Subgroups — C₂×C₁₃×#3494 #15749136

Order 3328.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3494	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#555	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#551	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#547	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#546	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#540	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#532	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
21	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#555	C₂²	1	32	yes	complemented
25	C₁₃×#553	C₂²	1	32	yes	complemented
26	C₁₃×#553	C₂²	1	32	yes	complemented
27	C₁₃×#551	C₂²	1	64	yes	complemented
28	C₁₃×#547	C₂²	1	32	yes	complemented
29	C₁₃×#546	C₂²	1	64	yes	complemented
30	C₁₃×#544	C₂²	1	16	yes	complemented
31	C₁₃×#542	C₂²	1	32	yes	complemented
32	C₁₃×#540	C₂²	1	32	yes	complemented
33	C₁₃×#535	C₂²	1	16	yes	complemented
34	C₁₃×#532	C₂²	1	32	yes	complemented
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
38	C₁₃×#529	C₂²	1	32	yes	complemented
39	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#126	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	complemented
44	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
45	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
46	C₁₃×#525	C₂²	1	16	yes	complemented
47	C₂×C₁₃×#123	C₂²	1	2	yes	—
48	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
49	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
50	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
51	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
52	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
53	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
56	C₂×C₁₃×#121	C₂²	1	2	yes	—
57	C₂×C₁₃×#121	C₂²	1	2	yes	—
58	C₂×C₁₃×#121	C₂²	1	2	yes	—
59	C₂×C₁₃×#121	C₂²	1	2	yes	—
60	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
61	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
64	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
65	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
66	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
67	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
68	C₂×C₁₃×#120	C₂²	1	2	yes	—
69	C₂×C₁₃×#120	C₂²	1	4	yes	—
70	C₁₃×#520	C₂²	1	16	yes	complemented
71	C₁₃×#518	C₂²	1	16	yes	complemented
72	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
73	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
74	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
75	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
76	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
77	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
78	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
79	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
81	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	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	1	yes	characteristic
85	C₂×C₁₃×#117	C₂²	1	2	yes	—
86	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
87	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
88	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
91	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#117	C₂²	1	16	yes	complemented
93	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
99	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
101	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
102	C₂⁵×C₁₃	C₂³	1	2	yes	—
103	C₂×C₁₃×#41	—	2	8	no	—
104	C₂×C₁₃×#41	—	4	16	no	—
105	C₂×C₁₃×#41	C₂³	1	8	yes	—
106	C₂×C₁₃×#41	C₂³	1	32	yes	complemented
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
109	C₂²×D₄×C₁₃	—	2	8	no	—
110	C₂²×D₄×C₁₃	—	4	8	no	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
120	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
121	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
122	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
123	C₂³×C₄×C₁₃	—	2	8	no	—
124	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
135	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
136	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
137	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
139	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
140	C₁₃×#127	C₂³	1	16	yes	complemented
141	C₁₃×#126	C₂³	1	32	yes	complemented
142	C₁₃×#126	C₂³	1	32	yes	complemented
143	C₁₃×#125	C₂³	1	16	yes	complemented
144	C₁₃×#125	C₂³	1	16	yes	complemented
145	C₁₃×#124	C₂³	1	16	yes	complemented
146	C₁₃×#124	C₂³	1	32	yes	complemented
147	C₁₃×#124	C₂³	1	32	yes	complemented
148	C₁₃×#123	C₂³	1	16	yes	—
149	C₁₃×#123	C₂³	1	32	yes	complemented
150	C₁₃×#123	C₂³	1	32	yes	complemented
151	C₁₃×#123	C₂³	1	32	yes	complemented
152	C₁₃×#123	C₂³	1	32	yes	complemented
153	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
155	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
156	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
157	C₁₃×#121	C₂³	1	16	yes	—
158	C₁₃×#121	C₂³	1	16	yes	—
159	C₁₃×#121	C₂³	1	16	yes	—
160	C₁₃×#121	C₂³	1	16	yes	—
161	C₁₃×#121	C₂³	1	8	yes	complemented
162	C₁₃×#121	C₂³	1	8	yes	complemented
163	C₁₃×#121	C₂³	1	32	yes	complemented
164	C₁₃×#121	C₂³	1	16	yes	complemented
165	C₁₃×#121	C₂³	1	16	yes	complemented
