Subgroups — #16797531

Order 3328.

1038 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
3	#13130637	C₂	1	4	yes	maximal, complemented
4	#13130630	C₂	1	2	yes	maximal, complemented
5	C₈×C₄⋊#261	C₂	1	2	yes	maximal, complemented
6	#13130564	C₂	1	2	yes	maximal
7	C₂²⋊C₈×#261	C₂	1	2	yes	maximal
8	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊#261	C₄	1	2	yes	—
10	C₂²×C₄×#261	C₂²	1	2	yes	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
13	#11719130	C₄	1	2	yes	complemented
14	#11719128	C₄	1	2	yes	complemented
15	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
16	C₂×#88100	C₂²	1	4	yes	—
17	C₂×C₈×#261	C₂²	1	4	yes	—
18	C₄×C₄⋊#261	C₄	1	2	yes	—
19	C₄×C₄⋊#261	C₄	1	2	yes	—
20	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊#261	C₂²	1	2	yes	—
23	#11719055	C₄	1	2	yes	complemented
24	#11719054	C₄	1	2	yes	complemented
25	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
26	#11719047	C₂²	1	2	yes	—
27	C₁₃×#431	C₄	1	1	yes	characteristic, complemented
28	#11718586	C₄	1	1	yes	characteristic, complemented
29	#11718494	C₄	1	2	yes	complemented
30	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
31	D₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	D₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	#11718379	C₄	1	1	yes	characteristic, complemented
34	#11718379	C₄	1	1	yes	characteristic, complemented
35	#11718346	C₄	1	2	yes	complemented
36	C₄×C₈×D₁₃	C₂²	1	2	yes	—
37	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
38	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
39	C₂³×#261	C₂×C₄	1	4	yes	—
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊#261	—	2	8	no	—
44	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
47	C₂×C₄×#261	—	4	4	no	—
48	C₂×C₄×#261	C₂×C₄	1	4	yes	—
49	C₂×C₄×#261	C₂³	1	2	yes	—
50	C₂×C₄×#261	C₂³	1	2	yes	—
51	C₂×D₁₃⋊C₈	C₂³	1	4	yes	—
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂³	1	2	yes	—
57	C₂×C₈×D₁₃	C₂³	1	2	yes	—
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	C₄²×D₁₃	C₂³	1	1	yes	characteristic
66	C₂²⋊#1057	C₂×C₄	1	4	yes	—
67	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
68	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
69	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
70	#88112	C₂×C₄	1	4	yes	complemented
71	#88111	C₂×C₄	1	4	yes	—
72	#88110	C₂×C₄	1	4	yes	complemented
73	#88110	C₂×C₄	1	4	yes	complemented
74	C₄⋊#1057	C₂×C₄	1	4	yes	complemented
75	#88100	—	4	4	no	—
76	C₈×#261	—	4	4	no	—
77	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
78	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
81	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
83	#88060	C₂×C₄	1	2	yes	—
84	#88060	C₂×C₄	1	2	yes	—
85	#88054	C₂×C₄	1	2	yes	complemented
86	#88054	C₂×C₄	1	2	yes	complemented
87	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
88	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
89	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
90	C₄×#1055	C₂×C₄	1	2	yes	complemented
91	#20535	—	13	1	no	maximal, Sylow
92	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×#261	—	2	8	no	—
94	C₂²×#261	—	2	8	no	—
95	C₂²×#261	—	4	4	no	—
96	C₂²×#261	C₂²×C₄	1	4	yes	—
