Subgroups — C₂×C₁₃×#3460 #15749018

Order 3328.

7994 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3460	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#542	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#540	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#538	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#535	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#532	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#525	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#544	C₂²	1	16	yes	complemented
18	C₁₃×#542	C₂²	1	64	yes	complemented
19	C₁₃×#540	C₂²	1	64	yes	complemented
20	C₁₃×#538	C₂²	1	64	yes	complemented
21	C₁₃×#537	C₂²	1	16	yes	complemented
22	C₁₃×#535	C₂²	1	32	yes	complemented
23	C₁₃×#532	C₂²	1	64	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#127	C₂²	1	4	yes	—
26	C₁₃×#529	C₂²	1	64	yes	complemented
27	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
28	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#124	C₂²	1	4	yes	—
30	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
31	C₁₃×#525	C₂²	1	64	yes	complemented
32	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#121	C₂²	1	4	yes	—
38	C₂×C₁₃×#121	C₂²	1	4	yes	—
39	C₂×C₁₃×#121	C₂²	1	4	yes	—
40	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
42	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#120	C₂²	1	8	yes	—
44	C₄×C₁₃×#41	C₂²	1	32	yes	complemented
45	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
46	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
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	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
51	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
52	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
53	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
55	C₂×C₁₃×#117	C₂²	1	2	yes	—
56	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
57	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
58	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
60	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
61	C₂²×C₄²×C₁₃	C₂²	1	4	yes	complemented
62	C₂⁵×C₁₃	C₂³	1	2	yes	—
63	C₂×C₁₃×#41	—	2	16	no	—
64	C₂×C₁₃×#41	—	4	16	no	—
65	C₂×C₁₃×#41	C₂³	1	16	yes	—
66	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
67	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃	—	2	8	no	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	—	4	8	no	—
78	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	complemented
89	C₁₃×#127	C₂³	1	32	yes	—
90	C₁₃×#126	C₂³	1	64	yes	complemented
91	C₁₃×#125	C₂³	1	32	yes	complemented
92	C₁₃×#124	C₂³	1	32	yes	—
93	C₁₃×#124	C₂³	1	64	yes	complemented
94	C₁₃×#123	C₂³	1	64	yes	complemented
95	C₁₃×#123	C₂³	1	64	yes	complemented
96	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
97	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
98	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
99	C₁₃×#121	C₂³	1	32	yes	—
100	C₁₃×#121	C₂³	1	32	yes	—
101	C₁₃×#121	C₂³	1	32	yes	—
102	C₁₃×#121	C₂³	1	32	yes	complemented
103	C₁₃×#121	C₂³	1	32	yes	complemented
104	C₁₃×#121	C₂³	1	64	yes	complemented
105	C₁₃×#120	C₂³	1	64	yes	—
106	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
107	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
108	C₄×D₄×C₁₃	C₂³	1	32	yes	—
109	C₄×D₄×C₁₃	C₂³	1	32	yes	—
110	C₄×D₄×C₁₃	C₂³	1	32	yes	—
111	C₄×D₄×C₁₃	C₂³	1	32	yes	—
112	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
113	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
114	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
115	C₁₃×#117	C₂³	1	16	yes	—
116	C₁₃×#117	C₂³	1	32	yes	complemented
117	C₁₃×#117	C₂³	1	32	yes	complemented
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	4	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	32	yes	complemented
