Subgroups — C₂×C₁₃×#3475 #15749047

Order 3328.

7954 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3475	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#551	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#546	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#117	C₂	1	2	yes	maximal, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×#41	C₂²	1	2	yes	—
21	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#556	C₂²	1	16	yes	complemented
24	C₁₃×#555	C₂²	1	16	yes	complemented
25	C₁₃×#554	C₂²	1	16	yes	complemented
26	C₁₃×#553	C₂²	1	32	yes	complemented
27	C₁₃×#552	C₂²	1	32	yes	complemented
28	C₁₃×#552	C₂²	1	32	yes	complemented
29	C₁₃×#551	C₂²	1	64	yes	complemented
30	C₁₃×#547	C₂²	1	16	yes	complemented
31	C₁₃×#546	C₂²	1	32	yes	complemented
32	C₁₃×#533	C₂²	1	16	yes	complemented
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#529	C₂²	1	64	yes	complemented
36	C₁₃×#529	C₂²	1	32	yes	complemented
37	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
38	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
39	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#124	C₂²	1	2	yes	—
44	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
45	C₁₃×#525	C₂²	1	32	yes	complemented
46	C₂×C₁₃×#123	C₂²	1	4	yes	—
47	C₂×C₁₃×#123	C₂²	1	4	yes	—
48	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
49	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
50	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
53	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
54	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
55	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
56	C₂×C₁₃×#121	C₂²	1	4	yes	—
57	C₂×C₁₃×#121	C₂²	1	2	yes	—
58	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
59	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
60	C₂×C₁₃×#120	C₂²	1	4	yes	—
61	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
62	C₄×C₁₃×#41	C₂²	1	32	yes	complemented
63	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
64	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
66	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
68	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
69	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
70	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
71	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
72	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
73	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
74	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
75	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
76	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
77	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
78	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
83	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
84	C₂×C₁₃×#117	C₂²	1	2	yes	—
85	C₂×C₁₃×#117	C₂²	1	4	yes	—
86	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
87	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
88	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
89	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
90	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
91	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
92	C₂×C₁₃×#117	C₂²	1	32	yes	complemented
93	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
95	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
97	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
99	C₂²×C₄²×C₁₃	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
101	C₂⁵×C₁₃	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	—	2	16	no	—
103	C₂×C₁₃×#41	—	2	8	no	—
104	C₂×C₁₃×#41	C₂³	1	8	yes	—
105	C₂×C₁₃×#41	C₂³	1	16	yes	—
106	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	—	2	8	no	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	—	2	16	no	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
134	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
135	C₁₃×#126	C₂³	1	32	yes	complemented
136	C₁₃×#126	C₂³	1	32	yes	complemented
137	C₁₃×#126	C₂³	1	32	yes	complemented
138	C₁₃×#125	C₂³	1	32	yes	complemented
139	C₁₃×#125	C₂³	1	16	yes	complemented
140	C₁₃×#125	C₂³	1	16	yes	complemented
141	C₁₃×#124	C₂³	1	16	yes	—
142	C₁₃×#124	C₂³	1	32	yes	complemented
143	C₁₃×#123	C₂³	1	32	yes	—
144	C₁₃×#123	C₂³	1	32	yes	—
145	C₁₃×#123	C₂³	1	32	yes	complemented
146	C₁₃×#123	C₂³	1	32	yes	complemented
147	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
150	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
