Subgroups — C₂×C₁₃×#3493 #15749115

Order 3328.

7302 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3493	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#556	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#555	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#553	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#552	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#538	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#556	C₂²	1	64	yes	complemented
16	C₁₃×#555	C₂²	1	64	yes	complemented
17	C₁₃×#553	C₂²	1	64	yes	complemented
18	C₁₃×#552	C₂²	1	64	yes	complemented
19	C₁₃×#544	C₂²	1	16	yes	complemented
20	C₁₃×#538	C₂²	1	64	yes	complemented
21	C₁₃×#537	C₂²	1	16	yes	complemented
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
23	C₁₃×#529	C₂²	1	64	yes	complemented
24	C₂×C₁₃×#126	C₂²	1	8	yes	—
25	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
26	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
27	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
28	C₂×C₁₃×#124	C₂²	1	8	yes	—
29	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
30	C₁₃×#525	C₂²	1	32	yes	complemented
31	C₂×C₁₃×#123	C₂²	1	4	yes	—
32	C₂×C₁₃×#123	C₂²	1	8	yes	—
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#121	C₂²	1	2	yes	—
38	C₂×C₁₃×#121	C₂²	1	2	yes	—
39	C₂×C₁₃×#121	C₂²	1	4	yes	—
40	C₂×C₁₃×#121	C₂²	1	8	yes	—
41	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
42	C₂×C₁₃×#120	C₂²	1	4	yes	—
43	C₁₃×#520	C₂²	1	32	yes	complemented
44	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
45	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
46	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
50	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
51	C₂×C₁₃×#117	C₂²	1	4	yes	—
52	C₂×C₁₃×#117	C₂²	1	4	yes	—
53	C₂×C₁₃×#117	C₂²	1	2	yes	—
54	C₂×C₁₃×#117	C₂²	1	16	yes	complemented
55	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
56	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
57	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
60	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
61	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
62	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	16	no	—
64	C₂×C₁₃×#41	C₂³	1	16	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	—	2	8	no	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	complemented
83	C₁₃×#126	C₂³	1	64	yes	—
84	C₁₃×#126	C₂³	1	64	yes	complemented
85	C₁₃×#125	C₂³	1	32	yes	complemented
86	C₁₃×#125	C₂³	1	32	yes	complemented
87	C₁₃×#124	C₂³	1	64	yes	—
88	C₁₃×#124	C₂³	1	32	yes	complemented
89	C₁₃×#123	C₂³	1	32	yes	—
90	C₁₃×#123	C₂³	1	64	yes	—
91	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
92	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
93	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
94	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
95	C₁₃×#121	C₂³	1	16	yes	—
96	C₁₃×#121	C₂³	1	16	yes	—
97	C₁₃×#121	C₂³	1	32	yes	—
98	C₁₃×#121	C₂³	1	64	yes	—
99	C₁₃×#121	C₂³	1	32	yes	complemented
100	C₁₃×#120	C₂³	1	32	yes	—
101	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
102	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
103	C₄×D₄×C₁₃	C₂³	1	64	yes	—
104	C₄×D₄×C₁₃	C₂³	1	32	yes	—
105	C₄×D₄×C₁₃	C₂³	1	32	yes	—
106	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
107	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
108	C₁₃×#117	C₂³	1	32	yes	—
109	C₁₃×#117	C₂³	1	32	yes	—
110	C₁₃×#117	C₂³	1	16	yes	—
111	C₁₃×#117	C₂³	1	32	yes	complemented
112	C₁₃×#117	C₂³	1	64	yes	complemented
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	complemented
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
140	C₂×#3493	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	4	no	—
142	C₂⁴×C₁₃	—	4	2	no	—
143	C₂⁴×C₁₃	—	4	2	no	—
144	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
145	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
146	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
148	C₁₃×#41	—	2	64	no	—
149	C₂×Q₈×C₁₃	—	2	8	no	—
150	C₂×Q₈×C₁₃	—	4	8	no	—
151	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
152	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
153	C₂×D₄×C₁₃	—	2	16	no	—
154	C₂×D₄×C₁₃	—	2	8	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	8	no	—
