Subgroups — C₂×C₁₃×#3205 #15747113

Order 3328.

3102 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3205	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#493	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#486	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#459	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#447	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂³×D₄×C₁₃	—	2	1	no	—
11	C₂³×D₄×C₁₃	—	2	1	no	—
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	8	yes	complemented
14	C₁₃×#532	—	2	4	no	—
15	C₁₃×#532	C₂²	1	8	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×#127	—	2	1	no	—
18	C₂×C₁₃×#127	—	2	1	no	—
19	C₂×C₁₃×#127	—	2	4	no	—
20	C₂×C₁₃×#127	C₂²	1	2	yes	—
21	C₂×C₁₃×#127	C₂²	1	2	yes	—
22	C₂×C₁₃×#127	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#124	—	2	1	no	—
25	C₂×C₁₃×#121	—	2	1	no	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#493	C₂²	1	16	yes	complemented
31	C₁₃×#486	C₂²	1	16	yes	complemented
32	C₁₃×#459	C₂²	1	32	yes	complemented
33	C₁₃×#447	C₂²	1	32	yes	complemented
34	C₁₃×#431	C₂²	1	8	yes	complemented
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
39	C₂⁵×C₁₃	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	8	no	—
41	C₂×C₁₃×#41	—	4	8	no	—
42	C₂²×Q₈×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	4	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	—	2	8	no	—
53	C₂²×D₄×C₁₃	—	2	8	no	—
54	C₂²×D₄×C₁₃	—	4	8	no	—
55	C₂²×D₄×C₁₃	—	4	8	no	—
56	C₂²×D₄×C₁₃	—	4	8	no	—
57	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
60	C₂³×C₄×C₁₃	—	2	2	no	—
61	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×D₈	—	4	16	no	—
65	C₂×C₁₃×D₈	C₂³	1	32	yes	complemented
66	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
67	C₁₃×C₄⋊Q₈	—	2	2	no	—
68	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
69	C₁₃×#127	—	2	4	no	—
70	C₁₃×#127	—	2	4	no	—
71	C₁₃×#127	—	2	8	no	—
72	C₁₃×#127	—	2	8	no	—
73	C₁₃×#127	—	2	2	no	—
74	C₁₃×#127	C₂³	1	8	yes	—
75	C₁₃×#127	C₂³	1	8	yes	—
76	C₁₃×#127	C₂³	1	4	yes	complemented
77	C₁₃×#124	—	2	8	no	—
78	C₁₃×#121	—	2	8	no	—
79	C₁₃×#121	—	2	4	no	—
80	C₁₃×#121	C₂³	1	8	yes	—
81	C₄×D₄×C₁₃	—	2	8	no	—
82	C₄×D₄×C₁₃	—	2	4	no	—
83	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	D₄	1	4	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
94	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
95	C₁₃×#102	C₂³	1	32	yes	complemented
96	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
97	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
98	C₂×#3205	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	8	no	—
100	C₂⁴×C₁₃	—	2	2	no	—
101	C₂⁴×C₁₃	—	2	4	no	—
102	C₂⁴×C₁₃	—	4	8	no	—
103	C₂⁴×C₁₃	—	4	8	no	—
104	C₂⁴×C₁₃	—	4	8	no	—
105	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₁₃×#41	—	4	32	no	—
107	C₂×Q₈×C₁₃	—	2	4	no	—
108	C₂×Q₈×C₁₃	—	4	4	no	—
109	C₂×D₄×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	4	no	—
112	C₂×D₄×C₁₃	—	2	4	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂×D₄×C₁₃	—	2	8	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	—	2	8	no	—
120	C₂×D₄×C₁₃	—	2	16	no	—
121	C₂×D₄×C₁₃	—	4	16	no	—
122	C₂×D₄×C₁₃	—	4	8	no	—
123	C₂×D₄×C₁₃	—	4	8	no	—
124	C₂×D₄×C₁₃	—	4	16	no	—
125	C₂×D₄×C₁₃	—	4	32	no	—
126	C₂×D₄×C₁₃	—	4	8	no	—
127	C₂×D₄×C₁₃	—	4	8	no	—
128	C₂×D₄×C₁₃	—	4	8	no	—
129	C₂×D₄×C₁₃	—	4	4	no	—
130	C₂×D₄×C₁₃	—	4	32	no	—
131	C₂×D₄×C₁₃	—	4	4	no	—
132	C₂×D₄×C₁₃	—	4	8	no	—
133	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
134	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	4	8	no	—
