Subgroups — #16727095

Order 3328.

2706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128039	C₂	1	2	yes	maximal, complemented
2	#13123720	C₂	1	4	yes	maximal, complemented
3	#13123712	C₂	1	4	yes	maximal, complemented
4	#13123704	C₂	1	2	yes	maximal, complemented
5	#13123696	C₂	1	4	yes	maximal, complemented
6	#13123688	C₂	1	2	yes	maximal, complemented
7	#13123637	C₂	1	4	yes	maximal, complemented
8	#135×Dic₁₃	C₂	1	4	yes	maximal, complemented
9	C₂×#11718767	C₂	1	1	yes	maximal, characteristic, complemented
10	#13123355	C₂	1	2	yes	maximal, complemented
11	C₂×#11718762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₄	1	16	yes	complemented
15	C₂×C₁₃×#135	C₂²	1	2	yes	—
16	C₂×C₁₃×#135	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	2	yes	—
18	C₂×C₁₃×#135	C₂²	1	2	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	#11719532	—	2	4	no	—
24	#11719532	C₂²	1	8	yes	complemented
25	#41×Dic₁₃	—	2	4	no	—
26	#41×Dic₁₃	C₂²	1	8	yes	complemented
27	#11719517	C₂²	1	4	yes	—
28	#11719503	—	2	4	no	—
29	#11719503	C₂²	1	4	yes	—
30	C₂×#88180	—	2	4	no	—
31	C₂×#88180	C₂²	1	2	yes	—
32	C₂×#88180	C₂²	1	1	yes	characteristic
33	C₂²×#6099	C₂²	1	1	yes	characteristic
34	#11718894	C₂²	1	8	yes	complemented
35	#11718893	C₂²	1	8	yes	complemented
36	#11718886	C₂²	1	4	yes	—
37	#11718876	C₂²	1	4	yes	—
38	#11718845	C₂²	1	8	yes	complemented
39	Q₁₆×Dic₁₃	C₂²	1	8	yes	complemented
40	#11718825	C₂²	1	16	yes	complemented
41	SD₁₆×Dic₁₃	C₂²	1	16	yes	complemented
42	#11718813	C₂²	1	8	yes	complemented
43	D₈×Dic₁₃	C₂²	1	8	yes	complemented
44	#11718767	C₂²	1	2	yes	—
45	#11718767	C₂²	1	2	yes	—
46	#11718767	C₂²	1	2	yes	complemented
47	#11718767	C₂²	1	2	yes	complemented
48	C₂×#88058	C₂²	1	2	yes	complemented
49	C₂×#88057	C₂²	1	2	yes	complemented
50	#11718762	C₂²	1	2	yes	—
51	#11718762	C₂²	1	2	yes	—
52	#11718762	C₂²	1	2	yes	complemented
53	#11718762	C₂²	1	2	yes	complemented
54	C₂×#88055	C₂²	1	2	yes	complemented
55	C₂×C₈×Dic₁₃	C₂²	1	2	yes	complemented
56	C₂×C₁₃×#41	—	2	2	no	—
57	C₂×C₁₃×#41	—	2	2	no	—
58	C₂×C₁₃×#41	—	2	8	no	—
59	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
60	C₂×C₁₃×#41	C₂³	1	4	yes	—
61	C₂×C₁₃×#41	C₂³	1	4	yes	—
62	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	—	2	2	no	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#135	C₂×C₄	1	16	yes	complemented
68	C₁₃×#135	C₂×C₄	1	16	yes	complemented
69	C₁₃×#135	C₂×C₄	1	16	yes	complemented
70	C₁₃×#135	C₂×C₄	1	16	yes	complemented
71	C₂×C₁₃×Q₁₆	C₂×C₄	1	8	yes	complemented
72	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×SD₁₆	C₂×C₄	1	16	yes	complemented
75	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
77	C₂×C₁₃×D₈	C₂×C₄	1	8	yes	complemented
78	C₂×C₁₃×D₈	C₂³	1	2	yes	—
79	C₂×C₁₃×D₈	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
88	C₂×C₂²⋊Dic₁₃	—	2	8	no	—
89	C₂×C₂²⋊Dic₁₃	D₄	1	2	yes	—
