Subgroups — #16797272

Order 3328.

1174 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	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×#88237	C₂	1	1	yes	maximal, characteristic
3	#13130629	C₂	1	4	yes	maximal, complemented
4	#13130571	C₂	1	4	yes	maximal
5	#13130549	C₂	1	2	yes	maximal, complemented
6	C₄×C₈×#261	C₂	1	2	yes	maximal, complemented
7	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
8	C₂×#88237	C₄	1	2	yes	—
9	C₂²×D₁₃⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	C₄×C₂²⋊#261	C₄	1	2	yes	—
12	C₄×C₂²⋊#261	C₂²	1	2	yes	—
13	C₂×C₄×#1057	C₄	1	2	yes	complemented
14	C₂×C₄×#1057	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	C₄×D₁₃⋊C₈	C₄	1	2	yes	complemented
21	C₄×D₁₃⋊C₈	C₄	1	2	yes	complemented
22	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
24	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
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	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
37	C₂×C₂²⋊#261	C₂×C₄	1	4	yes	—
38	C₂²×#1057	C₂×C₄	1	4	yes	—
39	#88237	C₈	1	16	yes	complemented
40	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
41	C₂×C₄×#261	C₂×C₄	1	4	yes	—
42	C₂×C₄×#261	C₂×C₄	1	4	yes	—
43	C₂×C₄×#261	C₂³	1	4	yes	—
44	C₂×D₁₃⋊C₈	—	2	8	no	—
45	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
46	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
47	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂³	1	4	yes	—
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	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂³	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
62	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
63	C₄×#1057	C₂×C₄	1	2	yes	—
64	C₄×#1057	C₂×C₄	1	2	yes	—
65	C₄×#1057	C₂×C₄	1	4	yes	—
66	C₄×#1057	C₂×C₄	1	4	yes	—
67	C₄×#1057	C₂×C₄	1	2	yes	—
68	C₄×#1057	C₂×C₄	1	2	yes	—
69	C₈×#261	—	2	16	no	—
70	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
71	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
72	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
73	C₂²⋊#1055	C₂×C₄	1	2	yes	—
74	#88060	C₂×C₄	1	4	yes	—
75	#88054	C₂×C₄	1	4	yes	—
76	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
77	C₄⋊#1055	C₂×C₄	1	2	yes	—
78	C₄×#1055	C₂×C₄	1	2	yes	—
79	C₈×#117	—	13	1	no	maximal, Sylow
80	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×#261	C₂²×C₄	1	8	yes	—
82	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
86	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
87	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	—	2	4	no	—
89	C₂×C₄×D₁₃	—	2	4	no	—
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	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
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	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
103	C₂²⋊#261	C₂×C₈	1	16	yes	—
104	C₂×#1057	—	2	8	no	—
105	C₂×#1057	C₂²×C₄	1	4	yes	—
106	C₂×#1057	C₂²×C₄	1	4	yes	—
107	C₄⋊#261	C₂×C₈	1	16	yes	complemented
108	C₄×#261	—	2	8	no	—
109	C₄×#261	—	2	8	no	—
110	C₄×#261	C₂×C₈	1	16	yes	complemented
111	D₁₃⋊C₈	—	2	4	no	—
112	D₁₃⋊C₈	—	2	8	no	—
113	D₁₃⋊C₈	#41	1	8	yes	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
115	C₄²×C₁₃	C₄²	1	1	yes	characteristic
116	C₄²×C₁₃	C₄²	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
120	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
121	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
122	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
123	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
124	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×#1055	C₂²×C₄	1	4	yes	—
