Subgroups — C₂×C₁₃×#3488 #15749133

Order 3328.

12366 conjugacy classes of subgroups.

The subgroup lattice has 644 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×#3488	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₁₃×#550	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#546	C₂	1	6	yes	maximal, complemented
7	C₂×D₄²×C₁₃	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₃×#537	C₂	1	3	yes	maximal, complemented
9	C₂×C₁₃×#535	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#525	C₂	1	3	yes	maximal, complemented
11	C₂²×C₁₃×#121	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×H(5,𝔽₂)	—	2	16	no	—
14	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	16	yes	complemented
15	C₂²×C₁₃×#41	—	2	16	no	—
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
18	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
21	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×#41	C₂²	1	16	yes	complemented
23	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×D₄×C₁₃	C₂²	1	3	yes	complemented
25	C₂³×D₄×C₁₃	C₂²	1	3	yes	complemented
26	C₂³×D₄×C₁₃	C₂²	1	6	yes	complemented
27	C₂³×D₄×C₁₃	C₂²	1	6	yes	complemented
28	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	complemented
29	C₁₃×#550	C₂²	1	32	yes	complemented
30	C₁₃×#548	C₂²	1	32	yes	complemented
31	C₁₃×#546	C₂²	1	96	yes	complemented
32	D₄²×C₁₃	C₂²	1	96	yes	complemented
33	C₁₃×#537	C₂²	1	48	yes	complemented
34	C₁₃×#535	C₂²	1	48	yes	complemented
35	C₂×C₁₃×#127	C₂²	1	6	yes	complemented
36	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
37	C₁₃×#525	C₂²	1	48	yes	complemented
38	C₂×C₁₃×#123	C₂²	1	6	yes	complemented
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
41	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
42	C₂×C₁₃×#121	C₂²	1	3	yes	complemented
43	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
44	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
45	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
46	C₂×C₁₃×#121	C₂²	1	3	yes	complemented
47	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
48	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
49	C₂×C₁₃×#121	C₂²	1	48	yes	complemented
50	C₂×C₁₃×#120	C₂²	1	6	yes	complemented
51	C₂×C₁₃×#120	C₂²	1	12	yes	complemented
52	C₁₃×#520	C₂²	1	16	yes	complemented
53	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
55	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
56	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
57	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
58	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	complemented
59	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	6	yes	complemented
60	C₂⁵×C₁₃	C₂³	1	3	yes	—
61	C₂⁵×C₁₃	C₂³	1	6	yes	—
62	C₁₃×H(5,𝔽₂)	—	2	128	no	—
63	C₂×C₁₃×#41	—	2	128	no	—
64	C₂×C₁₃×#41	—	2	8	no	—
65	C₂×C₁₃×#41	—	2	16	no	—
66	C₂×C₁₃×#41	—	2	24	no	—
67	C₂×C₁₃×#41	—	2	24	no	—
68	C₂×C₁₃×#41	—	2	24	no	—
69	C₂×C₁₃×#41	D₄	1	16	yes	complemented
70	C₂×C₁₃×#41	C₂³	1	8	yes	—
71	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
72	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
73	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
74	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
75	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
76	C₂²×Q₈×C₁₃	—	2	8	no	—
77	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
81	C₂²×D₄×C₁₃	—	2	24	no	—
82	C₂²×D₄×C₁₃	—	2	48	no	—
83	C₂²×D₄×C₁₃	—	2	24	no	—
84	C₂²×D₄×C₁₃	—	4	24	no	—
85	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
95	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
96	C₂²×D₄×C₁₃	C₂³	1	48	yes	complemented
97	C₂²×D₄×C₁₃	C₂³	1	48	yes	complemented