166	C₁₃×#121	C₂³	1	32	yes	complemented
167	C₁₃×#121	C₂³	1	32	yes	complemented
168	C₁₃×#120	C₂³	1	16	yes	—
169	C₁₃×#120	C₂³	1	32	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
171	C₄×D₄×C₁₃	C₂³	1	32	yes	—
172	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
173	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
174	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
175	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
176	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
177	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
178	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
179	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
180	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
181	C₁₃×#117	C₂³	1	8	yes	—
182	C₁₃×#117	C₂³	1	8	yes	—
183	C₁₃×#117	C₂³	1	16	yes	—
184	C₁₃×#117	C₂³	1	8	yes	—
185	C₁₃×#117	C₂³	1	16	yes	complemented
186	C₁₃×#117	C₂³	1	8	yes	complemented
187	C₁₃×#117	C₂³	1	8	yes	complemented
188	C₁₃×#117	C₂³	1	16	yes	complemented
189	C₁₃×#117	C₂³	1	32	yes	complemented
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
222	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
224	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
230	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
234	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
235	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
236	C₂×#3494	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂⁴×C₁₃	—	2	4	no	—
238	C₂⁴×C₁₃	—	2	4	no	—
239	C₂⁴×C₁₃	—	2	8	no	—
240	C₂⁴×C₁₃	—	4	2	no	—
241	C₂⁴×C₁₃	—	4	4	no	—
242	C₂⁴×C₁₃	—	4	4	no	—
243	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
245	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
246	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
247	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
250	C₁₃×#41	—	2	32	no	—
251	C₁₃×#41	—	4	64	no	—
252	C₂×Q₈×C₁₃	—	2	4	no	—
253	C₂×Q₈×C₁₃	—	4	8	no	—
254	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
255	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
256	C₂×D₄×C₁₃	—	2	8	no	—
257	C₂×D₄×C₁₃	—	2	16	no	—
258	C₂×D₄×C₁₃	—	2	8	no	—
259	C₂×D₄×C₁₃	—	2	8	no	—
260	C₂×D₄×C₁₃	—	2	8	no	—
261	C₂×D₄×C₁₃	—	2	4	no	—
262	C₂×D₄×C₁₃	—	2	32	no	—
263	C₂×D₄×C₁₃	—	4	8	no	—
264	C₂×D₄×C₁₃	—	4	4	no	—
265	C₂×D₄×C₁₃	—	4	8	no	—
266	C₂×D₄×C₁₃	—	4	8	no	—
267	C₂×D₄×C₁₃	—	4	32	no	—
268	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
269	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
270	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
271	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
272	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
273	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
274	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
275	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
277	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
278	C₂²×C₄×C₁₃	—	2	4	no	—
279	C₂²×C₄×C₁₃	—	2	8	no	—
280	C₂²×C₄×C₁₃	—	2	4	no	—
281	C₂²×C₄×C₁₃	—	2	4	no	—
282	C₂²×C₄×C₁₃	—	2	4	no	—
283	C₂²×C₄×C₁₃	—	2	4	no	—
284	C₂²×C₄×C₁₃	—	2	8	no	—
285	C₂²×C₄×C₁₃	—	2	32	no	—
286	C₂²×C₄×C₁₃	—	4	8	no	—
287	C₂²×C₄×C₁₃	—	4	4	no	—
288	C₂²×C₄×C₁₃	—	4	4	no	—
289	C₂²×C₄×C₁₃	—	4	8	no	—
290	C₂²×C₄×C₁₃	—	4	8	no	—
291	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
292	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
308	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
310	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
311	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
312	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
313	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
335	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
336	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
337	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
338	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
339	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
340	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
341	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
342	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
343	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
344	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
345	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
346	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
347	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
349	C₄²×C₁₃	C₂⁴	1	8	yes	—
350	C₄²×C₁₃	C₂⁴	1	8	yes	—
351	C₄²×C₁₃	C₂⁴	1	8	yes	—
352	C₄²×C₁₃	C₂⁴	1	8	yes	—
353	C₄²×C₁₃	C₂⁴	1	8	yes	—
354	C₄²×C₁₃	C₂⁴	1	16	yes	—
355	#3494	C₂×C₁₃	1	32	yes	direct product factor
356	C₂×#555	C₂×C₁₃	1	2	yes	complemented
357	C₂×#553	C₂×C₁₃	1	2	yes	complemented
358	C₂×#553	C₂×C₁₃	1	2	yes	complemented
359	C₂×#551	C₂×C₁₃	1	4	yes	complemented
360	C₂×#547	C₂×C₁₃	1	2	yes	complemented
361	C₂×#546	C₂×C₁₃	1	4	yes	complemented
362	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
363	C₂×#542	C₂×C₁₃	1	2	yes	complemented
364	C₂×#540	C₂×C₁₃	1	2	yes	complemented
365	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
366	C₂×#532	C₂×C₁₃	1	2	yes	complemented
367	C₂×#529	C₂×C₁₃	1	2	yes	complemented
368	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
