Subgroups — #16727262

Order 3328.

2604 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129607	C₂	1	1	yes	maximal, characteristic
2	#13129547	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123751	C₂	1	6	yes	maximal, complemented
4	#13123743	C₂	1	6	yes	maximal, complemented
5	#13123737	C₂	1	6	yes	maximal, complemented
6	C₂×#11718806	C₂	1	6	yes	maximal, complemented
7	#13123445	C₂	1	1	yes	maximal, characteristic, complemented
8	#13123383	C₂	1	1	yes	maximal, characteristic, complemented
9	#13123381	C₂	1	1	yes	maximal, characteristic, complemented
10	#13123262	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3573	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#585	C₂²	1	1	yes	characteristic
13	#11719648	C₂²	1	1	yes	characteristic
14	C₁₃×#568	—	2	4	no	—
15	C₁₃×#568	C₂²	1	1	yes	characteristic
16	C₁₃×#568	C₂²	1	6	yes	complemented
17	C₂×C₁₃×#131	—	2	4	no	—
18	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	6	yes	complemented
20	#11719543	C₄	1	4	yes	complemented
21	#11719542	C₄	1	4	yes	complemented
22	#11719541	C₄	1	4	yes	complemented
23	#11719540	C₄	1	4	yes	complemented
24	#41×Dic₁₃	C₂²	1	1	yes	characteristic
25	#11719527	C₂²	1	6	yes	—
26	C₂×#88204	C₂²	1	6	yes	—
27	#11719524	C₂²	1	1	yes	characteristic
28	C₂×#88202	C₂²	1	1	yes	characteristic
29	#11719455	—	2	4	no	—
30	D₁₃×#131	—	2	4	no	—
31	#11719450	C₂²	1	6	yes	complemented
32	C₂×#88155	C₂²	1	6	yes	complemented
33	#11718897	C₂²	1	6	yes	complemented
34	C₂×#88077	C₂²	1	6	yes	complemented
35	#11718806	C₂²	1	4	yes	complemented
36	#11718806	C₂²	1	12	yes	complemented
37	#11718806	C₂²	1	12	yes	complemented
38	#11718806	C₂²	1	12	yes	complemented
39	#11718805	C₂²	1	24	yes	complemented
40	#11718800	C₂²	1	6	yes	complemented
41	C₂×#88065	C₂²	1	6	yes	complemented
42	#11718785	C₂²	1	6	yes	complemented
43	C₂×#88062	C₂²	1	6	yes	complemented
44	#11718783	C₂²	1	3	yes	complemented
45	M₁₆×Dic₁₃	C₂²	1	3	yes	complemented
46	#11718762	C₂²	1	3	yes	complemented
47	C₂×#88055	C₂²	1	3	yes	complemented
48	C₁₃×2₋¹⁺⁴	—	2	1	no	—
49	C₁₃×2₋¹⁺⁴	C₂×C₄	1	4	yes	—
50	C₁₃×H(5,𝔽₂)	—	2	3	no	—
51	C₁₃×H(5,𝔽₂)	C₂×C₄	1	4	yes	—
52	C₂×C₁₃×#41	—	2	4	no	—
53	C₂×C₁₃×#41	C₂³	1	6	yes	—
54	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
