Subgroups — #15861806

Order 3328.

1222 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718495	C₂	1	1	yes	maximal, characteristic
3	C₄×#88147	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#6103	C₂	1	2	yes	maximal, complemented
7	#13114606	C₂	1	2	yes	maximal, complemented
8	C₄×#88060	C₂	1	2	yes	maximal, complemented
9	#13114581	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×#336	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
13	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
14	C₂×#88147	C₄	1	2	yes	—
15	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₁₃	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×#88060	C₂²	1	2	yes	—
22	C₂×#88060	C₂²	1	2	yes	—
23	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
24	C₄⋊C₄×Dic₁₃	C₄	1	2	yes	—
25	C₄×#6103	C₂²	1	2	yes	—
26	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×C₄×#1055	C₂²	1	2	yes	—
29	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
30	#11718495	C₄	1	8	yes	complemented
31	C₈×D₅₂	C₄	1	8	yes	complemented
32	#11718327	C₄	1	4	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	#11718142	C₂²	1	2	yes	—
35	#11718142	C₂²	1	1	yes	characteristic
36	#11718142	C₂²	1	1	yes	characteristic
37	#11718142	C₂²	1	1	yes	characteristic
38	#11718142	C₂²	1	1	yes	characteristic
39	#11718116	C₂²	1	2	yes	—
40	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂×C₄	1	4	yes	—
42	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×#6103	C₂×C₄	1	2	yes	—
50	C₂×#6103	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
53	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
57	C₂²×#1055	C₂³	1	1	yes	characteristic
58	C₂²×#1055	C₂³	1	2	yes	—
59	C₂²×#1055	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₁₃	—	4	2	no	—
61	C₂×C₈×D₁₃	—	4	2	no	—
62	C₂×C₈×D₁₃	—	4	2	no	—
63	C₂×C₈×D₁₃	—	4	2	no	—
64	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	complemented
65	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	complemented
66	#88147	C₈	1	16	yes	complemented
67	C₄×D₅₂	C₂×C₄	1	4	yes	—
68	C₄×D₅₂	C₂×C₄	1	4	yes	—
69	C₄²×D₁₃	—	4	2	no	—
70	C₄²×D₁₃	—	4	2	no	—
71	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
72	C₄×C₈×C₁₃	—	4	2	no	—
73	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
74	C₁₃×#95	C₂×C₄	1	2	yes	—
75	#88071	C₂×C₄	1	4	yes	—
76	#88060	C₂×C₄	1	8	yes	complemented
77	#88060	C₂×C₄	1	8	yes	complemented
78	C₈×Dic₁₃	—	4	2	no	—
79	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
80	C₄×#1055	—	4	2	no	—
81	C₄×#1055	C₂×C₄	1	4	yes	complemented
82	#20555	—	13	1	no	maximal, Sylow
83	C₂³×D₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
91	C₂×D₅₂	C₄²	1	4	yes	—
92	C₂×D₅₂	C₂×C₈	1	8	yes	—
93	C₂×C₄×D₁₃	—	2	2	no	—
94	C₂×C₄×D₁₃	—	2	2	no	—
95	C₂×C₄×D₁₃	—	2	2	no	—
96	C₂×C₄×D₁₃	—	2	2	no	—
97	C₂×C₄×D₁₃	—	4	4	no	—
98	C₂×C₄×D₁₃	—	4	4	no	—
99	C₂×C₄×D₁₃	C₂×C₈	1	16	yes	complemented
100	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
101	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
111	C₁₃×C₄⋊C₄	C₂×C₈	1	8	yes	complemented
112	C₄²×C₁₃	—	2	2	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
