Subgroups — C₁₃×#35001 #15721340

Order 3328.

4298 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#534	C₂	1	4	yes	maximal, complemented
2	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2856	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2656	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2539	C₂	1	8	yes	maximal, complemented
6	C₁₃×#2501	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2433	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
10	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
11	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#534	—	2	32	no	—
13	C₂×C₁₃×#127	C₂²	1	4	yes	complemented
14	C₂×C₁₃×#123	C₂²	1	16	yes	complemented
15	C₂×C₁₃×#121	—	2	16	no	—
16	C₂×C₁₃×#121	C₂²	1	4	yes	—
17	C₂×C₁₃×#121	C₂²	1	4	yes	—
18	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
20	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#120	C₂²	1	16	yes	complemented
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
26	C₁₃×#399	C₂²	1	16	yes	complemented
27	C₁₃×#392	C₂²	1	16	yes	complemented
28	C₁₃×#390	C₂²	1	8	yes	complemented
29	C₁₃×#390	C₂²	1	16	yes	complemented
30	C₁₃×#384	C₂²	1	4	yes	complemented
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
33	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
34	C₂⁵×C₁₃	C₂³	1	4	yes	—
35	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₃	—	2	16	no	—
37	C₂²×D₄×C₁₃	—	2	32	no	—
38	C₂²×D₄×C₁₃	—	2	8	no	—
39	C₂²×D₄×C₁₃	—	4	8	no	—
40	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
41	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
44	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃	—	4	4	no	—
46	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
47	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
53	C₁₃×#127	—	4	8	no	—
54	C₁₃×#123	—	2	64	no	—
55	C₁₃×#121	—	2	16	no	—
56	C₁₃×#121	—	2	16	no	—
57	C₁₃×#121	—	2	16	no	—
58	C₁₃×#121	—	2	16	no	—
59	C₁₃×#121	—	2	64	no	—
60	C₁₃×#120	—	2	64	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
66	C₂×C₁₃×C₂²⋊C₄	D₄	1	16	yes	complemented
67	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
68	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₂×C₄²×C₁₃	—	4	4	no	—
72	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
74	C₁₃×#95	C₂³	1	8	yes	—
75	#35001	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	—	2	8	no	—
77	C₂⁴×C₁₃	—	2	16	no	—
78	C₂⁴×C₁₃	—	4	2	no	—
79	C₂⁴×C₁₃	—	4	2	no	—
80	C₂⁴×C₁₃	—	4	8	no	—
81	C₂⁴×C₁₃	—	4	8	no	—
82	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
83	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
84	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
85	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
86	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
87	C₂×D₄×C₁₃	—	2	32	no	—
88	C₂×D₄×C₁₃	—	2	16	no	—
89	C₂×D₄×C₁₃	—	2	16	no	—
90	C₂×D₄×C₁₃	—	2	32	no	—
91	C₂×D₄×C₁₃	—	2	8	no	—
92	C₂×D₄×C₁₃	—	2	8	no	—
93	C₂×D₄×C₁₃	—	2	32	no	—
94	C₂×D₄×C₁₃	—	2	16	no	—
95	C₂×D₄×C₁₃	—	4	8	no	—
96	C₂×D₄×C₁₃	—	4	32	no	—
97	C₂×D₄×C₁₃	—	4	16	no	—
98	C₂×D₄×C₁₃	—	4	16	no	—
99	C₂×D₄×C₁₃	—	4	64	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	8	no	—
102	C₂²×C₄×C₁₃	—	2	8	no	—
103	C₂²×C₄×C₁₃	—	2	16	no	—
104	C₂²×C₄×C₁₃	—	4	16	no	—
105	C₂²×C₄×C₁₃	—	4	4	no	—
106	C₂²×C₄×C₁₃	—	4	4	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
114	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×C₄⋊C₄	—	2	8	no	—
120	C₁₃×C₄⋊C₄	—	2	8	no	—
121	C₁₃×C₄⋊C₄	—	2	32	no	—
122	C₁₃×C₂²⋊C₄	—	2	16	no	—
123	C₁₃×C₂²⋊C₄	—	2	16	no	—
124	C₁₃×C₂²⋊C₄	—	2	64	no	—
125	C₁₃×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
126	C₄²×C₁₃	—	2	8	no	—
