Subgroups — #16797537

Order 3328.

1026 conjugacy classes of subgroups.

The subgroup lattice has 416 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×C₄×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
3	#13130633	C₂	1	4	yes	maximal, complemented
4	#13130630	C₂	1	4	yes	maximal, complemented
5	#13130564	C₂	1	4	yes	maximal
6	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄⋊#261	C₄	1	2	yes	—
8	C₂²×C₄×#261	C₂²	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×(C₂×#261)⋊C₄	C₄	1	2	yes	—
11	#11719125	C₄	1	2	yes	complemented
12	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
13	#11719119	C₄	1	2	yes	complemented
14	C₂×#88100	C₂²	1	8	yes	—
15	C₄×C₄⋊#261	C₄	1	2	yes	—
16	C₄×C₄⋊#261	C₄	1	2	yes	—
17	C₄×C₄⋊#261	C₂²	1	2	yes	—
18	C₄×C₄⋊#261	C₂²	1	2	yes	—
19	#11719051	C₄	1	2	yes	complemented
20	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
21	#11719049	C₄	1	2	yes	complemented
22	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
23	C₁₃×#431	C₄	1	1	yes	characteristic, complemented
24	#11718586	C₄	1	1	yes	characteristic, complemented
25	#11718494	C₄	1	2	yes	complemented
26	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
27	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	#11718379	C₄	1	2	yes	complemented
29	#11718346	C₄	1	2	yes	complemented
30	C₄×C₈×D₁₃	C₂²	1	2	yes	—
31	(C₂×#261)⋊C₈	C₂²	1	8	yes	—
32	C₂³×#261	C₂×C₄	1	4	yes	—
33	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊#261	—	2	8	no	—
37	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
38	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
39	C₂×C₄×#261	—	4	4	no	—
40	C₂×C₄×#261	C₂×C₄	1	4	yes	—
41	C₂×C₄×#261	C₂³	1	4	yes	—
42	C₂×D₁₃⋊C₈	C₂³	1	4	yes	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	C₂³	1	4	yes	—
48	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	C₂³	1	1	yes	characteristic
55	C₄²×D₁₃	C₂³	1	1	yes	characteristic
56	C₂²⋊#1057	C₂×C₄	1	4	yes	—
57	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
58	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
59	#88112	C₂×C₄	1	4	yes	complemented
60	#88111	C₂×C₄	1	4	yes	—
61	C₄⋊#1057	C₂×C₄	1	4	yes	complemented
62	C₄×#1057	C₂×C₄	1	4	yes	complemented
63	C₄×#1057	C₂×C₄	1	4	yes	complemented
64	#88100	—	4	8	no	—
65	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
66	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
68	C₂²⋊#1055	C₂×C₄	1	2	yes	—
69	#88060	C₂×C₄	1	4	yes	—
70	#88054	C₂×C₄	1	4	yes	complemented
71	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
72	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
73	C₄×#1055	C₂×C₄	1	2	yes	complemented
74	#20536	—	13	1	no	maximal, Sylow
75	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×#261	—	2	8	no	—
77	C₂²×#261	—	4	4	no	—
78	C₂²×#261	—	4	4	no	—
79	C₂²×#261	C₂²×C₄	1	8	yes	—
80	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
84	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	—	2	2	no	—
87	C₂×C₄×D₁₃	—	2	2	no	—
