Subgroups — #16727096

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	C₂²×#88158	C₂	1	1	yes	maximal, characteristic
2	#13128037	C₂	1	2	yes	maximal, complemented
3	#13123721	C₂	1	4	yes	maximal, complemented
4	#13123713	C₂	1	4	yes	maximal, complemented
5	#13123705	C₂	1	2	yes	maximal, complemented
6	#13123697	C₂	1	4	yes	maximal, complemented
7	#13123689	C₂	1	2	yes	maximal, complemented
8	#13123638	C₂	1	4	yes	maximal, complemented
9	C₄×#88158	C₂	1	4	yes	maximal, complemented
10	C₂×#11718767	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123356	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#6127	C₂²	1	2	yes	—
14	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂×#88180	C₂²	1	2	yes	—
18	C₂²×Dic₅₂	C₂²	1	1	yes	characteristic
19	C₂×#88158	C₄	1	16	yes	complemented
20	C₂×#88158	C₂²	1	2	yes	—
21	C₂×#88158	C₂²	1	2	yes	—
22	C₂×#88158	C₂²	1	2	yes	—
23	C₂×#88158	C₂²	1	2	yes	—
24	C₂²×D₁₀₄	C₂²	1	1	yes	characteristic
25	C₂²×#6095	C₂²	1	2	yes	—
26	#11719228	C₂²	1	8	yes	complemented
27	#11719227	—	2	4	no	—
28	#11719226	C₂²	1	4	yes	—
29	D₁₃×#117	—	2	4	no	—
30	#11719221	C₂²	1	4	yes	—
31	#11719209	—	2	4	no	—
32	#11719191	—	2	4	no	—
33	C₄×#6127	C₂²	1	8	yes	complemented
34	C₁₃×#405	C₂²	1	2	yes	—
35	C₁₃×#405	C₂²	1	2	yes	—
36	C₁₃×#405	C₂²	1	2	yes	complemented
37	C₁₃×#405	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
39	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
40	#11718794	C₂²	1	8	yes	complemented
41	#11718792	C₂²	1	4	yes	—
42	#11718781	C₂²	1	4	yes	—
43	#11718774	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	#11718377	C₂²	1	8	yes	complemented
51	#11718372	C₂²	1	8	yes	complemented
52	#11718371	C₂²	1	16	yes	complemented
53	C₄×Dic₅₂	C₂²	1	8	yes	complemented
54	C₄×D₁₀₄	C₂²	1	8	yes	complemented
55	C₄×#6095	C₂²	1	16	yes	complemented
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₂²⋊D₁₃	—	2	2	no	—
58	C₂×#6127	—	2	2	no	—
59	C₂×#6127	—	2	2	no	—
60	C₂×#6127	—	2	8	no	—
61	C₂×#6127	C₂×C₄	1	16	yes	complemented
62	C₂×#6127	C₂³	1	4	yes	—
63	C₂×#6127	C₂³	1	4	yes	—
64	C₂²×D₅₂	C₂³	1	2	yes	—
65	C₂²×C₄×D₁₃	—	2	2	no	—
66	C₂²×Dic₂₆	C₂³	1	2	yes	—
67	C₂×C₁₃×M₁₆	—	2	4	no	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
71	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#117	D₄	1	2	yes	—
79	C₁₃×#117	D₄	1	2	yes	—
80	C₁₃×#117	C₂³	1	2	yes	—
81	C₁₃×#117	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
83	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
85	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
86	C₄×C₂²⋊D₁₃	—	2	16	no	—
87	#88180	—	2	2	no	—
88	#88180	—	2	2	no	—
89	#88180	C₂³	1	4	yes	—
90	#88180	C₂³	1	4	yes	—
91	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
92	C₂×C₄×Dic₁₃	—	2	2	no	—
93	C₂×Dic₅₂	C₂×C₄	1	8	yes	complemented
94	C₂×Dic₅₂	C₂³	1	2	yes	—
95	C₂×Dic₅₂	C₂³	1	2	yes	—
96	#88158	C₂×C₄	1	16	yes	complemented
97	#88158	C₂×C₄	1	16	yes	complemented
98	#88158	C₂×C₄	1	16	yes	complemented
99	#88158	C₂×C₄	1	16	yes	complemented