152	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	C₁₃×#121	C₂³	1	32	yes	—
154	C₁₃×#121	C₂³	1	16	yes	—
155	C₁₃×#121	C₂³	1	16	yes	complemented
156	C₁₃×#121	C₂³	1	16	yes	complemented
157	C₁₃×#120	C₂³	1	32	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
159	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
160	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
161	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
162	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
163	C₄×D₄×C₁₃	C₂³	1	8	yes	—
164	C₄×D₄×C₁₃	C₂³	1	8	yes	—
165	C₄×D₄×C₁₃	C₂³	1	16	yes	—
166	C₄×D₄×C₁₃	C₂³	1	8	yes	—
167	C₄×D₄×C₁₃	C₂³	1	16	yes	—
168	C₄×D₄×C₁₃	C₂³	1	8	yes	—
169	C₄×D₄×C₁₃	C₂³	1	16	yes	—
170	C₄×D₄×C₁₃	C₂³	1	16	yes	—
171	C₄×D₄×C₁₃	C₂³	1	16	yes	—
172	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
173	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
174	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
175	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
176	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
177	C₁₃×#117	C₂³	1	8	yes	—
178	C₁₃×#117	C₂³	1	16	yes	—
179	C₁₃×#117	C₂³	1	32	yes	—
180	C₁₃×#117	C₂³	1	32	yes	complemented
181	C₁₃×#117	C₂³	1	16	yes	complemented
182	C₁₃×#117	C₂³	1	16	yes	complemented
183	C₁₃×#117	C₂³	1	16	yes	complemented
184	C₁₃×#117	C₂³	1	32	yes	complemented
185	C₁₃×#117	C₂³	1	16	yes	complemented
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
206	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
208	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
216	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
225	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
226	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
227	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
229	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
233	C₂×C₄²×C₁₃	C₂³	1	32	yes	complemented
234	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
235	C₂×#3475	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂⁴×C₁₃	—	2	8	no	—
237	C₂⁴×C₁₃	—	2	8	no	—
238	C₂⁴×C₁₃	—	4	4	no	—
239	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
240	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
241	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
242	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
244	C₁₃×#41	—	2	64	no	—
245	C₁₃×#41	—	2	32	no	—
246	C₂×Q₈×C₁₃	—	2	4	no	—
247	C₂×Q₈×C₁₃	—	2	8	no	—
248	C₂×Q₈×C₁₃	—	4	4	no	—
249	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
250	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
251	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
252	C₂×D₄×C₁₃	—	2	8	no	—
253	C₂×D₄×C₁₃	—	2	8	no	—
254	C₂×D₄×C₁₃	—	2	16	no	—
255	C₂×D₄×C₁₃	—	2	32	no	—
256	C₂×D₄×C₁₃	—	2	4	no	—
257	C₂×D₄×C₁₃	—	2	4	no	—
258	C₂×D₄×C₁₃	—	4	8	no	—
259	C₂×D₄×C₁₃	#41	1	8	yes	complemented
260	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
261	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
263	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
264	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₁₃	—	2	8	no	—
268	C₂²×C₄×C₁₃	—	2	16	no	—
269	C₂²×C₄×C₁₃	—	2	8	no	—
270	C₂²×C₄×C₁₃	—	2	8	no	—
271	C₂²×C₄×C₁₃	—	2	8	no	—
272	C₂²×C₄×C₁₃	—	2	8	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	8	no	—
275	C₂²×C₄×C₁₃	—	2	8	no	—
276	C₂²×C₄×C₁₃	—	2	64	no	—
277	C₂²×C₄×C₁₃	—	4	4	no	—
278	C₂²×C₄×C₁₃	—	4	8	no	—
279	C₂²×C₄×C₁₃	—	4	2	no	—
280	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
306	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
325	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
326	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
327	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
328	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
329	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
330	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
335	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
337	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
338	C₄²×C₁₃	C₂⁴	1	4	yes	—
339	C₄²×C₁₃	C₂⁴	1	4	yes	—
340	C₄²×C₁₃	C₂⁴	1	4	yes	—
341	C₄²×C₁₃	C₂⁴	1	4	yes	—
342	C₄²×C₁₃	C₂⁴	1	8	yes	—
343	C₄²×C₁₃	C₂⁴	1	16	yes	—
344	C₄²×C₁₃	C₂⁴	1	16	yes	—
345	C₄²×C₁₃	C₂⁴	1	16	yes	—
346	C₄²×C₁₃	C₂⁴	1	8	yes	—
347	C₄²×C₁₃	C₂⁴	1	8	yes	—
348	#3475	C₂×C₁₃	1	32	yes	direct product factor
349	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
351	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#553	C₂×C₁₃	1	2	yes	complemented
353	C₂×#552	C₂×C₁₃	1	2	yes	complemented