97	C₂²×#261	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	—	2	4	no	—
105	C₂×C₄×D₁₃	—	2	4	no	—
106	C₂×C₄×D₁₃	—	2	2	no	—
107	C₂×C₄×D₁₃	—	2	2	no	—
108	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×#1057	C₂²×C₄	1	8	yes	—
121	C₄⋊#261	—	2	8	no	—
122	C₄⋊#261	—	2	4	no	—
123	C₄⋊#261	M₁₆	1	8	yes	—
124	C₄×#261	—	2	4	no	—
125	C₄×#261	—	2	4	no	—
126	C₄×#261	—	4	4	no	—
127	D₁₃⋊C₈	—	2	4	no	—
128	D₁₃⋊C₈	—	2	4	no	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
131	C₄²×C₁₃	C₄²	1	1	yes	characteristic
132	C₄²×C₁₃	C₄²	1	1	yes	characteristic
133	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
136	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
137	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
138	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
139	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
140	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×#1055	C₂²×C₄	1	2	yes	—
148	C₂×#1055	C₂²×C₄	1	2	yes	—
149	C₈×D₁₃	—	2	2	no	—
150	C₈×D₁₃	—	2	2	no	—
151	C₈×D₁₃	—	2	2	no	—
152	C₈×D₁₃	—	2	2	no	—
153	C₂×#432	—	13	1	no	—
154	C₂×#431	—	13	1	no	—
155	C₂×C₄×C₄⋊C₄	—	13	1	no	—
156	#1771	—	13	4	no	—
157	#1770	—	13	2	no	—
158	C₈×C₄⋊C₄	—	13	2	no	—
159	#1749	—	13	2	no	—
160	C₄×C₂²⋊C₈	—	13	2	no	—
161	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂²×D₁₃	—	2	1	no	—
163	C₂²×D₁₃	—	2	1	no	—
164	C₂²×D₁₃	—	2	2	no	—
165	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂²×D₁₃	#131	1	4	yes	—
167	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×#261	—	2	4	no	—
169	C₂×#261	—	2	4	no	—
170	C₂×#261	—	2	4	no	—
171	C₂×#261	—	2	4	no	—
172	C₂×#261	—	2	4	no	—
173	C₂×#261	—	4	16	no	—
174	C₂×#261	C₂×M₁₆	1	8	yes	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×Dic₁₃	—	2	2	no	—
185	C₂×Dic₁₃	—	2	2	no	—
186	C₂×Dic₁₃	—	2	2	no	—
187	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
193	C₄×D₁₃	—	2	1	no	—
194	C₄×D₁₃	—	2	1	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	2	2	no	—
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	—	2	2	no	—
199	C₄×D₁₃	—	2	2	no	—
200	C₄×D₁₃	—	2	2	no	—
201	C₄×D₁₃	—	2	2	no	—
202	C₄×D₁₃	—	2	2	no	—
203	C₄×D₁₃	—	2	2	no	—
204	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
205	C₄×D₁₃	H(5,𝔽₂)	1	2	yes	—
206	C₄×D₁₃	2₋¹⁺⁴	1	2	yes	—
207	#1057	—	2	8	no	—
208	C₈×C₁₃	—	2	2	no	—
209	C₈×C₁₃	—	2	2	no	—
210	#1055	—	2	2	no	—
211	#1055	—	2	2	no	—
212	C₂²×C₄⋊C₄	—	13	2	no	—
213	C₂²×C₄²	—	13	1	no	—
214	C₂²×C₄²	—	13	2	no	—
215	#432	—	13	2	no	—
216	#432	—	13	2	no	—
217	#432	—	13	2	no	—
218	#432	—	13	2	no	—
219	#431	—	13	1	no	—
220	#431	—	13	2	no	—
221	#431	—	13	1	no	—
222	#431	—	13	1	no	—
223	#431	—	13	2	no	—
224	#431	#261	1	1	yes	characteristic, complemented
225	C₂×C₄⋊C₈	—	13	2	no	—
226	C₂×C₄⋊C₈	—	13	2	no	—
227	C₂×C₂²⋊C₈	—	13	2	no	—
228	C₂×C₂²⋊C₈	—	13	1	no	—
229	C₂×C₂²⋊C₈	—	13	1	no	—
230	C₂×#97	—	13	2	no	—
231	C₂×#97	—	13	4	no	—
232	C₂×C₄×C₈	—	13	2	no	—
233	C₂×C₄×C₈	—	13	4	no	—
234	C₄×C₄⋊C₄	—	13	2	no	—
235	C₄×C₄⋊C₄	—	13	2	no	—
236	C₄×C₄⋊C₄	—	13	1	no	—
237	C₄×C₄⋊C₄	—	13	1	no	—
238	C₄×C₄⋊C₄	—	13	2	no	—
239	C₂×#95	—	13	2	no	—
240	#336	—	13	4	no	—
241	#336	—	13	4	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	#405	1	2	yes	—
245	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