140	C₂²×C₄×C₁₃	D₈	1	8	yes	complemented
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×D₈	—	4	32	no	—
152	C₂×C₈×C₁₃	—	2	8	no	—
153	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₄²×C₁₃	C₂×D₄	1	4	yes	—
160	C₄²×C₁₃	C₂×D₄	1	2	yes	—
161	C₄²×C₁₃	C₂×D₄	1	4	yes	—
162	C₄²×C₁₃	C₂×D₄	1	2	yes	—
163	C₄²×C₁₃	C₂⁴	1	2	yes	—
164	C₄²×C₁₃	C₂⁴	1	2	yes	—
165	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#3205	C₂×C₁₃	1	16	yes	direct product factor
168	C₂×#493	C₂×C₁₃	1	2	yes	complemented
169	C₂×#486	C₂×C₁₃	1	2	yes	complemented
170	C₂×#459	C₂×C₁₃	1	4	yes	complemented
171	C₂×#447	C₂×C₁₃	1	4	yes	complemented
172	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	2	8	no	—
177	C₂³×C₁₃	—	4	16	no	—
178	C₂³×C₁₃	—	4	16	no	—
179	C₂³×C₁₃	—	4	8	no	—
180	C₂³×C₁₃	—	4	4	no	—
181	C₂³×C₁₃	—	4	4	no	—
182	C₂³×C₁₃	—	4	16	no	—
183	C₂³×C₁₃	—	4	8	no	—
184	C₂³×C₁₃	—	4	8	no	—
185	C₂³×C₁₃	—	4	4	no	—
186	C₂³×C₁₃	—	8	32	no	—
187	C₂³×C₁₃	C₂×D₈	1	4	yes	—
188	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
189	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₃	—	4	8	no	—
191	D₄×C₁₃	—	2	8	no	—
192	D₄×C₁₃	—	2	16	no	—
193	D₄×C₁₃	—	4	16	no	—
194	D₄×C₁₃	—	4	16	no	—
195	D₄×C₁₃	—	4	16	no	—
196	D₄×C₁₃	—	4	4	no	—
197	D₄×C₁₃	—	4	8	no	—
198	D₄×C₁₃	—	4	16	no	—
199	D₄×C₁₃	—	4	16	no	—
200	D₄×C₁₃	—	4	8	no	—
201	D₄×C₁₃	—	4	8	no	—
202	D₄×C₁₃	—	4	16	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	4	16	no	—
211	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
212	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
213	C₂×C₄×C₁₃	C₂×D₈	1	16	yes	complemented
214	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
222	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
223	C₈×C₁₃	—	2	8	no	—
224	C₂²×#41	—	2	1	no	—
225	C₂³×D₄	—	2	1	no	—
226	C₂³×D₄	—	2	1	no	—
227	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
228	C₂²×D₈	C₂²×C₁₃	1	8	yes	complemented
229	#532	—	2	4	no	—
230	#532	C₂²×C₁₃	1	8	yes	complemented
231	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
232	C₂×#127	—	2	1	no	—
233	C₂×#127	—	2	1	no	—
234	C₂×#127	—	2	4	no	—
235	C₂×#127	C₂²×C₁₃	1	2	yes	—
236	C₂×#127	C₂²×C₁₃	1	2	yes	—
237	C₂×#127	C₂²×C₁₃	1	8	yes	complemented
238	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
239	C₂×#124	—	2	1	no	—
240	C₂×#121	—	2	1	no	—
241	C₂×#121	C₂²×C₁₃	1	2	yes	—
242	C₂×C₄×D₄	—	2	1	no	—
243	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
244	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
245	#493	C₂²×C₁₃	1	16	yes	complemented
246	#486	C₂²×C₁₃	1	16	yes	complemented
247	#459	C₂²×C₁₃	1	32	yes	complemented
248	#447	C₂²×C₁₃	1	32	yes	complemented
249	#431	C₂²×C₁₃	1	8	yes	complemented
250	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
251	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
252	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	2	8	no	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	4	8	no	—
258	C₂²×C₁₃	—	4	4	no	—
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	8	no	—
261	C₂²×C₁₃	—	4	8	no	—
262	C₂²×C₁₃	—	4	4	no	—
263	C₂²×C₁₃	—	8	32	no	—
264	C₂²×C₁₃	—	8	8	no	—
265	C₂²×C₁₃	—	8	16	no	—
266	C₂²×C₁₃	#535	1	2	yes	—
267	C₂²×C₁₃	C₂²×D₈	1	4	yes	—
268	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
269	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
270	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	4	4	no	—
274	C₄×C₁₃	#535	1	2	yes	—
275	C₄×C₁₃	C₂²×D₈	1	4	yes	—
276	C₄×C₁₃	C₂²×D₈	1	4	yes	—
277	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