354	C₂×#552	C₂×C₁₃	1	2	yes	complemented
355	C₂×#551	C₂×C₁₃	1	4	yes	complemented
356	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₂×#546	C₂×C₁₃	1	2	yes	complemented
358	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₂×#529	C₂×C₁₃	1	4	yes	complemented
360	C₂×#529	C₂×C₁₃	1	2	yes	complemented
361	C₂×#525	C₂×C₁₃	1	2	yes	complemented
362	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
363	C₂×C₄×#41	C₂×C₁₃	1	2	yes	complemented
364	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
365	C₂²×#117	C₂×C₁₃	1	2	yes	complemented
366	C₂³×C₁₃	—	2	4	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	4	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	16	no	—
371	C₂³×C₁₃	—	2	4	no	—
372	C₂³×C₁₃	—	2	4	no	—
373	C₂³×C₁₃	—	2	4	no	—
374	C₂³×C₁₃	—	2	16	no	—
375	C₂³×C₁₃	—	2	4	no	—
376	C₂³×C₁₃	—	2	4	no	—
377	C₂³×C₁₃	—	2	4	no	—
378	C₂³×C₁₃	—	4	8	no	—
379	C₂³×C₁₃	—	4	32	no	—
380	C₂³×C₁₃	C₂×#41	1	4	yes	—
381	C₂³×C₁₃	C₂×#41	1	8	yes	—
382	C₂³×C₁₃	C₂⁵	1	4	yes	—
383	C₂³×C₁₃	C₂⁵	1	4	yes	—
384	C₂³×C₁₃	C₂⁵	1	2	yes	—
385	C₂³×C₁₃	C₂⁵	1	4	yes	—
386	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
387	Q₈×C₁₃	—	2	8	no	—
388	Q₈×C₁₃	—	2	16	no	—
389	Q₈×C₁₃	—	4	8	no	—
390	D₄×C₁₃	—	2	16	no	—
391	D₄×C₁₃	—	2	16	no	—
392	D₄×C₁₃	—	2	32	no	—
393	D₄×C₁₃	—	2	8	no	—
394	D₄×C₁₃	—	2	8	no	—
395	D₄×C₁₃	—	4	16	no	—
396	D₄×C₁₃	C₂×#41	1	16	yes	complemented
397	C₂×C₄×C₁₃	—	2	16	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	4	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	8	no	—
403	C₂×C₄×C₁₃	—	2	4	no	—
404	C₂×C₄×C₁₃	—	2	32	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	4	no	—
407	C₂×C₄×C₁₃	—	2	8	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	16	no	—
410	C₂×C₄×C₁₃	—	2	16	no	—
411	C₂×C₄×C₁₃	—	2	16	no	—
412	C₂×C₄×C₁₃	—	2	16	no	—
413	C₂×C₄×C₁₃	—	2	8	no	—
414	C₂×C₄×C₁₃	—	2	16	no	—
415	C₂×C₄×C₁₃	—	2	16	no	—
416	C₂×C₄×C₁₃	—	4	8	no	—
417	C₂×C₄×C₁₃	—	4	16	no	—
418	C₂×C₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
420	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
421	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
422	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
423	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
424	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
425	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
426	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
427	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
428	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
429	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
430	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
431	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
432	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
433	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
434	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
435	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
436	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×#41	C₂²×C₁₃	1	2	yes	—
438	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
439	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
440	#556	C₂²×C₁₃	1	16	yes	complemented
441	#555	C₂²×C₁₃	1	16	yes	complemented
442	#554	C₂²×C₁₃	1	16	yes	complemented
443	#553	C₂²×C₁₃	1	32	yes	complemented
444	#552	C₂²×C₁₃	1	32	yes	complemented
445	#552	C₂²×C₁₃	1	32	yes	complemented
446	#551	C₂²×C₁₃	1	64	yes	complemented
447	#547	C₂²×C₁₃	1	16	yes	complemented
448	#546	C₂²×C₁₃	1	32	yes	complemented
449	#533	C₂²×C₁₃	1	16	yes	complemented
450	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#529	C₂²×C₁₃	1	64	yes	complemented
453	#529	C₂²×C₁₃	1	32	yes	complemented
454	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
455	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
456	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
457	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
458	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
459	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
460	C₂×#124	C₂²×C₁₃	1	2	yes	—
461	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
462	#525	C₂²×C₁₃	1	32	yes	complemented
463	C₂×#123	C₂²×C₁₃	1	4	yes	—
464	C₂×#123	C₂²×C₁₃	1	4	yes	—
465	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
466	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
467	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
468	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
469	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