55	#88257	C₂×C₄	1	4	yes	—
56	#88256	C₂×C₄	1	4	yes	—
57	#41×D₁₃	—	2	4	no	—
58	#88254	—	2	1	no	—
59	#88251	—	2	3	no	—
60	C₂×#6127	C₂³	1	6	yes	—
61	C₁₃×#131	—	2	4	no	—
62	C₁₃×#131	—	2	12	no	—
63	C₁₃×#131	—	2	6	no	—
64	C₁₃×#131	—	2	6	no	—
65	C₁₃×#131	D₄	1	4	yes	—
66	C₁₃×#131	D₄	1	4	yes	—
67	C₁₃×#131	C₂³	1	12	yes	—
68	C₁₃×#131	C₂³	1	4	yes	—
69	C₂×C₁₃×M₁₆	—	2	12	no	—
70	C₂×C₁₃×M₁₆	—	2	6	no	—
71	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
72	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
73	C₂²×C₈×C₁₃	—	2	6	no	—
74	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
75	#88205	C₂×C₄	1	12	yes	complemented
76	#88204	C₂×C₄	1	12	yes	complemented
77	#88204	C₂×C₄	1	12	yes	complemented
78	#88204	C₂³	1	4	yes	—
79	#88204	C₂³	1	12	yes	—
80	#88203	C₂×C₄	1	12	yes	complemented
81	#88202	—	2	4	no	—
82	#88202	C₂×C₄	1	4	yes	—
83	#88202	C₂×C₄	1	4	yes	—
84	Q₈×Dic₁₃	—	2	1	no	—
85	C₂×#6107	C₂×C₄	1	6	yes	complemented
86	#88196	C₂×C₄	1	12	yes	complemented
87	C₂×#6106	C₂×C₄	1	6	yes	complemented
88	D₄×Dic₁₃	—	2	3	no	—
89	C₂×#6105	C₂×C₄	1	6	yes	complemented
90	#88186	C₂×C₄	1	12	yes	complemented
91	C₂×#6104	C₂×C₄	1	6	yes	complemented
92	#88180	C₂³	1	3	yes	—
93	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
94	C₂×#6099	C₂³	1	6	yes	—
95	C₂×#6099	C₂³	1	3	yes	—
96	C₂²×#1055	C₂³	1	3	yes	—
97	#88161	—	2	12	no	—
98	M₁₆×D₁₃	—	2	12	no	—
99	#88155	—	2	6	no	—
100	#88155	—	2	6	no	—
101	#88155	C₂³	1	4	yes	—
102	#88155	C₂³	1	12	yes	—
103	C₂×#6094	—	2	6	no	—
104	C₂×C₈×D₁₃	—	2	6	no	—
105	#88077	C₂³	1	12	yes	—
106	#88077	C₂³	1	4	yes	—
107	#88065	C₂³	1	4	yes	—
108	#88065	C₂³	1	12	yes	—
109	#88062	C₂³	1	4	yes	—
110	#88062	C₂³	1	12	yes	—
111	#88055	C₂³	1	1	yes	characteristic
112	#88055	C₂³	1	3	yes	—
113	#88055	C₂³	1	3	yes	—
114	#88055	C₂³	1	3	yes	—
115	C₈×Dic₁₃	C₂³	1	6	yes	—
116	#60184	—	13	1	no	maximal, Sylow
117	C₁₃×#41	—	2	4	no	—
118	C₁₃×#41	—	2	12	no	—
119	C₁₃×#41	—	2	6	no	—
120	C₁₃×#41	—	2	6	no	—
121	C₁₃×#41	C₂²×C₄	1	12	yes	—
122	C₁₃×#41	C₂²×C₄	1	4	yes	—
123	C₁₃×#41	C₂×D₄	1	4	yes	—
124	C₁₃×#41	C₂⁴	1	4	yes	—
125	C₂×Q₈×C₁₃	—	2	4	no	—
126	C₂×Q₈×C₁₃	C₂²×C₄	1	6	yes	—
127	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
128	C₂×D₄×C₁₃	—	2	6	no	—
129	C₂×D₄×C₁₃	—	2	12	no	—
130	C₂×D₄×C₁₃	C₂²×C₄	1	6	yes	—