142	C₂×#3460	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	8	no	—
144	C₂⁴×C₁₃	—	4	4	no	—
145	C₂⁴×C₁₃	—	4	4	no	—
146	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
147	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
148	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
150	C₁₃×#41	—	2	64	no	—
151	C₁₃×#41	—	4	64	no	—
152	C₂×Q₈×C₁₃	—	2	8	no	—
153	C₂×Q₈×C₁₃	—	4	8	no	—
154	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
155	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
156	C₂×D₄×C₁₃	—	2	16	no	—
157	C₂×D₄×C₁₃	—	2	16	no	—
158	C₂×D₄×C₁₃	—	2	8	no	—
159	C₂×D₄×C₁₃	—	2	32	no	—
160	C₂×D₄×C₁₃	—	4	16	no	—
161	C₂×D₄×C₁₃	—	4	8	no	—
162	C₂×D₄×C₁₃	—	4	16	no	—
163	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
166	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
167	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
168	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
169	C₂²×C₄×C₁₃	—	2	16	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	16	no	—
172	C₂²×C₄×C₁₃	—	2	16	no	—
173	C₂²×C₄×C₁₃	—	4	32	no	—
174	C₂²×C₄×C₁₃	—	4	8	no	—
175	C₂²×C₄×C₁₃	—	4	4	no	—
176	C₂²×C₄×C₁₃	—	4	2	no	—
177	C₂²×C₄×C₁₃	—	4	8	no	—
178	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
204	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
205	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
206	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
207	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
208	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
209	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
210	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
211	C₄²×C₁₃	C₂⁴	1	8	yes	—
212	C₄²×C₁₃	C₂⁴	1	8	yes	—
213	C₄²×C₁₃	C₂⁴	1	16	yes	—
214	C₄²×C₁₃	C₂⁴	1	16	yes	—
215	C₄²×C₁₃	C₂⁴	1	16	yes	—
216	#3460	C₂×C₁₃	1	32	yes	direct product factor
217	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂×#542	C₂×C₁₃	1	4	yes	complemented
219	C₂×#540	C₂×C₁₃	1	4	yes	complemented
220	C₂×#538	C₂×C₁₃	1	4	yes	complemented
221	C₂×#537	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂×#535	C₂×C₁₃	1	2	yes	complemented
223	C₂×#532	C₂×C₁₃	1	4	yes	complemented
224	C₂×#529	C₂×C₁₃	1	4	yes	complemented
225	C₂×#525	C₂×C₁₃	1	4	yes	complemented
226	C₂×C₄×#41	C₂×C₁₃	1	2	yes	complemented
227	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	—	2	8	no	—
231	C₂³×C₁₃	—	2	16	no	—
232	C₂³×C₁₃	—	2	8	no	—
233	C₂³×C₁₃	—	2	8	no	—
234	C₂³×C₁₃	—	2	8	no	—
235	C₂³×C₁₃	—	2	8	no	—
236	C₂³×C₁₃	—	2	8	no	—
237	C₂³×C₁₃	—	4	8	no	—
238	C₂³×C₁₃	—	4	8	no	—
239	C₂³×C₁₃	—	4	32	no	—
240	C₂³×C₁₃	C₂×#41	1	4	yes	—
241	C₂³×C₁₃	C₂⁵	1	8	yes	—
242	C₂³×C₁₃	C₂⁵	1	8	yes	—
243	C₂³×C₁₃	C₂⁵	1	2	yes	—
244	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
245	Q₈×C₁₃	—	2	16	no	—
246	Q₈×C₁₃	—	4	16	no	—
247	D₄×C₁₃	—	2	32	no	—
248	D₄×C₁₃	—	2	32	no	—
249	D₄×C₁₃	—	2	16	no	—
250	D₄×C₁₃	—	4	32	no	—
251	D₄×C₁₃	—	4	16	no	—
252	D₄×C₁₃	—	4	32	no	—
253	C₂×C₄×C₁₃	—	2	8	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	8	no	—
256	C₂×C₄×C₁₃	—	2	8	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	8	no	—
259	C₂×C₄×C₁₃	—	2	32	no	—
260	C₂×C₄×C₁₃	—	2	8	no	—
261	C₂×C₄×C₁₃	—	2	32	no	—
262	C₂×C₄×C₁₃	—	2	32	no	—
263	C₂×C₄×C₁₃	—	4	16	no	—
264	C₂×C₄×C₁₃	—	4	8	no	—
265	C₂×C₄×C₁₃	—	4	4	no	—
266	C₂×C₄×C₁₃	—	4	16	no	—
267	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
268	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
269	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
270	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
271	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
272	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
273	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
274	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
275	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