470	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
471	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
472	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
473	C₂×#121	C₂²×C₁₃	1	4	yes	—
474	C₂×#121	C₂²×C₁₃	1	2	yes	—
475	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
476	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
477	C₂×#120	C₂²×C₁₃	1	4	yes	—
478	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
479	C₄×#41	C₂²×C₁₃	1	32	yes	complemented
480	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
481	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
483	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
485	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
486	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
487	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
490	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
491	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
492	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
493	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
494	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
495	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
496	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
498	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
500	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
501	C₂×#117	C₂²×C₁₃	1	2	yes	—
502	C₂×#117	C₂²×C₁₃	1	4	yes	—
503	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
504	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
505	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
506	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
507	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
508	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
509	C₂×#117	C₂²×C₁₃	1	32	yes	complemented
510	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
511	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
512	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
513	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
514	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
515	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
516	C₂²×C₄²	C₂²×C₁₃	1	4	yes	complemented
517	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
518	C₂²×C₁₃	—	2	4	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	4	no	—
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	2	8	no	—
523	C₂²×C₁₃	—	2	16	no	—
524	C₂²×C₁₃	—	2	4	no	—
525	C₂²×C₁₃	—	2	4	no	—
526	C₂²×C₁₃	—	2	4	no	—
527	C₂²×C₁₃	—	2	4	no	—
528	C₂²×C₁₃	—	2	4	no	—
529	C₂²×C₁₃	—	2	4	no	—
530	C₂²×C₁₃	—	4	32	no	—
531	C₂²×C₁₃	—	4	8	no	—
532	C₂²×C₁₃	—	4	8	no	—
533	C₂²×C₁₃	C₂²×#41	1	4	yes	—
534	C₂²×C₁₃	C₂²×#41	1	8	yes	—
535	C₂²×C₁₃	C₂²×#41	1	2	yes	—
536	C₂²×C₁₃	C₂²×#41	1	2	yes	—
537	C₂²×C₁₃	#585	1	2	yes	—
538	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
539	C₄×C₁₃	—	2	4	no	—
540	C₄×C₁₃	—	2	4	no	—
541	C₄×C₁₃	—	2	4	no	—
542	C₄×C₁₃	—	2	2	no	—
543	C₄×C₁₃	—	2	8	no	—
544	C₄×C₁₃	—	2	4	no	—
545	C₄×C₁₃	—	2	2	no	—
546	C₄×C₁₃	—	2	4	no	—
547	C₄×C₁₃	—	2	8	no	—
548	C₄×C₁₃	—	2	2	no	—
549	C₄×C₁₃	C₂²×#41	1	4	yes	—
550	C₄×C₁₃	C₂²×#41	1	4	yes	—
551	C₄×C₁₃	C₂²×#41	1	4	yes	—
552	C₂⁵	C₂³×C₁₃	1	2	yes	—
553	C₂×#41	—	2	16	no	—
554	C₂×#41	—	2	8	no	—
555	C₂×#41	C₂³×C₁₃	1	8	yes	—
556	C₂×#41	C₂³×C₁₃	1	16	yes	—
557	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
558	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
560	C₂²×D₄	—	2	8	no	—
561	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
562	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
563	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
564	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
565	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
567	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
568	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂³×C₄	—	2	16	no	—
570	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
571	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
572	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
574	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
575	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
576	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
577	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
578	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
579	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
580	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
