Subgroups — C₂×C₁₃×#3496 #15749103

Order 3328.

12378 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3496	C₂	1	32	yes	maximal, direct product factor
3	C₂×C₁₃×#547	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#546	C₂	1	8	yes	maximal, complemented
5	C₂×D₄²×C₁₃	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#537	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#534	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#532	C₂	1	2	yes	maximal, complemented
9	C₂²×C₁₃×#121	C₂	1	4	yes	maximal, complemented
10	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×H(5,𝔽₂)	—	2	32	no	—
12	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	32	yes	complemented
13	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
14	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	8	yes	complemented
17	C₂³×D₄×C₁₃	C₂²	1	8	yes	complemented
18	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
19	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
20	C₁₃×#547	C₂²	1	64	yes	complemented
21	C₁₃×#546	C₂²	1	128	yes	complemented
22	D₄²×C₁₃	C₂²	1	64	yes	complemented
23	C₁₃×#537	C₂²	1	32	yes	complemented
24	C₁₃×#534	C₂²	1	64	yes	complemented
25	C₁₃×#532	C₂²	1	32	yes	complemented
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#123	C₂²	1	16	yes	complemented
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
31	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
34	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
37	C₂×C₁₃×#121	C₂²	1	64	yes	complemented
38	C₂×C₁₃×#120	C₂²	1	16	yes	complemented
39	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
40	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
41	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
42	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
43	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
47	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
48	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₂⁵×C₁₃	C₂³	1	8	yes	—
50	C₂⁵×C₁₃	C₂³	1	2	yes	—
51	C₁₃×H(5,𝔽₂)	—	2	256	no	—
52	C₂×C₁₃×#41	—	2	64	no	—
53	C₂×C₁₃×#41	—	2	32	no	—
54	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
55	C₂×C₁₃×#41	C₂³	1	64	yes	complemented
56	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	—	2	64	no	—
58	C₂²×D₄×C₁₃	—	2	64	no	—
59	C₂²×D₄×C₁₃	—	4	16	no	—
60	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	64	yes	complemented
70	C₂²×D₄×C₁₃	C₂³	1	64	yes	complemented
71	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
72	C₂³×C₄×C₁₃	—	4	8	no	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
82	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
83	C₁₃×#127	C₂³	1	16	yes	complemented
84	C₁₃×#124	C₂³	1	32	yes	complemented
85	C₁₃×#123	C₂³	1	128	yes	complemented
86	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
87	C₁₃×#121	C₂³	1	32	yes	complemented
88	C₁₃×#121	C₂³	1	64	yes	complemented
89	C₁₃×#121	C₂³	1	64	yes	complemented
90	C₁₃×#121	C₂³	1	64	yes	complemented
91	C₁₃×#121	C₂³	1	32	yes	complemented
92	C₁₃×#121	C₂³	1	64	yes	complemented
93	C₁₃×#120	C₂³	1	128	yes	complemented
94	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
95	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
96	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
97	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	complemented
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	64	yes	complemented
110	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
113	C₂×#3496	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	32	no	—
115	C₂⁴×C₁₃	—	4	4	no	—
116	C₂⁴×C₁₃	—	4	4	no	—
117	C₂⁴×C₁₃	—	4	16	no	—
118	C₂⁴×C₁₃	—	4	16	no	—
119	C₂⁴×C₁₃	C₂×D₄	1	16	yes	complemented
120	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
121	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
122	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂⁴×C₁₃	C₂⁴	1	32	yes	—
