Subgroups — C₂×C₁₃×#3529 #15749030

Order 3328.

7418 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3529	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#563	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₃×#562	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#560	C₂	1	6	yes	maximal, complemented
6	C₂×C₁₃×#532	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₃×#529	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₃×#525	C₂	1	6	yes	maximal, complemented
9	C₂²×C₁₃×#41	C₂²	1	3	yes	—
10	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
12	C₁₃×#563	C₂²	1	48	yes	complemented
13	C₁₃×#562	C₂²	1	96	yes	complemented
14	C₁₃×H(3,𝔽₄)	C₂²	1	16	yes	complemented
15	C₁₃×#560	C₂²	1	96	yes	complemented
16	C₁₃×#532	C₂²	1	48	yes	complemented
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
18	C₂×C₁₃×#127	C₂²	1	3	yes	—
19	C₁₃×#529	C₂²	1	96	yes	complemented
20	C₂×C₁₃×#126	C₂²	1	12	yes	complemented
21	C₂×C₁₃×#125	C₂²	1	6	yes	complemented
22	C₂×C₁₃×#124	C₂²	1	6	yes	—
23	C₂×C₁₃×#124	C₂²	1	3	yes	—
24	C₂×C₁₃×#124	C₂²	1	3	yes	complemented
25	C₁₃×#525	C₂²	1	96	yes	complemented
26	C₂×C₁₃×#123	C₂²	1	6	yes	—
27	C₂×C₁₃×#123	C₂²	1	12	yes	complemented
28	C₂×C₁₃×#123	C₂²	1	6	yes	complemented
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	12	yes	complemented
31	C₂×C₁₃×#121	C₂²	1	6	yes	—
32	C₂×C₁₃×#121	C₂²	1	12	yes	—
33	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
34	C₂×C₁₃×#120	C₂²	1	6	yes	—
35	C₂×C₁₃×#120	C₂²	1	6	yes	complemented
36	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
37	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	12	yes	complemented
39	C₂×C₁₃×#117	C₂²	1	6	yes	complemented
40	C₂²×C₄²×C₁₃	C₂²	1	3	yes	complemented
41	C₂⁵×C₁₃	C₂³	1	2	yes	—
42	C₂×C₁₃×#41	—	4	12	no	—
43	C₂×C₁₃×#41	—	4	4	no	—
44	C₂×C₁₃×#41	C₂³	1	24	yes	—
45	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
54	C₂³×C₄×C₁₃	—	4	8	no	—
55	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
60	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	complemented
61	C₁₃×#127	C₂³	1	24	yes	—
62	C₁₃×#126	C₂³	1	96	yes	complemented
63	C₁₃×#125	C₂³	1	48	yes	complemented
64	C₁₃×#124	C₂³	1	48	yes	—
65	C₁₃×#124	C₂³	1	24	yes	—
66	C₁₃×#124	C₂³	1	24	yes	complemented
67	C₁₃×#123	C₂³	1	48	yes	—
68	C₁₃×#123	C₂³	1	48	yes	complemented
69	C₁₃×#123	C₂³	1	96	yes	complemented
70	C₁₃×C₂²⋊Q₈	C₂³	1	96	yes	complemented
71	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
72	C₁₃×#121	C₂³	1	96	yes	—
73	C₁₃×#121	C₂³	1	48	yes	—
74	C₁₃×#121	C₂³	1	96	yes	complemented
75	C₁₃×#120	C₂³	1	48	yes	—
76	C₁₃×#120	C₂³	1	48	yes	complemented
77	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
78	C₄×D₄×C₁₃	C₂³	1	48	yes	—
79	C₄×D₄×C₁₃	C₂³	1	96	yes	complemented
80	C₁₃×#117	C₂³	1	48	yes	complemented
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
94	C₂×#3529	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	4	4	no	—
96	C₂⁴×C₁₃	—	4	8	no	—
97	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
98	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
99	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
100	C₁₃×#41	—	4	48	no	—
101	C₁₃×#41	—	4	16	no	—
102	C₂×Q₈×C₁₃	—	4	4	no	—
103	C₂×Q₈×C₁₃	—	4	6	no	—
104	C₂×Q₈×C₁₃	—	4	2	no	—
105	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
106	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
107	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
