Subgroups — #16797566

Order 3328.

1090 conjugacy classes of subgroups.

The subgroup lattice has 412 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	C₄×#88237	C₂	1	1	yes	maximal, characteristic
3	#13130629	C₂	1	4	yes	maximal, complemented
4	C₄⋊C₈×#261	C₂	1	4	yes	maximal, complemented
5	C₈×C₂²⋊#261	C₂	1	4	yes	maximal
6	C₂×D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	C₄	1	2	yes	—
8	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	C₄×C₂²⋊#261	C₄	1	2	yes	—
11	C₄×C₂²⋊#261	C₂²	1	2	yes	—
12	#11719125	C₄	1	2	yes	complemented
13	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
14	#11719119	C₄	1	2	yes	complemented
15	C₂×C₈×#261	C₂²	1	8	yes	—
16	C₄×C₄⋊#261	C₄	1	2	yes	—
17	C₄×C₄⋊#261	C₂²	1	2	yes	—
18	#11719057	C₄	1	2	yes	—
19	C₄²×#261	C₂²	1	2	yes	—
20	#11719051	C₄	1	2	yes	complemented
21	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
22	#11719049	C₄	1	2	yes	complemented
23	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
25	C₂×#88054	C₄	1	2	yes	complemented
26	C₂×C₄⋊#1055	C₄	1	1	yes	characteristic, complemented
27	D₁₃×C₄⋊C₈	C₄	1	2	yes	complemented
28	D₁₃×C₄⋊C₈	C₄	1	2	yes	complemented
29	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
30	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
31	(C₂×#261)⋊C₈	C₂²	1	8	yes	—
32	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
35	C₂×C₂²⋊#261	C₂×C₄	1	4	yes	—
36	#88237	C₈	1	16	yes	complemented
37	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
38	C₂×C₄×#261	C₂×C₄	1	4	yes	—
39	C₂×C₄×#261	C₂×C₄	1	4	yes	—
40	C₂×C₄×#261	C₂³	1	4	yes	—
41	C₂×D₁₃⋊C₈	C₂³	1	4	yes	—
42	C₂²×C₈×C₁₃	C₂×C₄	1	2	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	C₂²×#1055	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₁₃	—	4	4	no	—
49	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
50	C₂×C₈×D₁₃	C₂³	1	4	yes	—
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	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂³	1	1	yes	characteristic
58	C₄²×D₁₃	C₂³	1	1	yes	characteristic
59	C₂²⋊#1057	C₂×C₄	1	4	yes	—
60	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
61	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
62	#88112	C₂×C₄	1	4	yes	—
63	#88111	C₂×C₄	1	4	yes	—
64	C₄⋊#1057	C₂×C₄	1	4	yes	—
65	C₄×#1057	C₂×C₄	1	4	yes	—
66	C₄×#1057	C₂×C₄	1	4	yes	—
67	C₈×#261	—	4	8	no	—
68	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
69	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	#88054	C₂×C₄	1	4	yes	—
71	#88054	C₂×C₄	1	4	yes	—
72	C₄⋊#1055	C₂×C₄	1	2	yes	—
73	C₄⋊#1055	C₂×C₄	1	2	yes	—
74	#20543	—	13	1	no	maximal, Sylow