88	C₂×C₄×D₁₃	—	4	2	no	—
89	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₁₃	M₁₆	1	8	yes	—
94	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
102	C₂×#1057	C₂²×C₄	1	8	yes	—
103	C₄⋊#261	—	2	8	no	—
104	C₄⋊#261	—	2	8	no	—
105	C₄×#261	—	2	8	no	—
106	C₄×#261	—	4	4	no	—
107	D₁₃⋊C₈	—	2	4	no	—
108	D₁₃⋊C₈	—	2	4	no	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
110	C₄²×C₁₃	C₄²	1	1	yes	characteristic
111	C₄²×C₁₃	C₄²	1	1	yes	characteristic
112	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
115	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
116	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
117	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
120	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×#1055	C₂²×C₄	1	4	yes	—
127	C₈×D₁₃	—	2	4	no	—
128	C₈×D₁₃	—	2	4	no	—
129	C₂×#431	—	13	1	no	—
130	C₂×#431	—	13	1	no	—
131	C₂×C₄×C₄⋊C₄	—	13	1	no	—
132	#1770	—	13	4	no	—
133	#1770	—	13	4	no	—
134	#1749	—	13	4	no	—
135	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
136	C₂²×D₁₃	—	2	1	no	—
137	C₂²×D₁₃	—	2	1	no	—
138	C₂²×D₁₃	—	2	2	no	—
139	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
140	C₂²×D₁₃	C₂×M₁₆	1	4	yes	—
141	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
142	C₂×#261	—	2	8	no	—
143	C₂×#261	—	2	8	no	—
144	C₂×#261	—	2	8	no	—
145	C₂×#261	—	4	16	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	#97	1	4	yes	complemented
149	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×Dic₁₃	—	2	2	no	—
156	C₂×Dic₁₃	—	4	1	no	—
157	C₂×Dic₁₃	#97	1	4	yes	complemented
158	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
164	C₄×D₁₃	—	2	1	no	—
165	C₄×D₁₃	—	2	1	no	—
166	C₄×D₁₃	—	2	2	no	—
167	C₄×D₁₃	—	2	2	no	—
168	C₄×D₁₃	—	2	2	no	—
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	4	1	no	—
171	C₄×D₁₃	—	4	1	no	—
172	C₄×D₁₃	#97	1	4	yes	complemented
173	C₄×D₁₃	#97	1	4	yes	complemented
174	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
175	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
176	C₄×D₁₃	H(5,𝔽₂)	1	2	yes	—
177	C₄×D₁₃	2₋¹⁺⁴	1	2	yes	—
178	#1057	—	2	8	no	—
179	C₈×C₁₃	—	2	4	no	—
180	#1055	—	2	4	no	—
181	C₂²×C₄⋊C₄	—	13	2	no	—
182	C₂²×C₄²	—	13	1	no	—
183	C₂²×C₄²	—	13	2	no	—
184	#431	—	13	2	no	—
185	#431	—	13	2	no	—
186	#431	—	13	2	no	—
187	#431	—	13	2	no	—
188	#431	—	13	1	no	—
189	#431	—	13	2	no	—
190	#431	—	13	2	no	—
191	#431	—	13	2	no	—
192	#431	#261	1	1	yes	characteristic, complemented
193	C₂×C₄⋊C₈	—	13	2	no	—
194	C₂×C₄⋊C₈	—	13	2	no	—
195	C₂×C₂²⋊C₈	—	13	2	no	—
196	C₂×C₂²⋊C₈	—	13	2	no	—
197	C₂×#97	—	13	8	no	—
198	C₂×C₄×C₈	—	13	2	no	—
199	C₂×C₄×C₈	—	13	2	no	—
200	C₄×C₄⋊C₄	—	13	2	no	—
201	C₄×C₄⋊C₄	—	13	2	no	—
202	C₄×C₄⋊C₄	—	13	2	no	—
203	C₄×C₄⋊C₄	—	13	2	no	—
204	C₂×#95	—	13	2	no	—
205	#336	—	13	8	no	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	2	1	no	—
208	C₂²×C₁₃	C₂×#97	1	2	yes	—
209	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
210	C₂×D₁₃	—	2	1	no	—
211	C₂×D₁₃	—	2	1	no	—
212	C₂×D₁₃	—	2	4	no	—