131	C₂×D₄×C₁₃	#41	1	3	yes	—
132	C₂²×C₄×C₁₃	—	2	6	no	—
133	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
134	C₂×C₂²⋊D₁₃	—	2	6	no	—
135	C₂²×Dic₁₃	—	2	3	no	—
136	#6131	—	2	4	no	—
137	Q₈×D₁₃	—	2	4	no	—
138	#6129	—	2	12	no	—
139	D₄×D₁₃	—	2	12	no	—
140	#6127	—	2	6	no	—
141	#6127	—	2	6	no	—
142	#6127	C₂²×C₄	1	12	yes	—
143	#6127	C₂⁴	1	4	yes	—
144	C₂×D₅₂	C₂²×C₄	1	6	yes	—
145	C₂×C₄×D₁₃	—	2	6	no	—
146	C₂×Dic₂₆	C₂²×C₄	1	6	yes	—
147	C₁₃×M₁₆	—	2	6	no	—
148	C₁₃×M₁₆	—	2	4	no	—
149	C₁₃×M₁₆	—	2	12	no	—
150	C₁₃×M₁₆	C₂×D₄	1	12	yes	—
151	C₁₃×M₁₆	C₂⁴	1	4	yes	—
152	C₂×C₈×C₁₃	—	2	6	no	—
153	C₂×C₈×C₁₃	—	2	4	no	—
154	C₂×C₈×C₁₃	—	2	12	no	—
155	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
156	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
159	C₂²⋊Dic₁₃	—	2	3	no	—
160	#6107	C₂²×C₄	1	12	yes	—
161	#6107	C₂²×C₄	1	4	yes	—
162	#6106	C₂²×C₄	1	4	yes	—
163	#6106	C₂²×C₄	1	12	yes	—
164	#6105	C₂²×C₄	1	12	yes	—
165	#6105	C₂²×C₄	1	4	yes	—
166	#6104	C₂²×C₄	1	4	yes	—
167	#6104	C₂²×C₄	1	12	yes	—
168	C₄⋊Dic₁₃	—	2	3	no	—
169	C₄×Dic₁₃	—	2	3	no	—
170	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
171	C₄×Dic₁₃	C₂⁴	1	3	yes	—
172	#6099	—	2	6	no	—
173	#6099	C₂²×C₄	1	12	yes	—
174	#6099	C₂⁴	1	4	yes	—
175	C₂×#1055	—	2	6	no	—
176	C₂×#1055	C₂²×C₄	1	6	yes	—
177	C₂×#1055	C₂²×C₄	1	6	yes	—
178	C₂×#1055	C₂⁴	1	1	yes	characteristic
179	C₂×#1055	C₂⁴	1	3	yes	—
180	#6094	—	2	4	no	—
181	#6094	—	2	12	no	—
182	C₈×D₁₃	—	2	4	no	—
183	C₈×D₁₃	—	2	12	no	—
184	#3584	—	13	1	no	—
185	#3573	—	13	1	no	—
186	#3573	D₁₃	1	1	yes	characteristic, complemented
187	#2957	—	13	6	no	—
188	#2956	—	13	6	no	—
189	#2955	—	13	6	no	—
190	C₂×#444	—	13	6	no	—
191	#2916	—	13	1	no	—
192	#2901	—	13	1	no	—
193	#2901	—	13	1	no	—
194	#2875	—	13	1	no	—
195	C₂³×C₁₃	—	2	6	no	—
196	C₂³×C₁₃	C₂×#41	1	3	yes	—
197	C₂²×D₁₃	—	2	6	no	—
198	Q₈×C₁₃	—	2	6	no	—
199	Q₈×C₁₃	C₄×D₄	1	4	yes	—
200	Q₈×C₁₃	C₂³×C₄	1	4	yes	—
201	D₄×C₁₃	—	2	12	no	—
202	D₄×C₁₃	—	2	4	no	—
203	D₄×C₁₃	—	2	6	no	—
204	D₄×C₁₃	C₄×D₄	1	12	yes	—
205	D₄×C₁₃	C₂³×C₄	1	4	yes	—
206	C₂×C₄×C₁₃	—	2	6	no	—
207	C₂×C₄×C₁₃	—	2	12	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
211	C₂×C₄×C₁₃	C₂×#41	1	3	yes	—
212	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
213	C₂²⋊D₁₃	—	2	12	no	—