108	C₂×D₄×C₁₃	—	4	24	no	—
109	C₂×D₄×C₁₃	—	4	12	no	—
110	C₂×D₄×C₁₃	—	4	12	no	—
111	C₂×D₄×C₁₃	—	4	6	no	—
112	C₂×D₄×C₁₃	—	4	6	no	—
113	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
114	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
115	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
116	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
117	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
118	C₂²×C₄×C₁₃	—	2	24	no	—
119	C₂²×C₄×C₁₃	—	2	12	no	—
120	C₂²×C₄×C₁₃	—	4	32	no	—
121	C₂²×C₄×C₁₃	—	4	12	no	—
122	C₂²×C₄×C₁₃	—	4	12	no	—
123	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
133	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
134	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
135	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
136	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
137	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
138	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
139	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
140	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
141	C₄²×C₁₃	C₂⁴	1	24	yes	—
142	C₄²×C₁₃	C₂⁴	1	12	yes	—
143	C₄²×C₁₃	C₂⁴	1	12	yes	—
144	#3529	C₂×C₁₃	1	32	yes	direct product factor
145	C₂×#563	C₂×C₁₃	1	3	yes	complemented
146	C₂×#562	C₂×C₁₃	1	6	yes	complemented
147	C₂×H(3,𝔽₄)	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂×#560	C₂×C₁₃	1	6	yes	complemented
149	C₂×#532	C₂×C₁₃	1	3	yes	complemented
150	C₂×#529	C₂×C₁₃	1	6	yes	complemented
151	C₂×#525	C₂×C₁₃	1	6	yes	complemented
152	C₂³×C₁₃	—	2	12	no	—
153	C₂³×C₁₃	—	2	6	no	—
154	C₂³×C₁₃	—	2	12	no	—
155	C₂³×C₁₃	—	2	24	no	—
156	C₂³×C₁₃	—	4	8	no	—
157	C₂³×C₁₃	—	4	16	no	—
158	C₂³×C₁₃	—	4	32	no	—
159	C₂³×C₁₃	C₂⁵	1	12	yes	—
160	C₂³×C₁₃	C₂⁵	1	6	yes	—
161	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
162	Q₈×C₁₃	—	4	8	no	—
163	Q₈×C₁₃	—	4	12	no	—
164	Q₈×C₁₃	—	4	4	no	—
165	D₄×C₁₃	—	4	48	no	—
166	D₄×C₁₃	—	4	24	no	—
167	D₄×C₁₃	—	4	24	no	—
168	D₄×C₁₃	—	4	12	no	—
169	D₄×C₁₃	—	4	12	no	—
170	C₂×C₄×C₁₃	—	2	12	no	—
171	C₂×C₄×C₁₃	—	2	6	no	—
172	C₂×C₄×C₁₃	—	2	12	no	—
173	C₂×C₄×C₁₃	—	2	12	no	—
174	C₂×C₄×C₁₃	—	2	48	no	—
175	C₂×C₄×C₁₃	—	2	24	no	—
176	C₂×C₄×C₁₃	—	4	24	no	—
177	C₂×C₄×C₁₃	—	4	24	no	—
178	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
179	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
180	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
181	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
182	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
183	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
184	C₂²×#41	C₂²×C₁₃	1	3	yes	—
185	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
186	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
187	#563	C₂²×C₁₃	1	48	yes	complemented
188	#562	C₂²×C₁₃	1	96	yes	complemented
189	H(3,𝔽₄)	C₂²×C₁₃	1	16	yes	complemented
190	#560	C₂²×C₁₃	1	96	yes	complemented
191	#532	C₂²×C₁₃	1	48	yes	complemented
192	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
193	C₂×#127	C₂²×C₁₃	1	3	yes	—
194	#529	C₂²×C₁₃	1	96	yes	complemented
195	C₂×#126	C₂²×C₁₃	1	12	yes	complemented
196	C₂×#125	C₂²×C₁₃	1	6	yes	complemented
197	C₂×#124	C₂²×C₁₃	1	6	yes	—
198	C₂×#124	C₂²×C₁₃	1	3	yes	—
199	C₂×#124	C₂²×C₁₃	1	3	yes	complemented
200	#525	C₂²×C₁₃	1	96	yes	complemented
201	C₂×#123	C₂²×C₁₃	1	6	yes	—
202	C₂×#123	C₂²×C₁₃	1	6	yes	complemented
203	C₂×#123	C₂²×C₁₃	1	12	yes	complemented