278	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
279	C₂⁵	—	2	2	no	—
280	C₂×#41	—	2	8	no	—
281	C₂×#41	—	4	8	no	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	4	no	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	8	no	—
293	C₂²×D₄	—	2	8	no	—
294	C₂²×D₄	—	4	8	no	—
295	C₂²×D₄	—	4	8	no	—
296	C₂²×D₄	—	4	8	no	—
297	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
298	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
299	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
302	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×D₈	—	4	16	no	—
305	C₂×D₈	C₂³×C₁₃	1	32	yes	complemented
306	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
309	#127	—	2	4	no	—
310	#127	—	2	4	no	—
311	#127	—	2	8	no	—
312	#127	—	2	8	no	—
313	#127	—	2	2	no	—
314	#127	C₂³×C₁₃	1	8	yes	—
315	#127	C₂³×C₁₃	1	8	yes	—
316	#127	C₂³×C₁₃	1	4	yes	complemented
317	#124	—	2	8	no	—
318	#121	—	2	8	no	—
319	#121	—	2	4	no	—
320	#121	C₂³×C₁₃	1	8	yes	—
321	C₄×D₄	—	2	8	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
330	C₂×C₄²	D₄×C₁₃	1	4	yes	—
331	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
334	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
335	#102	C₂³×C₁₃	1	32	yes	complemented
336	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
337	C₄×C₈	C₂³×C₁₃	1	8	yes	complemented
338	C₂×C₁₃	—	2	4	no	—
339	C₂×C₁₃	—	8	4	no	—
340	C₂×C₁₃	—	8	8	no	—
341	C₂×C₁₃	#3205	1	4	yes	direct product factor
342	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
343	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
344	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	8	no	—
347	C₂⁴	—	2	4	no	—
348	C₂⁴	—	4	8	no	—
349	C₂⁴	—	4	8	no	—
350	C₂⁴	—	4	8	no	—
351	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
352	#41	—	4	32	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	16	no	—
367	C₂×D₄	—	4	16	no	—
368	C₂×D₄	—	4	8	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	16	no	—
371	C₂×D₄	—	4	32	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	32	no	—
377	C₂×D₄	—	4	8	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
380	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	4	8	no	—
386	C₂²×C₄	C₁₃×D₈	1	8	yes	complemented
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
391	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
397	D₈	—	4	32	no	—
398	C₂×C₈	—	2	8	no	—
399	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₄²	C₂×D₄×C₁₃	1	4	yes	—
406	C₄²	C₂×D₄×C₁₃	1	2	yes	—
407	C₄²	C₂×D₄×C₁₃	1	4	yes	—
408	C₄²	C₂×D₄×C₁₃	1	2	yes	—
409	C₄²	C₂⁴×C₁₃	1	2	yes	—
410	C₄²	C₂⁴×C₁₃	1	2	yes	—
411	C₁₃	C₂×#3205	1	1	yes	characteristic, direct product factor, Sylow
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	4	16	no	—
417	C₂³	—	4	16	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	16	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	4	no	—
425	C₂³	—	8	32	no	—
426	C₂³	C₂×C₁₃×D₈	1	4	yes	—
427	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
428	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	Q₈	—	4	8	no	—
430	D₄	—	2	8	no	—
431	D₄	—	2	16	no	—
432	D₄	—	4	16	no	—
433	D₄	—	4	16	no	—
434	D₄	—	4	16	no	—
435	D₄	—	4	8	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	16	no	—
438	D₄	—	4	16	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	16	no	—
441	D₄	—	4	8	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	16	no	—
450	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
451	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
452	C₂×C₄	C₂×C₁₃×D₈	1	16	yes	complemented