369	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
370	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
371	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
372	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	2	no	—
375	C₂³×C₁₃	—	2	2	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	8	no	—
378	C₂³×C₁₃	—	2	2	no	—
379	C₂³×C₁₃	—	2	4	no	—
380	C₂³×C₁₃	—	2	8	no	—
381	C₂³×C₁₃	—	2	4	no	—
382	C₂³×C₁₃	—	2	8	no	—
383	C₂³×C₁₃	—	2	8	no	—
384	C₂³×C₁₃	—	2	2	no	—
385	C₂³×C₁₃	—	2	8	no	—
386	C₂³×C₁₃	—	2	4	no	—
387	C₂³×C₁₃	—	2	2	no	—
388	C₂³×C₁₃	—	2	16	no	—
389	C₂³×C₁₃	—	4	4	no	—
390	C₂³×C₁₃	—	4	8	no	—
391	C₂³×C₁₃	—	4	8	no	—
392	C₂³×C₁₃	—	4	16	no	—
393	C₂³×C₁₃	—	8	16	no	—
394	C₂³×C₁₃	C₂×#41	1	4	yes	—
395	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
396	C₂³×C₁₃	C₂⁵	1	2	yes	—
397	C₂³×C₁₃	C₂⁵	1	8	yes	—
398	C₂³×C₁₃	C₂⁵	1	4	yes	—
399	C₂³×C₁₃	C₂⁵	1	2	yes	—
400	C₂³×C₁₃	C₂⁵	1	2	yes	—
401	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
402	Q₈×C₁₃	—	2	8	no	—
403	Q₈×C₁₃	—	4	16	no	—
404	D₄×C₁₃	—	2	16	no	—
405	D₄×C₁₃	—	2	32	no	—
406	D₄×C₁₃	—	2	16	no	—
407	D₄×C₁₃	—	2	16	no	—
408	D₄×C₁₃	—	2	16	no	—
409	D₄×C₁₃	—	2	8	no	—
410	D₄×C₁₃	—	4	16	no	—
411	D₄×C₁₃	—	4	8	no	—
412	D₄×C₁₃	—	4	16	no	—
413	D₄×C₁₃	—	4	16	no	—
414	C₂×C₄×C₁₃	—	2	8	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	4	no	—
418	C₂×C₄×C₁₃	—	2	4	no	—
419	C₂×C₄×C₁₃	—	2	4	no	—
420	C₂×C₄×C₁₃	—	2	16	no	—
421	C₂×C₄×C₁₃	—	2	8	no	—
422	C₂×C₄×C₁₃	—	2	4	no	—
423	C₂×C₄×C₁₃	—	2	4	no	—
424	C₂×C₄×C₁₃	—	2	4	no	—
425	C₂×C₄×C₁₃	—	2	4	no	—
426	C₂×C₄×C₁₃	—	2	8	no	—
427	C₂×C₄×C₁₃	—	2	8	no	—
428	C₂×C₄×C₁₃	—	2	8	no	—
429	C₂×C₄×C₁₃	—	2	8	no	—
430	C₂×C₄×C₁₃	—	2	16	no	—
431	C₂×C₄×C₁₃	—	4	16	no	—
432	C₂×C₄×C₁₃	—	4	8	no	—
433	C₂×C₄×C₁₃	—	4	8	no	—
434	C₂×C₄×C₁₃	—	4	16	no	—
435	C₂×C₄×C₁₃	—	4	16	no	—
436	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
437	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
438	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
439	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
440	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
441	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
442	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
443	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
444	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
445	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
446	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
447	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
448	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
449	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
450	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
451	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
452	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
453	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
454	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
455	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
456	#555	C₂²×C₁₃	1	32	yes	complemented
457	#553	C₂²×C₁₃	1	32	yes	complemented
458	#553	C₂²×C₁₃	1	32	yes	complemented
459	#551	C₂²×C₁₃	1	64	yes	complemented
460	#547	C₂²×C₁₃	1	32	yes	complemented
461	#546	C₂²×C₁₃	1	64	yes	complemented
462	#544	C₂²×C₁₃	1	16	yes	complemented
463	#542	C₂²×C₁₃	1	32	yes	complemented
464	#540	C₂²×C₁₃	1	32	yes	complemented
465	#535	C₂²×C₁₃	1	16	yes	complemented
466	#532	C₂²×C₁₃	1	32	yes	complemented
467	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
468	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
469	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
470	#529	C₂²×C₁₃	1	32	yes	complemented
471	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
472	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
473	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
474	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
475	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
476	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
477	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
478	#525	C₂²×C₁₃	1	16	yes	complemented
479	C₂×#123	C₂²×C₁₃	1	2	yes	—
480	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
481	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
482	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
483	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
484	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
485	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
488	C₂×#121	C₂²×C₁₃	1	2	yes	—
489	C₂×#121	C₂²×C₁₃	1	2	yes	—
490	C₂×#121	C₂²×C₁₃	1	2	yes	—
491	C₂×#121	C₂²×C₁₃	1	2	yes	—
492	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
493	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
496	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
497	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
498	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
499	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
500	C₂×#120	C₂²×C₁₃	1	2	yes	—
501	C₂×#120	C₂²×C₁₃	1	4	yes	—
502	#520	C₂²×C₁₃	1	16	yes	complemented
503	#518	C₂²×C₁₃	1	16	yes	complemented
504	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
505	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
