Subgroups — C₂×C₁₃×#3485 #15749113

Order 3328.

11686 conjugacy classes of subgroups.

The subgroup lattice has 532 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	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3485	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₁₃×#547	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#546	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#534	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
9	C₂²×C₁₃×#123	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×H(5,𝔽₂)	—	2	16	no	—
12	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	16	yes	complemented
13	C₂²×C₁₃×#41	—	2	16	no	—
14	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
16	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
17	C₂²×C₁₃×#41	C₂²	1	16	yes	complemented
18	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
20	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
22	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
23	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
24	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#547	C₂²	1	128	yes	complemented
26	C₁₃×#546	C₂²	1	128	yes	complemented
27	C₁₃×#536	C₂²	1	32	yes	complemented
28	C₁₃×#534	C₂²	1	64	yes	complemented
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
31	C₁₃×#525	C₂²	1	32	yes	complemented
32	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
33	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
34	C₂×C₁₃×#123	C₂²	1	16	yes	complemented
35	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
36	C₂×C₁₃×#123	C₂²	1	64	yes	complemented
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
38	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
39	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
41	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
42	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
43	C₁₃×#518	C₂²	1	16	yes	complemented
44	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
45	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
46	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
47	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
48	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
49	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
50	C₂⁵×C₁₃	C₂³	1	4	yes	—
51	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
52	C₂⁵×C₁₃	C₂³	1	2	yes	—
53	C₁₃×H(5,𝔽₂)	—	2	128	no	—
54	C₂×C₁₃×#41	—	2	64	no	—
55	C₂×C₁₃×#41	—	2	32	no	—
56	C₂×C₁₃×#41	—	2	128	no	—
57	C₂×C₁₃×#41	—	2	16	no	—
58	C₂×C₁₃×#41	C₂³	1	16	yes	—
59	C₂×C₁₃×#41	C₂³	1	64	yes	complemented
60	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
61	C₂²×Q₈×C₁₃	—	2	8	no	—
62	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
63	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
64	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
65	C₂²×D₄×C₁₃	—	2	32	no	—
66	C₂²×D₄×C₁₃	—	2	16	no	—
67	C₂²×D₄×C₁₃	—	2	32	no	—
68	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
69	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	32	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
78	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
79	C₂³×C₄×C₁₃	—	2	16	no	—
80	C₂³×C₄×C₁₃	—	2	8	no	—
81	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
90	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
91	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	complemented
92	C₁₃×#124	C₂³	1	32	yes	complemented
93	C₁₃×#123	C₂³	1	32	yes	complemented
94	C₁₃×#123	C₂³	1	64	yes	complemented
95	C₁₃×#123	C₂³	1	128	yes	complemented
96	C₁₃×#123	C₂³	1	64	yes	complemented
97	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
98	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
99	C₁₃×#121	C₂³	1	32	yes	complemented
100	C₁₃×#121	C₂³	1	128	yes	complemented
