Subgroups — C₂×C₁₃×#3213 #15747122

Order 3328.

2522 conjugacy classes of subgroups.

The subgroup lattice has 536 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×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3213	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#496	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#463	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#448	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#447	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	—	2	1	no	—
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
14	C₂²×C₁₃×D₈	C₂²	1	4	yes	—
15	C₁₃×#532	—	2	4	no	—
16	C₁₃×#532	C₂²	1	8	yes	complemented
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₁₃×#124	—	2	1	no	—
20	C₂×C₁₃×#124	—	2	1	no	—
21	C₂×C₁₃×#124	—	2	4	no	—
22	C₂×C₁₃×#124	—	2	1	no	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#124	C₂²	1	2	yes	—
25	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
26	C₂×C₁₃×#121	—	2	1	no	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
30	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
31	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#496	C₂²	1	16	yes	complemented
34	C₁₃×#489	C₂²	1	16	yes	complemented
35	C₁₃×#463	C₂²	1	32	yes	complemented
36	C₁₃×#448	C₂²	1	16	yes	complemented
37	C₁₃×#447	C₂²	1	16	yes	complemented
38	C₁₃×#432	C₂²	1	8	yes	complemented
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#102	C₂²	1	4	yes	—
42	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
44	C₂⁵×C₁₃	—	2	1	no	—
45	C₂×C₁₃×#41	—	2	8	no	—
46	C₂×C₁₃×#41	—	4	8	no	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₂²×Q₈×C₁₃	—	4	4	no	—
51	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	—	2	1	no	—
55	C₂²×D₄×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	—	2	1	no	—
58	C₂²×D₄×C₁₃	—	4	4	no	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×SD₁₆	—	4	8	no	—
68	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	complemented
69	C₂×C₁₃×D₈	—	4	8	no	—
70	C₂×C₁₃×D₈	C₂³	1	16	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
72	C₁₃×C₄⋊Q₈	—	2	2	no	—
73	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
74	C₁₃×#127	—	2	2	no	—
75	C₁₃×#127	C₂³	1	4	yes	complemented
76	C₁₃×#124	—	2	4	no	—
77	C₁₃×#124	—	2	4	no	—
78	C₁₃×#124	—	2	8	no	—
79	C₁₃×#124	—	2	8	no	—
80	C₁₃×#124	—	2	8	no	—
81	C₁₃×#124	C₂³	1	8	yes	—
82	C₁₃×#124	C₂³	1	8	yes	—
83	C₁₃×#121	—	2	8	no	—
84	C₁₃×#121	—	2	4	no	—
85	C₁₃×#121	C₂³	1	8	yes	—
86	C₄×D₄×C₁₃	—	2	8	no	—
87	C₄×D₄×C₁₃	—	2	4	no	—
88	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	D₄	1	4	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
105	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
106	C₁₃×#103	C₂³	1	16	yes	complemented
107	C₁₃×#102	C₂³	1	16	yes	—
108	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
109	C₁₃×#97	C₂³	1	8	yes	complemented
110	C₂×#3213	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	—	4	4	no	—
115	C₂⁴×C₁₃	—	4	4	no	—
116	C₂⁴×C₁₃	—	4	4	no	—
117	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₁₃×#41	—	4	32	no	—
119	C₂×Q₈×C₁₃	—	2	4	no	—
120	C₂×Q₈×C₁₃	—	2	2	no	—
121	C₂×Q₈×C₁₃	—	2	4	no	—
122	C₂×Q₈×C₁₃	—	2	8	no	—
123	C₂×Q₈×C₁₃	—	4	8	no	—
124	C₂×Q₈×C₁₃	—	4	4	no	—
125	C₂×Q₈×C₁₃	—	4	8	no	—
126	C₂×Q₈×C₁₃	—	4	4	no	—
127	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
128	C₂×D₄×C₁₃	—	2	8	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	—	2	4	no	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	2	4	no	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	4	8	no	—