115	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
116	#6103	C₄²	1	8	yes	—
117	#6103	C₂×C₈	1	16	yes	complemented
118	C₄⋊Dic₁₃	C₄²	1	4	yes	—
119	C₄×Dic₁₃	—	2	1	no	—
120	C₄×Dic₁₃	—	2	1	no	—
121	C₄×Dic₁₃	—	2	1	no	—
122	C₄×Dic₁₃	—	2	1	no	—
123	C₄×Dic₁₃	—	4	4	no	—
124	C₄×Dic₁₃	—	4	2	no	—
125	C₄×Dic₁₃	C₂×C₈	1	8	yes	complemented
126	C₂×#1055	—	2	1	no	—
127	C₂×#1055	—	2	1	no	—
128	C₂×#1055	—	2	2	no	—
129	C₂×#1055	—	2	2	no	—
130	C₂×#1055	—	2	1	no	—
131	C₂×#1055	—	2	1	no	—
132	C₂×#1055	C₂²×C₄	1	2	yes	—
133	C₂×#1055	C₂²×C₄	1	4	yes	—
134	C₂×#1055	C₂²×C₄	1	2	yes	—
135	C₈×D₁₃	—	4	8	no	—
136	C₈×D₁₃	—	4	8	no	—
137	C₂×C₈×D₄	—	13	1	no	—
138	C₂×C₈×D₄	—	13	1	no	—
139	C₄²×D₄	—	13	1	no	—
140	C₈×C₄⋊C₄	—	13	1	no	—
141	C₈×C₄⋊C₄	D₁₃	1	1	yes	characteristic, complemented
142	C₄×C₄⋊C₈	—	13	1	no	—
143	C₈×C₂²⋊C₄	—	13	2	no	—
144	C₈×C₂²⋊C₄	—	13	2	no	—
145	C₄×C₂²⋊C₈	—	13	2	no	—
146	#1744	—	13	1	no	—
147	C₂×#336	—	13	2	no	—
148	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
149	C₂²×D₁₃	—	2	2	no	—
150	C₂²×D₁₃	—	2	2	no	—
151	C₂²×D₁₃	—	2	4	no	—
152	C₂²×D₁₃	C₂×C₄²	1	4	yes	—
153	C₂²×D₁₃	C₂²×C₈	1	8	yes	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
158	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
159	C₂×C₄×C₁₃	C₂²×C₈	1	8	yes	—
160	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	2	2	no	—
169	C₂×Dic₁₃	—	2	2	no	—
170	C₂×Dic₁₃	—	2	2	no	—
171	C₂×Dic₁₃	—	2	2	no	—
172	C₂×Dic₁₃	—	2	2	no	—
173	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
174	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
175	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
176	D₅₂	C₄×C₈	1	16	yes	complemented
177	C₄×D₁₃	—	2	4	no	—
178	C₄×D₁₃	—	2	4	no	—
179	C₄×D₁₃	—	2	4	no	—
180	C₄×D₁₃	—	2	4	no	—
181	C₄×D₁₃	—	4	16	no	—
182	C₈×C₁₃	—	2	2	no	—
183	C₈×C₁₃	—	2	4	no	—
184	C₈×C₁₃	—	2	2	no	—
185	#1055	—	2	2	no	—
186	#1055	—	2	4	no	—
187	#1055	—	2	2	no	—
188	C₂³×C₈	—	13	2	no	—
189	C₂³×C₈	—	13	2	no	—
190	C₂×C₄×D₄	—	13	2	no	—
191	C₂×C₄×D₄	—	13	1	no	—
192	C₂²×C₄²	—	13	2	no	—
193	C₈×D₄	—	13	8	no	—
194	C₈×D₄	—	13	8	no	—
195	C₂×C₄⋊C₈	—	13	1	no	—
196	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
197	C₂×C₂²⋊C₈	—	13	2	no	—
198	C₂×C₂²⋊C₈	—	13	2	no	—
199	C₂×C₄×C₈	—	13	1	no	—
200	C₂×C₄×C₈	—	13	2	no	—
201	C₂×C₄×C₈	—	13	2	no	—
202	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
203	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
204	C₄×C₄⋊C₄	—	13	2	no	—
205	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
206	C₄×C₂²⋊C₄	—	13	2	no	—
207	C₄×C₂²⋊C₄	—	13	4	no	—
208	C₄³	—	13	1	no	—
209	#336	—	13	1	no	—
210	#336	—	13	2	no	—
211	#336	—	13	1	no	—
212	#336	—	13	1	no	—
213	#336	—	13	1	no	—
214	#336	—	13	2	no	—
215	#336	C₂×D₁₃	1	2	yes	—
216	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
217	C₂²×C₁₃	#518	1	1	yes	characteristic
218	C₂²×C₁₃	#520	1	1	yes	characteristic
219	C₂²×C₁₃	C₂³×C₈	1	2	yes	—
220	C₂²×C₁₃	#568	1	2	yes	—
221	C₂×D₁₃	—	2	4	no	—
222	C₂×D₁₃	—	2	8	no	—
223	C₂×D₁₃	—	2	8	no	—
224	C₂×D₁₃	—	2	4	no	—
225	C₂×D₁₃	C₂×C₄×C₈	1	8	yes	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	8	no	—