213	C₂×D₁₃	—	2	4	no	—
214	C₂×D₁₃	C₂×#97	1	2	yes	—
215	C₂×D₁₃	#518	1	1	yes	characteristic
216	C₂×D₁₃	#519	1	1	yes	characteristic
217	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
218	C₂×D₁₃	#568	1	2	yes	—
219	#261	—	4	8	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	C₂×#97	1	2	yes	—
224	C₄×C₁₃	C₂×#97	1	2	yes	—
225	C₄×C₁₃	#520	1	2	yes	—
226	Dic₁₃	—	2	1	no	—
227	Dic₁₃	—	2	1	no	—
228	Dic₁₃	—	2	1	no	—
229	Dic₁₃	C₂×#97	1	2	yes	—
230	Dic₁₃	C₂×#97	1	2	yes	—
231	Dic₁₃	#520	1	2	yes	—
232	C₂³×C₄	—	13	1	no	—
233	C₂³×C₄	—	13	1	no	—
234	C₂³×C₄	—	13	1	no	—
235	C₂³×C₄	—	13	4	no	—
236	C₂²×C₈	—	13	4	no	—
237	C₂²×C₈	—	13	4	no	—
238	C₂×C₄⋊C₄	—	13	4	no	—
239	C₂×C₄⋊C₄	—	13	4	no	—
240	C₂×C₄⋊C₄	—	26	8	no	—
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₄²	—	13	1	no	—
243	C₂×C₄²	—	13	1	no	—
244	C₂×C₄²	—	13	1	no	—
245	C₂×C₄²	—	13	1	no	—
246	C₂×C₄²	—	13	1	no	—
247	C₂×C₄²	—	13	1	no	—
248	C₂×C₄²	—	13	1	no	—
249	C₂×C₄²	—	13	1	no	—
250	C₂×C₄²	—	13	1	no	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	—	13	4	no	—
253	C₂×C₄²	—	13	4	no	—
254	C₂×C₄²	—	52	4	no	—
255	C₂×C₄²	C₂×#261	1	1	yes	characteristic
256	C₄⋊C₈	—	13	4	no	—
257	C₄⋊C₈	—	13	4	no	—
258	C₄⋊C₈	—	13	4	no	—
259	C₄⋊C₈	—	13	2	no	—
260	C₄⋊C₈	C₂×#261	1	2	yes	complemented
261	C₂²⋊C₈	—	13	4	no	—
262	C₂²⋊C₈	—	13	4	no	—
263	C₂²⋊C₈	—	13	2	no	—
264	C₂²⋊C₈	—	13	4	no	—
265	C₂²⋊C₈	C₂×#261	1	2	yes	—
266	#97	—	52	8	no	—
267	C₄×C₈	—	13	4	no	—
268	C₄×C₈	—	13	4	no	—
269	C₄×C₈	—	13	4	no	—
270	C₄×C₈	—	13	2	no	—
271	C₄×C₈	C₂×#261	1	2	yes	complemented
272	#95	—	13	4	no	—
273	#95	—	13	4	no	—
274	C₂×C₁₃	—	2	2	no	—
275	C₂×C₁₃	#2274	1	1	yes	characteristic
276	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
277	C₂×C₁₃	#2873	1	1	yes	characteristic
278	D₁₃	—	2	2	no	—
279	D₁₃	#2975	1	2	yes	—
280	D₁₃	#2983	1	2	yes	—
281	C₂⁴	—	13	1	no	—
282	C₂²×C₄	—	13	1	no	—
283	C₂²×C₄	—	13	8	no	—
284	C₂²×C₄	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	1	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	1	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	8	no	—
299	C₂²×C₄	—	26	2	no	—
300	C₂²×C₄	—	26	2	no	—
301	C₂²×C₄	—	26	8	no	—
302	C₂²×C₄	—	52	2	no	—
303	C₂²×C₄	—	52	4	no	—
304	C₂²×C₄	—	52	4	no	—
305	C₂²×C₄	C₄×#261	1	1	yes	characteristic
306	C₂²×C₄	C₄×#261	1	1	yes	characteristic
307	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
308	C₂×C₈	—	13	8	no	—
309	C₂×C₈	—	13	4	no	—
310	C₂×C₈	—	26	4	no	—
311	C₂×C₈	—	26	4	no	—
312	C₂×C₈	—	26	4	no	—
313	C₂×C₈	—	26	4	no	—
314	C₂×C₈	C₂²×#261	1	4	yes	—
315	C₄⋊C₄	—	26	8	no	—
316	C₄⋊C₄	—	26	8	no	—
317	C₄²	—	13	1	no	—
318	C₄²	—	13	1	no	—
319	C₄²	—	13	1	no	—
320	C₄²	—	13	1	no	—
321	C₄²	—	13	1	no	—
322	C₄²	—	13	1	no	—
323	C₄²	—	13	1	no	—
324	C₄²	—	13	1	no	—
325	C₄²	—	13	1	no	—
326	C₄²	—	13	1	no	—
327	C₄²	—	13	1	no	—
328	C₄²	—	13	1	no	—
329	C₄²	—	26	8	no	—
330	C₄²	—	52	4	no	—
331	C₄²	C₄×#261	1	1	yes	characteristic
332	C₄²	C₄×#261	1	1	yes	characteristic
333	C₄²	C₂²×#261	1	1	yes	characteristic