506	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
507	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
508	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
509	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
510	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
511	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
512	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
513	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
514	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
515	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
516	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
517	C₂×#117	C₂²×C₁₃	1	2	yes	—
518	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
519	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
520	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
522	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
523	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
524	C₂×#117	C₂²×C₁₃	1	16	yes	complemented
525	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
526	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
527	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
528	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
529	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
530	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
531	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
532	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
533	C₂²×C₁₃	—	2	2	no	—
534	C₂²×C₁₃	—	2	2	no	—
535	C₂²×C₁₃	—	2	2	no	—
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	8	no	—
538	C₂²×C₁₃	—	2	8	no	—
539	C₂²×C₁₃	—	2	2	no	—
540	C₂²×C₁₃	—	2	4	no	—
541	C₂²×C₁₃	—	2	8	no	—
542	C₂²×C₁₃	—	2	4	no	—
543	C₂²×C₁₃	—	2	8	no	—
544	C₂²×C₁₃	—	2	2	no	—
545	C₂²×C₁₃	—	2	8	no	—
546	C₂²×C₁₃	—	2	4	no	—
547	C₂²×C₁₃	—	2	2	no	—
548	C₂²×C₁₃	—	4	16	no	—
549	C₂²×C₁₃	—	4	8	no	—
550	C₂²×C₁₃	—	4	4	no	—
551	C₂²×C₁₃	—	4	16	no	—
552	C₂²×C₁₃	—	8	16	no	—
553	C₂²×C₁₃	C₂²×#41	1	4	yes	—
554	C₂²×C₁₃	C₂²×#41	1	2	yes	—
555	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
556	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
557	C₂²×C₁₃	#585	1	2	yes	—
558	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
559	C₄×C₁₃	—	2	2	no	—
560	C₄×C₁₃	—	2	2	no	—
561	C₄×C₁₃	—	2	4	no	—
562	C₄×C₁₃	—	2	4	no	—
563	C₄×C₁₃	—	2	4	no	—
564	C₄×C₁₃	—	2	8	no	—
565	C₄×C₁₃	—	2	4	no	—
566	C₄×C₁₃	—	2	4	no	—
567	C₄×C₁₃	—	2	4	no	—
568	C₄×C₁₃	—	2	4	no	—
569	C₄×C₁₃	C₂²×#41	1	4	yes	—
570	C₄×C₁₃	C₂²×#41	1	4	yes	—
571	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
572	C₂⁵	C₂³×C₁₃	1	2	yes	—
573	C₂×#41	—	2	8	no	—
574	C₂×#41	—	4	16	no	—
575	C₂×#41	C₂³×C₁₃	1	8	yes	—
576	C₂×#41	C₂³×C₁₃	1	32	yes	complemented
577	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
578	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
579	C₂²×D₄	—	2	8	no	—
580	C₂²×D₄	—	4	8	no	—
581	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
582	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
583	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
584	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
586	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
587	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
588	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
589	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
590	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
591	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
592	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
593	C₂³×C₄	—	2	8	no	—
594	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
596	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
598	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
601	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
603	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
604	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
605	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
606	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
607	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
609	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
610	#127	C₂³×C₁₃	1	16	yes	complemented
611	#126	C₂³×C₁₃	1	32	yes	complemented
612	#126	C₂³×C₁₃	1	32	yes	complemented
613	#125	C₂³×C₁₃	1	16	yes	complemented
614	#125	C₂³×C₁₃	1	16	yes	complemented
615	#124	C₂³×C₁₃	1	16	yes	complemented
616	#124	C₂³×C₁₃	1	32	yes	complemented
617	#124	C₂³×C₁₃	1	32	yes	complemented
618	#123	C₂³×C₁₃	1	16	yes	—
619	#123	C₂³×C₁₃	1	32	yes	complemented
620	#123	C₂³×C₁₃	1	32	yes	complemented
621	#123	C₂³×C₁₃	1	32	yes	complemented
622	#123	C₂³×C₁₃	1	32	yes	complemented
623	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
624	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
625	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
626	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
627	#121	C₂³×C₁₃	1	16	yes	—
628	#121	C₂³×C₁₃	1	16	yes	—
629	#121	C₂³×C₁₃	1	16	yes	—
630	#121	C₂³×C₁₃	1	16	yes	—
631	#121	C₂³×C₁₃	1	8	yes	complemented
632	#121	C₂³×C₁₃	1	8	yes	complemented
633	#121	C₂³×C₁₃	1	32	yes	complemented
634	#121	C₂³×C₁₃	1	16	yes	complemented
635	#121	C₂³×C₁₃	1	16	yes	complemented
636	#121	C₂³×C₁₃	1	32	yes	complemented