278	C₂²×#41	C₂²×C₁₃	1	2	yes	—
279	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
280	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
281	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
282	#544	C₂²×C₁₃	1	16	yes	complemented
283	#542	C₂²×C₁₃	1	64	yes	complemented
284	#540	C₂²×C₁₃	1	64	yes	complemented
285	#538	C₂²×C₁₃	1	64	yes	complemented
286	#537	C₂²×C₁₃	1	16	yes	complemented
287	#535	C₂²×C₁₃	1	32	yes	complemented
288	#532	C₂²×C₁₃	1	64	yes	complemented
289	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
290	C₂×#127	C₂²×C₁₃	1	4	yes	—
291	#529	C₂²×C₁₃	1	64	yes	complemented
292	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
293	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
294	C₂×#124	C₂²×C₁₃	1	4	yes	—
295	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
296	#525	C₂²×C₁₃	1	64	yes	complemented
297	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
298	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
299	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
300	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
301	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
302	C₂×#121	C₂²×C₁₃	1	4	yes	—
303	C₂×#121	C₂²×C₁₃	1	4	yes	—
304	C₂×#121	C₂²×C₁₃	1	4	yes	—
305	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
306	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
307	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
308	C₂×#120	C₂²×C₁₃	1	8	yes	—
309	C₄×#41	C₂²×C₁₃	1	32	yes	complemented
310	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
311	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
312	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
313	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
314	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
315	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
316	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
317	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
318	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
319	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
320	C₂×#117	C₂²×C₁₃	1	2	yes	—
321	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
322	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
323	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
325	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
326	C₂²×C₄²	C₂²×C₁₃	1	4	yes	complemented
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	8	no	—
330	C₂²×C₁₃	—	2	8	no	—
331	C₂²×C₁₃	—	2	8	no	—
332	C₂²×C₁₃	—	2	8	no	—
333	C₂²×C₁₃	—	2	8	no	—
334	C₂²×C₁₃	—	2	8	no	—
335	C₂²×C₁₃	—	2	8	no	—
336	C₂²×C₁₃	—	4	32	no	—
337	C₂²×C₁₃	—	4	16	no	—
338	C₂²×C₁₃	—	4	16	no	—
339	C₂²×C₁₃	C₂²×#41	1	4	yes	—
340	C₂²×C₁₃	C₂²×#41	1	2	yes	—
341	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
342	C₂²×C₁₃	#585	1	2	yes	—
343	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
344	C₄×C₁₃	—	2	8	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	8	no	—
347	C₄×C₁₃	—	2	8	no	—
348	C₄×C₁₃	—	2	4	no	—
349	C₄×C₁₃	—	2	8	no	—
350	C₄×C₁₃	C₂²×#41	1	8	yes	—
351	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
352	C₂⁵	C₂³×C₁₃	1	2	yes	—
353	C₂×#41	—	2	16	no	—
354	C₂×#41	—	4	16	no	—
355	C₂×#41	C₂³×C₁₃	1	16	yes	—
356	C₂×#41	C₂³×C₁₃	1	32	yes	complemented
357	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
358	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
359	C₂²×D₄	—	2	8	no	—
360	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
361	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
362	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
363	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
364	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
365	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
366	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