127	C₄²×C₁₃	—	4	4	no	—
128	C₂×#534	C₂×C₁₃	1	4	yes	complemented
129	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
130	#2856	C₂×C₁₃	1	4	yes	complemented
131	#2656	C₂×C₁₃	1	4	yes	complemented
132	#2539	C₂×C₁₃	1	8	yes	complemented
133	#2501	C₂×C₁₃	1	4	yes	complemented
134	#2433	C₂×C₁₃	1	4	yes	complemented
135	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
136	C₂³×C₁₃	—	2	2	no	—
137	C₂³×C₁₃	—	2	4	no	—
138	C₂³×C₁₃	—	2	2	no	—
139	C₂³×C₁₃	—	2	4	no	—
140	C₂³×C₁₃	—	2	8	no	—
141	C₂³×C₁₃	—	2	16	no	—
142	C₂³×C₁₃	—	2	16	no	—
143	C₂³×C₁₃	—	2	16	no	—
144	C₂³×C₁₃	—	4	4	no	—
145	C₂³×C₁₃	—	4	4	no	—
146	C₂³×C₁₃	—	4	16	no	—
147	C₂³×C₁₃	—	4	16	no	—
148	C₂³×C₁₃	—	4	16	no	—
149	C₂³×C₁₃	—	4	16	no	—
150	C₂³×C₁₃	—	8	32	no	—
151	C₂³×C₁₃	#127	1	16	yes	complemented
152	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
153	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
154	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
155	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
156	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
157	D₄×C₁₃	—	4	16	no	—
158	D₄×C₁₃	—	4	32	no	—
159	D₄×C₁₃	—	4	32	no	—
160	D₄×C₁₃	—	4	16	no	—
161	D₄×C₁₃	—	8	32	no	—
162	C₂×C₄×C₁₃	—	2	8	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	8	no	—
166	C₂×C₄×C₁₃	—	2	8	no	—
167	C₂×C₄×C₁₃	—	2	16	no	—
168	C₂×C₄×C₁₃	—	2	8	no	—
169	C₂×C₄×C₁₃	—	2	16	no	—
170	C₂×C₄×C₁₃	—	4	8	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	—	4	16	no	—
173	C₂×C₄×C₁₃	—	4	16	no	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
176	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
179	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
180	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
181	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
182	#534	—	2	32	no	—
183	C₂×#127	C₂²×C₁₃	1	4	yes	complemented
184	C₂×#123	C₂²×C₁₃	1	16	yes	complemented
185	C₂×#121	—	2	16	no	—
186	C₂×#121	C₂²×C₁₃	1	4	yes	—
187	C₂×#121	C₂²×C₁₃	1	4	yes	—
188	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
189	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
190	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
191	C₂×#120	C₂²×C₁₃	1	16	yes	complemented
192	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
193	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
194	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
195	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
196	#399	C₂²×C₁₃	1	16	yes	complemented
197	#392	C₂²×C₁₃	1	16	yes	complemented
198	#390	C₂²×C₁₃	1	8	yes	complemented
199	#390	C₂²×C₁₃	1	16	yes	complemented
200	#384	C₂²×C₁₃	1	4	yes	complemented
201	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
202	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
203	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
204	C₂²×C₁₃	—	2	4	no	—
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	2	4	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	8	no	—
209	C₂²×C₁₃	—	2	16	no	—
210	C₂²×C₁₃	—	4	16	no	—
211	C₂²×C₁₃	—	4	8	no	—
212	C₂²×C₁₃	—	4	8	no	—
213	C₂²×C₁₃	—	4	8	no	—
214	C₂²×C₁₃	—	4	32	no	—
215	C₂²×C₁₃	—	8	32	no	—
216	C₂²×C₁₃	C₂×#127	1	8	yes	—
217	C₂²×C₁₃	C₂×#127	1	4	yes	—
218	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
219	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
220	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
221	C₂²×C₁₃	#585	1	2	yes	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	4	no	—
224	C₄×C₁₃	—	2	16	no	—
225	C₄×C₁₃	—	4	8	no	—
226	C₄×C₁₃	#534	1	4	yes	complemented
227	C₂⁵	C₂³×C₁₃	1	4	yes	—
228	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