101	C₁₃×#120	C₂³	1	32	yes	complemented
102	C₁₃×#120	C₂³	1	64	yes	complemented
103	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
104	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
105	C₁₃×#117	C₂³	1	16	yes	complemented
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	64	yes	complemented
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	64	yes	complemented
117	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
118	C₂×#3485	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	4	no	—
120	C₂⁴×C₁₃	—	2	16	no	—
121	C₂⁴×C₁₃	—	4	8	no	—
122	C₂⁴×C₁₃	—	4	4	no	—
123	C₂⁴×C₁₃	—	4	16	no	—
124	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
125	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
129	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
130	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
131	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
132	C₁₃×#41	—	2	256	no	—
133	C₁₃×#41	—	2	128	no	—
134	C₁₃×#41	—	2	64	no	—
135	C₂×Q₈×C₁₃	—	2	16	no	—
136	C₂×Q₈×C₁₃	—	2	32	no	—
137	C₂×Q₈×C₁₃	—	2	8	no	—
138	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
140	C₂×D₄×C₁₃	—	2	16	no	—
141	C₂×D₄×C₁₃	—	2	32	no	—
142	C₂×D₄×C₁₃	—	2	32	no	—
143	C₂×D₄×C₁₃	—	2	128	no	—
144	C₂×D₄×C₁₃	—	2	64	no	—
145	C₂×D₄×C₁₃	—	2	128	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	4	16	no	—
148	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	—
149	C₂×D₄×C₁₃	C₂×D₄	1	64	yes	complemented
150	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
151	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
152	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
154	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
155	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	8	no	—
158	C₂²×C₄×C₁₃	—	2	32	no	—
159	C₂²×C₄×C₁₃	—	2	64	no	—
160	C₂²×C₄×C₁₃	—	2	16	no	—
161	C₂²×C₄×C₁₃	—	2	16	no	—
162	C₂²×C₄×C₁₃	—	2	32	no	—
163	C₂²×C₄×C₁₃	—	2	16	no	—
164	C₂²×C₄×C₁₃	—	4	16	no	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	64	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
182	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
183	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
184	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
185	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
186	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
187	C₄²×C₁₃	C₂⁴	1	16	yes	—
188	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#3485	C₂×C₁₃	1	32	yes	direct product factor
191	C₂×#547	C₂×C₁₃	1	8	yes	complemented
192	C₂×#546	C₂×C₁₃	1	8	yes	complemented
193	C₂×#536	C₂×C₁₃	1	2	yes	complemented
194	C₂×#534	C₂×C₁₃	1	4	yes	complemented
195	C₂×#525	C₂×C₁₃	1	2	yes	complemented
196	C₂²×#123	C₂×C₁₃	1	4	yes	complemented
197	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂³×C₁₃	—	2	16	no	—
199	C₂³×C₁₃	—	2	4	no	—
200	C₂³×C₁₃	—	2	8	no	—
201	C₂³×C₁₃	—	2	4	no	—
202	C₂³×C₁₃	—	2	8	no	—
203	C₂³×C₁₃	—	2	8	no	—
204	C₂³×C₁₃	—	2	16	no	—
205	C₂³×C₁₃	—	2	32	no	—
206	C₂³×C₁₃	—	4	32	no	—
207	C₂³×C₁₃	—	4	16	no	—
208	C₂³×C₁₃	—	4	8	no	—
209	C₂³×C₁₃	—	4	32	no	—
210	C₂³×C₁₃	—	4	16	no	—
211	C₂³×C₁₃	—	8	32	no	—
212	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
213	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
214	C₂³×C₁₃	C₂²×D₄	1	32	yes	—
215	C₂³×C₁₃	C₂⁵	1	8	yes	—
216	C₂³×C₁₃	C₂⁵	1	4	yes	—
217	C₂³×C₁₃	C₂⁵	1	2	yes	—
218	C₂³×C₁₃	C₂⁵	1	8	yes	—
219	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	32	no	—
221	Q₈×C₁₃	—	2	16	no	—
222	D₄×C₁₃	—	2	32	no	—
223	D₄×C₁₃	—	2	64	no	—
224	D₄×C₁₃	—	2	64	no	—
225	D₄×C₁₃	—	2	16	no	—
226	D₄×C₁₃	—	4	32	no	—
227	D₄×C₁₃	C₂²×D₄	1	64	yes	—
228	C₂×C₄×C₁₃	—	2	8	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	16	no	—
232	C₂×C₄×C₁₃	—	2	8	no	—
233	C₂×C₄×C₁₃	—	2	64	no	—
234	C₂×C₄×C₁₃	—	2	32	no	—