98	C₂³×C₄×C₁₃	—	2	24	no	—
99	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
102	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
107	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
108	C₁₃×#127	C₂³	1	48	yes	complemented
109	C₁₃×#124	C₂³	1	48	yes	complemented
110	C₁₃×#123	C₂³	1	48	yes	complemented
111	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
112	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	complemented
113	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
114	C₁₃×#121	C₂³	1	24	yes	complemented
115	C₁₃×#121	C₂³	1	48	yes	complemented
116	C₁₃×#121	C₂³	1	48	yes	complemented
117	C₁₃×#121	C₂³	1	48	yes	complemented
118	C₁₃×#121	C₂³	1	24	yes	complemented
119	C₁₃×#121	C₂³	1	96	yes	complemented
120	C₁₃×#121	C₂³	1	48	yes	complemented
121	C₁₃×#120	C₂³	1	48	yes	complemented
122	C₁₃×#120	C₂³	1	96	yes	complemented
123	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
124	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
125	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
126	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
127	C₁₃×#117	C₂³	1	24	yes	complemented
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
141	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
142	C₂×#3488	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	12	no	—
144	C₂⁴×C₁₃	—	2	12	no	—
145	C₂⁴×C₁₃	—	2	24	no	—
146	C₂⁴×C₁₃	—	4	6	no	—
147	C₂⁴×C₁₃	—	4	12	no	—
148	C₂⁴×C₁₃	—	4	12	no	—
149	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
150	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
151	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
152	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
153	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
155	C₁₃×#41	—	2	32	no	—
156	C₁₃×#41	—	2	64	no	—
157	C₁₃×#41	—	2	96	no	—
158	C₁₃×#41	—	2	96	no	—
159	C₁₃×#41	—	2	96	no	—
160	C₁₃×#41	C₂×D₄	1	64	yes	complemented
161	C₂×Q₈×C₁₃	—	2	32	no	—
162	C₂×Q₈×C₁₃	—	2	12	no	—
163	C₂×Q₈×C₁₃	—	2	4	no	—
164	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
165	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
166	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
167	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
168	C₂×D₄×C₁₃	—	2	24	no	—
169	C₂×D₄×C₁₃	—	2	24	no	—
170	C₂×D₄×C₁₃	—	2	24	no	—
171	C₂×D₄×C₁₃	—	2	96	no	—
172	C₂×D₄×C₁₃	—	2	192	no	—
173	C₂×D₄×C₁₃	—	2	12	no	—
174	C₂×D₄×C₁₃	—	2	24	no	—
175	C₂×D₄×C₁₃	—	2	12	no	—
176	C₂×D₄×C₁₃	—	2	96	no	—
177	C₂×D₄×C₁₃	—	4	24	no	—
178	C₂×D₄×C₁₃	—	4	12	no	—
179	C₂×D₄×C₁₃	—	4	96	no	—
180	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	complemented
181	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
182	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
184	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
186	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
188	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
189	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
190	C₂²×C₄×C₁₃	—	2	12	no	—
191	C₂²×C₄×C₁₃	—	2	4	no	—
192	C₂²×C₄×C₁₃	—	2	12	no	—
193	C₂²×C₄×C₁₃	—	2	12	no	—
194	C₂²×C₄×C₁₃	—	2	12	no	—
195	C₂²×C₄×C₁₃	—	2	24	no	—
196	C₂²×C₄×C₁₃	—	2	96	no	—
197	C₂²×C₄×C₁₃	—	4	12	no	—
198	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
199	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
203	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
214	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
215	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
216	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
217	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