582	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
583	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
585	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
586	#126	C₂³×C₁₃	1	32	yes	complemented
587	#126	C₂³×C₁₃	1	32	yes	complemented
588	#126	C₂³×C₁₃	1	32	yes	complemented
589	#125	C₂³×C₁₃	1	32	yes	complemented
590	#125	C₂³×C₁₃	1	16	yes	complemented
591	#125	C₂³×C₁₃	1	16	yes	complemented
592	#124	C₂³×C₁₃	1	16	yes	—
593	#124	C₂³×C₁₃	1	32	yes	complemented
594	#123	C₂³×C₁₃	1	32	yes	—
595	#123	C₂³×C₁₃	1	32	yes	—
596	#123	C₂³×C₁₃	1	32	yes	complemented
597	#123	C₂³×C₁₃	1	32	yes	complemented
598	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
600	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
601	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
602	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
603	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
604	#121	C₂³×C₁₃	1	32	yes	—
605	#121	C₂³×C₁₃	1	16	yes	—
606	#121	C₂³×C₁₃	1	16	yes	complemented
607	#121	C₂³×C₁₃	1	16	yes	complemented
608	#120	C₂³×C₁₃	1	32	yes	—
609	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
610	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
611	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
612	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
613	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
614	C₄×D₄	C₂³×C₁₃	1	8	yes	—
615	C₄×D₄	C₂³×C₁₃	1	8	yes	—
616	C₄×D₄	C₂³×C₁₃	1	16	yes	—
617	C₄×D₄	C₂³×C₁₃	1	8	yes	—
618	C₄×D₄	C₂³×C₁₃	1	16	yes	—
619	C₄×D₄	C₂³×C₁₃	1	8	yes	—
620	C₄×D₄	C₂³×C₁₃	1	16	yes	—
621	C₄×D₄	C₂³×C₁₃	1	16	yes	—
622	C₄×D₄	C₂³×C₁₃	1	16	yes	—
623	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
624	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
625	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
626	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
627	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
628	#117	C₂³×C₁₃	1	8	yes	—
629	#117	C₂³×C₁₃	1	16	yes	—
630	#117	C₂³×C₁₃	1	32	yes	—
631	#117	C₂³×C₁₃	1	32	yes	complemented
632	#117	C₂³×C₁₃	1	16	yes	complemented
633	#117	C₂³×C₁₃	1	16	yes	complemented
634	#117	C₂³×C₁₃	1	16	yes	complemented
635	#117	C₂³×C₁₃	1	32	yes	complemented
636	#117	C₂³×C₁₃	1	16	yes	complemented
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
657	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
673	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
674	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
675	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
676	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
677	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
679	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
682	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
684	C₂×C₄²	C₂³×C₁₃	1	32	yes	complemented
685	C₂×C₄²	C₂³×C₁₃	1	16	yes	complemented
686	C₂×C₁₃	—	2	4	no	—
687	C₂×C₁₃	—	2	8	no	—
688	C₂×C₁₃	—	4	4	no	—
689	C₂×C₁₃	—	4	4	no	—
690	C₂×C₁₃	#3475	1	4	yes	direct product factor
691	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
692	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
693	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
694	C₂⁴	—	2	8	no	—
695	C₂⁴	—	2	8	no	—
696	C₂⁴	—	4	4	no	—
697	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
698	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
699	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
700	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
702	#41	—	2	64	no	—
703	#41	—	2	32	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	8	no	—
706	C₂×Q₈	—	4	4	no	—
707	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
708	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
709	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
710	C₂×D₄	—	2	8	no	—
711	C₂×D₄	—	2	8	no	—
712	C₂×D₄	—	2	16	no	—
713	C₂×D₄	—	2	32	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	4	8	no	—
717	C₂×D₄	C₁₃×#41	1	8	yes	complemented
718	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
719	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
720	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
721	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
722	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
723	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
724	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
725	C₂²×C₄	—	2	8	no	—
726	C₂²×C₄	—	2	16	no	—
727	C₂²×C₄	—	2	8	no	—
728	C₂²×C₄	—	2	8	no	—
729	C₂²×C₄	—	2	8	no	—
