Subgroups — #16797235

Order 3328.

1222 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×#261	C₂	1	1	yes	maximal, characteristic
3	#13130623	C₂	1	4	yes	maximal, complemented
4	#13130564	C₂	1	4	yes	maximal
5	#13130549	C₂	1	2	yes	maximal, complemented
6	C₄×#88100	C₂	1	2	yes	maximal, complemented
7	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×#261	C₄	1	2	yes	—
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	#11719125	C₄	1	2	yes	complemented
13	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
14	#11719119	C₄	1	2	yes	complemented
15	C₂×#88100	C₂²	1	8	yes	—
16	C₄²×#261	C₄	1	2	yes	—
17	C₄²×#261	C₄	1	2	yes	—
18	C₄²×#261	C₂²	1	1	yes	characteristic
19	C₄²×#261	C₂²	1	2	yes	—
20	C₄²×#261	C₂²	1	1	yes	characteristic
21	#11719051	C₄	1	2	yes	complemented
22	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
23	#11719049	C₄	1	2	yes	complemented
24	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
25	C₁₃×#431	C₄	1	1	yes	characteristic, complemented
26	#11718586	C₄	1	1	yes	characteristic, complemented
27	#11718494	C₄	1	2	yes	complemented
28	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
29	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
30	#11718379	C₄	1	2	yes	complemented
31	#11718346	C₄	1	2	yes	complemented
32	C₄×C₈×D₁₃	C₂²	1	2	yes	—
33	(C₂×#261)⋊C₈	C₂²	1	8	yes	—
34	C₂³×#261	C₂×C₄	1	4	yes	—
35	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₄×#261	—	2	8	no	—
39	C₂×C₄×#261	—	2	8	no	—
40	C₂×C₄×#261	—	2	8	no	—
41	C₂×C₄×#261	C₂×C₄	1	4	yes	—
42	C₂×C₄×#261	C₂×C₄	1	4	yes	—
43	C₂×C₄×#261	C₂×C₄	1	2	yes	—
44	C₂×C₄×#261	C₂×C₄	1	2	yes	—
45	C₂×C₄×#261	C₂×C₄	1	4	yes	—
46	C₂×C₄×#261	C₂×C₄	1	2	yes	—
47	C₂×C₄×#261	C₂×C₄	1	2	yes	—
48	C₂×C₄×#261	C₂³	1	2	yes	—
49	C₂×C₄×#261	C₂³	1	2	yes	—
50	C₂×D₁₃⋊C₈	C₂³	1	4	yes	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	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×C₈×D₁₃	C₂³	1	4	yes	—
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
63	C₄²×D₁₃	C₂³	1	1	yes	characteristic
64	C₂²⋊#1057	C₂×C₄	1	4	yes	—
65	#88112	C₂×C₄	1	4	yes	complemented
66	#88111	C₂×C₄	1	4	yes	—
67	C₄⋊#1057	C₂×C₄	1	4	yes	complemented
68	C₄×#1057	C₂×C₄	1	4	yes	complemented
69	C₄×#1057	C₂×C₄	1	4	yes	complemented
70	#88100	—	2	16	no	—
71	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
72	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
74	C₂²⋊#1055	C₂×C₄	1	2	yes	—
75	#88060	C₂×C₄	1	4	yes	—
76	#88054	C₂×C₄	1	4	yes	complemented
77	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
78	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
79	C₄×#1055	C₂×C₄	1	2	yes	complemented
80	#20463	—	13	1	no	maximal, Sylow
81	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×#261	—	2	8	no	—
83	C₂²×#261	—	2	8	no	—
84	C₂²×#261	—	2	8	no	—
85	C₂²×#261	C₂²×C₄	1	4	yes	—
86	C₂²×#261	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
91	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
92	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	—	2	4	no	—