124	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
125	C₁₃×#41	—	2	256	no	—
126	C₁₃×#41	—	2	128	no	—
127	C₂×Q₈×C₁₃	—	2	16	no	—
128	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
129	C₂×D₄×C₁₃	—	2	64	no	—
130	C₂×D₄×C₁₃	—	2	32	no	—
131	C₂×D₄×C₁₃	—	2	256	no	—
132	C₂×D₄×C₁₃	—	2	256	no	—
133	C₂×D₄×C₁₃	—	2	16	no	—
134	C₂×D₄×C₁₃	—	2	16	no	—
135	C₂×D₄×C₁₃	—	4	64	no	—
136	C₂×D₄×C₁₃	—	4	16	no	—
137	C₂×D₄×C₁₃	—	4	8	no	—
138	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	complemented
139	C₂×D₄×C₁₃	C₂×D₄	1	64	yes	complemented
140	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
141	C₂×D₄×C₁₃	C₂⁴	1	64	yes	—
142	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
144	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
145	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
147	C₂²×C₄×C₁₃	—	2	32	no	—
148	C₂²×C₄×C₁₃	—	2	32	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	16	no	—
151	C₂²×C₄×C₁₃	—	4	32	no	—
152	C₂²×C₄×C₁₃	—	4	8	no	—
153	C₂²×C₄×C₁₃	—	4	4	no	—
154	C₂²×C₄×C₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
156	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
173	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
174	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
175	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
176	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
177	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
178	C₄²×C₁₃	C₂⁴	1	8	yes	—
179	C₄²×C₁₃	C₂⁴	1	8	yes	—
180	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	2	yes	complemented
181	#3496	C₂×C₁₃	1	32	yes	direct product factor
182	C₂×#547	C₂×C₁₃	1	4	yes	complemented
183	C₂×#546	C₂×C₁₃	1	8	yes	complemented
184	C₂×D₄²	C₂×C₁₃	1	4	yes	complemented
185	C₂×#537	C₂×C₁₃	1	2	yes	complemented
186	C₂×#534	C₂×C₁₃	1	4	yes	complemented
187	C₂×#532	C₂×C₁₃	1	2	yes	complemented
188	C₂²×#121	C₂×C₁₃	1	4	yes	complemented
189	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	8	no	—
194	C₂³×C₁₃	—	2	16	no	—
195	C₂³×C₁₃	—	2	16	no	—
196	C₂³×C₁₃	—	2	16	no	—
197	C₂³×C₁₃	—	2	64	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	—	4	32	no	—
200	C₂³×C₁₃	—	4	8	no	—
201	C₂³×C₁₃	—	4	32	no	—
202	C₂³×C₁₃	—	4	32	no	—
203	C₂³×C₁₃	—	8	64	no	—
204	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
205	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
206	C₂³×C₁₃	C₂²×D₄	1	32	yes	complemented
207	C₂³×C₁₃	C₂⁵	1	16	yes	—
208	C₂³×C₁₃	C₂⁵	1	8	yes	—
209	C₂³×C₁₃	C₂⁵	1	2	yes	—
210	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	32	no	—
212	D₄×C₁₃	—	2	128	no	—
213	D₄×C₁₃	—	2	64	no	—
214	D₄×C₁₃	—	2	32	no	—
215	D₄×C₁₃	—	2	32	no	—
216	D₄×C₁₃	—	4	32	no	—
217	D₄×C₁₃	—	4	16	no	—
218	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
219	C₂×C₄×C₁₃	—	2	16	no	—
220	C₂×C₄×C₁₃	—	2	64	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	64	no	—
225	C₂×C₄×C₁₃	—	2	8	no	—
226	C₂×C₄×C₁₃	—	2	32	no	—
227	C₂×C₄×C₁₃	—	4	16	no	—
228	C₂×C₄×C₁₃	—	4	8	no	—
229	C₂×C₄×C₁₃	—	4	4	no	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	complemented
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
233	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
234	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
235	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
237	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
238	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
239	C₂×H(5,𝔽₂)	—	2	32	no	—
240	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	32	yes	complemented
241	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
242	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
243	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
244	C₂³×D₄	C₂²×C₁₃	1	8	yes	complemented
245	C₂³×D₄	C₂²×C₁₃	1	8	yes	complemented
246	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
247	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
248	#547	C₂²×C₁₃	1	64	yes	complemented