214	C₂²⋊D₁₃	—	2	4	no	—
215	C₂×Dic₁₃	—	2	6	no	—
216	C₂×Dic₁₃	—	2	1	no	—
217	C₂×Dic₁₃	—	2	3	no	—
218	C₂×Dic₁₃	—	8	3	no	—
219	D₅₂	—	2	6	no	—
220	D₅₂	C₂³×C₄	1	4	yes	—
221	C₄×D₁₃	—	2	12	no	—
222	C₄×D₁₃	—	2	4	no	—
223	Dic₂₆	—	2	6	no	—
224	Dic₂₆	C₂³×C₄	1	4	yes	—
225	C₈×C₁₃	—	2	4	no	—
226	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₈×C₁₃	C₂²×D₄	1	6	yes	—
228	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	#1055	—	2	4	no	—
230	#1055	C₂³×C₄	1	1	yes	characteristic
231	#1055	C₂³×C₄	1	1	yes	characteristic
232	#1055	C₂³×C₄	1	6	yes	—
233	#585	—	13	1	no	—
234	#585	C₂×D₁₃	1	1	yes	characteristic
235	#578	—	13	4	no	—
236	#577	—	13	4	no	—
237	#577	—	13	4	no	—
238	#576	—	13	4	no	—
239	#575	—	13	6	no	—
240	C₂×#135	—	13	6	no	—
241	#568	—	2	4	no	—
242	#568	—	13	1	no	—
243	#568	—	13	6	no	—
244	#568	—	26	4	no	—
245	#568	C₂×D₁₃	1	1	yes	characteristic
246	#568	C₂×D₁₃	1	6	yes	complemented
247	C₂×#131	—	2	4	no	—
248	C₂×#131	—	13	1	no	—
249	C₂×#131	—	13	6	no	—
250	C₂×#131	—	26	4	no	—
251	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
252	C₂×#131	C₂×D₁₃	1	6	yes	complemented
253	C₄×#41	—	13	1	no	—
254	#444	—	13	4	no	—
255	#444	—	13	12	no	—
256	#444	—	13	12	no	—
257	#444	—	13	12	no	—
258	#443	—	13	24	no	—
259	#430	—	13	6	no	—
260	C₂×#108	—	13	6	no	—
261	#421	—	13	6	no	—
262	#421	—	13	6	no	—
263	C₂×#104	—	13	6	no	—
264	C₂×#104	—	13	6	no	—
265	#405	—	13	3	no	—
266	#405	—	13	3	no	—
267	C₄×M₁₆	—	13	3	no	—
268	C₂×#97	—	13	3	no	—
269	C₂²×C₁₃	—	2	4	no	—
270	C₂²×C₁₃	—	4	3	no	—
271	C₂²×C₁₃	—	8	6	no	—
272	C₂²×C₁₃	C₂×C₄×D₄	1	6	yes	—
273	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
274	C₂×D₁₃	—	2	4	no	—
275	C₂×D₁₃	—	8	6	no	—
276	C₄×C₁₃	—	2	4	no	—
277	C₄×C₁₃	C₂×C₄×D₄	1	6	yes	—
278	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
279	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
280	Dic₁₃	—	2	4	no	—
281	Dic₁₃	—	4	3	no	—
282	Dic₁₃	—	4	1	no	—
283	2₋¹⁺⁴	—	2	1	no	—
284	2₋¹⁺⁴	—	13	4	no	—
285	2₋¹⁺⁴	—	26	1	no	—
286	2₋¹⁺⁴	C₄×D₁₃	1	4	yes	—
287	H(5,𝔽₂)	—	2	3	no	—
288	H(5,𝔽₂)	—	13	4	no	—
289	H(5,𝔽₂)	—	26	3	no	—
290	H(5,𝔽₂)	C₄×D₁₃	1	4	yes	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	13	6	no	—
293	C₂×#41	—	26	4	no	—
294	C₂×#41	C₂²×D₁₃	1	6	yes	—