229	C₂²×D₄	—	2	16	no	—
230	C₂²×D₄	—	2	32	no	—
231	C₂²×D₄	—	2	8	no	—
232	C₂²×D₄	—	4	8	no	—
233	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
234	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
235	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
236	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
237	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
238	C₂³×C₄	—	4	4	no	—
239	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
240	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
241	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
246	#127	—	4	8	no	—
247	#123	—	2	64	no	—
248	#121	—	2	16	no	—
249	#121	—	2	16	no	—
250	#121	—	2	16	no	—
251	#121	—	2	16	no	—
252	#121	—	2	64	no	—
253	#120	—	2	64	no	—
254	C₂×C₄⋊C₄	—	2	8	no	—
255	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
258	C₂×C₂²⋊C₄	—	2	16	no	—
259	C₂×C₂²⋊C₄	D₄×C₁₃	1	16	yes	complemented
260	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
262	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
263	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
264	C₂×C₄²	—	4	4	no	—
265	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
266	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
267	#95	C₂³×C₁₃	1	8	yes	—
268	C₂×C₁₃	—	2	8	no	—
269	C₂×C₁₃	—	2	4	no	—
270	C₂×C₁₃	—	8	8	no	—
271	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
272	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
273	C₂×C₁₃	#3449	1	1	yes	characteristic
274	C₂×C₁₃	#3496	1	4	yes	—
275	C₂⁴	—	2	8	no	—
276	C₂⁴	—	2	16	no	—
277	C₂⁴	—	4	2	no	—
278	C₂⁴	—	4	2	no	—
279	C₂⁴	—	4	8	no	—
280	C₂⁴	—	4	8	no	—
281	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
282	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
283	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
284	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
285	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
286	C₂×D₄	—	2	32	no	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	32	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	32	no	—
293	C₂×D₄	—	2	16	no	—
294	C₂×D₄	—	4	8	no	—
295	C₂×D₄	—	4	32	no	—
296	C₂×D₄	—	4	16	no	—
297	C₂×D₄	—	4	16	no	—
298	C₂×D₄	—	4	64	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	4	16	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
313	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
314	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
316	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	32	no	—
321	C₂²⋊C₄	—	2	16	no	—
322	C₂²⋊C₄	—	2	16	no	—
323	C₂²⋊C₄	—	2	64	no	—
324	C₂²⋊C₄	C₂×D₄×C₁₃	1	32	yes	complemented
325	C₄²	—	2	8	no	—
326	C₄²	—	4	4	no	—
327	C₁₃	#35001	1	1	yes	characteristic, direct product factor, Sylow
328	C₂³	—	2	2	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	2	16	no	—
334	C₂³	—	2	16	no	—
335	C₂³	—	2	16	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	16	no	—
340	C₂³	—	4	16	no	—
341	C₂³	—	4	16	no	—
342	C₂³	—	8	32	no	—
343	C₂³	C₁₃×#127	1	16	yes	complemented
344	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
345	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
346	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
347	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
348	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
349	D₄	—	4	16	no	—
350	D₄	—	4	32	no	—
351	D₄	—	4	32	no	—
352	D₄	—	4	16	no	—
353	D₄	—	8	32	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	16	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	4	8	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	16	no	—
365	C₂×C₄	—	4	16	no	—