75	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×#261	C₂²×C₄	1	8	yes	—
77	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
81	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
82	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₃	—	2	2	no	—
84	C₂×C₄×D₁₃	—	2	2	no	—
85	C₂×C₄×D₁₃	—	4	2	no	—
86	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
91	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
99	C₂²⋊#261	C₂×C₈	1	16	yes	—
100	C₂×#1057	C₂²×C₄	1	8	yes	—
101	C₄⋊#261	C₂×C₈	1	16	yes	complemented
102	C₄×#261	—	2	4	no	—
103	C₄×#261	—	2	4	no	—
104	C₄×#261	—	4	4	no	—
105	C₄×#261	C₂×C₈	1	16	yes	complemented
106	D₁₃⋊C₈	—	2	4	no	—
107	D₁₃⋊C₈	—	2	4	no	—
108	C₂×C₈×C₁₃	—	4	2	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	—	4	2	no	—
127	C₂×#1055	C₂²×C₄	1	4	yes	—
128	C₈×D₁₃	—	2	8	no	—
129	C₈×D₁₃	—	4	4	no	—
130	C₂×#431	—	13	1	no	—
131	C₂²×C₄⋊C₈	—	13	1	no	—
132	C₄×#117	—	13	1	no	—
133	C₈×C₄⋊C₄	—	13	4	no	—
134	C₄×C₄⋊C₈	—	13	4	no	—
135	C₈×C₂²⋊C₄	—	13	4	no	—
136	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
137	C₂²×D₁₃	—	2	2	no	—
138	C₂²×D₁₃	—	2	2	no	—
139	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
140	C₂²×D₁₃	C₂²×C₈	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	C₂²×C₈	1	16	yes	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	C₄×C₈	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	C₄×C₈	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	2	no	—
165	C₄×D₁₃	—	2	2	no	—
166	C₄×D₁₃	—	2	2	no	—
167	C₄×D₁₃	—	2	1	no	—
168	C₄×D₁₃	—	2	1	no	—
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	4	1	no	—
171	C₄×D₁₃	—	4	1	no	—
172	C₄×D₁₃	C₄×C₈	1	4	yes	complemented
173	C₄×D₁₃	C₄×C₈	1	4	yes	complemented
174	C₄×D₁₃	C₂²×C₈	1	4	yes	—
175	C₄×D₁₃	C₂²×C₈	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	C₂³×C₈	—	13	2	no	—
182	C₂×#117	—	13	2	no	—
183	C₂²×C₄²	—	13	1	no	—
184	#431	—	13	2	no	—
185	#431	—	13	2	no	—
186	#431	—	13	2	no	—
187	#431	—	13	2	no	—
188	C₂×C₄⋊C₈	—	13	2	no	—
189	C₂×C₄⋊C₈	—	13	2	no	—
190	C₂×C₄⋊C₈	—	13	1	no	—
191	C₂×C₄⋊C₈	—	13	2	no	—
192	C₂×C₄⋊C₈	—	13	2	no	—
193	C₂×C₄⋊C₈	—	13	2	no	—
194	C₂×C₄⋊C₈	—	13	2	no	—
195	C₂×C₄⋊C₈	#261	1	1	yes	characteristic, complemented
196	C₂×C₂²⋊C₈	—	13	2	no	—
197	C₂×C₄×C₈	—	13	2	no	—
198	C₂×C₄×C₈	—	13	8	no	—
199	C₄×C₄⋊C₄	—	13	2	no	—
200	C₄×C₄⋊C₄	—	13	2	no	—
201	C₄×C₂²⋊C₄	—	13	2	no	—
202	C₄×C₂²⋊C₄	—	13	2	no	—
203	#376	—	13	2	no	—
204	C₄³	—	13	2	no	—
205	#336	—	13	8	no	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	2	1	no	—
208	C₂²×C₁₃	C₂×C₄×C₈	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	8	no	—
213	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
214	C₂×D₁₃	#520	1	2	yes	—