219	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
220	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
221	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
222	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
223	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
224	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
225	C₄²×C₁₃	C₂⁴	1	24	yes	—
226	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#3488	C₂×C₁₃	1	32	yes	direct product factor
229	C₂×#550	C₂×C₁₃	1	2	yes	complemented
230	C₂×#548	C₂×C₁₃	1	2	yes	complemented
231	C₂×#546	C₂×C₁₃	1	6	yes	complemented
232	C₂×D₄²	C₂×C₁₃	1	6	yes	complemented
233	C₂×#537	C₂×C₁₃	1	3	yes	complemented
234	C₂×#535	C₂×C₁₃	1	3	yes	complemented
235	C₂×#525	C₂×C₁₃	1	3	yes	complemented
236	C₂²×#121	C₂×C₁₃	1	3	yes	complemented
237	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	6	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	6	no	—
242	C₂³×C₁₃	—	2	24	no	—
243	C₂³×C₁₃	—	2	6	no	—
244	C₂³×C₁₃	—	2	12	no	—
245	C₂³×C₁₃	—	2	12	no	—
246	C₂³×C₁₃	—	2	6	no	—
247	C₂³×C₁₃	—	2	24	no	—
248	C₂³×C₁₃	—	2	6	no	—
249	C₂³×C₁₃	—	2	12	no	—
250	C₂³×C₁₃	—	2	48	no	—
251	C₂³×C₁₃	—	4	12	no	—
252	C₂³×C₁₃	—	4	24	no	—
253	C₂³×C₁₃	—	4	24	no	—
254	C₂³×C₁₃	—	4	48	no	—
255	C₂³×C₁₃	—	8	48	no	—
256	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
257	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
258	C₂³×C₁₃	C₂⁵	1	12	yes	—
259	C₂³×C₁₃	C₂⁵	1	6	yes	—
260	C₂³×C₁₃	C₂⁵	1	6	yes	—
261	C₂³×C₁₃	C₂⁵	1	2	yes	—
262	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
263	Q₈×C₁₃	—	2	24	no	—
264	Q₈×C₁₃	—	2	8	no	—
265	Q₈×C₁₃	C₂²×D₄	1	16	yes	complemented
266	D₄×C₁₃	—	2	48	no	—
267	D₄×C₁₃	—	2	48	no	—
268	D₄×C₁₃	—	2	48	no	—
269	D₄×C₁₃	—	2	24	no	—
270	D₄×C₁₃	—	2	48	no	—
271	D₄×C₁₃	—	2	24	no	—
272	D₄×C₁₃	—	4	48	no	—
273	D₄×C₁₃	—	4	24	no	—
274	D₄×C₁₃	C₂²×D₄	1	48	yes	complemented
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	6	no	—
278	C₂×C₄×C₁₃	—	2	24	no	—
279	C₂×C₄×C₁₃	—	2	12	no	—
280	C₂×C₄×C₁₃	—	2	4	no	—
281	C₂×C₄×C₁₃	—	2	8	no	—
282	C₂×C₄×C₁₃	—	2	24	no	—
283	C₂×C₄×C₁₃	—	2	24	no	—
284	C₂×C₄×C₁₃	—	2	24	no	—
285	C₂×C₄×C₁₃	—	2	48	no	—
286	C₂×C₄×C₁₃	—	4	24	no	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	48	yes	complemented
290	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
291	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
292	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
293	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
294	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
295	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
296	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
297	C₂×H(5,𝔽₂)	—	2	16	no	—
298	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	16	yes	complemented
299	C₂²×#41	—	2	16	no	—
300	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
302	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
303	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
305	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
306	C₂²×#41	C₂²×C₁₃	1	16	yes	complemented
307	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	C₂³×D₄	C₂²×C₁₃	1	3	yes	complemented
309	C₂³×D₄	C₂²×C₁₃	1	3	yes	complemented
310	C₂³×D₄	C₂²×C₁₃	1	6	yes	complemented
311	C₂³×D₄	C₂²×C₁₃	1	6	yes	complemented
312	C₂⁴×C₄	C₂²×C₁₃	1	3	yes	complemented
313	#550	C₂²×C₁₃	1	32	yes	complemented
314	#548	C₂²×C₁₃	1	32	yes	complemented
315	#546	C₂²×C₁₃	1	96	yes	complemented
316	D₄²	C₂²×C₁₃	1	96	yes	complemented
317	#537	C₂²×C₁₃	1	48	yes	complemented
318	#535	C₂²×C₁₃	1	48	yes	complemented
319	C₂×#127	C₂²×C₁₃	1	6	yes	complemented
320	C₂×#124	C₂²×C₁₃	1	6	yes	complemented