100	C₂×D₁₀₄	C₂×C₄	1	8	yes	complemented
101	C₂×D₁₀₄	C₂³	1	2	yes	—
102	C₂×D₁₀₄	C₂³	1	2	yes	—
103	C₂×#6095	C₂×C₄	1	16	yes	complemented
104	C₂×#6095	C₂³	1	4	yes	—
105	C₂×#6095	C₂³	1	4	yes	—
106	#88147	—	2	8	no	—
107	#88146	—	2	8	no	—
108	C₄⋊C₄×D₁₃	—	2	8	no	—
109	#88141	—	2	8	no	—
110	#88135	—	2	16	no	—
111	C₂²⋊C₄×D₁₃	—	2	8	no	—
112	#88131	—	2	8	no	—
113	C₄×D₅₂	C₂³	1	16	yes	—
114	#88126	—	2	8	no	—
115	C₄²×D₁₃	—	2	8	no	—
116	C₄×Dic₂₆	C₂³	1	16	yes	—
117	C₁₃×#97	C₂³	1	4	yes	—
118	C₁₃×#97	C₂³	1	4	yes	—
119	C₄×C₈×C₁₃	C₂³	1	4	yes	—
120	C₄×C₈×C₁₃	C₂³	1	4	yes	—
121	#88061	C₂³	1	16	yes	—
122	#88058	C₂³	1	4	yes	—
123	#88058	C₂³	1	4	yes	—
124	#88057	C₂³	1	4	yes	—
125	#88057	C₂³	1	4	yes	—
126	#88056	C₂³	1	16	yes	—
127	#60167	—	13	1	no	maximal, Sylow
128	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂³×D₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	#41	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	—	2	16	no	—
140	C₂×C₂²⋊D₁₃	—	2	4	no	—
141	C₂×C₂²⋊D₁₃	—	2	4	no	—
142	C₂²×Dic₁₃	—	2	2	no	—
143	C₂²×Dic₁₃	—	2	4	no	—
144	#6127	—	2	16	no	—
145	#6127	—	2	16	no	—
146	#6127	—	2	8	no	—
147	#6127	—	2	8	no	—
148	#6127	C₂²×C₄	1	16	yes	—
149	#6127	C₂²×C₄	1	16	yes	—
150	C₂×D₅₂	—	2	2	no	—
151	C₂×D₅₂	—	2	4	no	—
152	C₂×D₅₂	C₂²×C₄	1	8	yes	—
153	C₂×D₅₂	C₂⁴	1	4	yes	—
154	C₂×C₄×D₁₃	—	2	16	no	—
155	C₂×C₄×D₁₃	—	2	4	no	—
156	C₂×C₄×D₁₃	—	2	4	no	—
157	C₂×C₄×D₁₃	—	2	16	no	—
158	C₂×Dic₂₆	—	2	2	no	—
159	C₂×Dic₂₆	—	2	4	no	—
160	C₂×Dic₂₆	C₂²×C₄	1	8	yes	—
161	C₂×Dic₂₆	C₂⁴	1	4	yes	—
162	C₁₃×M₁₆	—	2	4	no	—
163	C₁₃×M₁₆	—	2	4	no	—
164	C₂×C₈×C₁₃	—	2	4	no	—
165	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
166	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
167	C₂×C₈×C₁₃	C₂²×C₄	1	4	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	C₂⁴	1	4	yes	—
172	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
177	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
178	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
179	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
180	C₄²×C₁₃	C₂×D₄	1	4	yes	—
181	C₄²×C₁₃	C₂⁴	1	4	yes	—
182	C₂²⋊Dic₁₃	—	2	4	no	—
183	C₂²⋊Dic₁₃	—	2	4	no	—
184	#6103	—	2	16	no	—
185	C₄⋊Dic₁₃	—	2	4	no	—
186	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
187	#6101	—	2	16	no	—
188	C₄×Dic₁₃	—	2	16	no	—
189	C₄×Dic₁₃	—	2	4	no	—
190	C₄×Dic₁₃	—	2	4	no	—
191	Dic₅₂	C₂²×C₄	1	8	yes	—
192	Dic₅₂	C₂²×C₄	1	8	yes	—
193	D₁₀₄	C₂²×C₄	1	8	yes	—
194	D₁₀₄	C₂²×C₄	1	8	yes	—
195	#6095	C₂²×C₄	1	16	yes	—
196	#6095	C₂²×C₄	1	16	yes	—
197	C₂²×#135	—	13	1	no	—
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	D₁₃	1	1	yes	characteristic, complemented
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	C₄×D₄	1	4	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂²×D₁₃	—	2	4	no	—
215	C₂²×D₁₃	—	2	8	no	—
216	C₂²×D₁₃	—	8	4	no	—
217	C₂×C₄×C₁₃	—	4	4	no	—
218	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
219	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