334	C₄²	C₂²×#261	1	1	yes	characteristic
335	C₁₃	#20536	1	1	yes	characteristic, complemented, Sylow
336	C₂³	—	13	1	no	—
337	C₂³	—	13	4	no	—
338	C₂³	—	13	1	no	—
339	C₂³	—	26	1	no	—
340	C₂³	—	26	1	no	—
341	C₂³	—	26	2	no	—
342	C₂³	C₂×C₄×#261	1	1	yes	characteristic
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	13	4	no	—
346	C₂×C₄	—	13	1	no	—
347	C₂×C₄	—	13	1	no	—
348	C₂×C₄	—	13	1	no	—
349	C₂×C₄	—	13	4	no	—
350	C₂×C₄	—	13	4	no	—
351	C₂×C₄	—	13	4	no	—
352	C₂×C₄	—	13	4	no	—
353	C₂×C₄	—	13	2	no	—
354	C₂×C₄	—	13	2	no	—
355	C₂×C₄	—	13	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	1	no	—
358	C₂×C₄	—	26	2	no	—
359	C₂×C₄	—	26	1	no	—
360	C₂×C₄	—	26	1	no	—
361	C₂×C₄	—	26	2	no	—
362	C₂×C₄	—	26	2	no	—
363	C₂×C₄	—	26	2	no	—
364	C₂×C₄	—	26	2	no	—
365	C₂×C₄	—	26	8	no	—
366	C₂×C₄	—	26	8	no	—
367	C₂×C₄	—	26	8	no	—
368	C₂×C₄	—	52	1	no	—
369	C₂×C₄	—	52	1	no	—
370	C₂×C₄	—	52	1	no	—
371	C₂×C₄	—	52	16	no	—
372	C₂×C₄	#88100	1	4	yes	complemented
373	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
378	C₂×C₄	C₂³×#261	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	26	8	no	—
381	C₈	—	26	4	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	13	1	no	—
385	C₂²	—	13	1	no	—
386	C₂²	—	13	2	no	—
387	C₂²	—	13	2	no	—
388	C₂²	—	13	2	no	—
389	C₂²	—	26	4	no	—
390	C₂²	—	26	4	no	—
391	C₂²	—	26	1	no	—
392	C₂²	—	26	1	no	—
393	C₂²	C₂×#88100	1	2	yes	—
394	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	13	2	no	—
399	C₄	—	13	2	no	—
400	C₄	—	13	2	no	—
401	C₄	—	26	1	no	—
402	C₄	—	26	1	no	—
403	C₄	—	26	1	no	—
404	C₄	—	52	8	no	—
405	C₄	C₂×#88100	1	2	yes	—
406	C₄	C₂×#88100	1	2	yes	—
407	C₄	#11719631	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	13	2	no	—
410	C₂	—	13	2	no	—
411	C₂	—	26	2	no	—
412	C₂	#13131273	1	1	yes	characteristic
413	C₂	C₂²×#88100	1	1	yes	characteristic
414	C₂	#13131399	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	#20536
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. #13130633	C₂	semidirect
4. #13130630	C₂	semidirect
11. #11719125	C₄	semidirect
13. #11719119	C₄	semidirect
19. #11719051	C₄	semidirect
21. #11719049	C₄	semidirect
23. C₁₃×#431	C₄	semidirect
24. #11718586	C₄	semidirect
25. #11718494	C₄	semidirect
28. #11718379	C₄	semidirect
29. #11718346	C₄	semidirect
59. #88112	C₂×C₄	semidirect
61. C₄⋊#1057	C₂×C₄	semidirect
62. C₄×#1057	C₂×C₄	semidirect
63. C₄×#1057	C₂×C₄	semidirect
65. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
67. C₄×C₈×C₁₃	C₂×C₄	semidirect
70. #88054	C₂×C₄	semidirect
71. C₈×Dic₁₃	C₂×C₄	semidirect
72. C₄⋊#1055	C₂×C₄	semidirect
73. C₄×#1055	C₂×C₄	semidirect
148. C₂×C₄×C₁₃	#97	semidirect
157. C₂×Dic₁₃	#97	semidirect
172. C₄×D₁₃	#97	semidirect
173. C₄×D₁₃	#97	semidirect
192. #431	#261	semidirect
260. C₄⋊C₈	C₂×#261	semidirect
271. C₄×C₈	C₂×#261	semidirect
335. C₁₃	#20536	semidirect
372. 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×C₄×C₄⋊#261	2
#13130633	2
#13130630	2
#13130564	2
D₁₃×#431	2
#20536	13