235	C₂×C₄×C₁₃	—	2	16	no	—
236	C₂×C₄×C₁₃	—	2	32	no	—
237	C₂×C₄×C₁₃	—	2	32	no	—
238	C₂×C₄×C₁₃	—	4	32	no	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
242	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
243	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
244	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
245	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
246	C₂×H(5,𝔽₂)	—	2	16	no	—
247	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	16	yes	complemented
248	C₂²×#41	—	2	16	no	—
249	C₂²×#41	C₂²×C₁₃	1	2	yes	—
250	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
251	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
252	C₂²×#41	C₂²×C₁₃	1	16	yes	complemented
253	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
255	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
257	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
258	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
259	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
260	#547	C₂²×C₁₃	1	128	yes	complemented
261	#546	C₂²×C₁₃	1	128	yes	complemented
262	#536	C₂²×C₁₃	1	32	yes	complemented
263	#534	C₂²×C₁₃	1	64	yes	complemented
264	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
265	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
266	#525	C₂²×C₁₃	1	32	yes	complemented
267	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
268	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
269	C₂×#123	C₂²×C₁₃	1	16	yes	complemented
270	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
271	C₂×#123	C₂²×C₁₃	1	64	yes	complemented
272	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
273	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
274	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
275	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
276	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
277	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
278	#518	C₂²×C₁₃	1	16	yes	complemented
279	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
280	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
281	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
282	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
283	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
284	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
285	C₂²×C₁₃	—	2	16	no	—
286	C₂²×C₁₃	—	2	4	no	—
287	C₂²×C₁₃	—	2	8	no	—
288	C₂²×C₁₃	—	2	32	no	—
289	C₂²×C₁₃	—	2	4	no	—
290	C₂²×C₁₃	—	2	8	no	—
291	C₂²×C₁₃	—	2	8	no	—
292	C₂²×C₁₃	—	2	16	no	—
293	C₂²×C₁₃	—	4	32	no	—
294	C₂²×C₁₃	—	4	16	no	—
295	C₂²×C₁₃	—	4	8	no	—
296	C₂²×C₁₃	—	4	16	no	—
297	C₂²×C₁₃	—	8	32	no	—
298	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
299	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
300	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
301	C₂²×C₁₃	#585	1	4	yes	—
302	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
303	C₄×C₁₃	—	2	4	no	—
304	C₄×C₁₃	—	2	8	no	—
305	C₄×C₁₃	—	2	8	no	—
306	C₄×C₁₃	—	2	16	no	—
307	C₄×C₁₃	C₂³×D₄	1	8	yes	—
308	C₂⁵	C₂³×C₁₃	1	4	yes	—
309	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
310	C₂⁵	C₂³×C₁₃	1	2	yes	—
311	H(5,𝔽₂)	—	2	128	no	—
312	C₂×#41	—	2	64	no	—
313	C₂×#41	—	2	32	no	—
314	C₂×#41	—	2	128	no	—
315	C₂×#41	—	2	16	no	—
316	C₂×#41	C₂³×C₁₃	1	16	yes	—
317	C₂×#41	C₂³×C₁₃	1	64	yes	complemented
318	C₂×#41	C₂³×C₁₃	1	32	yes	complemented
319	C₂²×Q₈	—	2	8	no	—
320	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
321	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
322	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
323	C₂²×D₄	—	2	32	no	—
324	C₂²×D₄	—	2	16	no	—
325	C₂²×D₄	—	2	32	no	—
326	C₂²×D₄	D₄×C₁₃	1	16	yes	complemented
327	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
328	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