132	C₈×D₁₃	—	2	8	no	—
133	C₂×#431	—	13	1	no	—
134	C₂²×C₄×C₈	—	13	1	no	—
135	C₄×#117	—	13	1	no	—
136	C₈×C₄⋊C₄	—	13	4	no	—
137	C₈×C₂²⋊C₄	—	13	4	no	—
138	#1744	—	13	2	no	—
139	C₄²×C₈	—	13	2	no	—
140	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
141	C₂²×D₁₃	—	2	2	no	—
142	C₂²×D₁₃	—	2	2	no	—
143	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
144	C₂²×D₁₃	C₂²×C₈	1	4	yes	—
145	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
146	C₂×#261	—	2	8	no	—
147	C₂×#261	—	2	8	no	—
148	C₂×#261	C₂²×C₈	1	16	yes	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	complemented
152	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
158	C₂×Dic₁₃	—	2	2	no	—
159	C₂×Dic₁₃	—	2	2	no	—
160	C₂×Dic₁₃	C₄×C₈	1	4	yes	complemented
161	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₄×D₁₃	—	2	2	no	—
168	C₄×D₁₃	—	2	2	no	—
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	2	2	no	—
171	C₄×D₁₃	—	2	2	no	—
172	C₄×D₁₃	—	2	2	no	—
173	C₄×D₁₃	C₄×C₈	1	4	yes	complemented
174	C₄×D₁₃	C₄×C₈	1	4	yes	complemented
175	C₄×D₁₃	C₂²×C₈	1	4	yes	—
176	C₄×D₁₃	C₂²×C₈	1	4	yes	—
177	C₄×D₁₃	#131	1	4	yes	—
178	C₄×D₁₃	C₂×#41	1	4	yes	—
179	#1057	—	2	4	no	—
180	#1057	#117	1	8	yes	complemented
181	C₈×C₁₃	—	2	4	no	—
182	#1055	—	2	4	no	—
183	C₂³×C₈	—	13	2	no	—
184	C₂×#117	—	13	2	no	—
185	C₂²×C₄²	—	13	1	no	—
186	#431	—	13	1	no	—
187	#431	—	13	2	no	—
188	#431	—	13	2	no	—
189	#431	—	13	2	no	—
190	#431	#261	1	1	yes	characteristic, complemented
191	C₂×C₄⋊C₈	—	13	2	no	—
192	C₂×C₂²⋊C₈	—	13	2	no	—
193	C₂×C₄×C₈	—	13	2	no	—
194	C₂×C₄×C₈	—	13	2	no	—
195	C₂×C₄×C₈	—	13	1	no	—
196	C₂×C₄×C₈	—	13	1	no	—
197	C₂×C₄×C₈	—	13	2	no	—
198	C₂×C₄×C₈	—	13	2	no	—
199	C₂×C₄×C₈	—	13	2	no	—
200	C₂×C₄×C₈	—	13	2	no	—
201	C₂×C₄×C₈	—	13	8	no	—
202	C₄×C₄⋊C₄	—	13	2	no	—
203	C₄×C₄⋊C₄	—	13	2	no	—
204	C₄×C₂²⋊C₄	—	13	2	no	—
205	C₄×C₂²⋊C₄	—	13	2	no	—
206	#376	—	13	2	no	—
207	C₄³	—	13	2	no	—
208	#336	—	13	8	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
212	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
213	C₂×D₁₃	—	2	1	no	—
214	C₂×D₁₃	—	2	1	no	—
215	C₂×D₁₃	—	2	8	no	—
216	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
217	C₂×D₁₃	C₄×#41	1	2	yes	—
218	C₂×D₁₃	C₂³×C₈	1	2	yes	—
219	C₂×D₁₃	C₂×#131	1	2	yes	—
220	#261	—	2	16	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
224	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
225	C₄×C₁₃	#405	1	2	yes	—
226	C₄×C₁₃	C₄×#41	1	2	yes	—
227	Dic₁₃	—	2	1	no	—
228	Dic₁₃	—	2	1	no	—
229	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
230	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
231	Dic₁₃	#405	1	2	yes	—
232	Dic₁₃	C₂×#117	1	2	yes	—
233	C₂³×C₄	—	13	1	no	—
234	C₂³×C₄	—	13	1	no	—
235	C₂³×C₄	—	13	1	no	—
236	C₂²×C₈	—	13	2	no	—
237	C₂²×C₈	—	13	2	no	—
238	C₂²×C₈	—	13	4	no	—
239	C₂²×C₈	—	13	4	no	—
240	C₂²×C₈	—	13	4	no	—
241	C₂²×C₈	—	26	8	no	—
242	#117	—	13	16	no	—
243	C₂×C₄⋊C₄	—	13	4	no	—
244	C₂×C₂²⋊C₄	—	13	4	no	—
245	C₂×C₄²	—	13	4	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	1	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	4	no	—
258	C₂×C₄²	—	13	4	no	—
259	C₂×C₄²	C₂×#261	1	1	yes	characteristic
260	C₄⋊C₈	—	13	4	no	—
261	C₄⋊C₈	—	13	2	no	—
262	C₄⋊C₈	C₂×#261	1	2	yes	—
263	C₂²⋊C₈	—	13	2	no	—
264	C₂²⋊C₈	—	13	4	no	—
265	C₂²⋊C₈	C₂×#261	1	2	yes	—
266	C₄×C₈	—	13	2	no	—
267	C₄×C₈	—	13	2	no	—
268	C₄×C₈	—	13	4	no	—
269	C₄×C₈	—	13	4	no	—
270	C₄×C₈	—	13	2	no	—
271	C₄×C₈	—	13	2	no	—
272	C₄×C₈	—	13	4	no	—
273	C₄×C₈	—	13	2	no	—
274	C₄×C₈	—	26	16	no	—
275	C₄×C₈	C₂×#261	1	2	yes	—
276	#95	—	13	4	no	—
277	#95	—	13	4	no	—
278	C₂×C₁₃	—	2	2	no	—
279	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