321	#525	C₂²×C₁₃	1	48	yes	complemented
322	C₂×#123	C₂²×C₁₃	1	6	yes	complemented
323	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
324	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
325	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
326	C₂×#121	C₂²×C₁₃	1	3	yes	complemented
327	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
328	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
329	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
330	C₂×#121	C₂²×C₁₃	1	3	yes	complemented
331	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
332	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
333	C₂×#121	C₂²×C₁₃	1	48	yes	complemented
334	C₂×#120	C₂²×C₁₃	1	6	yes	complemented
335	C₂×#120	C₂²×C₁₃	1	12	yes	complemented
336	#520	C₂²×C₁₃	1	16	yes	complemented
337	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
338	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
339	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
340	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
341	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
342	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	complemented
343	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	6	yes	complemented
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	2	6	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	6	no	—
348	C₂²×C₁₃	—	2	8	no	—
349	C₂²×C₁₃	—	2	24	no	—
350	C₂²×C₁₃	—	2	6	no	—
351	C₂²×C₁₃	—	2	12	no	—
352	C₂²×C₁₃	—	2	12	no	—
353	C₂²×C₁₃	—	2	6	no	—
354	C₂²×C₁₃	—	2	6	no	—
355	C₂²×C₁₃	—	2	12	no	—
356	C₂²×C₁₃	—	4	48	no	—
357	C₂²×C₁₃	—	4	12	no	—
358	C₂²×C₁₃	—	4	24	no	—
359	C₂²×C₁₃	—	8	48	no	—
360	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
361	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
362	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
363	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
364	C₂²×C₁₃	#585	1	2	yes	—
365	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
366	C₄×C₁₃	—	2	2	no	—
367	C₄×C₁₃	—	2	4	no	—
368	C₄×C₁₃	—	2	6	no	—
369	C₄×C₁₃	—	2	12	no	—
370	C₄×C₁₃	—	2	4	no	—
371	C₄×C₁₃	C₂³×D₄	1	4	yes	—
372	C₄×C₁₃	C₂³×D₄	1	12	yes	—
373	C₂⁵	C₂³×C₁₃	1	3	yes	—
374	C₂⁵	C₂³×C₁₃	1	6	yes	—
375	H(5,𝔽₂)	—	2	128	no	—
376	C₂×#41	—	2	128	no	—
377	C₂×#41	—	2	8	no	—
378	C₂×#41	—	2	16	no	—
379	C₂×#41	—	2	24	no	—
380	C₂×#41	—	2	24	no	—
381	C₂×#41	—	2	24	no	—
382	C₂×#41	D₄×C₁₃	1	16	yes	complemented
383	C₂×#41	C₂³×C₁₃	1	8	yes	—
384	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
385	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
386	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
387	C₂×#41	C₂³×C₁₃	1	16	yes	complemented
388	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
389	C₂²×Q₈	—	2	8	no	—
390	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
392	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
394	C₂²×D₄	—	2	24	no	—
395	C₂²×D₄	—	2	48	no	—
396	C₂²×D₄	—	2	24	no	—
397	C₂²×D₄	—	4	24	no	—
398	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
399	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
400	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
401	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
402	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
403	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
404	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
405	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
406	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
407	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
408	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
409	C₂²×D₄	C₂³×C₁₃	1	48	yes	complemented