220	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
221	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
223	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	8	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	C₂×#41	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
231	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
232	C₂²⋊D₁₃	—	2	16	no	—
233	C₂²⋊D₁₃	—	2	16	no	—
234	C₂×Dic₁₃	—	2	8	no	—
235	C₂×Dic₁₃	—	2	4	no	—
236	C₂×Dic₁₃	—	2	8	no	—
237	C₂×Dic₁₃	—	8	4	no	—
238	D₅₂	—	2	8	no	—
239	D₅₂	—	2	4	no	—
240	D₅₂	C₂³×C₄	1	8	yes	—
241	C₄×D₁₃	—	2	16	no	—
242	C₄×D₁₃	—	2	16	no	—
243	C₄×D₁₃	—	8	16	no	—
244	Dic₂₆	—	2	8	no	—
245	Dic₂₆	—	2	4	no	—
246	Dic₂₆	C₂³×C₄	1	8	yes	—
247	C₈×C₁₃	—	2	4	no	—
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	C₈×C₁₃	C₂³×C₄	1	2	yes	—
252	C₂²×#41	—	13	2	no	—
253	C₂×#135	—	13	16	no	—
254	C₂×#135	—	13	2	no	—
255	C₂×#135	—	13	2	no	—
256	C₂×#135	—	13	2	no	—
257	C₂×#135	—	13	2	no	—
258	C₂²×Q₁₆	—	13	1	no	—
259	C₂²×SD₁₆	—	13	2	no	—
260	C₂²×D₈	—	13	1	no	—
261	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
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	2	no	—
271	C₂×#117	—	26	4	no	—
272	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
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	C₂×D₁₃	1	2	yes	—
290	#405	C₂×D₁₃	1	2	yes	—
291	#405	C₂×D₁₃	1	2	yes	complemented
292	#405	C₂×D₁₃	1	2	yes	complemented
293	C₂×#97	C₂×D₁₃	1	2	yes	complemented
294	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	complemented
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	4	4	no	—
299	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
300	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
301	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
302	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
303	C₂×D₁₃	—	2	8	no	—
304	C₂×D₁₃	—	4	8	no	—
305	C₂×D₁₃	—	8	8	no	—
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	—	13	16	no	—
315	C₂×#41	—	13	4	no	—
316	C₂×#41	—	13	4	no	—
317	C₂×#41	—	26	2	no	—
318	C₂×#41	—	26	2	no	—
319	C₂×#41	—	26	8	no	—
320	C₂²×Q₈	—	13	2	no	—
321	C₂²×D₄	—	13	2	no	—
322	C₂²×D₄	—	26	2	no	—
323	C₂³×C₄	—	26	2	no	—
324	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
325	#135	—	13	16	no	—
326	#135	—	13	16	no	—
327	#135	—	13	16	no	—
328	#135	—	13	16	no	—
329	C₂×Q₁₆	—	13	8	no	—
330	C₂×Q₁₆	—	13	2	no	—
331	C₂×Q₁₆	—	13	2	no	—
332	C₂×SD₁₆	—	13	16	no	—
333	C₂×SD₁₆	—	13	4	no	—
334	C₂×SD₁₆	—	13	4	no	—
335	C₂×D₈	—	13	8	no	—
336	C₂×D₈	—	13	2	no	—
337	C₂×D₈	—	13	2	no	—
338	C₂×M₁₆	—	2	4	no	—
339	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
340	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
341	C₂²×C₈	C₄×D₁₃	1	8	yes	complemented
342	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
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	4	no	—
356	#117	—	13	4	no	—
357	#117	—	26	2	no	—
358	#117	—	26	2	no	—
359	#117	—	26	8	no	—
360	#117	—	26	8	no	—
361	#117	—	26	8	no	—
362	#117	D₅₂	1	2	yes	—
363	#117	D₅₂	1	2	yes	—