453	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
454	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
460	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
461	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
462	C₈	—	2	8	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	8	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	8	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	32	no	—
473	C₂²	—	8	8	no	—
474	C₂²	—	8	16	no	—
475	C₂²	C₁₃×#535	1	2	yes	—
476	C₂²	C₂²×C₁₃×D₈	1	4	yes	—
477	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
478	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
479	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	4	no	—
483	C₄	C₁₃×#535	1	2	yes	—
484	C₄	C₂²×C₁₃×D₈	1	4	yes	—
485	C₄	C₂²×C₁₃×D₈	1	4	yes	—
486	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
487	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
488	C₂	—	2	4	no	—
489	C₂	—	8	8	no	—
490	C₂	—	8	4	no	—
491	C₂	C₁₃×#3205	1	4	yes	direct product factor
492	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
493	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
494	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₂²×C₁₃×#127	C₂	semidirect
3. C₁₃×#3205	C₂	direct (N × H)
4. C₂×C₁₃×#493	C₂	semidirect
5. C₂×C₁₃×#486	C₂	semidirect
6. C₂×C₁₃×#459	C₂	semidirect
7. C₂×C₁₃×#447	C₂	semidirect
8. C₂×C₁₃×#431	C₂	semidirect
13. C₂²×C₁₃×D₈	C₂²	semidirect
15. C₁₃×#532	C₂²	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×#127	C₂²	semidirect
23. C₂×C₁₃×#127	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
30. C₁₃×#493	C₂²	semidirect
31. C₁₃×#486	C₂²	semidirect
32. C₁₃×#459	C₂²	semidirect
33. C₁₃×#447	C₂²	semidirect
34. C₁₃×#431	C₂²	semidirect
35. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
36. C₂×C₁₃×#102	C₂²	semidirect
38. C₂×C₄×C₈×C₁₃	C₂²	semidirect
65. C₂×C₁₃×D₈	C₂³	semidirect
68. C₁₃×C₄⋊Q₈	C₂³	semidirect
76. C₁₃×#127	C₂³	semidirect
83. C₄×D₄×C₁₃	C₂³	semidirect
94. C₁₃×C₄⋊C₈	C₂³	semidirect
95. C₁₃×#102	C₂³	semidirect
97. C₄×C₈×C₁₃	C₂³	semidirect
98. C₂×#3205	C₁₃	direct (N × H)
140. C₂²×C₄×C₁₃	D₈	semidirect
165. C₂×#532	C₂×C₁₃	semidirect
166. C₂²×#127	C₂×C₁₃	semidirect
167. #3205	C₂×C₁₃	direct (N × H)
168. C₂×#493	C₂×C₁₃	semidirect
169. C₂×#486	C₂×C₁₃	semidirect
170. C₂×#459	C₂×C₁₃	semidirect
171. C₂×#447	C₂×C₁₃	semidirect
172. C₂×#431	C₂×C₁₃	semidirect
213. C₂×C₄×C₁₃	C₂×D₈	semidirect
228. C₂²×D₈	C₂²×C₁₃	semidirect
230. #532	C₂²×C₁₃	semidirect
231. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
237. C₂×#127	C₂²×C₁₃	semidirect
238. C₂×#127	C₂²×C₁₃	semidirect
243. C₂×C₄×D₄	C₂²×C₁₃	semidirect
245. #493	C₂²×C₁₃	semidirect
246. #486	C₂²×C₁₃	semidirect
247. #459	C₂²×C₁₃	semidirect
248. #447	C₂²×C₁₃	semidirect
249. #431	C₂²×C₁₃	semidirect
250. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
251. C₂×#102	C₂²×C₁₃	semidirect
253. C₂×C₄×C₈	C₂²×C₁₃	semidirect
305. C₂×D₈	C₂³×C₁₃	semidirect
308. C₄⋊Q₈	C₂³×C₁₃	semidirect
316. #127	C₂³×C₁₃	semidirect
323. C₄×D₄	C₂³×C₁₃	semidirect
334. C₄⋊C₈	C₂³×C₁₃	semidirect
335. #102	C₂³×C₁₃	semidirect
337. C₄×C₈	C₂³×C₁₃	semidirect
341. C₂×C₁₃	#3205	direct (N × H)
386. C₂²×C₄	C₁₃×D₈	semidirect
411. C₁₃	C₂×#3205	direct (N × H)
452. C₂×C₄	C₂×C₁₃×D₈	semidirect
491. C₂	C₁₃×#3205	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#532	2
C₂²×C₁₃×#127	2
C₁₃×#3205	2
C₂×C₁₃×#493	2
C₂×C₁₃×#486	2
C₂×C₁₃×#459	2
C₂×C₁₃×#447	2
C₂×C₁₃×#431	2
C₂×#3205	13

Subgroups — C2×C13×#3205 #15747113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3205 #15747113