410	C₂²×D₄	C₂³×C₁₃	1	48	yes	complemented
411	C₂³×C₄	—	2	24	no	—
412	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
413	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
414	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
415	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
416	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
418	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
419	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
420	C₂³×C₄	C₂³×C₁₃	1	24	yes	complemented
421	#127	C₂³×C₁₃	1	48	yes	complemented
422	#124	C₂³×C₁₃	1	48	yes	complemented
423	#123	C₂³×C₁₃	1	48	yes	complemented
424	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
425	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
426	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
427	#121	C₂³×C₁₃	1	24	yes	complemented
428	#121	C₂³×C₁₃	1	48	yes	complemented
429	#121	C₂³×C₁₃	1	48	yes	complemented
430	#121	C₂³×C₁₃	1	48	yes	complemented
431	#121	C₂³×C₁₃	1	24	yes	complemented
432	#121	C₂³×C₁₃	1	96	yes	complemented
433	#121	C₂³×C₁₃	1	48	yes	complemented
434	#120	C₂³×C₁₃	1	48	yes	complemented
435	#120	C₂³×C₁₃	1	96	yes	complemented
436	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
437	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
438	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
439	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
440	#117	C₂³×C₁₃	1	24	yes	complemented
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
447	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	complemented
454	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
455	C₂×C₁₃	—	2	4	no	—
456	C₂×C₁₃	—	2	12	no	—
457	C₂×C₁₃	—	4	6	no	—
458	C₂×C₁₃	—	4	12	no	—
459	C₂×C₁₃	#3488	1	4	yes	direct product factor
460	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
461	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
463	C₂⁴	—	2	12	no	—
464	C₂⁴	—	2	12	no	—
465	C₂⁴	—	2	24	no	—
466	C₂⁴	—	4	6	no	—
467	C₂⁴	—	4	12	no	—
468	C₂⁴	—	4	12	no	—
469	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
470	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
471	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
472	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
473	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
474	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
475	#41	—	2	32	no	—
476	#41	—	2	64	no	—
477	#41	—	2	96	no	—
478	#41	—	2	96	no	—
479	#41	—	2	96	no	—
480	#41	C₂×D₄×C₁₃	1	64	yes	complemented
481	C₂×Q₈	—	2	32	no	—
482	C₂×Q₈	—	2	12	no	—
483	C₂×Q₈	—	2	4	no	—
484	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	complemented
485	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
486	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
487	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
488	C₂×D₄	—	2	24	no	—
489	C₂×D₄	—	2	24	no	—
490	C₂×D₄	—	2	24	no	—
491	C₂×D₄	—	2	96	no	—
492	C₂×D₄	—	2	192	no	—
493	C₂×D₄	—	2	12	no	—
494	C₂×D₄	—	2	24	no	—
495	C₂×D₄	—	2	12	no	—
496	C₂×D₄	—	2	96	no	—
497	C₂×D₄	—	4	24	no	—
498	C₂×D₄	—	4	12	no	—
499	C₂×D₄	—	4	96	no	—
500	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	complemented
501	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
502	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
503	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
504	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
505	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
506	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
507	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
508	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