366	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₃	1	16	yes	—
368	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
369	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
370	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	2	16	no	—
377	C₂²	—	4	16	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	4	8	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	32	no	—
382	C₂²	—	8	32	no	—
383	C₂²	C₂×C₁₃×#127	1	8	yes	—
384	C₂²	C₂×C₁₃×#127	1	4	yes	—
385	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
386	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
387	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
388	C₂²	C₁₃×#585	1	2	yes	—
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	2	16	no	—
392	C₄	—	4	8	no	—
393	C₄	C₁₃×#534	1	4	yes	complemented
394	C₂	—	2	8	no	—
395	C₂	—	2	4	no	—
396	C₂	—	8	8	no	—
397	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
398	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
399	C₂	C₁₃×#3449	1	1	yes	characteristic
400	C₂	C₁₃×#3496	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#534	C₂	semidirect
2. C₂²×C₁₃×#121	C₂	semidirect
3. C₁₃×#2856	C₂	semidirect
4. C₁₃×#2656	C₂	semidirect
5. C₁₃×#2539	C₂	semidirect
6. C₁₃×#2501	C₂	semidirect
7. C₁₃×#2433	C₂	semidirect
8. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
10. C₂³×D₄×C₁₃	C₂²	semidirect
13. C₂×C₁₃×#127	C₂²	semidirect
14. C₂×C₁₃×#123	C₂²	semidirect
18. C₂×C₁₃×#121	C₂²	semidirect
19. C₂×C₁₃×#121	C₂²	semidirect
20. C₂×C₁₃×#121	C₂²	semidirect
21. C₂×C₁₃×#120	C₂²	semidirect
22. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₄²×C₁₃	C₂²	semidirect
26. C₁₃×#399	C₂²	semidirect
27. C₁₃×#392	C₂²	semidirect
28. C₁₃×#390	C₂²	semidirect
29. C₁₃×#390	C₂²	semidirect
30. C₁₃×#384	C₂²	semidirect
31. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
32. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
33. C₂×C₁₃×#95	C₂²	semidirect
46. C₂³×C₄×C₁₃	D₄	semidirect
66. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
75. #35001	C₁₃	direct (N × H)
113. C₂²×C₄×C₁₃	C₂×D₄	semidirect
125. C₁₃×C₂²⋊C₄	C₂×D₄	semidirect
128. C₂×#534	C₂×C₁₃	semidirect
129. C₂²×#121	C₂×C₁₃	semidirect
130. #2856	C₂×C₁₃	semidirect
131. #2656	C₂×C₁₃	semidirect
132. #2539	C₂×C₁₃	semidirect
133. #2501	C₂×C₁₃	semidirect
134. #2433	C₂×C₁₃	semidirect
135. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
151. C₂³×C₁₃	#127	semidirect
180. C₂³×D₄	C₂²×C₁₃	semidirect
183. C₂×#127	C₂²×C₁₃	semidirect
184. C₂×#123	C₂²×C₁₃	semidirect
188. C₂×#121	C₂²×C₁₃	semidirect
189. C₂×#121	C₂²×C₁₃	semidirect
190. C₂×#121	C₂²×C₁₃	semidirect
191. C₂×#120	C₂²×C₁₃	semidirect
192. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
194. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
195. C₂²×C₄²	C₂²×C₁₃	semidirect
196. #399	C₂²×C₁₃	semidirect
197. #392	C₂²×C₁₃	semidirect
198. #390	C₂²×C₁₃	semidirect
199. #390	C₂²×C₁₃	semidirect
200. #384	C₂²×C₁₃	semidirect
201. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
202. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
203. C₂×#95	C₂²×C₁₃	semidirect
226. C₄×C₁₃	#534	semidirect
239. C₂³×C₄	D₄×C₁₃	semidirect
259. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
312. C₂²×C₄	C₂×D₄×C₁₃	semidirect
324. C₂²⋊C₄	C₂×D₄×C₁₃	semidirect
327. C₁₃	#35001	direct (N × H)
343. C₂³	C₁₃×#127	semidirect
393. C₄	C₁₃×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#534	2
C₂²×C₁₃×#121	2
C₁₃×#2856	2
C₁₃×#2656	2
C₁₃×#2539	2
C₁₃×#2501	2
C₁₃×#2433	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35001	13

Subgroups — C13×#35001 #15721340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35001 #15721340