90	Q₈×Dic₁₃	—	2	8	no	—
91	Q₈×Dic₁₃	C₂³	1	16	yes	—
92	D₄×Dic₁₃	—	2	16	no	—
93	D₄×Dic₁₃	—	2	16	no	—
94	D₄×Dic₁₃	—	2	8	no	—
95	D₄×Dic₁₃	C₂³	1	16	yes	—
96	#88180	—	2	2	no	—
97	#88180	—	2	2	no	—
98	#88180	—	2	8	no	—
99	#88180	—	2	8	no	—
100	#88180	—	2	8	no	—
101	#88180	D₄	1	2	yes	—
102	#88180	D₄	1	2	yes	—
103	#88180	C₂³	1	4	yes	—
104	#88180	C₂³	1	4	yes	—
105	#88180	C₂³	1	2	yes	—
106	#88180	C₂³	1	2	yes	—
107	C₂×C₄⋊Dic₁₃	—	2	8	no	—
108	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
109	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
110	C₂×C₄×Dic₁₃	—	2	2	no	—
111	C₂×C₄×Dic₁₃	—	2	8	no	—
112	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
113	C₂×#6099	—	2	4	no	—
114	C₂×#6099	C₂³	1	2	yes	—
115	C₂×#6099	C₂³	1	2	yes	—
116	C₂²×#1055	C₂³	1	2	yes	—
117	#88075	C₂³	1	16	yes	—
118	#88072	C₂³	1	16	yes	—
119	#88058	C₂³	1	4	yes	—
120	#88058	C₂³	1	4	yes	—
121	#88057	C₂³	1	4	yes	—
122	#88057	C₂³	1	4	yes	—
123	#88055	C₂³	1	4	yes	—
124	#88055	C₂³	1	4	yes	—
125	C₈×Dic₁₃	C₂³	1	4	yes	—
126	C₈×Dic₁₃	C₂³	1	4	yes	—
127	#60167	—	13	1	no	maximal, Sylow
128	C₂⁴×C₁₃	—	2	2	no	—
129	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₁₃×#41	—	2	16	no	—
131	C₁₃×#41	—	2	16	no	—
132	C₁₃×#41	—	2	8	no	—
133	C₁₃×#41	—	2	8	no	—
134	C₁₃×#41	C₂²×C₄	1	16	yes	—
135	C₁₃×#41	C₂²×C₄	1	16	yes	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
140	C₂×D₄×C₁₃	—	2	16	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	16	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	#41	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂²×Dic₁₃	—	2	4	no	—
160	C₂²×Dic₁₃	—	2	16	no	—
161	C₂²×Dic₁₃	C₂×D₄	1	4	yes	—
162	C₁₃×Q₁₆	C₂²×C₄	1	8	yes	—
163	C₁₃×Q₁₆	C₂²×C₄	1	8	yes	—
164	C₁₃×SD₁₆	C₂²×C₄	1	16	yes	—
165	C₁₃×SD₁₆	C₂²×C₄	1	16	yes	—
166	C₁₃×D₈	C₂²×C₄	1	8	yes	—
167	C₁₃×D₈	C₂²×C₄	1	8	yes	—
168	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
169	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
170	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
171	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
172	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
173	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊Dic₁₃	—	2	4	no	—
179	C₂²⋊Dic₁₃	—	2	4	no	—
180	C₂²⋊Dic₁₃	—	2	16	no	—
181	C₂²⋊Dic₁₃	C₂×D₄	1	4	yes	—
182	C₂²⋊Dic₁₃	C₂×D₄	1	4	yes	—
183	C₄⋊Dic₁₃	—	2	4	no	—
184	C₄⋊Dic₁₃	—	2	16	no	—
185	C₄⋊Dic₁₃	C₂×D₄	1	4	yes	—
186	C₄⋊Dic₁₃	C₂×D₄	1	4	yes	—
187	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
188	C₄×Dic₁₃	—	2	4	no	—
189	C₄×Dic₁₃	—	2	4	no	—
190	C₄×Dic₁₃	—	2	16	no	—
191	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
192	C₄×Dic₁₃	C₂⁴	1	4	yes	—
193	#6099	—	2	4	no	—
194	#6099	—	2	4	no	—
195	C₂×#1055	—	2	4	no	—
196	C₂×#1055	C₂⁴	1	4	yes	—
197	C₂²×#135	D₁₃	1	1	yes	characteristic
198	#3428	—	13	2	no	—
199	#2952	—	13	4	no	—
200	#2951	—	13	4	no	—