637	#121	C₂³×C₁₃	1	32	yes	complemented
638	#120	C₂³×C₁₃	1	16	yes	—
639	#120	C₂³×C₁₃	1	32	yes	—
640	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
641	C₄×D₄	C₂³×C₁₃	1	32	yes	—
642	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
643	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
644	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
645	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
646	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
647	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
648	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
649	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
650	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
651	#117	C₂³×C₁₃	1	8	yes	—
652	#117	C₂³×C₁₃	1	8	yes	—
653	#117	C₂³×C₁₃	1	16	yes	—
654	#117	C₂³×C₁₃	1	8	yes	—
655	#117	C₂³×C₁₃	1	16	yes	complemented
656	#117	C₂³×C₁₃	1	8	yes	complemented
657	#117	C₂³×C₁₃	1	8	yes	complemented
658	#117	C₂³×C₁₃	1	16	yes	complemented
659	#117	C₂³×C₁₃	1	32	yes	complemented
660	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
663	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
670	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
674	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
675	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
676	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
679	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
680	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
699	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
700	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
701	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
702	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
703	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
704	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
705	C₂×C₄²	C₂³×C₁₃	1	16	yes	complemented
706	C₂×C₁₃	—	2	4	no	—
707	C₂×C₁₃	—	2	4	no	—
708	C₂×C₁₃	—	4	4	no	—
709	C₂×C₁₃	—	4	2	no	—
710	C₂×C₁₃	—	4	8	no	—
711	C₂×C₁₃	#3494	1	4	yes	direct product factor
712	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
713	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
715	C₂⁴	—	2	4	no	—
716	C₂⁴	—	2	4	no	—
717	C₂⁴	—	2	8	no	—
718	C₂⁴	—	4	2	no	—
719	C₂⁴	—	4	4	no	—
720	C₂⁴	—	4	4	no	—
721	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
723	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
724	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
725	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
728	#41	—	2	32	no	—
729	#41	—	4	64	no	—
730	C₂×Q₈	—	2	4	no	—
731	C₂×Q₈	—	4	8	no	—
732	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
733	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
734	C₂×D₄	—	2	8	no	—
735	C₂×D₄	—	2	16	no	—
736	C₂×D₄	—	2	8	no	—
737	C₂×D₄	—	2	8	no	—
738	C₂×D₄	—	2	8	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	32	no	—
741	C₂×D₄	—	4	8	no	—
742	C₂×D₄	—	4	8	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	8	no	—
745	C₂×D₄	—	4	32	no	—
746	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
747	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
748	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
749	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
750	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
751	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
752	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
753	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
754	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
755	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	8	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	8	no	—
763	C₂²×C₄	—	2	32	no	—
764	C₂²×C₄	—	4	4	no	—
765	C₂²×C₄	—	4	8	no	—
766	C₂²×C₄	—	4	8	no	—
767	C₂²×C₄	—	4	8	no	—
768	C₂²×C₄	—	4	4	no	—
769	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
770	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
779	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
780	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
781	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
783	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
784	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
785	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
786	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
787	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
788	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
789	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
790	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
791	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
792	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
795	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
796	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
797	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
798	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
799	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
800	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
801	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
802	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
803	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