367	C₂³×C₄	—	4	8	no	—
368	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
369	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
370	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
372	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
375	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
376	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
377	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
379	#127	C₂³×C₁₃	1	32	yes	—
380	#126	C₂³×C₁₃	1	64	yes	complemented
381	#125	C₂³×C₁₃	1	32	yes	complemented
382	#124	C₂³×C₁₃	1	32	yes	—
383	#124	C₂³×C₁₃	1	64	yes	complemented
384	#123	C₂³×C₁₃	1	64	yes	complemented
385	#123	C₂³×C₁₃	1	64	yes	complemented
386	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
387	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
388	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
389	#121	C₂³×C₁₃	1	32	yes	—
390	#121	C₂³×C₁₃	1	32	yes	—
391	#121	C₂³×C₁₃	1	32	yes	—
392	#121	C₂³×C₁₃	1	32	yes	complemented
393	#121	C₂³×C₁₃	1	32	yes	complemented
394	#121	C₂³×C₁₃	1	64	yes	complemented
395	#120	C₂³×C₁₃	1	64	yes	—
396	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
397	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
398	C₄×D₄	C₂³×C₁₃	1	32	yes	—
399	C₄×D₄	C₂³×C₁₃	1	32	yes	—
400	C₄×D₄	C₂³×C₁₃	1	32	yes	—
401	C₄×D₄	C₂³×C₁₃	1	32	yes	—
402	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
403	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
404	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
405	#117	C₂³×C₁₃	1	16	yes	—
406	#117	C₂³×C₁₃	1	32	yes	complemented
407	#117	C₂³×C₁₃	1	32	yes	complemented
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
425	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
426	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
429	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
431	C₂×C₄²	C₂³×C₁₃	1	32	yes	complemented
432	C₂×C₁₃	—	2	4	no	—
433	C₂×C₁₃	—	4	8	no	—
434	C₂×C₁₃	—	4	8	no	—
435	C₂×C₁₃	#3460	1	4	yes	direct product factor
436	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
437	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
439	C₂⁴	—	2	8	no	—
440	C₂⁴	—	4	4	no	—
441	C₂⁴	—	4	4	no	—
442	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
443	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
444	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
446	#41	—	2	64	no	—
447	#41	—	4	64	no	—
448	C₂×Q₈	—	2	8	no	—
449	C₂×Q₈	—	4	8	no	—
450	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
451	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
452	C₂×D₄	—	2	16	no	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	32	no	—
456	C₂×D₄	—	4	8	no	—
457	C₂×D₄	—	4	16	no	—
458	C₂×D₄	—	4	16	no	—
459	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
460	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
461	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
462	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
463	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
464	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
465	C₂²×C₄	—	2	16	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	16	no	—
468	C₂²×C₄	—	2	16	no	—
469	C₂²×C₄	—	4	32	no	—
470	C₂²×C₄	—	4	8	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	8	no	—
474	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
475	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
482	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
483	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
487	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
493	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
494	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
495	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
496	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
