₁₆	—	26	1	no	—
291	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
292	C₂×C₄×C₈	—	13	1	no	—
293	C₂×C₄×C₈	—	13	2	no	—
294	C₂×C₄×C₈	—	26	1	no	—
295	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
296	#341	—	13	2	no	—
297	#339	—	13	2	no	—
298	#336	—	13	2	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	2	no	—
304	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
305	C₂²×C₁₃	#529	1	1	yes	characteristic
306	C₂²×C₁₃	#532	1	1	yes	characteristic
307	C₂×D₁₃	—	2	2	no	—
308	C₂×D₁₃	—	4	1	no	—
309	C₂×D₁₃	—	4	1	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	#443	1	2	yes	complemented
316	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
317	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
318	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
319	C₄×C₁₃	#525	1	1	yes	characteristic
320	Dic₁₃	—	2	2	no	—
321	Dic₁₃	—	4	1	no	—
322	Dic₁₃	—	4	1	no	—
323	C₂×#41	—	13	1	no	—
324	C₂×#41	C₂²×D₁₃	1	2	yes	—
325	#135	—	26	4	no	—
326	#135	—	26	4	no	—
327	C₂×Q₁₆	—	13	2	no	—
328	C₂×SD₁₆	—	13	2	no	—
329	C₂×SD₁₆	—	13	2	no	—
330	C₂×D₈	—	13	2	no	—
331	#131	—	13	4	no	—
332	#131	—	26	2	no	—
333	#131	—	26	4	no	—
334	#131	—	26	4	no	—
335	#131	—	26	2	no	—
336	#131	—	26	2	no	—
337	C₂×M₁₆	—	13	2	no	—
338	C₂×M₁₆	—	26	1	no	—
339	C₂×M₁₆	—	26	1	no	—
340	C₂×M₁₆	—	26	2	no	—
341	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
342	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
343	C₂²×C₈	—	13	1	no	—
344	C₂²×C₈	—	13	1	no	—
345	C₂²×C₈	—	13	2	no	—
346	C₂²×C₈	—	26	1	no	—
347	C₂²×C₈	—	26	1	no	—
348	C₂²×C₈	—	26	2	no	—
349	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
350	#127	C₄×D₁₃	1	1	yes	characteristic
351	#124	C₄×D₁₃	1	2	yes	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	C₄×Q₈	—	13	1	no	—
355	C₄×Q₈	—	13	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	13	1	no	—
359	C₄×D₄	—	13	1	no	—
360	C₄×D₄	—	26	1	no	—
361	C₄×D₄	—	26	1	no	—
362	#117	—	13	1	no	—
363	#117	—	26	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄²	—	26	1	no	—
366	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
367	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
368	#108	—	26	4	no	—
369	C₄⋊C₈	—	13	1	no	—
370	C₄⋊C₈	—	13	1	no	—
371	C₄⋊C₈	—	13	2	no	—
372	C₄⋊C₈	—	26	1	no	—
373	C₄⋊C₈	—	26	1	no	—
374	#104	—	2	4	no	—
375	#104	—	2	4	no	—
376	#104	—	26	4	no	—
377	#103	—	13	2	no	—
378	#103	—	13	2	no	—
379	#102	—	13	2	no	—
380	#102	—	13	2	no	—
381	C₂²⋊C₈	—	26	2	no	—
382	C₂²⋊C₈	—	26	2	no	—
383	#97	—	2	1	no	—
384	#97	—	26	1	no	—
385	#97	—	26	1	no	—
386	C₄×C₈	—	2	1	no	—
387	C₄×C₈	—	13	1	no	—
388	C₄×C₈	—	13	1	no	—
389	C₄×C₈	—	13	1	no	—
390	C₄×C₈	—	13	1	no	—
391	C₄×C₈	—	26	4	no	—
392	C₄×C₈	—	26	1	no	—
393	C₄×C₈	—	26	1	no	—
394	#95	—	2	1	no	—
395	C₂×C₁₃	—	2	1	no	—
396	C₂×C₁₃	—	2	1	no	—
397	C₂×C₁₃	—	8	2	no	—
398	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
399	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
400	C₂×C₁₃	#2955	1	1	yes	characteristic
401	D₁₃	—	4	2	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	13	2	no	—
407	#41	—	13	2	no	—
408	#41	—	26	1	no	—
409	#41	—	26	1	no	—
410	C₂×Q₈	—	13	1	no	—
411	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	13	1	no	—
416	C₂×D₄	—	26	1	no	—
417	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	26	1	no	—
421	C₂²×C₄	—	26	1	no	—
422	C₂²×C₄	—	26	1	no	—
423	C₂²×C₄	#6129	1	1	yes	characteristic
424	C₂²×C₄	#6129	1	1	yes	characteristic
425	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
426	Q₁₆	—	26	4	no	—
427	SD₁₆	—	26	4	no	—
428	SD₁₆	—	26	4	no	—
429	D₈	—	26	4	no	—
430	M₁₆	—	2	1	no	—
431	M₁₆	—	2	1	no	—
432	M₁₆	—	26	4	no	—
433	M₁₆	—	26	4	no	—
434	M₁₆	—	26	2	no	—
435	M₁₆	—	26	2	no	—
436	M₁₆	—	52	4	no	—
437	M₁₆	D₄×D₁₃	1	2	yes	—
438	M₁₆	#6129	1	2	yes	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	13	2	no	—