509	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
510	C₂²×C₄	—	2	12	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	12	no	—
513	C₂²×C₄	—	2	12	no	—
514	C₂²×C₄	—	2	12	no	—
515	C₂²×C₄	—	2	24	no	—
516	C₂²×C₄	—	2	96	no	—
517	C₂²×C₄	—	4	12	no	—
518	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	complemented
519	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
530	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
531	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
532	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
534	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
535	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
536	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
537	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
538	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
539	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
540	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
541	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
542	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
543	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
544	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
545	C₄²	C₂⁴×C₁₃	1	24	yes	—
546	C₁₃	C₂×#3488	1	1	yes	characteristic, direct product factor, Sylow
547	C₂³	—	2	2	no	—
548	C₂³	—	2	6	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	6	no	—
551	C₂³	—	2	24	no	—
552	C₂³	—	2	6	no	—
553	C₂³	—	2	12	no	—
554	C₂³	—	2	12	no	—
555	C₂³	—	2	6	no	—
556	C₂³	—	2	24	no	—
557	C₂³	—	2	6	no	—
558	C₂³	—	2	12	no	—
559	C₂³	—	2	48	no	—
560	C₂³	—	4	12	no	—
561	C₂³	—	4	24	no	—
562	C₂³	—	4	24	no	—
563	C₂³	—	4	48	no	—
564	C₂³	—	8	48	no	—
565	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
566	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
567	C₂³	C₂⁵×C₁₃	1	12	yes	—
568	C₂³	C₂⁵×C₁₃	1	6	yes	—
569	C₂³	C₂⁵×C₁₃	1	6	yes	—
570	C₂³	C₂⁵×C₁₃	1	2	yes	—
571	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
572	Q₈	—	2	24	no	—
573	Q₈	—	2	8	no	—
574	Q₈	C₂²×D₄×C₁₃	1	16	yes	complemented
575	D₄	—	2	48	no	—
576	D₄	—	2	48	no	—
577	D₄	—	2	48	no	—
578	D₄	—	2	24	no	—
579	D₄	—	2	48	no	—
580	D₄	—	2	24	no	—
581	D₄	—	4	48	no	—
582	D₄	—	4	24	no	—
583	D₄	C₂²×D₄×C₁₃	1	48	yes	complemented
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	6	no	—
587	C₂×C₄	—	2	24	no	—
588	C₂×C₄	—	2	12	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	24	no	—
592	C₂×C₄	—	2	24	no	—
593	C₂×C₄	—	2	24	no	—
594	C₂×C₄	—	2	48	no	—
595	C₂×C₄	—	4	24	no	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
597	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃	1	48	yes	complemented
599	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
600	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
601	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
602	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
603	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
604	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
605	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	6	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	6	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	24	no	—
612	C₂²	—	2	6	no	—
613	C₂²	—	2	12	no	—
614	C₂²	—	2	12	no	—
615	C₂²	—	2	6	no	—
616	C₂²	—	2	6	no	—
617	C₂²	—	2	12	no	—
618	C₂²	—	4	48	no	—
619	C₂²	—	4	12	no	—
620	C₂²	—	4	24	no	—
621	C₂²	—	8	48	no	—
622	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
623	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
624	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
625	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	complemented
626	C₂²	C₁₃×#585	1	2	yes	—