157	C₂×D₄×C₁₃	—	4	8	no	—
158	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
160	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
161	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
162	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	8	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	—	2	32	no	—
167	C₂²×C₄×C₁₃	—	2	16	no	—
168	C₂²×C₄×C₁₃	—	4	4	no	—
169	C₂²×C₄×C₁₃	—	4	16	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	#41	1	8	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
190	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
191	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
192	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
198	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
199	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
200	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
201	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
202	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
203	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
204	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
205	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
206	C₄²×C₁₃	C₂⁴	1	16	yes	—
207	C₄²×C₁₃	C₂⁴	1	16	yes	—
208	C₄²×C₁₃	C₂⁴	1	16	yes	—
209	C₄²×C₁₃	C₂⁴	1	32	yes	—
210	#3493	C₂×C₁₃	1	32	yes	direct product factor
211	C₂×#556	C₂×C₁₃	1	4	yes	complemented
212	C₂×#555	C₂×C₁₃	1	4	yes	complemented
213	C₂×#553	C₂×C₁₃	1	4	yes	complemented
214	C₂×#552	C₂×C₁₃	1	4	yes	complemented
215	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#538	C₂×C₁₃	1	4	yes	complemented
217	C₂×#537	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂×#529	C₂×C₁₃	1	4	yes	complemented
219	C₂×#525	C₂×C₁₃	1	2	yes	complemented
220	C₂×#520	C₂×C₁₃	1	2	yes	complemented
221	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	8	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	8	no	—
227	C₂³×C₁₃	—	2	8	no	—
228	C₂³×C₁₃	—	2	8	no	—
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	4	4	no	—
232	C₂³×C₁₃	—	4	4	no	—
233	C₂³×C₁₃	—	4	16	no	—
234	C₂³×C₁₃	C₂×#41	1	4	yes	—
235	C₂³×C₁₃	C₂⁵	1	4	yes	—
236	C₂³×C₁₃	C₂⁵	1	8	yes	—
237	C₂³×C₁₃	C₂⁵	1	2	yes	—
238	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
239	Q₈×C₁₃	—	2	16	no	—
240	Q₈×C₁₃	—	4	16	no	—
241	D₄×C₁₃	—	2	32	no	—
242	D₄×C₁₃	—	2	16	no	—
243	D₄×C₁₃	—	4	16	no	—
244	D₄×C₁₃	—	4	16	no	—
245	D₄×C₁₃	—	4	16	no	—
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	8	no	—
250	C₂×C₄×C₁₃	—	2	8	no	—
251	C₂×C₄×C₁₃	—	2	8	no	—
252	C₂×C₄×C₁₃	—	2	8	no	—
253	C₂×C₄×C₁₃	—	2	8	no	—
254	C₂×C₄×C₁₃	—	2	16	no	—
255	C₂×C₄×C₁₃	—	2	16	no	—
256	C₂×C₄×C₁₃	—	2	32	no	—
257	C₂×C₄×C₁₃	—	4	8	no	—
258	C₂×C₄×C₁₃	—	4	32	no	—
259	C₂×C₄×C₁₃	—	4	8	no	—
260	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
261	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
262	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
263	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
264	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
265	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
266	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
267	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
268	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
269	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
270	C₂²×#41	C₂²×C₁₃	1	2	yes	—
271	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
272	#556	C₂²×C₁₃	1	64	yes	complemented
273	#555	C₂²×C₁₃	1	64	yes	complemented
274	#553	C₂²×C₁₃	1	64	yes	complemented
275	#552	C₂²×C₁₃	1	64	yes	complemented
276	#544	C₂²×C₁₃	1	16	yes	complemented
277	#538	C₂²×C₁₃	1	64	yes	complemented
278	#537	C₂²×C₁₃	1	16	yes	complemented
279	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
280	#529	C₂²×C₁₃	1	64	yes	complemented
281	C₂×#126	C₂²×C₁₃	1	8	yes	—
282	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
283	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
284	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
285	C₂×#124	C₂²×C₁₃	1	8	yes	—
286	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
287	#525	C₂²×C₁₃	1	32	yes	complemented
288	C₂×#123	C₂²×C₁₃	1	4	yes	—
289	C₂×#123	C₂²×C₁₃	1	8	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