730	C₂²×C₄	—	2	8	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	8	no	—
733	C₂²×C₄	—	2	8	no	—
734	C₂²×C₄	—	2	64	no	—
735	C₂²×C₄	—	4	4	no	—
736	C₂²×C₄	—	4	8	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
739	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
745	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
749	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
750	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
751	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
752	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
753	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
756	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
759	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
760	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
765	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
767	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
769	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
770	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
771	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
772	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
773	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
774	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
775	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
778	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
779	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
780	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
781	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
782	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
784	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
785	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
786	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
787	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
788	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
789	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
790	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
791	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
792	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
794	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
795	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
796	C₄²	C₂⁴×C₁₃	1	4	yes	—
797	C₄²	C₂⁴×C₁₃	1	4	yes	—
798	C₄²	C₂⁴×C₁₃	1	4	yes	—
799	C₄²	C₂⁴×C₁₃	1	4	yes	—
800	C₄²	C₂⁴×C₁₃	1	8	yes	—
801	C₄²	C₂⁴×C₁₃	1	16	yes	—
802	C₄²	C₂⁴×C₁₃	1	16	yes	—
803	C₄²	C₂⁴×C₁₃	1	16	yes	—
804	C₄²	C₂⁴×C₁₃	1	8	yes	—
805	C₄²	C₂⁴×C₁₃	1	8	yes	—
806	C₁₃	C₂×#3475	1	1	yes	characteristic, direct product factor, Sylow
807	C₂³	—	2	4	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	16	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	16	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	—	4	32	no	—
821	C₂³	C₂×C₁₃×#41	1	4	yes	—
822	C₂³	C₂×C₁₃×#41	1	8	yes	—
823	C₂³	C₂⁵×C₁₃	1	4	yes	—
824	C₂³	C₂⁵×C₁₃	1	4	yes	—
825	C₂³	C₂⁵×C₁₃	1	2	yes	—
826	C₂³	C₂⁵×C₁₃	1	4	yes	—
827	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
828	Q₈	—	2	8	no	—
829	Q₈	—	2	16	no	—
830	Q₈	—	4	8	no	—
831	D₄	—	2	16	no	—
832	D₄	—	2	16	no	—
833	D₄	—	2	32	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	8	no	—
836	D₄	—	4	16	no	—
837	D₄	C₂×C₁₃×#41	1	16	yes	complemented
838	C₂×C₄	—	2	16	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	32	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	16	no	—
851	C₂×C₄	—	2	16	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	2	16	no	—
854	C₂×C₄	—	2	8	no	—
855	C₂×C₄	—	2	16	no	—
856	C₂×C₄	—	2	16	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	16	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
861	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
862	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
863	C₂×C₄	C₂×C₁₃×#41	1	16	yes	complemented
864	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
865	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
866	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
867	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
868	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
869	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
870	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
871	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
872	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
873	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
874	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