249	#546	C₂²×C₁₃	1	128	yes	complemented
250	D₄²	C₂²×C₁₃	1	64	yes	complemented
251	#537	C₂²×C₁₃	1	32	yes	complemented
252	#534	C₂²×C₁₃	1	64	yes	complemented
253	#532	C₂²×C₁₃	1	32	yes	complemented
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
255	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
256	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
257	C₂×#123	C₂²×C₁₃	1	16	yes	complemented
258	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
259	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
260	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
261	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
262	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
263	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
264	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
265	C₂×#121	C₂²×C₁₃	1	64	yes	complemented
266	C₂×#120	C₂²×C₁₃	1	16	yes	complemented
267	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
268	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
269	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
270	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
271	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
272	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
273	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
274	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
275	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
276	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	8	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	2	8	no	—
281	C₂²×C₁₃	—	2	8	no	—
282	C₂²×C₁₃	—	2	32	no	—
283	C₂²×C₁₃	—	2	16	no	—
284	C₂²×C₁₃	—	2	16	no	—
285	C₂²×C₁₃	—	2	16	no	—
286	C₂²×C₁₃	—	4	32	no	—
287	C₂²×C₁₃	—	4	32	no	—
288	C₂²×C₁₃	—	8	64	no	—
289	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
290	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
291	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
292	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
293	C₂²×C₁₃	#585	1	2	yes	—
294	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
295	C₄×C₁₃	—	2	16	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	8	no	—
298	C₄×C₁₃	—	2	4	no	—
299	C₄×C₁₃	C₂³×D₄	1	8	yes	—
300	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
301	C₂⁵	C₂³×C₁₃	1	8	yes	—
302	C₂⁵	C₂³×C₁₃	1	2	yes	—
303	H(5,𝔽₂)	—	2	256	no	—
304	C₂×#41	—	2	64	no	—
305	C₂×#41	—	2	32	no	—
306	C₂×#41	C₂³×C₁₃	1	32	yes	complemented
307	C₂×#41	C₂³×C₁₃	1	64	yes	complemented
308	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
309	C₂²×D₄	—	2	64	no	—
310	C₂²×D₄	—	2	64	no	—
311	C₂²×D₄	—	4	16	no	—
312	C₂²×D₄	D₄×C₁₃	1	16	yes	complemented
313	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
314	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
315	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
316	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
317	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
318	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
319	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
320	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
321	C₂²×D₄	C₂³×C₁₃	1	64	yes	complemented
322	C₂²×D₄	C₂³×C₁₃	1	64	yes	complemented
323	C₂²×D₄	C₂³×C₁₃	1	32	yes	complemented
324	C₂³×C₄	—	4	8	no	—
325	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
327	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
328	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
330	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃	1	16	yes	complemented
334	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
335	#127	C₂³×C₁₃	1	16	yes	complemented
336	#124	C₂³×C₁₃	1	32	yes	complemented
337	#123	C₂³×C₁₃	1	128	yes	complemented
338	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
339	#121	C₂³×C₁₃	1	32	yes	complemented
340	#121	C₂³×C₁₃	1	64	yes	complemented
341	#121	C₂³×C₁₃	1	64	yes	complemented