228	C₄×C₁₃	C₂×C₄×C₈	1	4	yes	—
229	C₄×C₁₃	#518	1	1	yes	characteristic
230	C₄×C₁₃	#518	1	1	yes	characteristic
231	C₄×C₁₃	#520	1	1	yes	characteristic
232	C₄×C₁₃	#520	1	1	yes	characteristic
233	Dic₁₃	—	2	4	no	—
234	Dic₁₃	—	2	4	no	—
235	Dic₁₃	—	2	4	no	—
236	C₂²×D₄	—	13	1	no	—
237	C₂³×C₄	—	13	2	no	—
238	C₂³×C₄	—	13	4	no	—
239	C₂²×C₈	—	13	1	no	—
240	C₂²×C₈	—	13	2	no	—
241	C₂²×C₈	—	13	1	no	—
242	C₂²×C₈	—	13	8	no	—
243	C₂²×C₈	—	13	8	no	—
244	C₂²×C₈	—	52	2	no	—
245	C₂²×C₈	—	52	2	no	—
246	C₂²×C₈	—	52	2	no	—
247	C₂²×C₈	—	52	2	no	—
248	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
249	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
250	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
251	C₄×D₄	—	13	16	no	—
252	C₄×D₄	—	13	4	no	—
253	C₄×D₄	—	13	4	no	—
254	C₂×C₄⋊C₄	—	13	1	no	—
255	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
256	C₂×C₂²⋊C₄	—	13	2	no	—
257	C₂×C₂²⋊C₄	—	13	4	no	—
258	C₂×C₄²	—	13	2	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	—	13	2	no	—
262	C₂×C₄²	—	13	4	no	—
263	C₂×C₄²	—	52	2	no	—
264	C₂×C₄²	—	52	2	no	—
265	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
266	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
267	C₄⋊C₈	—	13	4	no	—
268	C₄⋊C₈	C₄×D₁₃	1	4	yes	complemented
269	C₂²⋊C₈	—	13	8	no	—
270	C₂²⋊C₈	—	13	8	no	—
271	C₄×C₈	—	4	2	no	—
272	C₄×C₈	—	13	4	no	—
273	C₄×C₈	—	52	2	no	—
274	C₄×C₈	—	52	2	no	—
275	C₄×C₈	C₄×D₁₃	1	4	yes	complemented
276	#95	—	13	4	no	—
277	#95	C₄×D₁₃	1	2	yes	—
278	C₂×C₁₃	#2275	1	1	yes	characteristic
279	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
280	C₂×C₁₃	#2875	1	1	yes	characteristic
281	C₂×C₁₃	#2972	1	2	yes	—
282	C₂×C₁₃	#2988	1	2	yes	—
283	D₁₃	—	2	8	no	—
284	C₂⁴	—	13	2	no	—
285	C₂×D₄	—	13	4	no	—
286	C₂×D₄	—	13	8	no	—
287	C₂²×C₄	—	13	2	no	—
288	C₂²×C₄	—	13	2	no	—
289	C₂²×C₄	—	13	2	no	—
290	C₂²×C₄	—	13	4	no	—
291	C₂²×C₄	—	13	4	no	—
292	C₂²×C₄	—	13	16	no	—
293	C₂²×C₄	—	26	2	no	—
294	C₂²×C₄	—	26	2	no	—
295	C₂²×C₄	—	26	2	no	—
296	C₂²×C₄	—	26	2	no	—
297	C₂²×C₄	—	52	4	no	—
298	C₂²×C₄	—	52	4	no	—
299	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
301	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	13	2	no	—
310	C₂×C₈	—	13	2	no	—
311	C₂×C₈	—	13	4	no	—
312	C₂×C₈	—	26	1	no	—
313	C₂×C₈	—	26	1	no	—
314	C₂×C₈	—	26	1	no	—
315	C₂×C₈	—	26	2	no	—
316	C₂×C₈	—	26	2	no	—
317	C₂×C₈	—	26	1	no	—
318	C₂×C₈	—	52	8	no	—
319	C₂×C₈	—	52	8	no	—
320	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
321	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
322	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
323	C₄⋊C₄	—	13	4	no	—
324	C₄⋊C₄	C₈×D₁₃	1	8	yes	complemented
325	C₂²⋊C₄	—	13	8	no	—
326	C₂²⋊C₄	—	13	16	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	13	8	no	—
330	C₄²	—	26	1	no	—
331	C₄²	—	26	1	no	—
332	C₄²	—	26	1	no	—
333	C₄²	—	26	1	no	—
334	C₄²	—	52	4	no	—
335	C₄²	—	52	2	no	—
336	C₄²	C₂×C₄×D₁₃	1	2	yes	—
337	C₄²	C₂×C₄×D₁₃	1	2	yes	—
338	C₁₃	#20555	1	1	yes	characteristic, complemented, Sylow
339	C₂³	—	13	4	no	—
340	C₂³	—	13	8	no	—