295	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
296	#137	—	13	12	no	—
297	#137	—	13	12	no	—
298	AGL(1,ℤ/8)	—	13	12	no	—
299	AGL(1,ℤ/8)	—	13	12	no	—
300	#135	—	13	12	no	—
301	#135	—	13	12	no	—
302	#135	—	13	4	no	—
303	#135	—	13	12	no	—
304	C₂×Q₁₆	—	13	6	no	—
305	C₂×SD₁₆	—	13	6	no	—
306	C₂×SD₁₆	—	13	6	no	—
307	C₂×D₈	—	13	6	no	—
308	#131	—	2	4	no	—
309	#131	—	2	12	no	—
310	#131	—	2	6	no	—
311	#131	—	2	6	no	—
312	#131	—	13	4	no	—
313	#131	—	13	4	no	—
314	#131	—	13	4	no	—
315	#131	—	13	12	no	—
316	#131	—	26	4	no	—
317	#131	—	26	12	no	—
318	#131	—	26	6	no	—
319	#131	—	26	6	no	—
320	#131	C₂²⋊D₁₃	1	4	yes	—
321	#131	C₂²⋊D₁₃	1	4	yes	—
322	#131	C₂²×D₁₃	1	4	yes	—
323	#131	C₂²×D₁₃	1	12	yes	—
324	C₂×M₁₆	—	2	12	no	—
325	C₂×M₁₆	—	2	6	no	—
326	C₂×M₁₆	—	13	3	no	—
327	C₂×M₁₆	—	13	6	no	—
328	C₂×M₁₆	—	26	12	no	—
329	C₂×M₁₆	—	26	6	no	—
330	C₂×M₁₆	C₂²×D₁₃	1	6	yes	—
331	C₂×M₁₆	C₂²×D₁₃	1	3	yes	—
332	C₂²×C₈	—	2	6	no	—
333	C₂²×C₈	—	13	3	no	—
334	C₂²×C₈	—	26	6	no	—
335	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
336	C₄×Q₈	—	26	1	no	—
337	C₄×D₄	—	26	3	no	—
338	#117	—	13	3	no	—
339	C₂×C₄²	—	13	3	no	—
340	#108	—	13	4	no	—
341	#108	—	13	12	no	—
342	#104	—	13	4	no	—
343	#104	—	13	12	no	—
344	#104	—	13	4	no	—
345	#104	—	13	12	no	—
346	#97	—	13	1	no	—
347	#97	—	13	3	no	—
348	#97	—	13	3	no	—
349	#97	—	13	3	no	—
350	C₄×C₈	—	13	6	no	—
351	C₂×C₁₃	—	2	1	no	—
352	C₂×C₁₃	—	2	6	no	—
353	C₂×C₁₃	—	4	4	no	—
354	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
355	D₁₃	—	4	4	no	—
356	#41	—	2	4	no	—
357	#41	—	2	12	no	—
358	#41	—	2	6	no	—
359	#41	—	2	6	no	—
360	#41	—	13	12	no	—
361	#41	—	13	4	no	—
362	#41	—	26	4	no	—
363	#41	—	26	12	no	—
364	#41	—	26	6	no	—
365	#41	—	26	6	no	—
366	#41	C₂×C₄×D₁₃	1	12	yes	—
367	#41	C₂×C₄×D₁₃	1	4	yes	—
368	#41	C₂×C₂²⋊D₁₃	1	4	yes	—
369	#41	C₂³×D₁₃	1	4	yes	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	13	6	no	—
372	C₂×Q₈	—	26	4	no	—
373	C₂×Q₈	C₂×C₄×D₁₃	1	6	yes	—
374	C₂×Q₈	#6127	1	1	yes	characteristic
375	C₂×D₄	—	2	6	no	—
376	C₂×D₄	—	2	12	no	—
377	C₂×D₄	—	13	6	no	—
378	C₂×D₄	—	26	6	no	—
379	C₂×D₄	—	26	12	no	—
380	C₂×D₄	C₂×C₄×D₁₃	1	6	yes	—
381	C₂×D₄	#6127	1	3	yes	—
382	C₂²×C₄	—	2	6	no	—
383	C₂²×C₄	—	26	6	no	—
384	C₂²×C₄	—	26	3	no	—
385	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