627	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	4	no	—
630	C₄	—	2	6	no	—
631	C₄	—	2	12	no	—
632	C₄	—	2	4	no	—
633	C₄	C₂³×D₄×C₁₃	1	4	yes	—
634	C₄	C₂³×D₄×C₁₃	1	12	yes	—
635	C₂	—	2	4	no	—
636	C₂	—	2	12	no	—
637	C₂	—	4	6	no	—
638	C₂	—	4	12	no	—
639	C₂	C₁₃×#3488	1	4	yes	direct product factor
640	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
641	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
642	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. C₂³×C₁₃×#41	C₂	semidirect
3. C₁₃×#3488	C₂	direct (N × H)
4. C₂×C₁₃×#550	C₂	semidirect
5. C₂×C₁₃×#548	C₂	semidirect
6. C₂×C₁₃×#546	C₂	semidirect
7. C₂×D₄²×C₁₃	C₂	semidirect
8. C₂×C₁₃×#537	C₂	semidirect
9. C₂×C₁₃×#535	C₂	semidirect
10. C₂×C₁₃×#525	C₂	semidirect
11. C₂²×C₁₃×#121	C₂	semidirect
12. C₂×C₁₃×#520	C₂	semidirect
14. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂²×C₁₃×#41	C₂²	semidirect
22. C₂²×C₁₃×#41	C₂²	semidirect
23. C₂³×Q₈×C₁₃	C₂²	semidirect
24. C₂³×D₄×C₁₃	C₂²	semidirect
25. C₂³×D₄×C₁₃	C₂²	semidirect
26. C₂³×D₄×C₁₃	C₂²	semidirect
27. C₂³×D₄×C₁₃	C₂²	semidirect
28. C₂⁴×C₄×C₁₃	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
30. C₁₃×#548	C₂²	semidirect
31. C₁₃×#546	C₂²	semidirect
32. D₄²×C₁₃	C₂²	semidirect
33. C₁₃×#537	C₂²	semidirect
34. C₁₃×#535	C₂²	semidirect
35. C₂×C₁₃×#127	C₂²	semidirect
36. C₂×C₁₃×#124	C₂²	semidirect
37. C₁₃×#525	C₂²	semidirect
38. C₂×C₁₃×#123	C₂²	semidirect
39. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
42. C₂×C₁₃×#121	C₂²	semidirect
43. C₂×C₁₃×#121	C₂²	semidirect
44. C₂×C₁₃×#121	C₂²	semidirect
45. C₂×C₁₃×#121	C₂²	semidirect
46. C₂×C₁₃×#121	C₂²	semidirect
47. C₂×C₁₃×#121	C₂²	semidirect
48. C₂×C₁₃×#121	C₂²	semidirect
49. C₂×C₁₃×#121	C₂²	semidirect
50. C₂×C₁₃×#120	C₂²	semidirect
51. C₂×C₁₃×#120	C₂²	semidirect
52. C₁₃×#520	C₂²	semidirect
53. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
54. C₂×C₄×D₄×C₁₃	C₂²	semidirect
55. C₂×C₄×D₄×C₁₃	C₂²	semidirect
56. C₂×C₄×D₄×C₁₃	C₂²	semidirect
57. C₂×C₁₃×#117	C₂²	semidirect
58. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
59. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
69. C₂×C₁₃×#41	D₄	semidirect
71. C₂×C₁₃×#41	C₂³	semidirect
72. C₂×C₁₃×#41	C₂³	semidirect
73. C₂×C₁₃×#41	C₂³	semidirect
74. C₂×C₁₃×#41	C₂³	semidirect
75. C₂×C₁₃×#41	C₂³	semidirect
80. C₂²×Q₈×C₁₃	C₂³	semidirect
94. C₂²×D₄×C₁₃	C₂³	semidirect
95. C₂²×D₄×C₁₃	C₂³	semidirect
96. C₂²×D₄×C₁₃	C₂³	semidirect
97. C₂²×D₄×C₁₃	C₂³	semidirect
107. C₂³×C₄×C₁₃	C₂³	semidirect
108. C₁₃×#127	C₂³	semidirect
109. C₁₃×#124	C₂³	semidirect
110. C₁₃×#123	C₂³	semidirect
111. C₁₃×C₂²⋊Q₈	C₂³	semidirect
112. C₁₃×C₂²⋊Q₈	C₂³	semidirect
113. C₁₃×C₂²⋊Q₈	C₂³	semidirect
114. C₁₃×#121	C₂³	semidirect
115. C₁₃×#121	C₂³	semidirect
116. C₁₃×#121	C₂³	semidirect
117. C₁₃×#121	C₂³	semidirect
118. C₁₃×#121	C₂³	semidirect
119. C₁₃×#121	C₂³	semidirect
120. C₁₃×#121	C₂³	semidirect
121. C₁₃×#120	C₂³	semidirect
122. C₁₃×#120	C₂³	semidirect
123. C₄×Q₈×C₁₃	C₂³	semidirect
124. C₄×D₄×C₁₃	C₂³	semidirect
125. C₄×D₄×C₁₃	C₂³	semidirect
126. C₄×D₄×C₁₃	C₂³	semidirect
127. C₁₃×#117	C₂³	semidirect
133. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
140. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
142. C₂×#3488	C₁₃	direct (N × H)
160. C₁₃×#41	C₂×D₄	semidirect
164. C₂×Q₈×C₁₃	C₂×D₄	semidirect
180. C₂×D₄×C₁₃	C₂×D₄	semidirect
198. C₂²×C₄×C₁₃	C₂×D₄	semidirect
226. C₂²×H(5,𝔽₂)	C₂×C₁₃	semidirect
227. C₂³×#41	C₂×C₁₃	semidirect
228. #3488	C₂×C₁₃	direct (N × H)
229. C₂×#550	C₂×C₁₃	semidirect
230. C₂×#548	C₂×C₁₃	semidirect
231. C₂×#546	C₂×C₁₃	semidirect
232. C₂×D₄²	C₂×C₁₃	semidirect
233. C₂×#537	C₂×C₁₃	semidirect
234. C₂×#535	C₂×C₁₃	semidirect