280	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
281	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
282	D₁₃	—	2	2	no	—
283	D₁₃	C₈×#41	1	4	yes	—
284	C₂⁴	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	8	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	8	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	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	26	4	no	—
303	C₂²×C₄	—	26	4	no	—
304	C₂²×C₄	C₄×#261	1	1	yes	characteristic
305	C₂²×C₄	C₄×#261	1	1	yes	characteristic
306	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
307	C₂×C₈	—	13	4	no	—
308	C₂×C₈	—	13	8	no	—
309	C₂×C₈	—	13	4	no	—
310	C₂×C₈	—	13	4	no	—
311	C₂×C₈	—	26	8	no	—
312	C₂×C₈	—	26	8	no	—
313	C₂×C₈	—	26	8	no	—
314	C₂×C₈	—	26	4	no	—
315	C₂×C₈	C₂²×#261	1	4	yes	—
316	C₄⋊C₄	—	13	16	no	—
317	C₂²⋊C₄	—	13	16	no	—
318	C₄²	—	13	16	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	—	13	1	no	—
330	C₄²	—	13	1	no	—
331	C₄²	—	26	8	no	—
332	C₄²	—	26	8	no	—
333	C₄²	C₄×#261	1	1	yes	characteristic
334	C₄²	C₄×#261	1	1	yes	characteristic
335	C₄²	C₂²×#261	1	1	yes	characteristic
336	C₄²	C₂²×#261	1	1	yes	characteristic
337	C₁₃	C₈×#117	1	1	yes	characteristic, complemented, Sylow
338	C₂³	—	13	1	no	—
339	C₂³	—	13	4	no	—
340	C₂³	—	13	1	no	—
341	C₂³	—	26	2	no	—
342	C₂³	—	26	2	no	—
343	C₂³	C₂×C₄×#261	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	13	4	no	—
347	C₂×C₄	—	13	1	no	—
348	C₂×C₄	—	13	1	no	—
349	C₂×C₄	—	13	1	no	—
350	C₂×C₄	—	13	1	no	—
351	C₂×C₄	—	13	4	no	—
352	C₂×C₄	—	13	4	no	—
353	C₂×C₄	—	13	4	no	—
354	C₂×C₄	—	13	4	no	—
355	C₂×C₄	—	13	4	no	—
356	C₂×C₄	—	13	4	no	—
357	C₂×C₄	—	13	16	no	—
358	C₂×C₄	—	13	1	no	—
359	C₂×C₄	—	13	1	no	—
360	C₂×C₄	—	26	2	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	2	no	—
366	C₂×C₄	—	26	8	no	—
367	C₂×C₄	—	26	8	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	—	26	2	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	—	13	8	no	—
379	C₈	—	26	4	no	—
380	C₈	—	26	4	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	13	2	no	—
384	C₂²	—	13	2	no	—
385	C₂²	—	13	2	no	—
386	C₂²	—	13	2	no	—
387	C₂²	—	26	8	no	—
388	C₂²	—	26	1	no	—
389	C₂²	—	26	1	no	—
390	C₂²	C₂×C₈×#261	1	2	yes	—
391	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
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	—	13	2	no	—
398	C₄	—	26	16	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	#11719099	1	2	yes	—
404	C₄	#41×#261	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	13	4	no	—
407	C₂	—	26	2	no	—
408	C₂	#117×#261	1	1	yes	characteristic
409	C₂	C₂²×C₈×#261	1	1	yes	characteristic
410	C₂	C₂×#11719099	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#431	C₄
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	C₈×#117
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130629	C₂	semidirect
5. #13130549	C₂	semidirect
6. C₄×C₈×#261	C₂	semidirect
13. C₂×C₄×#1057	C₄	semidirect
14. C₂×C₄×#1057	C₄	semidirect
20. C₄×D₁₃⋊C₈	C₄	semidirect
21. C₄×D₁₃⋊C₈	C₄	semidirect
25. C₁₃×#431	C₄	semidirect
26. #11718586	C₄	semidirect
27. #11718494	C₄	semidirect
30. #11718379	C₄	semidirect
31. #11718346	C₄	semidirect
39. #88237	C₈	semidirect
107. C₄⋊#261	C₂×C₈	semidirect
110. C₄×#261	C₂×C₈	semidirect
151. C₂×C₄×C₁₃	C₄×C₈	semidirect
160. C₂×Dic₁₃	C₄×C₈	semidirect
173. C₄×D₁₃	C₄×C₈	semidirect
174. C₄×D₁₃	C₄×C₈	semidirect
180. #1057	#117	semidirect
190. #431	#261	semidirect
337. C₁₃	C₈×#117	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
C₂×C₄×D₁₃⋊C₈	2
C₄×#88237	2
#13130629	2
#13130571	2
#13130549	2
C₄×C₈×#261	2
D₁₃×#431	2
C₈×#117	13