204	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	12	yes	complemented
205	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
206	C₂×#121	C₂²×C₁₃	1	12	yes	—
207	C₂×#121	C₂²×C₁₃	1	6	yes	—
208	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
209	C₂×#120	C₂²×C₁₃	1	6	yes	—
210	C₂×#120	C₂²×C₁₃	1	6	yes	complemented
211	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
212	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
213	C₂×C₄×D₄	C₂²×C₁₃	1	12	yes	complemented
214	C₂×#117	C₂²×C₁₃	1	6	yes	complemented
215	C₂²×C₄²	C₂²×C₁₃	1	3	yes	complemented
216	C₂²×C₁₃	—	2	12	no	—
217	C₂²×C₁₃	—	2	6	no	—
218	C₂²×C₁₃	—	2	12	no	—
219	C₂²×C₁₃	—	2	24	no	—
220	C₂²×C₁₃	—	4	32	no	—
221	C₂²×C₁₃	—	4	12	no	—
222	C₂²×C₁₃	—	4	24	no	—
223	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
224	C₂²×C₁₃	#585	1	4	yes	—
225	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
226	C₄×C₁₃	—	2	12	no	—
227	C₄×C₁₃	—	2	6	no	—
228	C₄×C₁₃	—	2	12	no	—
229	C₄×C₁₃	—	2	12	no	—
230	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
231	C₂⁵	C₂³×C₁₃	1	2	yes	—
232	C₂×#41	—	4	12	no	—
233	C₂×#41	—	4	4	no	—
234	C₂×#41	C₂³×C₁₃	1	24	yes	—
235	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
236	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
237	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
238	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
240	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
241	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
242	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
243	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
244	C₂³×C₄	—	4	8	no	—
245	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
246	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
247	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
248	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
249	C₂³×C₄	C₂³×C₁₃	1	16	yes	complemented
250	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
251	#127	C₂³×C₁₃	1	24	yes	—
252	#126	C₂³×C₁₃	1	96	yes	complemented
253	#125	C₂³×C₁₃	1	48	yes	complemented
254	#124	C₂³×C₁₃	1	48	yes	—
255	#124	C₂³×C₁₃	1	24	yes	—
256	#124	C₂³×C₁₃	1	24	yes	complemented
257	#123	C₂³×C₁₃	1	48	yes	—
258	#123	C₂³×C₁₃	1	48	yes	complemented
259	#123	C₂³×C₁₃	1	96	yes	complemented
260	C₂²⋊Q₈	C₂³×C₁₃	1	96	yes	complemented
261	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
262	#121	C₂³×C₁₃	1	96	yes	—
263	#121	C₂³×C₁₃	1	48	yes	—
264	#121	C₂³×C₁₃	1	96	yes	complemented
265	#120	C₂³×C₁₃	1	48	yes	—
266	#120	C₂³×C₁₃	1	48	yes	complemented
267	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
268	C₄×D₄	C₂³×C₁₃	1	48	yes	—
269	C₄×D₄	C₂³×C₁₃	1	96	yes	complemented
270	#117	C₂³×C₁₃	1	48	yes	complemented
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
280	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
281	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
282	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
283	C₂×C₄²	C₂³×C₁₃	1	24	yes	complemented
284	C₂×C₁₃	—	4	6	no	—
285	C₂×C₁₃	—	4	12	no	—
286	C₂×C₁₃	#3529	1	4	yes	direct product factor
287	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₁₃	C₂×#585	1	2	yes	—
289	C₂⁴	—	4	4	no	—
290	C₂⁴	—	4	8	no	—
291	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
292	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
293	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
294	#41	—	4	48	no	—
295	#41	—	4	16	no	—