235. C₂×#525	C₂×C₁₃	semidirect
236. C₂²×#121	C₂×C₁₃	semidirect
237. C₂×#520	C₂×C₁₃	semidirect
257. C₂³×C₁₃	H(5,𝔽₂)	semidirect
265. Q₈×C₁₃	C₂²×D₄	semidirect
274. D₄×C₁₃	C₂²×D₄	semidirect
289. C₂×C₄×C₁₃	C₂²×D₄	semidirect
298. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
301. C₂²×#41	C₂²×C₁₃	semidirect
302. C₂²×#41	C₂²×C₁₃	semidirect
303. C₂²×#41	C₂²×C₁₃	semidirect
304. C₂²×#41	C₂²×C₁₃	semidirect
305. C₂²×#41	C₂²×C₁₃	semidirect
306. C₂²×#41	C₂²×C₁₃	semidirect
307. C₂³×Q₈	C₂²×C₁₃	semidirect
308. C₂³×D₄	C₂²×C₁₃	semidirect
309. C₂³×D₄	C₂²×C₁₃	semidirect
310. C₂³×D₄	C₂²×C₁₃	semidirect
311. C₂³×D₄	C₂²×C₁₃	semidirect
312. C₂⁴×C₄	C₂²×C₁₃	semidirect
313. #550	C₂²×C₁₃	semidirect
314. #548	C₂²×C₁₃	semidirect
315. #546	C₂²×C₁₃	semidirect
316. D₄²	C₂²×C₁₃	semidirect
317. #537	C₂²×C₁₃	semidirect
318. #535	C₂²×C₁₃	semidirect
319. C₂×#127	C₂²×C₁₃	semidirect
320. C₂×#124	C₂²×C₁₃	semidirect
321. #525	C₂²×C₁₃	semidirect
322. C₂×#123	C₂²×C₁₃	semidirect
323. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
324. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
325. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
326. C₂×#121	C₂²×C₁₃	semidirect
327. C₂×#121	C₂²×C₁₃	semidirect
328. C₂×#121	C₂²×C₁₃	semidirect
329. C₂×#121	C₂²×C₁₃	semidirect
330. C₂×#121	C₂²×C₁₃	semidirect
331. C₂×#121	C₂²×C₁₃	semidirect
332. C₂×#121	C₂²×C₁₃	semidirect
333. C₂×#121	C₂²×C₁₃	semidirect
334. C₂×#120	C₂²×C₁₃	semidirect
335. C₂×#120	C₂²×C₁₃	semidirect
336. #520	C₂²×C₁₃	semidirect
337. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
338. C₂×C₄×D₄	C₂²×C₁₃	semidirect
339. C₂×C₄×D₄	C₂²×C₁₃	semidirect
340. C₂×C₄×D₄	C₂²×C₁₃	semidirect
341. C₂×#117	C₂²×C₁₃	semidirect
342. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
343. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
363. C₂²×C₁₃	C₂×H(5,𝔽₂)	semidirect
382. C₂×#41	D₄×C₁₃	semidirect
384. C₂×#41	C₂³×C₁₃	semidirect
385. C₂×#41	C₂³×C₁₃	semidirect
386. C₂×#41	C₂³×C₁₃	semidirect
387. C₂×#41	C₂³×C₁₃	semidirect
388. C₂×#41	C₂³×C₁₃	semidirect
393. C₂²×Q₈	C₂³×C₁₃	semidirect
407. C₂²×D₄	C₂³×C₁₃	semidirect
408. C₂²×D₄	C₂³×C₁₃	semidirect
409. C₂²×D₄	C₂³×C₁₃	semidirect
410. C₂²×D₄	C₂³×C₁₃	semidirect
420. C₂³×C₄	C₂³×C₁₃	semidirect
421. #127	C₂³×C₁₃	semidirect
422. #124	C₂³×C₁₃	semidirect
423. #123	C₂³×C₁₃	semidirect
424. C₂²⋊Q₈	C₂³×C₁₃	semidirect
425. C₂²⋊Q₈	C₂³×C₁₃	semidirect
426. C₂²⋊Q₈	C₂³×C₁₃	semidirect
427. #121	C₂³×C₁₃	semidirect
428. #121	C₂³×C₁₃	semidirect
429. #121	C₂³×C₁₃	semidirect
430. #121	C₂³×C₁₃	semidirect
431. #121	C₂³×C₁₃	semidirect
432. #121	C₂³×C₁₃	semidirect
433. #121	C₂³×C₁₃	semidirect
434. #120	C₂³×C₁₃	semidirect
435. #120	C₂³×C₁₃	semidirect
436. C₄×Q₈	C₂³×C₁₃	semidirect
437. C₄×D₄	C₂³×C₁₃	semidirect
438. C₄×D₄	C₂³×C₁₃	semidirect
439. C₄×D₄	C₂³×C₁₃	semidirect
440. #117	C₂³×C₁₃	semidirect
446. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
453. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
459. C₂×C₁₃	#3488	direct (N × H)
480. #41	C₂×D₄×C₁₃	semidirect
484. C₂×Q₈	C₂×D₄×C₁₃	semidirect
500. C₂×D₄	C₂×D₄×C₁₃	semidirect
518. C₂²×C₄	C₂×D₄×C₁₃	semidirect
546. C₁₃	C₂×#3488	direct (N × H)
566. C₂³	C₁₃×H(5,𝔽₂)	semidirect
574. Q₈	C₂²×D₄×C₁₃	semidirect
583. D₄	C₂²×D₄×C₁₃	semidirect
598. C₂×C₄	C₂²×D₄×C₁₃	semidirect
625. C₂²	C₂×C₁₃×H(5,𝔽₂)	semidirect
639. C₂	C₁₃×#3488	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×#3488	2
C₂×C₁₃×#550	2
C₂×C₁₃×#548	2
C₂×C₁₃×#546	2
C₂×D₄²×C₁₃	2
C₂×C₁₃×#537	2
C₂×C₁₃×#535	2
C₂×C₁₃×#525	2
C₂²×C₁₃×#121	2
C₂×C₁₃×#520	2
C₂×#3488	13

Subgroups — C2×C13×#3488 #15749133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3488 #15749133