329	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
330	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
331	C₂²×D₄	C₂³×C₁₃	1	32	yes	—
332	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
333	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
335	C₂²×D₄	C₂³×C₁₃	1	16	yes	complemented
336	C₂²×D₄	C₂³×C₁₃	1	32	yes	complemented
337	C₂³×C₄	—	2	16	no	—
338	C₂³×C₄	—	2	8	no	—
339	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
343	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₃	1	16	yes	complemented
348	C₂³×C₄	C₂³×C₁₃	1	8	yes	complemented
349	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
350	#124	C₂³×C₁₃	1	32	yes	complemented
351	#123	C₂³×C₁₃	1	32	yes	complemented
352	#123	C₂³×C₁₃	1	64	yes	complemented
353	#123	C₂³×C₁₃	1	128	yes	complemented
354	#123	C₂³×C₁₃	1	64	yes	complemented
355	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
356	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
357	#121	C₂³×C₁₃	1	32	yes	complemented
358	#121	C₂³×C₁₃	1	128	yes	complemented
359	#120	C₂³×C₁₃	1	32	yes	complemented
360	#120	C₂³×C₁₃	1	64	yes	complemented
361	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
362	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
363	#117	C₂³×C₁₃	1	16	yes	complemented
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	64	yes	complemented
368	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	64	yes	complemented
375	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
376	C₂×C₁₃	—	2	4	no	—
377	C₂×C₁₃	—	2	16	no	—
378	C₂×C₁₃	—	4	4	no	—
379	C₂×C₁₃	—	4	8	no	—
380	C₂×C₁₃	#3485	1	4	yes	direct product factor
381	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
382	C₂×C₁₃	C₂×#585	1	2	yes	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	16	no	—
385	C₂⁴	—	4	8	no	—
386	C₂⁴	—	4	4	no	—
387	C₂⁴	—	4	16	no	—
388	C₂⁴	C₂×D₄×C₁₃	1	16	yes	—
389	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
390	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
391	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
392	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
393	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
394	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
395	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
396	#41	—	2	256	no	—
397	#41	—	2	128	no	—
398	#41	—	2	64	no	—
399	C₂×Q₈	—	2	16	no	—
400	C₂×Q₈	—	2	32	no	—
401	C₂×Q₈	—	2	8	no	—
402	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
403	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
404	C₂×D₄	—	2	16	no	—
405	C₂×D₄	—	2	32	no	—
406	C₂×D₄	—	2	32	no	—
407	C₂×D₄	—	2	128	no	—
408	C₂×D₄	—	2	64	no	—
409	C₂×D₄	—	2	128	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	4	16	no	—
412	C₂×D₄	C₂×D₄×C₁₃	1	32	yes	—
413	C₂×D₄	C₂×D₄×C₁₃	1	64	yes	complemented
414	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
415	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
416	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
417	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
418	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
419	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	32	no	—
423	C₂²×C₄	—	2	64	no	—
424	C₂²×C₄	—	2	16	no	—
425	C₂²×C₄	—	2	16	no	—
426	C₂²×C₄	—	2	32	no	—
427	C₂²×C₄	—	2	16	no	—
428	C₂²×C₄	—	4	16	no	—
429	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
443	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
444	C₄⋊C₄	C₂⁴×C₁₃	1	64	yes	—
445	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
446	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
447	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
448	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
449	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