94	C₂×C₄×D₁₃	—	2	4	no	—
95	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
99	C₂×C₄×D₁₃	M₁₆	1	8	yes	—
100	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×#1057	C₂²×C₄	1	8	yes	—
109	C₄×#261	—	2	8	no	—
110	C₄×#261	—	2	8	no	—
111	C₄×#261	—	2	4	no	—
112	C₄×#261	—	2	8	no	—
113	C₄×#261	—	2	4	no	—
114	C₄×#261	—	2	4	no	—
115	C₄×#261	—	2	4	no	—
116	C₄×#261	M₁₆	1	8	yes	—
117	C₄×#261	#41	1	8	yes	—
118	D₁₃⋊C₈	—	2	8	no	—
119	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
120	C₄²×C₁₃	C₄²	1	1	yes	characteristic
121	C₄²×C₁₃	C₄²	1	1	yes	characteristic
122	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
125	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
127	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×#1055	C₂²×C₄	1	4	yes	—
137	C₈×D₁₃	—	2	8	no	—
138	C₂×#431	—	13	1	no	—
139	C₂×#431	—	13	1	no	—
140	C₂×C₄³	—	13	1	no	—
141	#1767	—	13	4	no	—
142	#1749	—	13	4	no	—
143	#1744	—	13	2	no	—
144	C₄×#97	—	13	2	no	—
145	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
146	C₂²×D₁₃	—	2	2	no	—
147	C₂²×D₁₃	—	2	2	no	—
148	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
149	C₂²×D₁₃	C₂×M₁₆	1	4	yes	—
150	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
151	C₂×#261	—	2	32	no	—
152	C₂×#261	—	2	4	no	—
153	C₂×#261	—	2	4	no	—
154	C₂×#261	—	2	4	no	—
155	C₂×#261	—	2	4	no	—
156	C₂×#261	#117	1	8	yes	—
157	C₂×#261	C₂×M₁₆	1	8	yes	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	#97	1	4	yes	complemented
161	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	2	2	no	—
169	C₂×Dic₁₃	#97	1	4	yes	complemented
170	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	#97	1	4	yes	complemented
183	C₄×D₁₃	#97	1	4	yes	complemented
184	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
185	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
186	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
187	C₄×D₁₃	C₂×#41	1	4	yes	—
188	#1057	—	2	8	no	—
189	C₈×C₁₃	—	2	4	no	—
190	#1055	—	2	4	no	—
191	C₂²×C₄²	—	13	1	no	—
192	C₂²×C₄²	—	13	2	no	—
193	C₂²×C₄²	—	13	2	no	—
194	C₂²×C₄²	—	13	2	no	—
195	#431	—	13	2	no	—
196	#431	—	13	2	no	—
197	#431	—	13	2	no	—
198	#431	—	13	2	no	—
199	#431	—	13	1	no	—
200	#431	—	13	2	no	—
201	#431	—	13	2	no	—
202	#431	—	13	2	no	—
203	#431	#261	1	1	yes	characteristic, complemented
204	C₂×C₄⋊C₈	—	13	2	no	—
205	C₂×C₄⋊C₈	—	13	2	no	—
206	C₂×C₂²⋊C₈	—	13	2	no	—
207	C₂×C₂²⋊C₈	—	13	2	no	—
208	C₂×#97	—	13	8	no	—
209	C₂×C₄×C₈	—	13	2	no	—
210	C₂×C₄×C₈	—	13	2	no	—
211	C₄³	—	13	2	no	—
212	C₄³	—	13	2	no	—
213	C₄³	—	13	1	no	—
214	C₄³	—	13	1	no	—
215	C₄³	—	13	2	no	—
216	#336	—	13	8	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	C₂×#97	1	2	yes	—
220	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
221	C₂×D₁₃	—	2	1	no	—
222	C₂×D₁₃	—	2	1	no	—
223	C₂×D₁₃	—	2	8	no	—
224	C₂×D₁₃	C₂×#97	1	2	yes	—
225	C₂×D₁₃	C₂×#117	1	2	yes	—
226	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
227	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
228	#261	—	2	8	no	—