386	Q₁₆	—	13	4	no	—
387	Q₁₆	—	13	12	no	—
388	SD₁₆	—	13	4	no	—
389	SD₁₆	—	13	12	no	—
390	SD₁₆	—	13	4	no	—
391	SD₁₆	—	13	12	no	—
392	D₈	—	13	4	no	—
393	D₈	—	13	12	no	—
394	M₁₆	—	2	6	no	—
395	M₁₆	—	2	12	no	—
396	M₁₆	—	2	4	no	—
397	M₁₆	—	13	12	no	—
398	M₁₆	—	13	4	no	—
399	M₁₆	—	26	6	no	—
400	M₁₆	—	26	4	no	—
401	M₁₆	—	26	12	no	—
402	M₁₆	C₂×C₂²⋊D₁₃	1	12	yes	—
403	M₁₆	C₂³×D₁₃	1	4	yes	—
404	C₂×C₈	—	2	6	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	12	no	—
407	C₂×C₈	—	13	6	no	—
408	C₂×C₈	—	13	6	no	—
409	C₂×C₈	—	13	3	no	—
410	C₂×C₈	—	13	1	no	—
411	C₂×C₈	—	26	6	no	—
412	C₂×C₈	—	26	4	no	—
413	C₂×C₈	—	26	12	no	—
414	C₂×C₈	C₂×C₂²⋊D₁₃	1	6	yes	—
415	C₂×C₈	C₂×C₂²⋊D₁₃	1	6	yes	—
416	C₂×C₈	C₂³×D₁₃	1	3	yes	—
417	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
418	C₄⋊C₄	—	26	3	no	—
419	C₂²⋊C₄	—	26	3	no	—
420	C₄²	—	13	3	no	—
421	C₄²	—	13	1	no	—
422	C₄²	—	26	3	no	—
423	C₁₃	#60184	1	1	yes	characteristic, complemented, Sylow
424	C₂³	—	2	6	no	—
425	C₂³	—	26	6	no	—
426	C₂³	C₂×#6127	1	3	yes	—
427	Q₈	—	2	6	no	—
428	Q₈	—	13	4	no	—
429	Q₈	—	26	6	no	—
430	Q₈	C₄×C₂²⋊D₁₃	1	4	yes	—
431	Q₈	C₂²×C₄×D₁₃	1	4	yes	—
432	D₄	—	2	12	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	6	no	—
435	D₄	—	13	4	no	—
436	D₄	—	26	12	no	—
437	D₄	—	26	4	no	—
438	D₄	—	26	6	no	—
439	D₄	C₄×C₂²⋊D₁₃	1	12	yes	—
440	D₄	C₂²×C₄×D₁₃	1	4	yes	—
441	C₂×C₄	—	2	6	no	—
442	C₂×C₄	—	2	12	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	26	6	no	—
445	C₂×C₄	—	26	12	no	—
446	C₂×C₄	—	26	4	no	—
447	C₂×C₄	—	26	1	no	—
448	C₂×C₄	—	26	3	no	—
449	C₂×C₄	—	104	3	no	—
450	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
451	C₂×C₄	C₂×#6127	1	3	yes	—
452	C₂×C₄	C₂²×C₂²⋊D₁₃	1	6	yes	—
453	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
454	C₈	—	2	4	no	—
455	C₈	—	13	1	no	—
456	C₈	—	13	1	no	—
457	C₈	—	13	6	no	—
458	C₈	—	26	4	no	—
459	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
460	C₈	C₂²×C₂²⋊D₁₃	1	6	yes	—
461	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
462	C₂²	—	2	4	no	—
463	C₂²	—	4	3	no	—
464	C₂²	—	8	6	no	—
465	C₂²	—	26	4	no	—
466	C₂²	—	104	6	no	—
467	C₂²	C₂×C₄×C₂²⋊D₁₃	1	6	yes	—
468	C₂²	C₂²×#6127	1	1	yes	characteristic
469	C₄	—	2	4	no	—
470	C₄	—	26	4	no	—
471	C₄	—	52	3	no	—
472	C₄	—	52	1	no	—