296	C₂×Q₈	—	4	6	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	—	4	4	no	—
299	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
300	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
301	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
302	C₂×D₄	—	4	12	no	—
303	C₂×D₄	—	4	6	no	—
304	C₂×D₄	—	4	6	no	—
305	C₂×D₄	—	4	24	no	—
306	C₂×D₄	—	4	12	no	—
307	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
308	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
309	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
310	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
311	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
312	C₂²×C₄	—	2	24	no	—
313	C₂²×C₄	—	2	12	no	—
314	C₂²×C₄	—	4	32	no	—
315	C₂²×C₄	—	4	12	no	—
316	C₂²×C₄	—	4	12	no	—
317	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
318	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
319	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
320	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
321	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
322	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
323	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
324	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
325	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
327	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
328	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
329	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
330	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
331	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
332	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
333	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
334	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
335	C₄²	C₂⁴×C₁₃	1	24	yes	—
336	C₄²	C₂⁴×C₁₃	1	12	yes	—
337	C₄²	C₂⁴×C₁₃	1	12	yes	—
338	C₁₃	C₂×#3529	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	2	12	no	—
340	C₂³	—	2	6	no	—
341	C₂³	—	2	12	no	—
342	C₂³	—	2	24	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	16	no	—
345	C₂³	—	4	32	no	—
346	C₂³	C₂⁵×C₁₃	1	12	yes	—
347	C₂³	C₂⁵×C₁₃	1	6	yes	—
348	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
349	Q₈	—	4	12	no	—
350	Q₈	—	4	4	no	—
351	Q₈	—	4	8	no	—
352	D₄	—	4	48	no	—
353	D₄	—	4	24	no	—
354	D₄	—	4	24	no	—
355	D₄	—	4	12	no	—
356	D₄	—	4	12	no	—
357	C₂×C₄	—	2	12	no	—
358	C₂×C₄	—	2	6	no	—
359	C₂×C₄	—	2	12	no	—
360	C₂×C₄	—	2	12	no	—
361	C₂×C₄	—	2	48	no	—
362	C₂×C₄	—	2	24	no	—
363	C₂×C₄	—	4	24	no	—
364	C₂×C₄	—	4	24	no	—
365	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
366	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
367	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
368	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
369	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
370	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
371	C₂²	—	2	12	no	—
372	C₂²	—	2	6	no	—
373	C₂²	—	2	12	no	—
374	C₂²	—	2	24	no	—
375	C₂²	—	4	32	no	—
376	C₂²	—	4	12	no	—
377	C₂²	—	4	24	no	—
378	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
379	C₂²	C₁₃×#585	1	4	yes	—
380	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
381	C₄	—	2	12	no	—
382	C₄	—	2	6	no	—
383	C₄	—	2	12	no	—
384	C₄	—	2	12	no	—
385	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
386	C₂	—	4	12	no	—
387	C₂	—	4	6	no	—
388	C₂	C₁₃×#3529	1	4	yes	direct product factor