137	C₂×D₄×C₁₃	—	4	4	no	—
138	C₂×D₄×C₁₃	—	4	4	no	—
139	C₂×D₄×C₁₃	—	4	8	no	—
140	C₂×D₄×C₁₃	—	4	4	no	—
141	C₂×D₄×C₁₃	—	4	8	no	—
142	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₃	—	4	2	no	—
151	C₂²×C₄×C₁₃	—	4	8	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×SD₁₆	—	4	16	no	—
164	C₁₃×D₈	—	4	16	no	—
165	C₂×C₈×C₁₃	—	2	8	no	—
166	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	8	no	—
174	C₁₃×C₂²⋊C₄	—	2	8	no	—
175	C₁₃×C₂²⋊C₄	—	2	8	no	—
176	C₄²×C₁₃	C₂×D₄	1	4	yes	—
177	C₄²×C₁₃	C₂×D₄	1	2	yes	—
178	C₄²×C₁₃	C₂×D₄	1	4	yes	—
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₃	C₂⁴	1	2	yes	—
181	C₄²×C₁₃	C₂⁴	1	2	yes	—
182	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#3213	C₂×C₁₃	1	16	yes	direct product factor
185	C₂×#496	C₂×C₁₃	1	2	yes	complemented
186	C₂×#489	C₂×C₁₃	1	2	yes	complemented
187	C₂×#463	C₂×C₁₃	1	4	yes	complemented
188	C₂×#448	C₂×C₁₃	1	2	yes	complemented
189	C₂×#447	C₂×C₁₃	1	2	yes	complemented
190	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	—	4	8	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	—	4	4	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	8	no	—
201	C₂³×C₁₃	—	4	4	no	—
202	C₂³×C₁₃	—	4	4	no	—
203	C₂³×C₁₃	—	4	4	no	—
204	C₂³×C₁₃	—	8	16	no	—
205	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
206	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₃	—	2	8	no	—
209	Q₈×C₁₃	—	4	8	no	—
210	Q₈×C₁₃	—	4	8	no	—
211	Q₈×C₁₃	—	4	4	no	—
212	D₄×C₁₃	—	2	8	no	—
213	D₄×C₁₃	—	2	8	no	—
214	D₄×C₁₃	—	4	8	no	—
215	D₄×C₁₃	—	4	8	no	—
216	D₄×C₁₃	—	4	8	no	—
217	D₄×C₁₃	—	4	16	no	—
218	D₄×C₁₃	—	4	4	no	—
219	D₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	8	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	16	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	4	4	no	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
242	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
243	C₈×C₁₃	—	2	8	no	—
244	C₂²×#41	—	2	1	no	—
245	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
246	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
248	C₂²×D₈	C₂²×C₁₃	1	4	yes	—
249	#532	—	2	4	no	—
250	#532	C₂²×C₁₃	1	8	yes	complemented
251	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
252	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
253	C₂×#124	—	2	1	no	—
254	C₂×#124	—	2	1	no	—
255	C₂×#124	—	2	4	no	—
256	C₂×#124	—	2	1	no	—
257	C₂×#124	C₂²×C₁₃	1	2	yes	—
258	C₂×#124	C₂²×C₁₃	1	2	yes	—
259	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
260	C₂×#121	—	2	1	no	—
261	C₂×#121	C₂²×C₁₃	1	2	yes	—
262	C₂×C₄×D₄	—	2	1	no	—
263	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
264	C₂²×C₂²⋊C₄	—	2	1	no	—
265	C₂²×C₂²⋊C₄	—	2	1	no	—
266	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
267	#496	C₂²×C₁₃	1	16	yes	complemented
268	#489	C₂²×C₁₃	1	16	yes	complemented
269	#463	C₂²×C₁₃	1	32	yes	complemented
270	#448	C₂²×C₁₃	1	16	yes	complemented
271	#447	C₂²×C₁₃	1	16	yes	complemented
272	#432	C₂²×C₁₃	1	8	yes	complemented
273	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
274	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
275	C₂×#102	C₂²×C₁₃	1	4	yes	—
276	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
277	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	8	no	—
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	4	no	—
283	C₂²×C₁₃	—	4	4	no	—
284	C₂²×C₁₃	—	4	4	no	—
285	C₂²×C₁₃	—	4	4	no	—
286	C₂²×C₁₃	—	4	4	no	—
287	C₂²×C₁₃	—	8	16	no	—
288	C₂²×C₁₃	—	8	8	no	—
289	C₂²×C₁₃	—	8	8	no	—
290	C₂²×C₁₃	#535	1	2	yes	—
291	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