342	#121	C₂³×C₁₃	1	64	yes	complemented
343	#121	C₂³×C₁₃	1	32	yes	complemented
344	#121	C₂³×C₁₃	1	64	yes	complemented
345	#120	C₂³×C₁₃	1	128	yes	complemented
346	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
347	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
348	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
349	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	complemented
356	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
361	C₂×C₂²⋊C₄	C₂³×C₁₃	1	64	yes	complemented
362	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
363	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
364	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
365	C₂×C₁₃	—	2	4	no	—
366	C₂×C₁₃	—	2	16	no	—
367	C₂×C₁₃	—	4	16	no	—
368	C₂×C₁₃	#3496	1	4	yes	direct product factor
369	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
370	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
372	C₂⁴	—	2	32	no	—
373	C₂⁴	—	4	4	no	—
374	C₂⁴	—	4	4	no	—
375	C₂⁴	—	4	16	no	—
376	C₂⁴	—	4	16	no	—
377	C₂⁴	C₂×D₄×C₁₃	1	16	yes	complemented
378	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
379	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
380	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
381	C₂⁴	C₂⁴×C₁₃	1	32	yes	—
382	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
383	#41	—	2	256	no	—
384	#41	—	2	128	no	—
385	C₂×Q₈	—	2	16	no	—
386	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
387	C₂×D₄	—	2	64	no	—
388	C₂×D₄	—	2	32	no	—
389	C₂×D₄	—	2	256	no	—
390	C₂×D₄	—	2	256	no	—
391	C₂×D₄	—	2	16	no	—
392	C₂×D₄	—	2	16	no	—
393	C₂×D₄	—	4	64	no	—
394	C₂×D₄	—	4	16	no	—
395	C₂×D₄	—	4	8	no	—
396	C₂×D₄	C₂×D₄×C₁₃	1	32	yes	complemented
397	C₂×D₄	C₂×D₄×C₁₃	1	64	yes	complemented
398	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
399	C₂×D₄	C₂⁴×C₁₃	1	64	yes	—
400	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
401	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
402	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
403	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
404	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
405	C₂²×C₄	—	2	32	no	—
406	C₂²×C₄	—	2	32	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	16	no	—
409	C₂²×C₄	—	4	32	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	complemented
414	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
419	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
420	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
422	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
428	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
429	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
430	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
431	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
432	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
433	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
434	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
435	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
436	C₄²	C₂⁴×C₁₃	1	8	yes	—
437	C₄²	C₂⁴×C₁₃	1	8	yes	—
438	C₁₃	C₂×#3496	1	1	yes	characteristic, direct product factor, Sylow
439	C₂³	—	2	2	no	—
440	C₂³	—	2	8	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	8	no	—
443	C₂³	—	2	16	no	—
444	C₂³	—	2	16	no	—
445	C₂³	—	2	16	no	—
446	C₂³	—	2	64	no	—
447	C₂³	—	4	8	no	—
448	C₂³	—	4	32	no	—
449	C₂³	—	4	8	no	—
450	C₂³	—	4	32	no	—
451	C₂³	—	4	32	no	—
452	C₂³	—	8	64	no	—
453	C₂³	C₂²×D₄×C₁₃	1	16	yes	—
454	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
455	C₂³	C₂²×D₄×C₁₃	1	32	yes	complemented
456	C₂³	C₂⁵×C₁₃	1	16	yes	—
457	C₂³	C₂⁵×C₁₃	1	8	yes	—
458	C₂³	C₂⁵×C₁₃	1	2	yes	—
459	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
460	Q₈	—	2	32	no	—
461	D₄	—	2	128	no	—
462	D₄	—	2	64	no	—
463	D₄	—	2	32	no	—
464	D₄	—	2	32	no	—
465	D₄	—	4	32	no	—
466	D₄	—	4	16	no	—