246	C₂×D₁₃	—	2	1	no	—
247	C₂×D₁₃	—	2	1	no	—
248	C₂×D₁₃	—	2	4	no	—
249	C₂×D₁₃	—	2	4	no	—
250	C₂×D₁₃	#405	1	2	yes	—
251	C₂×D₁₃	#518	1	1	yes	characteristic
252	C₂×D₁₃	#519	1	1	yes	characteristic
253	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
254	C₂×D₁₃	C₂×#131	1	2	yes	—
255	#261	—	2	8	no	—
256	#261	—	4	4	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
262	C₄×C₁₃	#520	1	2	yes	—
263	Dic₁₃	—	2	1	no	—
264	Dic₁₃	—	2	1	no	—
265	Dic₁₃	—	2	1	no	—
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	C₄×M₁₆	1	2	yes	—
268	Dic₁₃	#520	1	2	yes	—
269	C₂³×C₄	—	13	1	no	—
270	C₂³×C₄	—	13	1	no	—
271	C₂³×C₄	—	13	1	no	—
272	C₂³×C₄	—	13	4	no	—
273	C₂²×C₈	—	13	4	no	—
274	C₂²×C₈	—	13	2	no	—
275	C₂²×C₈	—	13	2	no	—
276	C₂×C₄⋊C₄	—	13	2	no	—
277	C₂×C₄⋊C₄	—	13	2	no	—
278	C₂×C₄⋊C₄	—	13	4	no	—
279	C₂×C₄⋊C₄	—	26	8	no	—
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	1	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	2	no	—
292	C₂×C₄²	—	13	2	no	—
293	C₂×C₄²	—	13	4	no	—
294	C₂×C₄²	—	52	4	no	—
295	C₂×C₄²	C₂×#261	1	1	yes	characteristic
296	C₄⋊C₈	—	13	4	no	—
297	C₄⋊C₈	—	13	4	no	—
298	C₄⋊C₈	—	13	2	no	—
299	C₄⋊C₈	—	13	2	no	—
300	C₄⋊C₈	—	13	2	no	—
301	C₄⋊C₈	C₂×#261	1	2	yes	complemented
302	C₂²⋊C₈	—	13	4	no	—
303	C₂²⋊C₈	—	13	4	no	—
304	C₂²⋊C₈	—	13	1	no	—
305	C₂²⋊C₈	—	13	1	no	—
306	C₂²⋊C₈	—	13	2	no	—
307	C₂²⋊C₈	—	13	2	no	—
308	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
309	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
310	#97	—	13	4	no	—
311	#97	—	13	4	no	—
312	#97	—	52	4	no	—
313	C₄×C₈	—	13	2	no	—
314	C₄×C₈	—	13	2	no	—
315	C₄×C₈	—	13	2	no	—
316	C₄×C₈	—	52	4	no	—
317	C₄×C₈	C₂×#261	1	2	yes	complemented
318	#95	—	13	2	no	—
319	#95	—	13	4	no	—
320	#95	—	13	2	no	—
321	C₂×C₁₃	—	2	2	no	—
322	C₂×C₁₃	#2274	1	1	yes	characteristic
323	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
325	D₁₃	—	2	2	no	—
326	D₁₃	#2974	1	2	yes	—
327	D₁₃	#2984	1	2	yes	—
328	C₂⁴	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	13	4	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	1	no	—
343	C₂²×C₄	—	13	1	no	—
344	C₂²×C₄	—	13	1	no	—
345	C₂²×C₄	—	13	4	no	—
346	C₂²×C₄	—	26	2	no	—
347	C₂²×C₄	—	26	4	no	—
348	C₂²×C₄	—	26	2	no	—
349	C₂²×C₄	—	26	4	no	—
350	C₂²×C₄	—	26	8	no	—
351	C₂²×C₄	—	26	8	no	—
352	C₂²×C₄	—	52	4	no	—
353	C₂²×C₄	C₄×#261	1	1	yes	characteristic
354	C₂²×C₄	C₄×#261	1	1	yes	characteristic
355	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
356	C₂×C₈	—	13	8	no	—
357	C₂×C₈	—	13	2	no	—
358	C₂×C₈	—	13	2	no	—
359	C₂×C₈	—	26	2	no	—
360	C₂×C₈	—	26	2	no	—
361	C₂×C₈	—	26	2	no	—
362	C₂×C₈	—	26	2	no	—
363	C₂×C₈	—	26	4	no	—
364	C₂×C₈	—	26	4	no	—
365	C₂×C₈	C₂²×#261	1	2	yes	—
366	C₂×C₈	C₂²×#261	1	2	yes	—
367	C₄⋊C₄	—	13	8	no	—
368	C₄⋊C₄	—	26	4	no	—
369	C₄⋊C₄	—	26	8	no	—
370	C₄²	—	13	1	no	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	1	no	—
374	C₄²	—	13	1	no	—
375	C₄²	—	13	1	no	—
376	C₄²	—	13	1	no	—
377	C₄²	—	13	1	no	—
378	C₄²	—	13	1	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	1	no	—
381	C₄²	—	13	1	no	—
382	C₄²	—	26	4	no	—
383	C₄²	—	26	4	no	—
384	C₄²	—	52	4	no	—
385	C₄²	C₄×#261	1	1	yes	characteristic
386	C₄²	C₄×#261	1	1	yes	characteristic
387	C₄²	C₂²×#261	1	1	yes	characteristic