201	#2950	—	13	2	no	—
202	#2949	—	13	4	no	—
203	#2948	—	13	2	no	—
204	#2943	—	13	4	no	—
205	C₄×#135	—	13	4	no	—
206	C₂×#427	—	13	1	no	—
207	#2896	—	13	2	no	—
208	C₂×#405	—	13	1	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	8	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	8	4	no	—
213	C₂³×C₁₃	C₄×D₄	1	4	yes	—
214	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	8	no	—
218	Q₈×C₁₃	—	2	4	no	—
219	Q₈×C₁₃	C₂³×C₄	1	8	yes	—
220	D₄×C₁₃	—	2	16	no	—
221	D₄×C₁₃	—	2	16	no	—
222	D₄×C₁₃	—	2	8	no	—
223	D₄×C₁₃	—	2	4	no	—
224	D₄×C₁₃	C₂³×C₄	1	8	yes	—
225	C₂×C₄×C₁₃	—	2	8	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	16	no	—
228	C₂×C₄×C₁₃	—	2	16	no	—
229	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
230	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
231	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
232	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
239	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
240	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
242	C₂×Dic₁₃	—	2	8	no	—
243	C₂×Dic₁₃	—	4	4	no	—
244	C₂×Dic₁₃	—	8	16	no	—
245	C₂×Dic₁₃	—	8	4	no	—
246	C₂×Dic₁₃	C₂²×D₄	1	8	yes	—
247	C₈×C₁₃	C₂³×C₄	1	2	yes	—
248	C₈×C₁₃	C₂³×C₄	1	2	yes	—
249	C₈×C₁₃	C₂³×C₄	1	2	yes	—
250	C₈×C₁₃	C₂³×C₄	1	2	yes	—
251	#1055	—	2	4	no	—
252	C₂²×#41	C₂×D₁₃	1	2	yes	—
253	C₂×#135	Dic₁₃	1	16	yes	complemented
254	C₂×#135	C₂×D₁₃	1	2	yes	—
255	C₂×#135	C₂×D₁₃	1	2	yes	—
256	C₂×#135	C₂×D₁₃	1	2	yes	—
257	C₂×#135	C₂×D₁₃	1	2	yes	—
258	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
259	C₂²×SD₁₆	C₂×D₁₃	1	2	yes	—
260	C₂²×D₈	C₂×D₁₃	1	1	yes	characteristic
261	C₂²×M₁₆	—	13	1	no	—
262	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
263	#520	—	13	8	no	—
264	#520	—	26	4	no	—
265	#519	—	13	4	no	—
266	#518	—	13	4	no	—
267	#518	—	26	4	no	—
268	C₄×#41	—	13	8	no	—
269	C₄×#41	—	26	4	no	—
270	C₂×#117	—	13	1	no	—
271	C₂×#117	—	13	2	no	—
272	C₂×#117	—	26	4	no	—
273	#442	—	13	8	no	—
274	#441	—	13	8	no	—
275	#440	—	13	16	no	—
276	C₄×Q₁₆	—	13	8	no	—
277	C₄×SD₁₆	—	13	16	no	—
278	C₄×D₈	—	13	8	no	—
279	#427	—	13	2	no	—
280	#427	—	13	2	no	—
281	#427	—	13	2	no	—
282	#427	—	13	2	no	—
283	C₂×#107	—	13	2	no	—
284	C₂×#106	—	13	2	no	—
285	#419	—	13	4	no	—
286	#418	—	13	4	no	—
287	#417	—	13	8	no	—
288	#416	—	13	8	no	—
289	#405	—	13	2	no	—
290	#405	—	13	2	no	—
291	#405	—	13	2	no	—
292	#405	—	13	2	no	—
293	C₂×#97	—	13	2	no	—
294	C₂×C₄×C₈	—	13	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	8	no	—
299	C₂²×C₁₃	—	4	4	no	—
300	C₂²×C₁₃	—	4	8	no	—
301	C₂²×C₁₃	—	8	8	no	—
302	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
303	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
304	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
305	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
306	C₄×C₁₃	—	2	8	no	—