389	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3529	C₂	direct (N × H)
2. C₂×C₁₃×#563	C₂	semidirect
3. C₂×C₁₃×#562	C₂	semidirect
4. C₂×C₁₃×H(3,𝔽₄)	C₂	semidirect
5. C₂×C₁₃×#560	C₂	semidirect
6. C₂×C₁₃×#532	C₂	semidirect
7. C₂×C₁₃×#529	C₂	semidirect
8. C₂×C₁₃×#525	C₂	semidirect
10. C₂²×C₁₃×#41	C₂²	semidirect
11. C₂⁴×C₄×C₁₃	C₂²	semidirect
12. C₁₃×#563	C₂²	semidirect
13. C₁₃×#562	C₂²	semidirect
14. C₁₃×H(3,𝔽₄)	C₂²	semidirect
15. C₁₃×#560	C₂²	semidirect
16. C₁₃×#532	C₂²	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₁₃×#529	C₂²	semidirect
20. C₂×C₁₃×#126	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
25. C₁₃×#525	C₂²	semidirect
27. C₂×C₁₃×#123	C₂²	semidirect
28. C₂×C₁₃×#123	C₂²	semidirect
29. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×#121	C₂²	semidirect
35. C₂×C₁₃×#120	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃	C₂²	semidirect
39. C₂×C₁₃×#117	C₂²	semidirect
40. C₂²×C₄²×C₁₃	C₂²	semidirect
45. C₂×C₁₃×#41	C₂³	semidirect
59. C₂³×C₄×C₁₃	C₂³	semidirect
60. C₁₃×C₄⋊Q₈	C₂³	semidirect
62. C₁₃×#126	C₂³	semidirect
63. C₁₃×#125	C₂³	semidirect
66. C₁₃×#124	C₂³	semidirect
68. C₁₃×#123	C₂³	semidirect
69. C₁₃×#123	C₂³	semidirect
70. C₁₃×C₂²⋊Q₈	C₂³	semidirect
71. C₁₃×C₂²⋊Q₈	C₂³	semidirect
74. C₁₃×#121	C₂³	semidirect
76. C₁₃×#120	C₂³	semidirect
77. C₄×Q₈×C₁₃	C₂³	semidirect
79. C₄×D₄×C₁₃	C₂³	semidirect
80. C₁₃×#117	C₂³	semidirect
93. C₂×C₄²×C₁₃	C₂³	semidirect
94. C₂×#3529	C₁₃	direct (N × H)
144. #3529	C₂×C₁₃	direct (N × H)
145. C₂×#563	C₂×C₁₃	semidirect
146. C₂×#562	C₂×C₁₃	semidirect
147. C₂×H(3,𝔽₄)	C₂×C₁₃	semidirect
148. C₂×#560	C₂×C₁₃	semidirect
149. C₂×#532	C₂×C₁₃	semidirect
150. C₂×#529	C₂×C₁₃	semidirect
151. C₂×#525	C₂×C₁₃	semidirect
185. C₂²×#41	C₂²×C₁₃	semidirect
186. C₂⁴×C₄	C₂²×C₁₃	semidirect
187. #563	C₂²×C₁₃	semidirect
188. #562	C₂²×C₁₃	semidirect
189. H(3,𝔽₄)	C₂²×C₁₃	semidirect
190. #560	C₂²×C₁₃	semidirect
191. #532	C₂²×C₁₃	semidirect
192. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
194. #529	C₂²×C₁₃	semidirect
195. C₂×#126	C₂²×C₁₃	semidirect
196. C₂×#125	C₂²×C₁₃	semidirect
199. C₂×#124	C₂²×C₁₃	semidirect
200. #525	C₂²×C₁₃	semidirect
202. C₂×#123	C₂²×C₁₃	semidirect
203. C₂×#123	C₂²×C₁₃	semidirect
204. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
205. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
208. C₂×#121	C₂²×C₁₃	semidirect
210. C₂×#120	C₂²×C₁₃	semidirect
211. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
213. C₂×C₄×D₄	C₂²×C₁₃	semidirect
214. C₂×#117	C₂²×C₁₃	semidirect
215. C₂²×C₄²	C₂²×C₁₃	semidirect
235. C₂×#41	C₂³×C₁₃	semidirect
249. C₂³×C₄	C₂³×C₁₃	semidirect
250. C₄⋊Q₈	C₂³×C₁₃	semidirect
252. #126	C₂³×C₁₃	semidirect
253. #125	C₂³×C₁₃	semidirect
256. #124	C₂³×C₁₃	semidirect
258. #123	C₂³×C₁₃	semidirect
259. #123	C₂³×C₁₃	semidirect
260. C₂²⋊Q₈	C₂³×C₁₃	semidirect
261. C₂²⋊Q₈	C₂³×C₁₃	semidirect
264. #121	C₂³×C₁₃	semidirect
266. #120	C₂³×C₁₃	semidirect
267. C₄×Q₈	C₂³×C₁₃	semidirect
269. C₄×D₄	C₂³×C₁₃	semidirect
270. #117	C₂³×C₁₃	semidirect
283. C₂×C₄²	C₂³×C₁₃	semidirect
286. C₂×C₁₃	#3529	direct (N × H)
338. C₁₃	C₂×#3529	direct (N × H)
388. C₂	C₁₃×#3529	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3529	2
C₂×C₁₃×#563	2
C₂×C₁₃×#562	2
C₂×C₁₃×H(3,𝔽₄)	2
C₂×C₁₃×#560	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂×#3529	13

Subgroups — C2×C13×#3529 #15749030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3529 #15749030