215	C₂×D₁₃	C₂³×C₈	1	2	yes	—
216	C₂×D₁₃	#568	1	2	yes	—
217	#261	—	2	16	no	—
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	1	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
222	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
223	C₄×C₁₃	#518	1	1	yes	characteristic
224	C₄×C₁₃	#519	1	1	yes	characteristic
225	Dic₁₃	—	2	1	no	—
226	Dic₁₃	—	2	1	no	—
227	Dic₁₃	—	2	1	no	—
228	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
229	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
230	Dic₁₃	#520	1	2	yes	—
231	C₂³×C₄	—	13	1	no	—
232	C₂³×C₄	—	13	1	no	—
233	C₂³×C₄	—	13	1	no	—
234	C₂²×C₈	—	13	4	no	—
235	C₂²×C₈	—	13	2	no	—
236	C₂²×C₈	—	13	4	no	—
237	C₂²×C₈	—	13	4	no	—
238	C₂²×C₈	—	52	4	no	—
239	C₂²×C₈	C₂×#261	1	2	yes	—
240	#117	—	13	16	no	—
241	C₂×C₄⋊C₄	—	13	4	no	—
242	C₂×C₂²⋊C₄	—	13	4	no	—
243	C₂×C₄²	—	13	4	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	1	no	—
253	C₂×C₄²	—	13	1	no	—
254	C₂×C₄²	—	13	1	no	—
255	C₂×C₄²	—	13	4	no	—
256	C₂×C₄²	—	13	4	no	—
257	C₂×C₄²	C₂×#261	1	1	yes	characteristic
258	C₄⋊C₈	—	13	4	no	—
259	C₄⋊C₈	—	13	4	no	—
260	C₄⋊C₈	—	13	4	no	—
261	C₄⋊C₈	—	13	4	no	—
262	C₄⋊C₈	—	13	2	no	—
263	C₄⋊C₈	—	13	2	no	—
264	C₄⋊C₈	C₂×#261	1	2	yes	—
265	C₄⋊C₈	C₂×#261	1	2	yes	—
266	C₂²⋊C₈	—	13	4	no	—
267	C₂²⋊C₈	—	13	4	no	—
268	C₄×C₈	—	13	4	no	—
269	C₄×C₈	—	13	4	no	—
270	C₄×C₈	—	52	8	no	—
271	#95	—	13	4	no	—
272	#95	—	13	4	no	—
273	C₂×C₁₃	—	2	2	no	—
274	C₂×C₁₃	#2274	1	1	yes	characteristic
275	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
276	C₂×C₁₃	#2873	1	1	yes	characteristic
277	D₁₃	—	2	2	no	—
278	D₁₃	#2988	1	4	yes	—
279	C₂⁴	—	13	1	no	—
280	C₂²×C₄	—	13	1	no	—
281	C₂²×C₄	—	13	8	no	—
282	C₂²×C₄	—	13	1	no	—
283	C₂²×C₄	—	13	1	no	—
284	C₂²×C₄	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	8	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	—	26	2	no	—
298	C₂²×C₄	—	26	2	no	—
299	C₂²×C₄	—	52	2	no	—
300	C₂²×C₄	C₄×#261	1	1	yes	characteristic
301	C₂²×C₄	C₄×#261	1	1	yes	characteristic
302	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	13	8	no	—
305	C₂×C₈	—	13	4	no	—
306	C₂×C₈	—	26	8	no	—
307	C₂×C₈	—	26	4	no	—
308	C₂×C₈	—	26	4	no	—
309	C₂×C₈	—	52	4	no	—
310	C₂×C₈	—	52	2	no	—
311	C₂×C₈	C₂²×#261	1	4	yes	—
312	C₄⋊C₄	—	13	16	no	—
313	C₂²⋊C₄	—	13	16	no	—
314	C₄²	—	13	16	no	—
315	C₄²	—	13	1	no	—
316	C₄²	—	13	1	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	—	26	4	no	—
328	C₄²	—	26	4	no	—
329	C₄²	—	52	4	no	—
330	C₄²	C₄×#261	1	1	yes	characteristic
331	C₄²	C₄×#261	1	1	yes	characteristic
332	C₄²	C₂²×#261	1	1	yes	characteristic
333	C₄²	C₂²×#261	1	1	yes	characteristic