292	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
293	C₂²×C₁₃	#575	1	2	yes	—
294	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
295	C₄×C₁₃	—	2	2	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	4	4	no	—
301	C₄×C₁₃	—	4	4	no	—
302	C₄×C₁₃	#535	1	2	yes	—
303	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
304	C₂⁵	—	2	1	no	—
305	C₂×#41	—	2	8	no	—
306	C₂×#41	—	4	8	no	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	—	4	4	no	—
311	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
312	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	4	4	no	—
319	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
320	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
321	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×SD₁₆	—	4	8	no	—
328	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	complemented
329	C₂×D₈	—	4	8	no	—
330	C₂×D₈	C₂³×C₁₃	1	16	yes	—
331	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
334	#127	—	2	2	no	—
335	#127	C₂³×C₁₃	1	4	yes	complemented
336	#124	—	2	4	no	—
337	#124	—	2	4	no	—
338	#124	—	2	8	no	—
339	#124	—	2	8	no	—
340	#124	—	2	8	no	—
341	#124	C₂³×C₁₃	1	8	yes	—
342	#124	C₂³×C₁₃	1	8	yes	—
343	#121	—	2	8	no	—
344	#121	—	2	4	no	—
345	#121	C₂³×C₁₃	1	8	yes	—
346	C₄×D₄	—	2	8	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	8	no	—
356	C₂×C₂²⋊C₄	—	2	8	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄²	D₄×C₁₃	1	4	yes	—
362	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
365	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
366	#103	C₂³×C₁₃	1	16	yes	complemented
367	#102	C₂³×C₁₃	1	16	yes	—
368	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
369	#97	C₂³×C₁₃	1	8	yes	complemented
370	C₂×C₁₃	—	2	4	no	—
371	C₂×C₁₃	—	8	4	no	—
372	C₂×C₁₃	—	8	4	no	—
373	C₂×C₁₃	#3213	1	4	yes	direct product factor
374	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
375	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
376	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
377	C₂⁴	—	2	4	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	4	4	no	—
381	C₂⁴	—	4	4	no	—
382	C₂⁴	—	4	4	no	—
383	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
384	#41	—	4	32	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	8	no	—
389	C₂×Q₈	—	4	8	no	—
390	C₂×Q₈	—	4	4	no	—
391	C₂×Q₈	—	4	8	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	4	8	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	8	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	8	no	—
408	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
409	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	—	4	8	no	—
418	C₂²×C₄	—	4	4	no	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
429	SD₁₆	—	4	16	no	—
430	D₈	—	4	16	no	—
431	C₂×C₈	—	2	8	no	—
432	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₄²	C₂×D₄×C₁₃	1	4	yes	—
443	C₄²	C₂×D₄×C₁₃	1	2	yes	—
444	C₄²	C₂×D₄×C₁₃	1	4	yes	—
445	C₄²	C₂×D₄×C₁₃	1	2	yes	—
446	C₄²	C₂⁴×C₁₃	1	2	yes	—
447	C₄²	C₂⁴×C₁₃	1	2	yes	—
448	C₁₃	C₂×#3213	1	1	yes	characteristic, direct product factor, Sylow
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	4	8	no	—
454	C₂³	—	4	8	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	4	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	8	16	no	—
463	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
464	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
465	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
466	Q₈	—	2	8	no	—
467	Q₈	—	4	8	no	—
468	Q₈	—	4	8	no	—
469	Q₈	—	4	4	no	—
470	D₄	—	2	8	no	—