307	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
308	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
309	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
310	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
311	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
312	Dic₁₃	—	2	8	no	—
313	Dic₁₃	—	4	8	no	—
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	8	no	—
317	C₂×#41	C₂×Dic₁₃	1	16	yes	complemented
318	C₂×#41	C₂²×D₁₃	1	4	yes	—
319	C₂×#41	C₂²×D₁₃	1	4	yes	—
320	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
325	#135	C₂×Dic₁₃	1	16	yes	complemented
326	#135	C₂×Dic₁₃	1	16	yes	complemented
327	#135	C₂×Dic₁₃	1	16	yes	complemented
328	#135	C₂×Dic₁₃	1	16	yes	complemented
329	C₂×Q₁₆	C₂×Dic₁₃	1	8	yes	complemented
330	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
331	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
332	C₂×SD₁₆	C₂×Dic₁₃	1	16	yes	complemented
333	C₂×SD₁₆	C₂²×D₁₃	1	4	yes	—
334	C₂×SD₁₆	C₂²×D₁₃	1	4	yes	—
335	C₂×D₈	C₂×Dic₁₃	1	8	yes	complemented
336	C₂×D₈	C₂²×D₁₃	1	2	yes	—
337	C₂×D₈	C₂²×D₁₃	1	2	yes	—
338	C₂×M₁₆	—	13	2	no	—
339	C₂×M₁₆	—	13	2	no	—
340	C₂×M₁₆	—	26	4	no	—
341	C₂²×C₈	—	13	2	no	—
342	C₂²×C₈	C₂×Dic₁₃	1	8	yes	complemented
343	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
344	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
347	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
348	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
349	C₄×Q₈	—	13	16	no	—
350	C₄×Q₈	—	26	8	no	—
351	C₄×D₄	—	13	16	no	—
352	C₄×D₄	—	26	16	no	—
353	C₄×D₄	—	26	8	no	—
354	C₄×D₄	—	26	16	no	—
355	#117	—	13	2	no	—
356	#117	—	13	2	no	—
357	#117	—	13	2	no	—
358	#117	—	13	2	no	—
359	#117	—	13	4	no	—
360	#117	—	13	4	no	—
361	#117	—	26	8	no	—
362	#117	—	26	8	no	—
363	#117	—	26	8	no	—
364	#117	—	26	2	no	—
365	#117	—	26	2	no	—
366	C₂×C₄⋊C₄	—	13	2	no	—
367	C₂×C₄⋊C₄	—	13	4	no	—
368	C₂×C₄⋊C₄	—	26	8	no	—
369	C₂×C₂²⋊C₄	—	13	2	no	—
370	C₂×C₂²⋊C₄	—	26	8	no	—
371	C₂×C₂²⋊C₄	—	26	2	no	—
372	C₂×C₄²	—	13	2	no	—
373	C₂×C₄²	—	26	8	no	—
374	C₂×C₄²	—	26	2	no	—
375	#107	—	13	4	no	—
376	#107	—	13	4	no	—
377	#106	—	13	4	no	—
378	#106	—	13	4	no	—
379	#103	—	13	16	no	—
380	#102	—	13	16	no	—
381	#97	—	13	4	no	—
382	#97	—	13	4	no	—
383	C₄×C₈	—	13	4	no	—
384	C₄×C₈	—	13	4	no	—
385	C₂×C₁₃	—	2	2	no	—
386	C₂×C₁₃	—	2	2	no	—
387	C₂×C₁₃	—	2	2	no	—
388	C₂×C₁₃	—	4	8	no	—
389	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
390	C₂×C₁₃	#3584	1	2	yes	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	D₄×D₁₃	1	1	yes	characteristic
393	#41	—	2	16	no	—
394	#41	—	2	16	no	—
395	#41	—	2	8	no	—
396	#41	—	2	8	no	—
397	#41	C₂²×Dic₁₃	1	16	yes	—
398	#41	C₂²×Dic₁₃	1	16	yes	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	C₂²×Dic₁₃	1	8	yes	—
402	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