364	#117	C₂²×D₁₃	1	2	yes	—
365	#117	C₂²×D₁₃	1	2	yes	—
366	C₂×C₄⋊C₄	—	13	4	no	—
367	C₂×C₄⋊C₄	—	26	8	no	—
368	C₂×C₄⋊C₄	D₅₂	1	2	yes	—
369	C₂×C₂²⋊C₄	—	26	2	no	—
370	C₂×C₂²⋊C₄	—	26	8	no	—
371	C₂×C₂²⋊C₄	D₅₂	1	2	yes	—
372	C₂×C₄²	—	26	2	no	—
373	C₂×C₄²	—	26	8	no	—
374	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
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	C₂²×D₁₃	1	4	yes	—
382	#97	C₂²×D₁₃	1	4	yes	—
383	C₄×C₈	C₂²×D₁₃	1	4	yes	—
384	C₄×C₈	C₂²×D₁₃	1	4	yes	—
385	C₂×C₁₃	—	2	2	no	—
386	C₂×C₁₃	—	2	2	no	—
387	C₂×C₁₃	—	2	2	no	—
388	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
389	C₂×C₁₃	#3584	1	2	yes	—
390	D₁₃	—	4	8	no	—
391	C₂⁴	—	26	2	no	—
392	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
393	#41	—	13	16	no	—
394	#41	—	13	16	no	—
395	#41	—	26	16	no	—
396	#41	—	26	16	no	—
397	#41	—	26	8	no	—
398	#41	—	26	8	no	—
399	C₂×Q₈	—	13	8	no	—
400	C₂×Q₈	—	13	4	no	—
401	C₂×Q₈	—	26	2	no	—
402	C₂×Q₈	—	26	4	no	—
403	C₂×D₄	—	13	8	no	—
404	C₂×D₄	—	13	4	no	—
405	C₂×D₄	—	26	16	no	—
406	C₂×D₄	—	26	4	no	—
407	C₂×D₄	—	26	4	no	—
408	C₂×D₄	—	26	2	no	—
409	C₂×D₄	—	26	4	no	—
410	C₂²×C₄	—	26	2	no	—
411	C₂²×C₄	—	26	16	no	—
412	C₂²×C₄	—	26	4	no	—
413	C₂²×C₄	—	26	4	no	—
414	C₂²×C₄	—	26	4	no	—
415	C₂²×C₄	—	26	16	no	—
416	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
417	C₂²×C₄	C₂×D₅₂	1	4	yes	—
418	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
421	C₂²×C₄	#6127	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	—	13	8	no	—
426	Q₁₆	—	13	8	no	—
427	SD₁₆	—	13	16	no	—
428	SD₁₆	—	13	16	no	—
429	D₈	—	13	8	no	—
430	D₈	—	13	8	no	—
431	M₁₆	—	2	4	no	—
432	M₁₆	—	2	4	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
435	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
436	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
437	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
438	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
439	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
440	C₂×C₈	C₂³×D₁₃	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	8	no	—
446	C₄⋊C₄	—	26	4	no	—
447	C₄⋊C₄	—	26	16	no	—
448	C₄⋊C₄	C₂×D₅₂	1	4	yes	—
449	C₄⋊C₄	C₂×D₅₂	1	4	yes	—
450	C₂²⋊C₄	—	26	4	no	—
451	C₂²⋊C₄	—	26	4	no	—
452	C₂²⋊C₄	—	26	16	no	—
453	C₂²⋊C₄	C₂×D₅₂	1	4	yes	—
454	C₂²⋊C₄	C₂×D₅₂	1	4	yes	—
455	C₄²	—	26	4	no	—
456	C₄²	—	26	16	no	—
457	C₄²	—	26	4	no	—
458	C₄²	C₂×D₅₂	1	4	yes	—
459	C₄²	C₂³×D₁₃	1	4	yes	—
460	C₁₃	#60167	1	1	yes	characteristic, complemented, Sylow
461	C₂³	—	4	2	no	—
462	C₂³	—	26	4	no	—
463	C₂³	—	26	8	no	—
464	C₂³	—	104	4	no	—
465	C₂³	C₄×D₅₂	1	4	yes	—
466	C₂³	C₂²×D₅₂	1	1	yes	characteristic
467	C₂³	C₂²×D₅₂	1	1	yes	characteristic
468	C₂³	C₂²×D₅₂	1	1	yes	characteristic
469	Q₈	—	13	8	no	—
470	Q₈	—	26	8	no	—
471	Q₈	—	26	4	no	—
472	D₄	—	13	8	no	—
473	D₄	—	26	16	no	—
474	D₄	—	26	16	no	—
475	D₄	—	26	8	no	—
476	D₄	—	26	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	26	8	no	—
479	C₂×C₄	—	26	4	no	—
480	C₂×C₄	—	26	16	no	—
481	C₂×C₄	—	26	16	no	—