334	C₁₃	#20543	1	1	yes	characteristic, complemented, Sylow
335	C₂³	—	13	1	no	—
336	C₂³	—	13	4	no	—
337	C₂³	—	13	1	no	—
338	C₂³	—	26	2	no	—
339	C₂³	—	26	2	no	—
340	C₂³	C₂×C₄×#261	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	13	4	no	—
345	C₂×C₄	—	13	1	no	—
346	C₂×C₄	—	13	1	no	—
347	C₂×C₄	—	13	1	no	—
348	C₂×C₄	—	13	4	no	—
349	C₂×C₄	—	13	4	no	—
350	C₂×C₄	—	13	4	no	—
351	C₂×C₄	—	13	4	no	—
352	C₂×C₄	—	13	2	no	—
353	C₂×C₄	—	13	2	no	—
354	C₂×C₄	—	13	16	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	2	no	—
360	C₂×C₄	—	26	2	no	—
361	C₂×C₄	—	26	2	no	—
362	C₂×C₄	—	26	2	no	—
363	C₂×C₄	—	26	8	no	—
364	C₂×C₄	—	26	8	no	—
365	C₂×C₄	—	26	1	no	—
366	C₂×C₄	—	26	1	no	—
367	C₂×C₄	—	52	1	no	—
368	C₂×C₄	—	52	1	no	—
369	C₂×C₄	—	52	1	no	—
370	C₂×C₄	C₈×#261	1	4	yes	complemented
371	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
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	C₂³×#261	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	26	8	no	—
379	C₈	—	26	4	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	13	2	no	—
383	C₂²	—	13	2	no	—
384	C₂²	—	13	2	no	—
385	C₂²	—	13	2	no	—
386	C₂²	—	26	8	no	—
387	C₂²	—	26	1	no	—
388	C₂²	—	26	1	no	—
389	C₂²	C₂×C₈×#261	1	2	yes	—
390	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	13	2	no	—
395	C₄	—	13	2	no	—
396	C₄	—	13	2	no	—
397	C₄	—	26	16	no	—
398	C₄	—	26	1	no	—
399	C₄	—	26	1	no	—
400	C₄	—	26	1	no	—
401	C₄	C₂×C₈×#261	1	2	yes	—
402	C₄	C₂×C₈×#261	1	2	yes	—
403	C₄	#11719623	1	1	yes	characteristic
404	C₄	#11719627	1	1	yes	characteristic
405	C₂	—	2	2	no	—
406	C₂	—	13	4	no	—
407	C₂	—	26	2	no	—
408	C₂	#13131274	1	1	yes	characteristic
409	C₂	C₂²×C₈×#261	1	1	yes	characteristic
410	C₂	#13131399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Fitting	C₂×C₁₃×C₄⋊C₈	C₄
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄⋊C₈	#261
hypocenter	C₁₃	#20543
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13130629	C₂	semidirect
4. C₄⋊C₈×#261	C₂	semidirect
12. #11719125	C₄	semidirect
14. #11719119	C₄	semidirect
20. #11719051	C₄	semidirect
22. #11719049	C₄	semidirect
24. C₂×C₁₃×C₄⋊C₈	C₄	semidirect
25. C₂×#88054	C₄	semidirect
26. C₂×C₄⋊#1055	C₄	semidirect
27. D₁₃×C₄⋊C₈	C₄	semidirect
28. D₁₃×C₄⋊C₈	C₄	semidirect
36. #88237	C₈	semidirect
101. C₄⋊#261	C₂×C₈	semidirect
105. C₄×#261	C₂×C₈	semidirect
148. C₂×C₄×C₁₃	C₄×C₈	semidirect
157. C₂×Dic₁₃	C₄×C₈	semidirect
172. C₄×D₁₃	C₄×C₈	semidirect
173. C₄×D₁₃	C₄×C₈	semidirect
195. C₂×C₄⋊C₈	#261	semidirect
334. C₁₃	#20543	semidirect
370. C₂×C₄	C₈×#261	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
C₄×#88237	2
#13130629	2
C₄⋊C₈×#261	2
C₈×C₂²⋊#261	2
C₂×D₁₃×C₄⋊C₈	2
#20543	13