291	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
292	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
293	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
294	C₂×#121	C₂²×C₁₃	1	2	yes	—
295	C₂×#121	C₂²×C₁₃	1	2	yes	—
296	C₂×#121	C₂²×C₁₃	1	4	yes	—
297	C₂×#121	C₂²×C₁₃	1	8	yes	—
298	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
299	C₂×#120	C₂²×C₁₃	1	4	yes	—
300	#520	C₂²×C₁₃	1	32	yes	complemented
301	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
302	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
303	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
304	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
305	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
306	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
307	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
308	C₂×#117	C₂²×C₁₃	1	4	yes	—
309	C₂×#117	C₂²×C₁₃	1	4	yes	—
310	C₂×#117	C₂²×C₁₃	1	2	yes	—
311	C₂×#117	C₂²×C₁₃	1	16	yes	complemented
312	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
313	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
314	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
315	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
317	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
318	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	8	no	—
322	C₂²×C₁₃	—	2	4	no	—
323	C₂²×C₁₃	—	2	8	no	—
324	C₂²×C₁₃	—	2	8	no	—
325	C₂²×C₁₃	—	2	8	no	—
326	C₂²×C₁₃	—	2	4	no	—
327	C₂²×C₁₃	—	2	4	no	—
328	C₂²×C₁₃	—	4	16	no	—
329	C₂²×C₁₃	—	4	16	no	—
330	C₂²×C₁₃	—	4	8	no	—
331	C₂²×C₁₃	C₂²×#41	1	4	yes	—
332	C₂²×C₁₃	C₂²×#41	1	2	yes	—
333	C₂²×C₁₃	#585	1	2	yes	—
334	C₂²×C₁₃	#585	1	2	yes	—
335	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	8	no	—
339	C₄×C₁₃	—	2	8	no	—
340	C₄×C₁₃	—	2	8	no	—
341	C₄×C₁₃	—	2	8	no	—
342	C₄×C₁₃	—	2	8	no	—
343	C₄×C₁₃	C₂²×#41	1	8	yes	—
344	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×#41	—	2	16	no	—
346	C₂×#41	C₂³×C₁₃	1	16	yes	—
347	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
348	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
349	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
350	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
351	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
352	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
353	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
354	C₂³×C₄	—	2	8	no	—
355	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
356	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
359	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
361	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
363	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
365	#126	C₂³×C₁₃	1	64	yes	—
366	#126	C₂³×C₁₃	1	64	yes	complemented
367	#125	C₂³×C₁₃	1	32	yes	complemented
368	#125	C₂³×C₁₃	1	32	yes	complemented
369	#124	C₂³×C₁₃	1	64	yes	—
370	#124	C₂³×C₁₃	1	32	yes	complemented
371	#123	C₂³×C₁₃	1	32	yes	—
372	#123	C₂³×C₁₃	1	64	yes	—
373	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
374	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
375	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
376	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
377	#121	C₂³×C₁₃	1	16	yes	—
378	#121	C₂³×C₁₃	1	16	yes	—
379	#121	C₂³×C₁₃	1	32	yes	—
380	#121	C₂³×C₁₃	1	64	yes	—
381	#121	C₂³×C₁₃	1	32	yes	complemented
382	#120	C₂³×C₁₃	1	32	yes	—
383	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
384	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
385	C₄×D₄	C₂³×C₁₃	1	64	yes	—
386	C₄×D₄	C₂³×C₁₃	1	32	yes	—
387	C₄×D₄	C₂³×C₁₃	1	32	yes	—
388	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
389	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
390	#117	C₂³×C₁₃	1	32	yes	—
391	#117	C₂³×C₁₃	1	32	yes	—
392	#117	C₂³×C₁₃	1	16	yes	—
393	#117	C₂³×C₁₃	1	32	yes	complemented
394	#117	C₂³×C₁₃	1	64	yes	complemented
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	complemented
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
417	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
419	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
422	C₂×C₁₃	—	2	4	no	—
423	C₂×C₁₃	—	4	8	no	—
424	C₂×C₁₃	—	4	4	no	—