467	D₄	C₂²×D₄×C₁₃	1	64	yes	complemented
468	C₂×C₄	—	2	16	no	—
469	C₂×C₄	—	2	64	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	64	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	2	32	no	—
476	C₂×C₄	—	4	16	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	16	yes	complemented
481	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
482	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
483	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
484	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
485	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
486	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
487	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	8	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	8	no	—
493	C₂²	—	2	32	no	—
494	C₂²	—	2	16	no	—
495	C₂²	—	2	16	no	—
496	C₂²	—	2	16	no	—
497	C₂²	—	4	32	no	—
498	C₂²	—	4	32	no	—
499	C₂²	—	8	64	no	—
500	C₂²	C₂³×D₄×C₁₃	1	16	yes	—
501	C₂²	C₂³×D₄×C₁₃	1	4	yes	—
502	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
503	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
504	C₂²	C₁₃×#585	1	2	yes	—
505	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
506	C₄	—	2	16	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	8	no	—
509	C₄	—	2	4	no	—
510	C₄	C₂³×D₄×C₁₃	1	8	yes	—
511	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	complemented
512	C₂	—	2	4	no	—
513	C₂	—	2	16	no	—
514	C₂	—	4	16	no	—
515	C₂	C₁₃×#3496	1	4	yes	direct product factor
516	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
517	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×H(5,𝔽₂)	C₂	semidirect
2. C₁₃×#3496	C₂	direct (N × H)
3. C₂×C₁₃×#547	C₂	semidirect
4. C₂×C₁₃×#546	C₂	semidirect
5. C₂×D₄²×C₁₃	C₂	semidirect
6. C₂×C₁₃×#537	C₂	semidirect
7. C₂×C₁₃×#534	C₂	semidirect
8. C₂×C₁₃×#532	C₂	semidirect
9. C₂²×C₁₃×#121	C₂	semidirect
10. C₂²×C₄×D₄×C₁₃	C₂	semidirect
12. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
14. C₂²×C₁₃×#41	C₂²	semidirect
16. C₂³×D₄×C₁₃	C₂²	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₂⁴×C₄×C₁₃	C₂²	semidirect
20. C₁₃×#547	C₂²	semidirect
21. C₁₃×#546	C₂²	semidirect
22. D₄²×C₁₃	C₂²	semidirect
23. C₁₃×#537	C₂²	semidirect
24. C₁₃×#534	C₂²	semidirect
25. C₁₃×#532	C₂²	semidirect
26. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₁₃×#127	C₂²	semidirect
28. C₂×C₁₃×#124	C₂²	semidirect
29. C₂×C₁₃×#123	C₂²	semidirect
30. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×#121	C₂²	semidirect
32. C₂×C₁₃×#121	C₂²	semidirect
33. C₂×C₁₃×#121	C₂²	semidirect
34. C₂×C₁₃×#121	C₂²	semidirect
35. C₂×C₁₃×#121	C₂²	semidirect
36. C₂×C₁₃×#121	C₂²	semidirect
37. C₂×C₁₃×#121	C₂²	semidirect
38. C₂×C₁₃×#120	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₂×C₄×D₄×C₁₃	C₂²	semidirect
41. C₂×C₄×D₄×C₁₃	C₂²	semidirect
42. C₂×C₄×D₄×C₁₃	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃	C₂²	semidirect
44. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
45. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
46. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
47. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
48. C₂²×C₄²×C₁₃	C₂²	semidirect
54. C₂×C₁₃×#41	C₂³	semidirect
55. C₂×C₁₃×#41	C₂³	semidirect
60. C₂²×D₄×C₁₃	D₄	semidirect
69. C₂²×D₄×C₁₃	C₂³	semidirect
70. C₂²×D₄×C₁₃	C₂³	semidirect
71. C₂²×D₄×C₁₃	C₂³	semidirect
81. C₂³×C₄×C₁₃	C₂³	semidirect
82. C₁₃×C₄⋊Q₈	C₂³	semidirect
83. C₁₃×#127	C₂³	semidirect
84. C₁₃×#124	C₂³	semidirect
85. C₁₃×#123	C₂³	semidirect
86. C₁₃×C₂²⋊Q₈	C₂³	semidirect
87. C₁₃×#121	C₂³	semidirect
88. C₁₃×#121	C₂³	semidirect
89. C₁₃×#121	C₂³	semidirect
90. C₁₃×#121	C₂³	semidirect
91. C₁₃×#121	C₂³	semidirect
92. C₁₃×#121	C₂³	semidirect
93. C₁₃×#120	C₂³	semidirect
94. C₄×D₄×C₁₃	C₂³	semidirect
95. C₄×D₄×C₁₃	C₂³	semidirect
96. C₄×D₄×C₁₃	C₂³	semidirect
97. C₄×D₄×C₁₃	C₂³	semidirect
102. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
103. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
108. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
109. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
112. C₂×C₄²×C₁₃	C₂³	semidirect
113. C₂×#3496	C₁₃	direct (N × H)
119. C₂⁴×C₁₃	C₂×D₄	semidirect
138. C₂×D₄×C₁₃	C₂×D₄	semidirect
139. C₂×D₄×C₁₃	C₂×D₄	semidirect
155. C₂²×C₄×C₁₃	C₂×D₄	semidirect
180. C₂²×H(5,𝔽₂)	C₂×C₁₃	semidirect
181. #3496	C₂×C₁₃	direct (N × H)
182. C₂×#547	C₂×C₁₃	semidirect
183. C₂×#546	C₂×C₁₃	semidirect
184. C₂×D₄²	C₂×C₁₃	semidirect
185. C₂×#537	C₂×C₁₃	semidirect
186. C₂×#534	C₂×C₁₃	semidirect
187. C₂×#532	C₂×C₁₃	semidirect
188. C₂²×#121	C₂×C₁₃	semidirect
189. C₂²×C₄×D₄	C₂×C₁₃	semidirect
206. C₂³×C₁₃	C₂²×D₄	semidirect
218. D₄×C₁₃	C₂²×D₄	semidirect
231. C₂×C₄×C₁₃	C₂²×D₄	semidirect
232. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
240. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
241. C₂²×#41	C₂²×C₁₃	semidirect
242. C₂²×#41	C₂²×C₁₃	semidirect
244. C₂³×D₄	C₂²×C₁₃	semidirect
245. C₂³×D₄	C₂²×C₁₃	semidirect
246. C₂³×D₄	C₂²×C₁₃	semidirect
247. C₂⁴×C₄	C₂²×C₁₃	semidirect
248. #547	C₂²×C₁₃	semidirect
249. #546	C₂²×C₁₃	semidirect
250. D₄²	C₂²×C₁₃	semidirect
251. #537	C₂²×C₁₃	semidirect
252. #534	C₂²×C₁₃	semidirect
253. #532	C₂²×C₁₃	semidirect
254. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
255. C₂×#127	C₂²×C₁₃	semidirect
256. C₂×#124	C₂²×C₁₃	semidirect
257. C₂×#123	C₂²×C₁₃	semidirect
258. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
259. C₂×#121	C₂²×C₁₃	semidirect
260. C₂×#121	C₂²×C₁₃	semidirect
261. C₂×#121	C₂²×C₁₃	semidirect
262. C₂×#121	C₂²×C₁₃	semidirect
263. C₂×#121	C₂²×C₁₃	semidirect
264. C₂×#121	C₂²×C₁₃	semidirect
265. C₂×#121	C₂²×C₁₃	semidirect
266. C₂×#120	C₂²×C₁₃	semidirect
267. C₂×C₄×D₄	C₂²×C₁₃	semidirect
268. C₂×C₄×D₄	C₂²×C₁₃	semidirect
269. C₂×C₄×D₄	C₂²×C₁₃	semidirect
270. C₂×C₄×D₄	C₂²×C₁₃	semidirect
271. C₂×C₄×D₄	C₂²×C₁₃	semidirect
272. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
273. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
274. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
275. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
276. C₂²×C₄²	C₂²×C₁₃	semidirect
300. C₄×C₁₃	C₂×H(5,𝔽₂)	semidirect
306. C₂×#41	C₂³×C₁₃	semidirect
307. C₂×#41	C₂³×C₁₃	semidirect
312. C₂²×D₄	D₄×C₁₃	semidirect
321. C₂²×D₄	C₂³×C₁₃	semidirect
322. C₂²×D₄	C₂³×C₁₃	semidirect
323. C₂²×D₄	C₂³×C₁₃	semidirect
333. C₂³×C₄	C₂³×C₁₃	semidirect
334. C₄⋊Q₈	C₂³×C₁₃	semidirect
335. #127	C₂³×C₁₃	semidirect
336. #124	C₂³×C₁₃	semidirect
337. #123	C₂³×C₁₃	semidirect
338. C₂²⋊Q₈	C₂³×C₁₃	semidirect
339. #121	C₂³×C₁₃	semidirect
340. #121	C₂³×C₁₃	semidirect
341. #121	C₂³×C₁₃	semidirect
342. #121	C₂³×C₁₃	semidirect
343. #121	C₂³×C₁₃	semidirect
344. #121	C₂³×C₁₃	semidirect
345. #120	C₂³×C₁₃	semidirect
346. C₄×D₄	C₂³×C₁₃	semidirect
347. C₄×D₄	C₂³×C₁₃	semidirect
348. C₄×D₄	C₂³×C₁₃	semidirect
349. C₄×D₄	C₂³×C₁₃	semidirect
354. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
355. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
360. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
361. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
364. C₂×C₄²	C₂³×C₁₃	semidirect
368. C₂×C₁₃	#3496	direct (N × H)
377. C₂⁴	C₂×D₄×C₁₃	semidirect
396. C₂×D₄	C₂×D₄×C₁₃	semidirect
397. C₂×D₄	C₂×D₄×C₁₃	semidirect
413. C₂²×C₄	C₂×D₄×C₁₃	semidirect
438. C₁₃	C₂×#3496	direct (N × H)
455. C₂³	C₂²×D₄×C₁₃	semidirect
467. D₄	C₂²×D₄×C₁₃	semidirect
480. C₂×C₄	C₂²×D₄×C₁₃	semidirect
481. C₂×C₄	C₁₃×H(5,𝔽₂)	semidirect
511. C₄	C₂×C₁₃×H(5,𝔽₂)	semidirect
515. C₂	C₁₃×#3496	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×H(5,𝔽₂)	2
C₁₃×#3496	2
C₂×C₁₃×#547	2
C₂×C₁₃×#546	2
C₂×D₄²×C₁₃	2
C₂×C₁₃×#537	2
C₂×C₁₃×#534	2
C₂×C₁₃×#532	2
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3496	13

Subgroups — C2×C13×#3496 #15749103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3496 #15749103