473	C₄	C₂×C₄×C₂²⋊D₁₃	1	6	yes	—
474	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
475	C₄	C₂³×C₂²⋊D₁₃	1	1	yes	characteristic
476	C₂	—	2	1	no	—
477	C₂	—	2	6	no	—
478	C₂	—	4	4	no	—
479	C₂	—	52	4	no	—
480	C₂	C₂²×C₄×C₂²⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂³×C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₁₃×#3573	C₂
socle	C₂×C₁₃	C₂²×C₄×D₄
prime radical	#13129607	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	#3573	D₁₃
hypocenter	C₁₃	#60184
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×#131 ◁ #3573

Complements

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

N	H ≅ G/N	type
2. #13129547	C₂	semidirect
3. #13123751	C₂	semidirect
4. #13123743	C₂	semidirect
5. #13123737	C₂	semidirect
6. C₂×#11718806	C₂	semidirect
7. #13123445	C₂	semidirect
8. #13123383	C₂	semidirect
9. #13123381	C₂	semidirect
10. #13123262	C₂	semidirect
11. C₁₃×#3573	C₂	semidirect
16. C₁₃×#568	C₂²	semidirect
19. C₂×C₁₃×#131	C₂²	semidirect
20. #11719543	C₄	semidirect
21. #11719542	C₄	semidirect
22. #11719541	C₄	semidirect
23. #11719540	C₄	semidirect
31. #11719450	C₂²	semidirect
32. C₂×#88155	C₂²	semidirect
33. #11718897	C₂²	semidirect
34. C₂×#88077	C₂²	semidirect
35. #11718806	C₂²	semidirect
36. #11718806	C₂²	semidirect
37. #11718806	C₂²	semidirect
38. #11718806	C₂²	semidirect
39. #11718805	C₂²	semidirect
40. #11718800	C₂²	semidirect
41. C₂×#88065	C₂²	semidirect
42. #11718785	C₂²	semidirect
43. C₂×#88062	C₂²	semidirect
44. #11718783	C₂²	semidirect
45. M₁₆×Dic₁₃	C₂²	semidirect
46. #11718762	C₂²	semidirect
47. C₂×#88055	C₂²	semidirect
75. #88205	C₂×C₄	semidirect
76. #88204	C₂×C₄	semidirect
77. #88204	C₂×C₄	semidirect
80. #88203	C₂×C₄	semidirect
85. C₂×#6107	C₂×C₄	semidirect
86. #88196	C₂×C₄	semidirect
87. C₂×#6106	C₂×C₄	semidirect
89. C₂×#6105	C₂×C₄	semidirect
90. #88186	C₂×C₄	semidirect
91. C₂×#6104	C₂×C₄	semidirect
186. #3573	D₁₃	semidirect
246. #568	C₂×D₁₃	semidirect
252. C₂×#131	C₂×D₁₃	semidirect
423. C₁₃	#60184	semidirect

Maximal subgroups

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

subgroup	index
#13129607	2
#13129547	2
#13123751	2
#13123743	2
#13123737	2
C₂×#11718806	2
#13123445	2
#13123383	2
#13123381	2
#13123262	2
C₁₃×#3573	2
#60184	13