425	C₂×C₁₃	#3493	1	4	yes	direct product factor
426	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
427	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
428	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
429	C₂⁴	—	2	4	no	—
430	C₂⁴	—	4	2	no	—
431	C₂⁴	—	4	2	no	—
432	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
433	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
434	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
436	#41	—	2	64	no	—
437	C₂×Q₈	—	2	8	no	—
438	C₂×Q₈	—	4	8	no	—
439	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
440	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
441	C₂×D₄	—	2	16	no	—
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	4	8	no	—
444	C₂×D₄	—	4	8	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
447	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
448	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
449	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
450	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	8	no	—
453	C₂²×C₄	—	2	8	no	—
454	C₂²×C₄	—	2	32	no	—
455	C₂²×C₄	—	2	16	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	16	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	C₁₃×#41	1	8	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
468	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
469	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
472	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
473	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
474	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
476	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
477	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
478	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
479	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
480	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
481	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
482	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
483	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
484	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
485	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
486	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
487	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
488	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
489	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
490	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
491	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
492	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
493	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
494	C₄²	C₂⁴×C₁₃	1	16	yes	—
495	C₄²	C₂⁴×C₁₃	1	16	yes	—
496	C₄²	C₂⁴×C₁₃	1	16	yes	—
497	C₄²	C₂⁴×C₁₃	1	32	yes	—
498	C₁₃	C₂×#3493	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	8	no	—
504	C₂³	—	2	8	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	4	no	—
510	C₂³	—	4	16	no	—
511	C₂³	C₂×C₁₃×#41	1	4	yes	—
512	C₂³	C₂⁵×C₁₃	1	4	yes	—
513	C₂³	C₂⁵×C₁₃	1	8	yes	—
514	C₂³	C₂⁵×C₁₃	1	2	yes	—
515	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
516	Q₈	—	2	16	no	—
517	Q₈	—	4	16	no	—
518	D₄	—	2	32	no	—
519	D₄	—	2	16	no	—
520	D₄	—	4	16	no	—
521	D₄	—	4	16	no	—
522	D₄	—	4	16	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	16	no	—
532	C₂×C₄	—	2	16	no	—
533	C₂×C₄	—	2	32	no	—
534	C₂×C₄	—	4	8	no	—
535	C₂×C₄	—	4	32	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
538	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
539	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
540	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
541	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
542	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
543	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
544	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
545	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
546	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	8	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	8	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	4	16	no	—
557	C₂²	—	4	16	no	—
558	C₂²	—	4	8	no	—
559	C₂²	C₂²×C₁₃×#41	1	4	yes	—
560	C₂²	C₂²×C₁₃×#41	1	2	yes	—
561	C₂²	C₁₃×#585	1	2	yes	—
562	C₂²	C₁₃×#585	1	2	yes	—