450	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
451	C₄²	C₂⁴×C₁₃	1	16	yes	—
452	C₁₃	C₂×#3485	1	1	yes	characteristic, direct product factor, Sylow
453	C₂³	—	2	16	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	8	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	8	no	—
458	C₂³	—	2	8	no	—
459	C₂³	—	2	16	no	—
460	C₂³	—	2	32	no	—
461	C₂³	—	4	32	no	—
462	C₂³	—	4	16	no	—
463	C₂³	—	4	8	no	—
464	C₂³	—	4	32	no	—
465	C₂³	—	4	16	no	—
466	C₂³	—	8	32	no	—
467	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
468	C₂³	C₂²×D₄×C₁₃	1	16	yes	—
469	C₂³	C₂²×D₄×C₁₃	1	32	yes	—
470	C₂³	C₂⁵×C₁₃	1	8	yes	—
471	C₂³	C₂⁵×C₁₃	1	4	yes	—
472	C₂³	C₂⁵×C₁₃	1	2	yes	—
473	C₂³	C₂⁵×C₁₃	1	8	yes	—
474	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
475	Q₈	—	2	32	no	—
476	Q₈	—	2	16	no	—
477	D₄	—	2	32	no	—
478	D₄	—	2	64	no	—
479	D₄	—	2	64	no	—
480	D₄	—	2	16	no	—
481	D₄	—	4	32	no	—
482	D₄	C₂²×D₄×C₁₃	1	64	yes	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	16	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	64	no	—
489	C₂×C₄	—	2	32	no	—
490	C₂×C₄	—	2	16	no	—
491	C₂×C₄	—	2	32	no	—
492	C₂×C₄	—	2	32	no	—
493	C₂×C₄	—	4	32	no	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
495	C₂×C₄	C₂²×D₄×C₁₃	1	16	yes	—
496	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
497	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
498	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
499	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
500	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
501	C₂²	—	2	16	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	32	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	2	16	no	—
509	C₂²	—	4	32	no	—
510	C₂²	—	4	16	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	16	no	—
513	C₂²	—	8	32	no	—
514	C₂²	C₂³×D₄×C₁₃	1	4	yes	—
515	C₂²	C₂³×D₄×C₁₃	1	16	yes	—
516	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
517	C₂²	C₁₃×#585	1	4	yes	—
518	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
519	C₄	—	2	4	no	—
520	C₄	—	2	8	no	—
521	C₄	—	2	8	no	—
522	C₄	—	2	16	no	—
523	C₄	C₂³×D₄×C₁₃	1	8	yes	—
524	C₂	—	2	4	no	—
525	C₂	—	2	16	no	—
526	C₂	—	4	4	no	—
527	C₂	—	4	8	no	—
528	C₂	C₁₃×#3485	1	4	yes	direct product factor
529	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
530	C₂	C₂×C₁₃×#585	1	2	yes	—

	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. C₂³×C₁₃×#41	C₂	semidirect
3. C₁₃×#3485	C₂	direct (N × H)
4. C₂×C₁₃×#547	C₂	semidirect
5. C₂×C₁₃×#546	C₂	semidirect
6. C₂×C₁₃×#536	C₂	semidirect
7. C₂×C₁₃×#534	C₂	semidirect
8. C₂×C₁₃×#525	C₂	semidirect
9. C₂²×C₁₃×#123	C₂	semidirect
10. C₂×C₁₃×#518	C₂	semidirect
12. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
15. C₂²×C₁₃×#41	C₂²	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂³×Q₈×C₁₃	C₂²	semidirect
21. C₂³×D₄×C₁₃	C₂²	semidirect
22. C₂³×D₄×C₁₃	C₂²	semidirect
23. C₂⁴×C₄×C₁₃	C₂²	semidirect
24. C₂⁴×C₄×C₁₃	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
26. C₁₃×#546	C₂²	semidirect
27. C₁₃×#536	C₂²	semidirect
28. C₁₃×#534	C₂²	semidirect
29. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₁₃×#124	C₂²	semidirect
31. C₁₃×#525	C₂²	semidirect
32. C₂×C₁₃×#123	C₂²	semidirect
33. C₂×C₁₃×#123	C₂²	semidirect
34. C₂×C₁₃×#123	C₂²	semidirect
35. C₂×C₁₃×#123	C₂²	semidirect
36. C₂×C₁₃×#123	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×#121	C₂²	semidirect
40. C₂×C₁₃×#121	C₂²	semidirect
41. C₂×C₁₃×#120	C₂²	semidirect
42. C₂×C₁₃×#120	C₂²	semidirect
43. C₁₃×#518	C₂²	semidirect
44. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃	C₂²	semidirect
46. C₂×C₁₃×#117	C₂²	semidirect
47. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
48. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
49. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
59. C₂×C₁₃×#41	C₂³	semidirect