875	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
876	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	16	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	4	32	no	—
890	C₂²	—	4	8	no	—
891	C₂²	—	4	8	no	—
892	C₂²	C₂²×C₁₃×#41	1	4	yes	—
893	C₂²	C₂²×C₁₃×#41	1	8	yes	—
894	C₂²	C₂²×C₁₃×#41	1	2	yes	—
895	C₂²	C₂²×C₁₃×#41	1	2	yes	—
896	C₂²	C₁₃×#585	1	2	yes	—
897	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
898	C₄	—	2	4	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	8	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	8	no	—
907	C₄	—	2	2	no	—
908	C₄	C₂²×C₁₃×#41	1	4	yes	—
909	C₄	C₂²×C₁₃×#41	1	4	yes	—
910	C₄	C₂²×C₁₃×#41	1	4	yes	—
911	C₂	—	2	4	no	—
912	C₂	—	2	8	no	—
913	C₂	—	4	4	no	—
914	C₂	—	4	4	no	—
915	C₂	C₁₃×#3475	1	4	yes	direct product factor
916	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
917	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
918	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×#3475	C₂	direct (N × H)
2. C₂×C₁₃×#556	C₂	semidirect
3. C₂×C₁₃×#555	C₂	semidirect
4. C₂×C₁₃×#554	C₂	semidirect
5. C₂×C₁₃×#553	C₂	semidirect
6. C₂×C₁₃×#552	C₂	semidirect
7. C₂×C₁₃×#552	C₂	semidirect
8. C₂×C₁₃×#551	C₂	semidirect
9. C₂×C₁₃×#547	C₂	semidirect
10. C₂×C₁₃×#546	C₂	semidirect
11. C₂×C₁₃×#533	C₂	semidirect
12. C₂×C₁₃×#529	C₂	semidirect
13. C₂×C₁₃×#529	C₂	semidirect
14. C₂×C₁₃×#525	C₂	semidirect
15. C₂×C₄×C₁₃×#41	C₂	semidirect
16. C₂×C₄×C₁₃×#41	C₂	semidirect
17. C₂²×C₄×D₄×C₁₃	C₂	semidirect
18. C₂²×C₁₃×#117	C₂	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
27. C₁₃×#552	C₂²	semidirect
28. C₁₃×#552	C₂²	semidirect
29. C₁₃×#551	C₂²	semidirect
30. C₁₃×#547	C₂²	semidirect
31. C₁₃×#546	C₂²	semidirect
32. C₁₃×#533	C₂²	semidirect
33. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
35. C₁₃×#529	C₂²	semidirect
36. C₁₃×#529	C₂²	semidirect
37. C₂×C₁₃×#126	C₂²	semidirect
38. C₂×C₁₃×#126	C₂²	semidirect
39. C₂×C₁₃×#126	C₂²	semidirect
40. C₂×C₁₃×#125	C₂²	semidirect
41. C₂×C₁₃×#125	C₂²	semidirect
42. C₂×C₁₃×#125	C₂²	semidirect
44. C₂×C₁₃×#124	C₂²	semidirect
45. C₁₃×#525	C₂²	semidirect
48. C₂×C₁₃×#123	C₂²	semidirect
49. C₂×C₁₃×#123	C₂²	semidirect
52. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₁₃×#121	C₂²	semidirect
59. C₂×C₁₃×#121	C₂²	semidirect
61. C₄×C₁₃×#41	C₂²	semidirect
62. C₄×C₁₃×#41	C₂²	semidirect
63. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
64. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
65. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
66. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
67. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
77. C₂×C₄×D₄×C₁₃	C₂²	semidirect
78. C₂×C₄×D₄×C₁₃	C₂²	semidirect
79. C₂×C₄×D₄×C₁₃	C₂²	semidirect
80. C₂×C₄×D₄×C₁₃	C₂²	semidirect
81. C₂×C₄×D₄×C₁₃	C₂²	semidirect
82. C₂×C₄×D₄×C₁₃	C₂²	semidirect
86. C₂×C₁₃×#117	C₂²	semidirect
87. C₂×C₁₃×#117	C₂²	semidirect
88. C₂×C₁₃×#117	C₂²	semidirect
89. C₂×C₁₃×#117	C₂²	semidirect
90. C₂×C₁₃×#117	C₂²	semidirect
91. C₂×C₁₃×#117	C₂²	semidirect
92. C₂×C₁₃×#117	C₂²	semidirect
94. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
95. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
99. C₂²×C₄²×C₁₃	C₂²	semidirect
100. C₂²×C₄²×C₁₃	C₂²	semidirect
133. C₁₃×C₄⋊Q₈	C₂³	semidirect
134. C₁₃×C₄⋊Q₈	C₂³	semidirect
135. C₁₃×#126	C₂³	semidirect
136. C₁₃×#126	C₂³	semidirect
137. C₁₃×#126	C₂³	semidirect
138. C₁₃×#125	C₂³	semidirect
139. C₁₃×#125	C₂³	semidirect
140. C₁₃×#125	C₂³	semidirect
142. C₁₃×#124	C₂³	semidirect
145. C₁₃×#123	C₂³	semidirect
146. C₁₃×#123	C₂³	semidirect
149. C₁₃×C₂²⋊Q₈	C₂³	semidirect
150. C₁₃×C₂²⋊Q₈	C₂³	semidirect
151. C₁₃×C₂²⋊Q₈	C₂³	semidirect
152. C₁₃×C₂²⋊Q₈	C₂³	semidirect
155. C₁₃×#121	C₂³	semidirect
156. C₁₃×#121	C₂³	semidirect
158. C₄×Q₈×C₁₃	C₂³	semidirect
159. C₄×Q₈×C₁₃	C₂³	semidirect
160. C₄×Q₈×C₁₃	C₂³	semidirect
161. C₄×Q₈×C₁₃	C₂³	semidirect
162. C₄×Q₈×C₁₃	C₂³	semidirect
172. C₄×D₄×C₁₃	C₂³	semidirect
173. C₄×D₄×C₁₃	C₂³	semidirect
174. C₄×D₄×C₁₃	C₂³	semidirect
175. C₄×D₄×C₁₃	C₂³	semidirect
176. C₄×D₄×C₁₃	C₂³	semidirect
180. C₁₃×#117	C₂³	semidirect
181. C₁₃×#117	C₂³	semidirect
182. C₁₃×#117	C₂³	semidirect
183. C₁₃×#117	C₂³	semidirect
184. C₁₃×#117	C₂³	semidirect
185. C₁₃×#117	C₂³	semidirect
204. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
205. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
233. C₂×C₄²×C₁₃	C₂³	semidirect
234. C₂×C₄²×C₁₃	C₂³	semidirect
235. C₂×#3475	C₁₃	direct (N × H)
259. C₂×D₄×C₁₃	#41	semidirect
280. C₂²×C₄×C₁₃	#41	semidirect