471	D₄	—	2	8	no	—
472	D₄	—	4	8	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	8	no	—
475	D₄	—	4	16	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	16	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
496	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
497	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
500	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
501	C₈	—	2	8	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	8	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	8	16	no	—
512	C₂²	—	8	8	no	—
513	C₂²	—	8	8	no	—
514	C₂²	C₁₃×#535	1	2	yes	—
515	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
516	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
517	C₂²	C₁₃×#575	1	2	yes	—
518	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	4	no	—
526	C₄	C₁₃×#535	1	2	yes	—
527	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
528	C₂	—	2	4	no	—
529	C₂	—	8	4	no	—
530	C₂	—	8	4	no	—
531	C₂	C₁₃×#3213	1	4	yes	direct product factor
532	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
533	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
534	C₂	C₂×C₁₃×#575	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×#124	C₂	semidirect
3. C₁₃×#3213	C₂	direct (N × H)
4. C₂×C₁₃×#496	C₂	semidirect
5. C₂×C₁₃×#489	C₂	semidirect
6. C₂×C₁₃×#463	C₂	semidirect
7. C₂×C₁₃×#448	C₂	semidirect
8. C₂×C₁₃×#447	C₂	semidirect
9. C₂×C₁₃×#432	C₂	semidirect
13. C₂²×C₁₃×SD₁₆	C₂²	semidirect
16. C₁₃×#532	C₂²	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₁₃×#127	C₂²	semidirect
25. C₂×C₁₃×#124	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₁₃×#496	C₂²	semidirect
34. C₁₃×#489	C₂²	semidirect
35. C₁₃×#463	C₂²	semidirect
36. C₁₃×#448	C₂²	semidirect
37. C₁₃×#447	C₂²	semidirect
38. C₁₃×#432	C₂²	semidirect
39. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
40. C₂×C₁₃×#103	C₂²	semidirect
43. C₂×C₁₃×#97	C₂²	semidirect
68. C₂×C₁₃×SD₁₆	C₂³	semidirect
73. C₁₃×C₄⋊Q₈	C₂³	semidirect
75. C₁₃×#127	C₂³	semidirect
88. C₄×D₄×C₁₃	C₂³	semidirect
105. C₁₃×C₄⋊C₈	C₂³	semidirect
106. C₁₃×#103	C₂³	semidirect
109. C₁₃×#97	C₂³	semidirect
110. C₂×#3213	C₁₃	direct (N × H)
182. C₂×#532	C₂×C₁₃	semidirect
183. C₂²×#124	C₂×C₁₃	semidirect
184. #3213	C₂×C₁₃	direct (N × H)
185. C₂×#496	C₂×C₁₃	semidirect
186. C₂×#489	C₂×C₁₃	semidirect
187. C₂×#463	C₂×C₁₃	semidirect
188. C₂×#448	C₂×C₁₃	semidirect
189. C₂×#447	C₂×C₁₃	semidirect
190. C₂×#432	C₂×C₁₃	semidirect
247. C₂²×SD₁₆	C₂²×C₁₃	semidirect
250. #532	C₂²×C₁₃	semidirect
251. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
252. C₂×#127	C₂²×C₁₃	semidirect
259. C₂×#124	C₂²×C₁₃	semidirect
263. C₂×C₄×D₄	C₂²×C₁₃	semidirect
267. #496	C₂²×C₁₃	semidirect
268. #489	C₂²×C₁₃	semidirect
269. #463	C₂²×C₁₃	semidirect
270. #448	C₂²×C₁₃	semidirect
271. #447	C₂²×C₁₃	semidirect
272. #432	C₂²×C₁₃	semidirect
273. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
274. C₂×#103	C₂²×C₁₃	semidirect
277. C₂×#97	C₂²×C₁₃	semidirect
328. C₂×SD₁₆	C₂³×C₁₃	semidirect
333. C₄⋊Q₈	C₂³×C₁₃	semidirect
335. #127	C₂³×C₁₃	semidirect
348. C₄×D₄	C₂³×C₁₃	semidirect
365. C₄⋊C₈	C₂³×C₁₃	semidirect
366. #103	C₂³×C₁₃	semidirect
369. #97	C₂³×C₁₃	semidirect
373. C₂×C₁₃	#3213	direct (N × H)
448. C₁₃	C₂×#3213	direct (N × H)
531. C₂	C₁₃×#3213	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×#124	2
C₁₃×#3213	2
C₂×C₁₃×#496	2
C₂×C₁₃×#489	2
C₂×C₁₃×#463	2
C₂×C₁₃×#448	2
C₂×C₁₃×#447	2
C₂×C₁₃×#432	2
C₂×#3213	13

Subgroups — C2×C13×#3213 #15747122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3213 #15747122