482	C₂×C₄	—	26	8	no	—
483	C₂×C₄	—	104	16	no	—
484	C₂×C₄	—	104	4	no	—
485	C₂×C₄	C₄×D₅₂	1	4	yes	—
486	C₂×C₄	C₄×D₅₂	1	4	yes	—
487	C₂×C₄	C₄×D₅₂	1	4	yes	—
488	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
489	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
490	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
491	C₂×C₄	C₂²×D₅₂	1	8	yes	—
492	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
495	C₂×C₄	C₂×#6127	1	2	yes	—
496	C₂×C₄	C₂×#6127	1	2	yes	—
497	C₂×C₄	C₂×#6127	1	2	yes	—
498	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
499	C₈	—	2	4	no	—
500	C₈	C₂²×C₄×D₁₃	1	2	yes	—
501	C₈	C₂²×C₄×D₁₃	1	2	yes	—
502	C₈	C₂²×C₄×D₁₃	1	2	yes	—
503	C₈	C₂²×C₄×D₁₃	1	2	yes	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	26	8	no	—
509	C₂²	—	52	8	no	—
510	C₂²	—	104	8	no	—
511	C₂²	C₂×C₄×D₅₂	1	2	yes	—
512	C₂²	C₂×C₄×D₅₂	1	2	yes	—
513	C₂²	C₂×C₄×D₅₂	1	2	yes	—
514	C₂²	C₂³×D₅₂	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	26	8	no	—
517	C₄	—	52	8	no	—
518	C₄	C₂×C₄×D₅₂	1	2	yes	—
519	C₄	C₂×C₄×D₅₂	1	2	yes	—
520	C₄	C₂×C₄×D₅₂	1	2	yes	—
521	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
522	C₄	C₂²×#6127	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	52	8	no	—
527	C₂	C₂²×C₄×D₅₂	1	1	yes	characteristic
528	C₂	#13129610	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂²×#88158	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#60167
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #13128037	C₂	semidirect
3. #13123721	C₂	semidirect
4. #13123713	C₂	semidirect
5. #13123705	C₂	semidirect
6. #13123697	C₂	semidirect
7. #13123689	C₂	semidirect
8. #13123638	C₂	semidirect
9. C₄×#88158	C₂	semidirect
10. C₂×#11718767	C₂	semidirect
11. #13123356	C₂	semidirect
12. C₂×C₁₃×#405	C₂	semidirect
19. C₂×#88158	C₄	semidirect
26. #11719228	C₂²	semidirect
33. C₄×#6127	C₂²	semidirect
36. C₁₃×#405	C₂²	semidirect
37. C₁₃×#405	C₂²	semidirect
38. C₂×C₁₃×#97	C₂²	semidirect
39. C₂×C₄×C₈×C₁₃	C₂²	semidirect
40. #11718794	C₂²	semidirect
43. #11718774	C₂²	semidirect
46. #11718767	C₂²	semidirect
47. #11718767	C₂²	semidirect
48. C₂×#88058	C₂²	semidirect
49. C₂×#88057	C₂²	semidirect
50. #11718377	C₂²	semidirect
51. #11718372	C₂²	semidirect
52. #11718371	C₂²	semidirect
53. C₄×Dic₅₂	C₂²	semidirect
54. C₄×D₁₀₄	C₂²	semidirect
55. C₄×#6095	C₂²	semidirect
61. C₂×#6127	C₂×C₄	semidirect
70. C₂²×C₈×C₁₃	C₂×C₄	semidirect
93. C₂×Dic₅₂	C₂×C₄	semidirect
96. #88158	C₂×C₄	semidirect
97. #88158	C₂×C₄	semidirect
98. #88158	C₂×C₄	semidirect
99. #88158	C₂×C₄	semidirect
100. C₂×D₁₀₄	C₂×C₄	semidirect
103. C₂×#6095	C₂×C₄	semidirect
208. C₂×#405	D₁₃	semidirect
291. #405	C₂×D₁₃	semidirect
292. #405	C₂×D₁₃	semidirect
293. C₂×#97	C₂×D₁₃	semidirect
294. C₂×C₄×C₈	C₂×D₁₃	semidirect
341. C₂²×C₈	C₄×D₁₃	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
C₂²×#88158	2
#13128037	2
#13123721	2
#13123713	2
#13123705	2
#13123697	2
#13123689	2
#13123638	2
C₄×#88158	2
C₂×#11718767	2
#13123356	2
C₂×C₁₃×#405	2
#60167	13