388	C₄²	C₂²×#261	1	1	yes	characteristic
389	C₁₃	#20535	1	1	yes	characteristic, complemented, Sylow
390	C₂³	—	13	1	no	—
391	C₂³	—	13	4	no	—
392	C₂³	—	13	1	no	—
393	C₂³	—	26	2	no	—
394	C₂³	—	26	1	no	—
395	C₂³	—	26	1	no	—
396	C₂³	C₂×C₄×#261	1	1	yes	characteristic
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	4	no	—
403	C₂×C₄	—	13	2	no	—
404	C₂×C₄	—	13	2	no	—
405	C₂×C₄	—	13	8	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	13	1	no	—
408	C₂×C₄	—	13	1	no	—
409	C₂×C₄	—	13	1	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	26	1	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	1	no	—
415	C₂×C₄	—	26	2	no	—
416	C₂×C₄	—	26	2	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	2	no	—
420	C₂×C₄	—	26	2	no	—
421	C₂×C₄	—	26	4	no	—
422	C₂×C₄	—	26	4	no	—
423	C₂×C₄	—	26	2	no	—
424	C₂×C₄	—	26	2	no	—
425	C₂×C₄	—	26	2	no	—
426	C₂×C₄	—	26	4	no	—
427	C₂×C₄	—	26	4	no	—
428	C₂×C₄	—	26	4	no	—
429	C₂×C₄	—	52	16	no	—
430	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
431	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
432	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
435	C₂×C₄	C₂³×#261	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	2	2	no	—
438	C₈	—	26	8	no	—
439	C₈	—	26	2	no	—
440	C₈	—	26	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	13	1	no	—
444	C₂²	—	13	1	no	—
445	C₂²	—	13	2	no	—
446	C₂²	—	13	2	no	—
447	C₂²	—	13	2	no	—
448	C₂²	—	26	4	no	—
449	C₂²	—	26	4	no	—
450	C₂²	—	26	1	no	—
451	C₂²	—	26	1	no	—
452	C₂²	#11719089	1	2	yes	—
453	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	13	2	no	—
459	C₄	—	13	2	no	—
460	C₄	—	26	8	no	—
461	C₄	—	26	1	no	—
462	C₄	—	26	1	no	—
463	C₄	—	26	1	no	—
464	C₄	—	26	1	no	—
465	C₄	—	52	4	no	—
466	C₄	M₁₆×#261	1	2	yes	—
467	C₄	#11719631	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	13	2	no	—
470	C₂	—	13	2	no	—
471	C₂	—	26	2	no	—
472	C₂	#13131273	1	1	yes	characteristic
473	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
474	C₂	C₂×#11719089	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#431	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#20535
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130637	C₂	semidirect
4. #13130630	C₂	semidirect
5. C₈×C₄⋊#261	C₂	semidirect
13. #11719130	C₄	semidirect
14. #11719128	C₄	semidirect
23. #11719055	C₄	semidirect
24. #11719054	C₄	semidirect
27. C₁₃×#431	C₄	semidirect
28. #11718586	C₄	semidirect
29. #11718494	C₄	semidirect
33. #11718379	C₄	semidirect
34. #11718379	C₄	semidirect
35. #11718346	C₄	semidirect
70. #88112	C₂×C₄	semidirect
72. #88110	C₂×C₄	semidirect
73. #88110	C₂×C₄	semidirect
74. C₄⋊#1057	C₂×C₄	semidirect
77. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
80. C₄×C₈×C₁₃	C₂×C₄	semidirect
85. #88054	C₂×C₄	semidirect
86. #88054	C₂×C₄	semidirect
87. C₈×Dic₁₃	C₂×C₄	semidirect
88. C₈×Dic₁₃	C₂×C₄	semidirect
89. C₄⋊#1055	C₂×C₄	semidirect
90. C₄×#1055	C₂×C₄	semidirect
224. #431	#261	semidirect
301. C₄⋊C₈	C₂×#261	semidirect
317. C₄×C₈	C₂×#261	semidirect
389. C₁₃	#20535	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#432	2
C₂×C₄×C₄⋊#261	2
#13130637	2
#13130630	2
C₈×C₄⋊#261	2
#13130564	2
C₂²⋊C₈×#261	2
D₁₃×#431	2
#20535	13