403	C₂×D₄	—	2	16	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	C₂²×Dic₁₃	1	8	yes	—
409	C₂×D₄	C₂³×D₁₃	1	4	yes	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	16	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	13	4	no	—
415	C₂²×C₄	—	26	16	no	—
416	C₂²×C₄	—	26	4	no	—
417	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
418	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
419	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
420	C₂²×C₄	#6129	1	4	yes	—
421	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
422	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
425	Q₁₆	C₂²×Dic₁₃	1	8	yes	—
426	Q₁₆	C₂²×Dic₁₃	1	8	yes	—
427	SD₁₆	C₂²×Dic₁₃	1	16	yes	—
428	SD₁₆	C₂²×Dic₁₃	1	16	yes	—
429	D₈	C₂²×Dic₁₃	1	8	yes	—
430	D₈	C₂²×Dic₁₃	1	8	yes	—
431	M₁₆	—	26	4	no	—
432	M₁₆	—	26	4	no	—
433	C₂×C₈	—	13	4	no	—
434	C₂×C₈	—	26	4	no	—
435	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
436	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
437	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
438	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
439	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
440	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
441	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
442	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
443	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
444	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
445	C₄⋊C₄	—	13	4	no	—
446	C₄⋊C₄	—	13	4	no	—
447	C₄⋊C₄	—	13	8	no	—
448	C₄⋊C₄	—	26	16	no	—
449	C₄⋊C₄	—	26	4	no	—
450	C₂²⋊C₄	—	13	4	no	—
451	C₂²⋊C₄	—	13	4	no	—
452	C₂²⋊C₄	—	26	16	no	—
453	C₂²⋊C₄	—	26	4	no	—
454	C₂²⋊C₄	—	26	4	no	—
455	C₄²	—	13	4	no	—
456	C₄²	—	13	4	no	—
457	C₄²	—	26	16	no	—
458	C₄²	—	26	4	no	—
459	C₄²	—	26	4	no	—
460	C₁₃	#60167	1	1	yes	characteristic, complemented, Sylow
461	C₂³	—	2	4	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	8	4	no	—
465	C₂³	D₄×Dic₁₃	1	4	yes	—
466	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
467	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
468	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
469	Q₈	—	2	8	no	—
470	Q₈	—	2	4	no	—
471	Q₈	C₂³×Dic₁₃	1	8	yes	—
472	D₄	—	2	16	no	—
473	D₄	—	2	16	no	—
474	D₄	—	2	8	no	—
475	D₄	—	2	4	no	—
476	D₄	C₂³×Dic₁₃	1	8	yes	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	16	no	—
480	C₂×C₄	—	2	16	no	—
481	C₂×C₄	—	13	8	no	—
482	C₂×C₄	—	26	8	no	—
483	C₂×C₄	—	52	4	no	—
484	C₂×C₄	—	104	16	no	—
485	C₂×C₄	—	104	4	no	—
486	C₂×C₄	D₄×Dic₁₃	1	4	yes	—
487	C₂×C₄	D₄×Dic₁₃	1	4	yes	—
488	C₂×C₄	D₄×Dic₁₃	1	4	yes	—
489	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂×#6129	1	2	yes	—
493	C₂×C₄	C₂×#6129	1	2	yes	—
494	C₂×C₄	C₂×#6129	1	2	yes	—
495	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
496	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