348. #3475	C₂×C₁₃	direct (N × H)
349. C₂×#556	C₂×C₁₃	semidirect
350. C₂×#555	C₂×C₁₃	semidirect
351. C₂×#554	C₂×C₁₃	semidirect
352. C₂×#553	C₂×C₁₃	semidirect
353. C₂×#552	C₂×C₁₃	semidirect
354. C₂×#552	C₂×C₁₃	semidirect
355. C₂×#551	C₂×C₁₃	semidirect
356. C₂×#547	C₂×C₁₃	semidirect
357. C₂×#546	C₂×C₁₃	semidirect
358. C₂×#533	C₂×C₁₃	semidirect
359. C₂×#529	C₂×C₁₃	semidirect
360. C₂×#529	C₂×C₁₃	semidirect
361. C₂×#525	C₂×C₁₃	semidirect
362. C₂×C₄×#41	C₂×C₁₃	semidirect
363. C₂×C₄×#41	C₂×C₁₃	semidirect
364. C₂²×C₄×D₄	C₂×C₁₃	semidirect
365. C₂²×#117	C₂×C₁₃	semidirect
396. D₄×C₁₃	C₂×#41	semidirect
422. C₂×C₄×C₁₃	C₂×#41	semidirect
440. #556	C₂²×C₁₃	semidirect
441. #555	C₂²×C₁₃	semidirect
442. #554	C₂²×C₁₃	semidirect
443. #553	C₂²×C₁₃	semidirect
444. #552	C₂²×C₁₃	semidirect
445. #552	C₂²×C₁₃	semidirect
446. #551	C₂²×C₁₃	semidirect
447. #547	C₂²×C₁₃	semidirect
448. #546	C₂²×C₁₃	semidirect
449. #533	C₂²×C₁₃	semidirect
450. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
451. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
452. #529	C₂²×C₁₃	semidirect
453. #529	C₂²×C₁₃	semidirect
454. C₂×#126	C₂²×C₁₃	semidirect
455. C₂×#126	C₂²×C₁₃	semidirect
456. C₂×#126	C₂²×C₁₃	semidirect
457. C₂×#125	C₂²×C₁₃	semidirect
458. C₂×#125	C₂²×C₁₃	semidirect
459. C₂×#125	C₂²×C₁₃	semidirect
461. C₂×#124	C₂²×C₁₃	semidirect
462. #525	C₂²×C₁₃	semidirect
465. C₂×#123	C₂²×C₁₃	semidirect
466. C₂×#123	C₂²×C₁₃	semidirect
469. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
470. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
471. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
472. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
475. C₂×#121	C₂²×C₁₃	semidirect
476. C₂×#121	C₂²×C₁₃	semidirect
478. C₄×#41	C₂²×C₁₃	semidirect
479. C₄×#41	C₂²×C₁₃	semidirect
480. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
481. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
482. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
483. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
484. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
494. C₂×C₄×D₄	C₂²×C₁₃	semidirect
495. C₂×C₄×D₄	C₂²×C₁₃	semidirect
496. C₂×C₄×D₄	C₂²×C₁₃	semidirect
497. C₂×C₄×D₄	C₂²×C₁₃	semidirect
498. C₂×C₄×D₄	C₂²×C₁₃	semidirect
499. C₂×C₄×D₄	C₂²×C₁₃	semidirect
503. C₂×#117	C₂²×C₁₃	semidirect
504. C₂×#117	C₂²×C₁₃	semidirect
505. C₂×#117	C₂²×C₁₃	semidirect
506. C₂×#117	C₂²×C₁₃	semidirect
507. C₂×#117	C₂²×C₁₃	semidirect
508. C₂×#117	C₂²×C₁₃	semidirect
509. C₂×#117	C₂²×C₁₃	semidirect
511. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
512. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
516. C₂²×C₄²	C₂²×C₁₃	semidirect
517. C₂²×C₄²	C₂²×C₁₃	semidirect
584. C₄⋊Q₈	C₂³×C₁₃	semidirect
585. C₄⋊Q₈	C₂³×C₁₃	semidirect
586. #126	C₂³×C₁₃	semidirect
587. #126	C₂³×C₁₃	semidirect
588. #126	C₂³×C₁₃	semidirect
589. #125	C₂³×C₁₃	semidirect
590. #125	C₂³×C₁₃	semidirect
591. #125	C₂³×C₁₃	semidirect
593. #124	C₂³×C₁₃	semidirect
596. #123	C₂³×C₁₃	semidirect
597. #123	C₂³×C₁₃	semidirect
600. C₂²⋊Q₈	C₂³×C₁₃	semidirect
601. C₂²⋊Q₈	C₂³×C₁₃	semidirect
602. C₂²⋊Q₈	C₂³×C₁₃	semidirect
603. C₂²⋊Q₈	C₂³×C₁₃	semidirect
606. #121	C₂³×C₁₃	semidirect
607. #121	C₂³×C₁₃	semidirect
609. C₄×Q₈	C₂³×C₁₃	semidirect
610. C₄×Q₈	C₂³×C₁₃	semidirect
611. C₄×Q₈	C₂³×C₁₃	semidirect
612. C₄×Q₈	C₂³×C₁₃	semidirect
613. C₄×Q₈	C₂³×C₁₃	semidirect
623. C₄×D₄	C₂³×C₁₃	semidirect
624. C₄×D₄	C₂³×C₁₃	semidirect
625. C₄×D₄	C₂³×C₁₃	semidirect
626. C₄×D₄	C₂³×C₁₃	semidirect
627. C₄×D₄	C₂³×C₁₃	semidirect
631. #117	C₂³×C₁₃	semidirect
632. #117	C₂³×C₁₃	semidirect
633. #117	C₂³×C₁₃	semidirect
634. #117	C₂³×C₁₃	semidirect
635. #117	C₂³×C₁₃	semidirect
636. #117	C₂³×C₁₃	semidirect
655. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
656. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
684. C₂×C₄²	C₂³×C₁₃	semidirect
685. C₂×C₄²	C₂³×C₁₃	semidirect
690. C₂×C₁₃	#3475	direct (N × H)
717. C₂×D₄	C₁₃×#41	semidirect
738. C₂²×C₄	C₁₃×#41	semidirect
806. C₁₃	C₂×#3475	direct (N × H)
837. D₄	C₂×C₁₃×#41	semidirect
863. C₂×C₄	C₂×C₁₃×#41	semidirect
915. C₂	C₁₃×#3475	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×#3475	2
C₂×C₁₃×#556	2
C₂×C₁₃×#555	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#552	2
C₂×C₁₃×#551	2
C₂×C₁₃×#547	2
C₂×C₁₃×#546	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂×C₄×C₁₃×#41	2
C₂²×C₄×D₄×C₁₃	2
C₂²×C₁₃×#117	2
C₂×#3475	13

Subgroups — C2×C13×#3475 #15749047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3475 #15749047