60. C₂×C₁₃×#41	C₂³	semidirect
64. C₂²×Q₈×C₁₃	C₂³	semidirect
68. C₂²×D₄×C₁₃	D₄	semidirect
77. C₂²×D₄×C₁₃	C₂³	semidirect
78. C₂²×D₄×C₁₃	C₂³	semidirect
89. C₂³×C₄×C₁₃	C₂³	semidirect
90. C₂³×C₄×C₁₃	C₂³	semidirect
91. C₁₃×C₄⋊Q₈	C₂³	semidirect
92. C₁₃×#124	C₂³	semidirect
93. C₁₃×#123	C₂³	semidirect
94. C₁₃×#123	C₂³	semidirect
95. C₁₃×#123	C₂³	semidirect
96. C₁₃×#123	C₂³	semidirect
97. C₁₃×C₂²⋊Q₈	C₂³	semidirect
98. C₁₃×C₂²⋊Q₈	C₂³	semidirect
99. C₁₃×#121	C₂³	semidirect
100. C₁₃×#121	C₂³	semidirect
101. C₁₃×#120	C₂³	semidirect
102. C₁₃×#120	C₂³	semidirect
103. C₄×D₄×C₁₃	C₂³	semidirect
104. C₄×D₄×C₁₃	C₂³	semidirect
105. C₁₃×#117	C₂³	semidirect
109. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
115. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
116. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
118. C₂×#3485	C₁₃	direct (N × H)
149. C₂×D₄×C₁₃	C₂×D₄	semidirect
188. C₂²×H(5,𝔽₂)	C₂×C₁₃	semidirect
189. C₂³×#41	C₂×C₁₃	semidirect
190. #3485	C₂×C₁₃	direct (N × H)
191. C₂×#547	C₂×C₁₃	semidirect
192. C₂×#546	C₂×C₁₃	semidirect
193. C₂×#536	C₂×C₁₃	semidirect
194. C₂×#534	C₂×C₁₃	semidirect
195. C₂×#525	C₂×C₁₃	semidirect
196. C₂²×#123	C₂×C₁₃	semidirect
197. C₂×#518	C₂×C₁₃	semidirect
247. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
250. C₂²×#41	C₂²×C₁₃	semidirect
251. C₂²×#41	C₂²×C₁₃	semidirect
252. C₂²×#41	C₂²×C₁₃	semidirect
253. C₂³×Q₈	C₂²×C₁₃	semidirect
256. C₂³×D₄	C₂²×C₁₃	semidirect
257. C₂³×D₄	C₂²×C₁₃	semidirect
258. C₂⁴×C₄	C₂²×C₁₃	semidirect
259. C₂⁴×C₄	C₂²×C₁₃	semidirect
260. #547	C₂²×C₁₃	semidirect
261. #546	C₂²×C₁₃	semidirect
262. #536	C₂²×C₁₃	semidirect
263. #534	C₂²×C₁₃	semidirect
264. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
265. C₂×#124	C₂²×C₁₃	semidirect
266. #525	C₂²×C₁₃	semidirect
267. C₂×#123	C₂²×C₁₃	semidirect
268. C₂×#123	C₂²×C₁₃	semidirect
269. C₂×#123	C₂²×C₁₃	semidirect
270. C₂×#123	C₂²×C₁₃	semidirect
271. C₂×#123	C₂²×C₁₃	semidirect
272. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
273. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
274. C₂×#121	C₂²×C₁₃	semidirect
275. C₂×#121	C₂²×C₁₃	semidirect
276. C₂×#120	C₂²×C₁₃	semidirect
277. C₂×#120	C₂²×C₁₃	semidirect
278. #518	C₂²×C₁₃	semidirect
279. C₂×C₄×D₄	C₂²×C₁₃	semidirect
280. C₂×C₄×D₄	C₂²×C₁₃	semidirect
281. C₂×#117	C₂²×C₁₃	semidirect
282. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
283. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
284. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
317. C₂×#41	C₂³×C₁₃	semidirect
318. C₂×#41	C₂³×C₁₃	semidirect
322. C₂²×Q₈	C₂³×C₁₃	semidirect
326. C₂²×D₄	D₄×C₁₃	semidirect
335. C₂²×D₄	C₂³×C₁₃	semidirect
336. C₂²×D₄	C₂³×C₁₃	semidirect
347. C₂³×C₄	C₂³×C₁₃	semidirect
348. C₂³×C₄	C₂³×C₁₃	semidirect
349. C₄⋊Q₈	C₂³×C₁₃	semidirect
350. #124	C₂³×C₁₃	semidirect
351. #123	C₂³×C₁₃	semidirect
352. #123	C₂³×C₁₃	semidirect
353. #123	C₂³×C₁₃	semidirect
354. #123	C₂³×C₁₃	semidirect
355. C₂²⋊Q₈	C₂³×C₁₃	semidirect
356. C₂²⋊Q₈	C₂³×C₁₃	semidirect
357. #121	C₂³×C₁₃	semidirect
358. #121	C₂³×C₁₃	semidirect
359. #120	C₂³×C₁₃	semidirect
360. #120	C₂³×C₁₃	semidirect
361. C₄×D₄	C₂³×C₁₃	semidirect
362. C₄×D₄	C₂³×C₁₃	semidirect
363. #117	C₂³×C₁₃	semidirect
367. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
373. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
374. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
380. C₂×C₁₃	#3485	direct (N × H)
413. C₂×D₄	C₂×D₄×C₁₃	semidirect
452. C₁₃	C₂×#3485	direct (N × H)
528. C₂	C₁₃×#3485	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
C₂³×C₁₃×#41	2
C₁₃×#3485	2
C₂×C₁₃×#547	2
C₂×C₁₃×#546	2
C₂×C₁₃×#536	2
C₂×C₁₃×#534	2
C₂×C₁₃×#525	2
C₂²×C₁₃×#123	2
C₂×C₁₃×#518	2
C₂×#3485	13

Subgroups — C2×C13×#3485 #15749113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3485 #15749113