229	#261	—	2	8	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	C₂×#97	1	2	yes	—
233	C₄×C₁₃	C₂×#97	1	2	yes	—
234	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
235	C₄×C₁₃	C₄×#41	1	2	yes	—
236	Dic₁₃	—	2	1	no	—
237	Dic₁₃	—	2	1	no	—
238	Dic₁₃	C₂×#97	1	2	yes	—
239	Dic₁₃	C₂×#97	1	2	yes	—
240	Dic₁₃	C₄×M₁₆	1	2	yes	—
241	Dic₁₃	C₄×#41	1	2	yes	—
242	C₂³×C₄	—	13	1	no	—
243	C₂³×C₄	—	13	1	no	—
244	C₂³×C₄	—	13	1	no	—
245	C₂³×C₄	—	13	4	no	—
246	C₂²×C₈	—	13	4	no	—
247	C₂²×C₈	—	13	4	no	—
248	C₂×C₄²	—	13	2	no	—
249	C₂×C₄²	—	13	2	no	—
250	C₂×C₄²	—	13	1	no	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	—	13	1	no	—
253	C₂×C₄²	—	13	1	no	—
254	C₂×C₄²	—	13	1	no	—
255	C₂×C₄²	—	13	1	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	1	no	—
258	C₂×C₄²	—	13	1	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	—	13	2	no	—
262	C₂×C₄²	—	13	2	no	—
263	C₂×C₄²	—	13	2	no	—
264	C₂×C₄²	—	13	2	no	—
265	C₂×C₄²	—	13	4	no	—
266	C₂×C₄²	—	13	4	no	—
267	C₂×C₄²	—	13	4	no	—
268	C₂×C₄²	—	26	8	no	—
269	C₂×C₄²	—	26	8	no	—
270	C₂×C₄²	—	26	8	no	—
271	C₂×C₄²	C₂×#261	1	1	yes	characteristic
272	C₄⋊C₈	—	13	4	no	—
273	C₄⋊C₈	—	13	4	no	—
274	C₄⋊C₈	—	13	4	no	—
275	C₄⋊C₈	—	13	2	no	—
276	C₄⋊C₈	C₂×#261	1	2	yes	complemented
277	C₂²⋊C₈	—	13	4	no	—
278	C₂²⋊C₈	—	13	4	no	—
279	C₂²⋊C₈	—	13	2	no	—
280	C₂²⋊C₈	—	13	4	no	—
281	C₂²⋊C₈	C₂×#261	1	2	yes	—
282	#97	—	26	16	no	—
283	C₄×C₈	—	13	4	no	—
284	C₄×C₈	—	13	4	no	—
285	C₄×C₈	—	13	4	no	—
286	C₄×C₈	—	13	2	no	—
287	C₄×C₈	C₂×#261	1	2	yes	complemented
288	C₂×C₁₃	—	2	2	no	—
289	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
290	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
291	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
292	D₁₃	—	2	2	no	—
293	D₁₃	#2920	1	4	yes	—
294	C₂⁴	—	13	1	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	8	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	4	no	—
304	C₂²×C₄	—	13	4	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	26	4	no	—
314	C₂²×C₄	—	26	4	no	—
315	C₂²×C₄	—	26	8	no	—
316	C₂²×C₄	—	26	8	no	—
317	C₂²×C₄	—	26	8	no	—
318	C₂²×C₄	C₄×#261	1	1	yes	characteristic
319	C₂²×C₄	C₄×#261	1	1	yes	characteristic
320	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
321	C₂×C₈	—	13	8	no	—
322	C₂×C₈	—	13	4	no	—
323	C₂×C₈	—	26	8	no	—
324	C₂×C₈	—	26	8	no	—
325	C₂×C₈	C₂²×#261	1	4	yes	—
326	C₄²	—	13	8	no	—
327	C₄²	—	13	8	no	—
328	C₄²	—	13	1	no	—
329	C₄²	—	13	1	no	—
330	C₄²	—	13	1	no	—
331	C₄²	—	13	1	no	—
332	C₄²	—	13	1	no	—
333	C₄²	—	13	1	no	—
334	C₄²	—	13	1	no	—
335	C₄²	—	13	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	—	13	1	no	—
340	C₄²	—	26	4	no	—
341	C₄²	—	26	4	no	—
342	C₄²	—	26	8	no	—
343	C₄²	—	26	4	no	—
344	C₄²	—	26	4	no	—
345	C₄²	—	26	8	no	—
346	C₄²	—	26	8	no	—
347	C₄²	C₄×#261	1	1	yes	characteristic
348	C₄²	C₄×#261	1	1	yes	characteristic
349	C₄²	C₂²×#261	1	1	yes	characteristic
350	C₄²	C₂²×#261	1	1	yes	characteristic
351	C₁₃	#20463	1	1	yes	characteristic, complemented, Sylow
352	C₂³	—	13	1	no	—
353	C₂³	—	13	4	no	—