341	C₂³	—	26	4	no	—
342	C₂³	—	26	2	no	—
343	C₂³	—	26	2	no	—
344	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
345	D₄	—	13	16	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	13	4	no	—
350	C₂×C₄	—	13	4	no	—
351	C₂×C₄	—	13	4	no	—
352	C₂×C₄	—	26	2	no	—
353	C₂×C₄	—	26	2	no	—
354	C₂×C₄	—	26	2	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	2	no	—
357	C₂×C₄	—	26	2	no	—
358	C₂×C₄	—	26	4	no	—
359	C₂×C₄	—	26	4	no	—
360	C₂×C₄	—	26	4	no	—
361	C₂×C₄	—	26	4	no	—
362	C₂×C₄	—	52	16	no	—
363	C₂×C₄	C₄²×D₁₃	1	2	yes	—
364	C₂×C₄	C₄²×D₁₃	1	2	yes	—
365	C₂×C₄	C₂×C₈×D₁₃	1	8	yes	—
366	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
367	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
369	C₂×C₄	#88251	1	1	yes	characteristic
370	C₂×C₄	#88254	1	1	yes	characteristic
371	C₂×C₄	#88256	1	1	yes	characteristic
372	C₂×C₄	#88256	1	1	yes	characteristic
373	C₈	—	2	2	no	—
374	C₈	—	2	2	no	—
375	C₈	—	2	4	no	—
376	C₈	—	26	4	no	—
377	C₈	—	26	2	no	—
378	C₈	—	26	2	no	—
379	C₂²	—	13	8	no	—
380	C₂²	—	26	4	no	—
381	C₂²	—	26	8	no	—
382	C₂²	—	26	8	no	—
383	C₂²	—	26	4	no	—
384	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
385	C₂²	#11719250	1	1	yes	characteristic
386	C₂²	#11719279	1	1	yes	characteristic
387	C₂²	C₂²×C₈×D₁₃	1	2	yes	—
388	C₂²	#11719455	1	2	yes	—
389	C₄	—	2	8	no	—
390	C₄	—	2	2	no	—
391	C₄	—	26	4	no	—
392	C₄	—	26	4	no	—
393	C₄	—	26	4	no	—
394	C₄	C₄×C₈×D₁₃	1	4	yes	—
395	C₄	#11719209	1	1	yes	characteristic
396	C₄	#11719226	1	1	yes	characteristic
397	C₄	#11719250	1	1	yes	characteristic
398	C₄	#11719279	1	1	yes	characteristic
399	C₂	—	26	8	no	—
400	C₂	#13117196	1	1	yes	characteristic
401	C₂	C₂×C₄×C₈×D₁₃	1	1	yes	characteristic
402	C₂	#13123263	1	1	yes	characteristic
403	C₂	#13123857	1	2	yes	—
404	C₂	#13123946	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂×C₁₃	C₂²×C₄×C₈
Fitting	C₈×C₁₃×C₄⋊C₄	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₁₃
hypocenter	C₁₃	#20555
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₄⋊C₄×#1055	C₂	semidirect
5. C₄⋊C₈×Dic₁₃	C₂	semidirect
6. C₈×#6103	C₂	semidirect
7. #13114606	C₂	semidirect
8. C₄×#88060	C₂	semidirect
9. #13114581	C₂	semidirect
10. D₁₃×#336	C₂	semidirect
11. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
30. #11718495	C₄	semidirect
31. C₈×D₅₂	C₄	semidirect
64. C₂×C₈×D₁₃	C₂×C₄	semidirect
65. C₂×C₈×D₁₃	C₂×C₄	semidirect
66. #88147	C₈	semidirect
71. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
73. C₄×C₈×C₁₃	C₂×C₄	semidirect
76. #88060	C₂×C₄	semidirect
77. #88060	C₂×C₄	semidirect
79. C₄⋊#1055	C₂×C₄	semidirect
81. C₄×#1055	C₂×C₄	semidirect
99. C₂×C₄×D₁₃	C₂×C₈	semidirect
111. C₁₃×C₄⋊C₄	C₂×C₈	semidirect
117. #6103	C₂×C₈	semidirect
125. C₄×Dic₁₃	C₂×C₈	semidirect
141. C₈×C₄⋊C₄	D₁₃	semidirect
176. D₅₂	C₄×C₈	semidirect
268. C₄⋊C₈	C₄×D₁₃	semidirect
275. C₄×C₈	C₄×D₁₃	semidirect
324. C₄⋊C₄	C₈×D₁₃	semidirect
338. C₁₃	#20555	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₅₂	2
C₂×#11718495	2
C₄×#88147	2
C₄⋊C₄×#1055	2
C₄⋊C₈×Dic₁₃	2
C₈×#6103	2
#13114606	2
C₄×#88060	2
#13114581	2
D₁₃×#336	2
C₈×C₁₃×C₄⋊C₄	2
#20555	13