497	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
498	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
499	C₈	—	26	4	no	—
500	C₈	C₂³×Dic₁₃	1	2	yes	—
501	C₈	C₂³×Dic₁₃	1	2	yes	—
502	C₈	C₂³×Dic₁₃	1	2	yes	—
503	C₈	C₂³×Dic₁₃	1	2	yes	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₂×D₄×Dic₁₃	1	2	yes	—
512	C₂²	C₂×D₄×Dic₁₃	1	2	yes	—
513	C₂²	C₂×D₄×Dic₁₃	1	2	yes	—
514	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	26	8	no	—
517	C₄	—	52	8	no	—
518	C₄	C₂×D₄×Dic₁₃	1	2	yes	—
519	C₄	C₂×D₄×Dic₁₃	1	2	yes	—
520	C₄	C₂×D₄×Dic₁₃	1	2	yes	—
521	C₄	C₂²×#6129	1	1	yes	characteristic
522	C₄	C₂⁴×Dic₁₃	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	4	8	no	—
527	C₂	C₂²×D₄×Dic₁₃	1	1	yes	characteristic
528	C₂	#13129605	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting, prime radical	C₂²×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂³×D₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂²×#135	D₁₃
hypocenter	C₁₃	#60167
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. #13128039	C₂	semidirect
2. #13123720	C₂	semidirect
3. #13123712	C₂	semidirect
4. #13123704	C₂	semidirect
5. #13123696	C₂	semidirect
6. #13123688	C₂	semidirect
7. #13123637	C₂	semidirect
8. #135×Dic₁₃	C₂	semidirect
9. C₂×#11718767	C₂	semidirect
10. #13123355	C₂	semidirect
11. C₂×#11718762	C₂	semidirect
14. C₂×C₁₃×#135	C₄	semidirect
24. #11719532	C₂²	semidirect
26. #41×Dic₁₃	C₂²	semidirect
34. #11718894	C₂²	semidirect
35. #11718893	C₂²	semidirect
38. #11718845	C₂²	semidirect
39. Q₁₆×Dic₁₃	C₂²	semidirect
40. #11718825	C₂²	semidirect
41. SD₁₆×Dic₁₃	C₂²	semidirect
42. #11718813	C₂²	semidirect
43. D₈×Dic₁₃	C₂²	semidirect
46. #11718767	C₂²	semidirect
47. #11718767	C₂²	semidirect
48. C₂×#88058	C₂²	semidirect
49. C₂×#88057	C₂²	semidirect
52. #11718762	C₂²	semidirect
53. #11718762	C₂²	semidirect
54. C₂×#88055	C₂²	semidirect
55. C₂×C₈×Dic₁₃	C₂²	semidirect
59. C₂×C₁₃×#41	C₂×C₄	semidirect
67. C₁₃×#135	C₂×C₄	semidirect
68. C₁₃×#135	C₂×C₄	semidirect
69. C₁₃×#135	C₂×C₄	semidirect
70. C₁₃×#135	C₂×C₄	semidirect
71. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
74. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
77. C₂×C₁₃×D₈	C₂×C₄	semidirect
80. C₂²×C₈×C₁₃	C₂×C₄	semidirect
253. C₂×#135	Dic₁₃	semidirect
317. C₂×#41	C₂×Dic₁₃	semidirect
325. #135	C₂×Dic₁₃	semidirect
326. #135	C₂×Dic₁₃	semidirect
327. #135	C₂×Dic₁₃	semidirect
328. #135	C₂×Dic₁₃	semidirect
329. C₂×Q₁₆	C₂×Dic₁₃	semidirect
332. C₂×SD₁₆	C₂×Dic₁₃	semidirect
335. C₂×D₈	C₂×Dic₁₃	semidirect
342. C₂²×C₈	C₂×Dic₁₃	semidirect
460. C₁₃	#60167	semidirect

Maximal subgroups

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

subgroup	index
#13128039	2
#13123720	2
#13123712	2
#13123704	2
#13123696	2
#13123688	2
#13123637	2
#135×Dic₁₃	2
C₂×#11718767	2
#13123355	2
C₂×#11718762	2
C₂²×C₁₃×#135	2
#60167	13