497	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
498	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
499	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
500	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
501	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
502	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
503	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
504	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
505	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
506	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
507	C₄²	C₂⁴×C₁₃	1	8	yes	—
508	C₄²	C₂⁴×C₁₃	1	8	yes	—
509	C₄²	C₂⁴×C₁₃	1	16	yes	—
510	C₄²	C₂⁴×C₁₃	1	16	yes	—
511	C₄²	C₂⁴×C₁₃	1	16	yes	—
512	C₁₃	C₂×#3460	1	1	yes	characteristic, direct product factor, Sylow
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	8	no	—
516	C₂³	—	2	16	no	—
517	C₂³	—	2	8	no	—
518	C₂³	—	2	8	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	4	8	no	—
523	C₂³	—	4	8	no	—
524	C₂³	—	4	32	no	—
525	C₂³	C₂×C₁₃×#41	1	4	yes	—
526	C₂³	C₂⁵×C₁₃	1	8	yes	—
527	C₂³	C₂⁵×C₁₃	1	8	yes	—
528	C₂³	C₂⁵×C₁₃	1	2	yes	—
529	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
530	Q₈	—	2	16	no	—
531	Q₈	—	4	16	no	—
532	D₄	—	2	32	no	—
533	D₄	—	2	32	no	—
534	D₄	—	2	16	no	—
535	D₄	—	4	32	no	—
536	D₄	—	4	16	no	—
537	D₄	—	4	32	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	32	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	32	no	—
547	C₂×C₄	—	2	32	no	—
548	C₂×C₄	—	4	16	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	16	no	—
552	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
553	C₂×C₄	C₂×C₁₃×#41	1	16	yes	complemented
554	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
555	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
556	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
557	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
558	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
559	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
560	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
561	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
562	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	8	no	—
566	C₂²	—	2	8	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	8	no	—
569	C₂²	—	2	8	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	4	32	no	—
573	C₂²	—	4	16	no	—
574	C₂²	—	4	16	no	—
575	C₂²	C₂²×C₁₃×#41	1	4	yes	—
576	C₂²	C₂²×C₁₃×#41	1	2	yes	—
577	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
578	C₂²	C₁₃×#585	1	2	yes	—
579	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
580	C₄	—	2	8	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	8	no	—
583	C₄	—	2	8	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	8	no	—
586	C₄	C₂²×C₁₃×#41	1	8	yes	—
587	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
588	C₂	—	2	4	no	—
589	C₂	—	4	8	no	—
590	C₂	—	4	8	no	—
591	C₂	C₁₃×#3460	1	4	yes	direct product factor
592	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
593	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3460	C₂	direct (N × H)
2. C₂×C₁₃×#544	C₂	semidirect
3. C₂×C₁₃×#542	C₂	semidirect
4. C₂×C₁₃×#540	C₂	semidirect
5. C₂×C₁₃×#538	C₂	semidirect
6. C₂×C₁₃×#537	C₂	semidirect
7. C₂×C₁₃×#535	C₂	semidirect
8. C₂×C₁₃×#532	C₂	semidirect
9. C₂×C₁₃×#529	C₂	semidirect
10. C₂×C₁₃×#525	C₂	semidirect
11. C₂×C₄×C₁₃×#41	C₂	semidirect
12. C₂²×C₄×D₄×C₁₃	C₂	semidirect
14. C₂²×C₁₃×#41	C₂²	semidirect
17. C₁₃×#544	C₂²	semidirect
18. C₁₃×#542	C₂²	semidirect
19. C₁₃×#540	C₂²	semidirect
20. C₁₃×#538	C₂²	semidirect
21. C₁₃×#537	C₂²	semidirect
22. C₁₃×#535	C₂²	semidirect
23. C₁₃×#532	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₁₃×#529	C₂²	semidirect
27. C₂×C₁₃×#126	C₂²	semidirect
28. C₂×C₁₃×#125	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
35. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₁₃×#121	C₂²	semidirect
41. C₂×C₁₃×#121	C₂²	semidirect
42. C₂×C₁₃×#121	C₂²	semidirect
44. C₄×C₁₃×#41	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
46. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
51. C₂×C₄×D₄×C₁₃	C₂²	semidirect
52. C₂×C₄×D₄×C₁₃	C₂²	semidirect
53. C₂×C₄×D₄×C₁₃	C₂²	semidirect
54. C₂×C₄×D₄×C₁₃	C₂²	semidirect
56. C₂×C₁₃×#117	C₂²	semidirect
57. C₂×C₁₃×#117	C₂²	semidirect
61. C₂²×C₄²×C₁₃	C₂²	semidirect
66. C₂×C₁₃×#41	C₂³	semidirect
88. C₁₃×C₄⋊Q₈	C₂³	semidirect
90. C₁₃×#126	C₂³	semidirect
91. C₁₃×#125	C₂³	semidirect
93. C₁₃×#124	C₂³	semidirect
94. C₁₃×#123	C₂³	semidirect
95. C₁₃×#123	C₂³	semidirect
97. C₁₃×C₂²⋊Q₈	C₂³	semidirect
98. C₁₃×C₂²⋊Q₈	C₂³	semidirect
102. C₁₃×#121	C₂³	semidirect
103. C₁₃×#121	C₂³	semidirect
104. C₁₃×#121	C₂³	semidirect
106. C₄×Q₈×C₁₃	C₂³	semidirect
107. C₄×Q₈×C₁₃	C₂³	semidirect
112. C₄×D₄×C₁₃	C₂³	semidirect
113. C₄×D₄×C₁₃	C₂³	semidirect
114. C₄×D₄×C₁₃	C₂³	semidirect
116. C₁₃×#117	C₂³	semidirect
117. C₁₃×#117	C₂³	semidirect
141. C₂×C₄²×C₁₃	C₂³	semidirect
142. C₂×#3460	C₁₃	direct (N × H)
178. C₂²×C₄×C₁₃	#41	semidirect
216. #3460	C₂×C₁₃	direct (N × H)
217. C₂×#544	C₂×C₁₃	semidirect
218. C₂×#542	C₂×C₁₃	semidirect
219. C₂×#540	C₂×C₁₃	semidirect
220. C₂×#538	C₂×C₁₃	semidirect
221. C₂×#537	C₂×C₁₃	semidirect
222. C₂×#535	C₂×C₁₃	semidirect
223. C₂×#532	C₂×C₁₃	semidirect
224. C₂×#529	C₂×C₁₃	semidirect
225. C₂×#525	C₂×C₁₃	semidirect
226. C₂×C₄×#41	C₂×C₁₃	semidirect
227. C₂²×C₄×D₄	C₂×C₁₃	semidirect
268. C₂×C₄×C₁₃	C₂×#41	semidirect
279. C₂²×#41	C₂²×C₁₃	semidirect
282. #544	C₂²×C₁₃	semidirect
283. #542	C₂²×C₁₃	semidirect
284. #540	C₂²×C₁₃	semidirect
285. #538	C₂²×C₁₃	semidirect
286. #537	C₂²×C₁₃	semidirect
287. #535	C₂²×C₁₃	semidirect
288. #532	C₂²×C₁₃	semidirect
289. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
291. #529	C₂²×C₁₃	semidirect
292. C₂×#126	C₂²×C₁₃	semidirect
293. C₂×#125	C₂²×C₁₃	semidirect
295. C₂×#124	C₂²×C₁₃	semidirect
296. #525	C₂²×C₁₃	semidirect
297. C₂×#123	C₂²×C₁₃	semidirect
298. C₂×#123	C₂²×C₁₃	semidirect
300. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
301. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
305. C₂×#121	C₂²×C₁₃	semidirect
306. C₂×#121	C₂²×C₁₃	semidirect
307. C₂×#121	C₂²×C₁₃	semidirect
309. C₄×#41	C₂²×C₁₃	semidirect
310. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
311. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
316. C₂×C₄×D₄	C₂²×C₁₃	semidirect
317. C₂×C₄×D₄	C₂²×C₁₃	semidirect
318. C₂×C₄×D₄	C₂²×C₁₃	semidirect
319. C₂×C₄×D₄	C₂²×C₁₃	semidirect
321. C₂×#117	C₂²×C₁₃	semidirect
322. C₂×#117	C₂²×C₁₃	semidirect
326. C₂²×C₄²	C₂²×C₁₃	semidirect
356. C₂×#41	C₂³×C₁₃	semidirect
378. C₄⋊Q₈	C₂³×C₁₃	semidirect
380. #126	C₂³×C₁₃	semidirect
381. #125	C₂³×C₁₃	semidirect
383. #124	C₂³×C₁₃	semidirect
384. #123	C₂³×C₁₃	semidirect
385. #123	C₂³×C₁₃	semidirect
387. C₂²⋊Q₈	C₂³×C₁₃	semidirect
388. C₂²⋊Q₈	C₂³×C₁₃	semidirect
392. #121	C₂³×C₁₃	semidirect
393. #121	C₂³×C₁₃	semidirect
394. #121	C₂³×C₁₃	semidirect
396. C₄×Q₈	C₂³×C₁₃	semidirect
397. C₄×Q₈	C₂³×C₁₃	semidirect
402. C₄×D₄	C₂³×C₁₃	semidirect
403. C₄×D₄	C₂³×C₁₃	semidirect
404. C₄×D₄	C₂³×C₁₃	semidirect
406. #117	C₂³×C₁₃	semidirect
407. #117	C₂³×C₁₃	semidirect
431. C₂×C₄²	C₂³×C₁₃	semidirect
435. C₂×C₁₃	#3460	direct (N × H)
474. C₂²×C₄	C₁₃×#41	semidirect
512. C₁₃	C₂×#3460	direct (N × H)
553. C₂×C₄	C₂×C₁₃×#41	semidirect
591. C₂	C₁₃×#3460	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×#3460	2
C₂×C₁₃×#544	2
C₂×C₁₃×#542	2
C₂×C₁₃×#540	2
C₂×C₁₃×#538	2
C₂×C₁₃×#537	2
C₂×C₁₃×#535	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂×C₄×C₁₃×#41	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3460	13

Subgroups — C2×C13×#3460 #15749018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3460 #15749018