563	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	8	no	—
567	C₄	—	2	8	no	—
568	C₄	—	2	8	no	—
569	C₄	—	2	8	no	—
570	C₄	—	2	8	no	—
571	C₄	C₂²×C₁₃×#41	1	8	yes	—
572	C₂	—	2	4	no	—
573	C₂	—	4	4	no	—
574	C₂	—	4	8	no	—
575	C₂	C₁₃×#3493	1	4	yes	direct product factor
576	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
577	C₂	C₂×C₁₃×#585	1	1	yes	characteristic
578	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. C₁₃×#3493	C₂	direct (N × H)
2. C₂×C₁₃×#556	C₂	semidirect
3. C₂×C₁₃×#555	C₂	semidirect
4. C₂×C₁₃×#553	C₂	semidirect
5. C₂×C₁₃×#552	C₂	semidirect
6. C₂×C₁₃×#544	C₂	semidirect
7. C₂×C₁₃×#538	C₂	semidirect
8. C₂×C₁₃×#537	C₂	semidirect
9. C₂×C₁₃×#529	C₂	semidirect
10. C₂×C₁₃×#525	C₂	semidirect
11. C₂×C₁₃×#520	C₂	semidirect
12. C₂²×C₁₃×#117	C₂	semidirect
15. C₁₃×#556	C₂²	semidirect
16. C₁₃×#555	C₂²	semidirect
17. C₁₃×#553	C₂²	semidirect
18. C₁₃×#552	C₂²	semidirect
19. C₁₃×#544	C₂²	semidirect
20. C₁₃×#538	C₂²	semidirect
21. C₁₃×#537	C₂²	semidirect
22. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₁₃×#529	C₂²	semidirect
25. C₂×C₁₃×#126	C₂²	semidirect
26. C₂×C₁₃×#125	C₂²	semidirect
27. C₂×C₁₃×#125	C₂²	semidirect
29. C₂×C₁₃×#124	C₂²	semidirect
30. C₁₃×#525	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₁₃×#121	C₂²	semidirect
43. C₁₃×#520	C₂²	semidirect
44. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₂×C₄×D₄×C₁₃	C₂²	semidirect
54. C₂×C₁₃×#117	C₂²	semidirect
55. C₂×C₁₃×#117	C₂²	semidirect
56. C₂×C₁₃×#117	C₂²	semidirect
59. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
82. C₁₃×C₄⋊Q₈	C₂³	semidirect
84. C₁₃×#126	C₂³	semidirect
85. C₁₃×#125	C₂³	semidirect
86. C₁₃×#125	C₂³	semidirect
88. C₁₃×#124	C₂³	semidirect
94. C₁₃×C₂²⋊Q₈	C₂³	semidirect
99. C₁₃×#121	C₂³	semidirect
101. C₄×Q₈×C₁₃	C₂³	semidirect
102. C₄×Q₈×C₁₃	C₂³	semidirect
106. C₄×D₄×C₁₃	C₂³	semidirect
107. C₄×D₄×C₁₃	C₂³	semidirect
111. C₁₃×#117	C₂³	semidirect
112. C₁₃×#117	C₂³	semidirect
125. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
140. C₂×#3493	C₁₃	direct (N × H)
210. #3493	C₂×C₁₃	direct (N × H)
211. C₂×#556	C₂×C₁₃	semidirect
212. C₂×#555	C₂×C₁₃	semidirect
213. C₂×#553	C₂×C₁₃	semidirect
214. C₂×#552	C₂×C₁₃	semidirect
215. C₂×#544	C₂×C₁₃	semidirect
216. C₂×#538	C₂×C₁₃	semidirect
217. C₂×#537	C₂×C₁₃	semidirect
218. C₂×#529	C₂×C₁₃	semidirect
219. C₂×#525	C₂×C₁₃	semidirect
220. C₂×#520	C₂×C₁₃	semidirect
221. C₂²×#117	C₂×C₁₃	semidirect
272. #556	C₂²×C₁₃	semidirect
273. #555	C₂²×C₁₃	semidirect
274. #553	C₂²×C₁₃	semidirect
275. #552	C₂²×C₁₃	semidirect
276. #544	C₂²×C₁₃	semidirect
277. #538	C₂²×C₁₃	semidirect
278. #537	C₂²×C₁₃	semidirect
279. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
280. #529	C₂²×C₁₃	semidirect
282. C₂×#126	C₂²×C₁₃	semidirect
283. C₂×#125	C₂²×C₁₃	semidirect
284. C₂×#125	C₂²×C₁₃	semidirect
286. C₂×#124	C₂²×C₁₃	semidirect
287. #525	C₂²×C₁₃	semidirect
293. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
298. C₂×#121	C₂²×C₁₃	semidirect
300. #520	C₂²×C₁₃	semidirect
301. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
302. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
306. C₂×C₄×D₄	C₂²×C₁₃	semidirect
307. C₂×C₄×D₄	C₂²×C₁₃	semidirect
311. C₂×#117	C₂²×C₁₃	semidirect
312. C₂×#117	C₂²×C₁₃	semidirect
313. C₂×#117	C₂²×C₁₃	semidirect
316. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
364. C₄⋊Q₈	C₂³×C₁₃	semidirect
366. #126	C₂³×C₁₃	semidirect
367. #125	C₂³×C₁₃	semidirect
368. #125	C₂³×C₁₃	semidirect
370. #124	C₂³×C₁₃	semidirect
376. C₂²⋊Q₈	C₂³×C₁₃	semidirect
381. #121	C₂³×C₁₃	semidirect
383. C₄×Q₈	C₂³×C₁₃	semidirect
384. C₄×Q₈	C₂³×C₁₃	semidirect
388. C₄×D₄	C₂³×C₁₃	semidirect
389. C₄×D₄	C₂³×C₁₃	semidirect
393. #117	C₂³×C₁₃	semidirect
394. #117	C₂³×C₁₃	semidirect
407. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
425. C₂×C₁₃	#3493	direct (N × H)
498. C₁₃	C₂×#3493	direct (N × H)
575. C₂	C₁₃×#3493	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×#3493	2
C₂×C₁₃×#556	2
C₂×C₁₃×#555	2
C₂×C₁₃×#553	2
C₂×C₁₃×#552	2
C₂×C₁₃×#544	2
C₂×C₁₃×#538	2
C₂×C₁₃×#537	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂×C₁₃×#520	2
C₂²×C₁₃×#117	2
C₂×#3493	13

Subgroups — C2×C13×#3493 #15749115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3493 #15749115