442	C₂×C₈	—	13	1	no	—
443	C₂×C₈	—	13	1	no	—
444	C₂×C₈	—	13	2	no	—
445	C₂×C₈	—	13	2	no	—
446	C₂×C₈	—	13	2	no	—
447	C₂×C₈	—	13	1	no	—
448	C₂×C₈	—	13	1	no	—
449	C₂×C₈	—	26	4	no	—
450	C₂×C₈	—	26	4	no	—
451	C₂×C₈	—	26	2	no	—
452	C₂×C₈	—	26	1	no	—
453	C₂×C₈	—	26	1	no	—
454	C₂×C₈	—	26	2	no	—
455	C₂×C₈	—	26	2	no	—
456	C₂×C₈	—	52	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	13	1	no	—
461	C₄⋊C₄	—	13	1	no	—
462	C₄⋊C₄	—	26	1	no	—
463	C₄⋊C₄	—	26	1	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	26	1	no	—
467	C₂²⋊C₄	—	26	1	no	—
468	C₂²⋊C₄	—	26	1	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	26	1	no	—
472	C₄²	—	26	1	no	—
473	C₄²	—	26	1	no	—
474	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
475	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
476	C₄²	D₄×D₁₃	1	1	yes	characteristic
477	C₄²	D₄×D₁₃	1	1	yes	characteristic
478	C₁₃	#21517	1	1	yes	characteristic, complemented, Sylow
479	C₂³	—	2	2	no	—
480	C₂³	—	26	1	no	—
481	C₂³	C₂×#6129	1	1	yes	characteristic
482	Q₈	—	2	2	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	13	2	no	—
485	Q₈	—	26	1	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	13	2	no	—
493	D₄	—	26	2	no	—
494	D₄	—	26	2	no	—
495	D₄	—	26	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	26	1	no	—
505	C₂×C₄	—	26	2	no	—
506	C₂×C₄	—	26	2	no	—
507	C₂×C₄	—	26	1	no	—
508	C₂×C₄	—	26	1	no	—
509	C₂×C₄	—	52	2	no	—
510	C₂×C₄	—	52	2	no	—
511	C₂×C₄	#88135	1	1	yes	characteristic
512	C₂×C₄	#88135	1	1	yes	characteristic
513	C₂×C₄	#88135	1	1	yes	characteristic
514	C₂×C₄	#88135	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
518	C₂×C₄	C₂×#6129	1	1	yes	characteristic
519	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
520	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	13	2	no	—
524	C₈	—	13	2	no	—
525	C₈	—	26	2	no	—
526	C₈	—	26	2	no	—
527	C₈	—	26	1	no	—
528	C₈	—	26	1	no	—
529	C₈	—	52	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	26	2	no	—
536	C₂²	—	52	1	no	—
537	C₂²	—	52	1	no	—
538	C₂²	C₂×#88135	1	1	yes	characteristic
539	C₂²	#11719385	1	1	yes	characteristic
540	C₂²	#11719421	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	26	2	no	—
547	C₄	—	52	1	no	—
548	C₄	—	52	1	no	—
549	C₄	#11718485	1	2	yes	complemented
550	C₄	C₄×#6129	1	1	yes	characteristic
551	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
552	C₄	D₁₃×#121	1	1	yes	characteristic
553	C₄	#11719311	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	8	2	no	—
557	C₂	—	52	2	no	—
558	C₂	#13117352	1	1	yes	characteristic
559	C₂	C₂×#11718485	1	1	yes	characteristic
560	C₂	#13123735	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1980	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124285	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1980	D₁₃
hypocenter	C₁₃	#21517
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1980

Complements

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

N	H ≅ G/N	type
2. C₂×#11718485	C₂	semidirect
3. #13123548	C₂	semidirect
4. C₄×#88161	C₂	semidirect
5. #13115611	C₂	semidirect
6. #13115487	C₂	semidirect
7. #13115160	C₂	semidirect
8. #13114857	C₂	semidirect
9. C₄⋊C₄×#1055	C₂	semidirect
10. #13114674	C₂	semidirect
11. C₁₃×#1980	C₂	semidirect
27. #11718751	C₄	semidirect
28. #11718744	C₄	semidirect
29. #11718736	C₄	semidirect
30. #11718733	C₄	semidirect
31. #11718718	C₄	semidirect
32. #11718715	C₄	semidirect
84. #88161	D₄	semidirect
203. #1980	D₁₃	semidirect
315. C₄×C₁₃	#443	semidirect
478. C₁₃	#21517	semidirect
549. C₄	#11718485	semidirect

Maximal subgroups

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

subgroup	index
#13124285	2
C₂×#11718485	2
#13123548	2
C₄×#88161	2
#13115611	2
#13115487	2
#13115160	2
#13114857	2
C₄⋊C₄×#1055	2
#13114674	2
C₁₃×#1980	2
#21517	13