354	C₂³	—	13	1	no	—
355	C₂³	—	26	2	no	—
356	C₂³	—	26	2	no	—
357	C₂³	C₂×C₄×#261	1	1	yes	characteristic
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	13	4	no	—
361	C₂×C₄	—	13	1	no	—
362	C₂×C₄	—	13	1	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	13	1	no	—
365	C₂×C₄	—	13	4	no	—
366	C₂×C₄	—	13	4	no	—
367	C₂×C₄	—	13	4	no	—
368	C₂×C₄	—	13	4	no	—
369	C₂×C₄	—	13	4	no	—
370	C₂×C₄	—	13	4	no	—
371	C₂×C₄	—	13	8	no	—
372	C₂×C₄	—	13	8	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	26	2	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	26	2	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	2	no	—
380	C₂×C₄	—	26	2	no	—
381	C₂×C₄	—	26	4	no	—
382	C₂×C₄	—	26	4	no	—
383	C₂×C₄	—	26	4	no	—
384	C₂×C₄	—	26	4	no	—
385	C₂×C₄	—	26	32	no	—
386	C₂×C₄	—	26	2	no	—
387	C₂×C₄	—	26	2	no	—
388	C₂×C₄	#88100	1	4	yes	complemented
389	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
393	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
394	C₂×C₄	C₂³×#261	1	1	yes	characteristic
395	C₈	—	2	4	no	—
396	C₈	—	26	8	no	—
397	C₈	—	26	4	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	13	2	no	—
401	C₂²	—	13	2	no	—
402	C₂²	—	13	2	no	—
403	C₂²	—	13	2	no	—
404	C₂²	—	26	8	no	—
405	C₂²	—	26	1	no	—
406	C₂²	—	26	1	no	—
407	C₂²	C₂×#88100	1	2	yes	—
408	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	13	2	no	—
412	C₄	—	13	2	no	—
413	C₄	—	13	2	no	—
414	C₄	—	13	2	no	—
415	C₄	—	26	8	no	—
416	C₄	—	26	8	no	—
417	C₄	—	26	1	no	—
418	C₄	—	26	1	no	—
419	C₄	C₂×#88100	1	2	yes	—
420	C₄	C₂×#88100	1	2	yes	—
421	C₄	M₁₆×#261	1	2	yes	—
422	C₄	#41×#261	1	2	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	13	4	no	—
425	C₂	—	26	2	no	—
426	C₂	#117×#261	1	1	yes	characteristic
427	C₂	C₂²×#88100	1	1	yes	characteristic
428	C₂	C₂×M₁₆×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#431	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#20463
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130623	C₂	semidirect
5. #13130549	C₂	semidirect
6. C₄×#88100	C₂	semidirect
12. #11719125	C₄	semidirect
14. #11719119	C₄	semidirect
21. #11719051	C₄	semidirect
23. #11719049	C₄	semidirect
25. C₁₃×#431	C₄	semidirect
26. #11718586	C₄	semidirect
27. #11718494	C₄	semidirect
30. #11718379	C₄	semidirect
31. #11718346	C₄	semidirect
65. #88112	C₂×C₄	semidirect
67. C₄⋊#1057	C₂×C₄	semidirect
68. C₄×#1057	C₂×C₄	semidirect
69. C₄×#1057	C₂×C₄	semidirect
71. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
73. C₄×C₈×C₁₃	C₂×C₄	semidirect
76. #88054	C₂×C₄	semidirect
77. C₈×Dic₁₃	C₂×C₄	semidirect
78. C₄⋊#1055	C₂×C₄	semidirect
79. C₄×#1055	C₂×C₄	semidirect
160. C₂×C₄×C₁₃	#97	semidirect
169. C₂×Dic₁₃	#97	semidirect
182. C₄×D₁₃	#97	semidirect
183. C₄×D₁₃	#97	semidirect
203. #431	#261	semidirect
276. C₄⋊C₈	C₂×#261	semidirect
287. C₄×C₈	C₂×#261	semidirect
351. C₁₃	#20463	semidirect
388. C₂×C₄	#88100	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#431	2
C₂×C₄²×#261	2
#13130623	2
#13130564	2
#13130549	2
C₄×#88100	2
D₁₃×#431	2
#20463	13