804	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
805	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
806	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
807	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
808	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
809	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
810	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
811	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
812	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
813	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
814	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
815	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
816	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
817	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
818	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
819	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
820	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
821	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
822	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
823	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
824	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
825	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
826	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
827	C₄²	C₂⁴×C₁₃	1	8	yes	—
828	C₄²	C₂⁴×C₁₃	1	8	yes	—
829	C₄²	C₂⁴×C₁₃	1	8	yes	—
830	C₄²	C₂⁴×C₁₃	1	8	yes	—
831	C₄²	C₂⁴×C₁₃	1	8	yes	—
832	C₄²	C₂⁴×C₁₃	1	16	yes	—
833	C₁₃	C₂×#3494	1	1	yes	characteristic, direct product factor, Sylow
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	8	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	8	no	—
844	C₂³	—	2	8	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	8	no	—
847	C₂³	—	2	4	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	16	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	8	no	—
852	C₂³	—	4	8	no	—
853	C₂³	—	4	16	no	—
854	C₂³	—	8	16	no	—
855	C₂³	C₂×C₁₃×#41	1	4	yes	—
856	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
857	C₂³	C₂⁵×C₁₃	1	2	yes	—
858	C₂³	C₂⁵×C₁₃	1	8	yes	—
859	C₂³	C₂⁵×C₁₃	1	4	yes	—
860	C₂³	C₂⁵×C₁₃	1	2	yes	—
861	C₂³	C₂⁵×C₁₃	1	2	yes	—
862	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
863	Q₈	—	2	8	no	—
864	Q₈	—	4	16	no	—
865	D₄	—	2	16	no	—
866	D₄	—	2	32	no	—
867	D₄	—	2	16	no	—
868	D₄	—	2	16	no	—
869	D₄	—	2	16	no	—
870	D₄	—	2	8	no	—
871	D₄	—	4	16	no	—
872	D₄	—	4	8	no	—
873	D₄	—	4	16	no	—
874	D₄	—	4	16	no	—
875	C₂×C₄	—	2	8	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	16	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	2	4	no	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	8	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	2	8	no	—
891	C₂×C₄	—	2	16	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	16	no	—
894	C₂×C₄	—	4	8	no	—
895	C₂×C₄	—	4	16	no	—
896	C₂×C₄	—	4	16	no	—
897	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
898	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
899	C₂×C₄	C₂×C₁₃×#41	1	16	yes	complemented
900	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
901	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
902	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
903	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
904	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
905	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
906	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
907	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
908	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
909	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
910	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
911	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	8	no	—
917	C₂²	—	2	8	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	8	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	8	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	8	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	4	16	no	—
928	C₂²	—	4	8	no	—
929	C₂²	—	4	4	no	—
930	C₂²	—	4	16	no	—
931	C₂²	—	8	16	no	—
932	C₂²	C₂²×C₁₃×#41	1	4	yes	—
933	C₂²	C₂²×C₁₃×#41	1	2	yes	—
934	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
935	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
936	C₂²	C₁₃×#585	1	2	yes	—
937	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	4	no	—
943	C₄	—	2	8	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	4	no	—
947	C₄	—	2	4	no	—
948	C₄	C₂²×C₁₃×#41	1	4	yes	—
949	C₄	C₂²×C₁₃×#41	1	4	yes	—
950	C₂	—	2	4	no	—
951	C₂	—	2	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	4	8	no	—
954	C₂	—	4	4	no	—
955	C₂	C₁₃×#3494	1	4	yes	direct product factor
956	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
957	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
958	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×#3494	C₂	direct (N × H)
2. C₂×C₁₃×#555	C₂	semidirect
3. C₂×C₁₃×#553	C₂	semidirect
4. C₂×C₁₃×#553	C₂	semidirect
5. C₂×C₁₃×#551	C₂	semidirect
6. C₂×C₁₃×#547	C₂	semidirect
7. C₂×C₁₃×#546	C₂	semidirect
8. C₂×C₁₃×#544	C₂	semidirect
9. C₂×C₁₃×#542	C₂	semidirect
10. C₂×C₁₃×#540	C₂	semidirect
11. C₂×C₁₃×#535	C₂	semidirect
12. C₂×C₁₃×#532	C₂	semidirect
13. C₂×C₁₃×#529	C₂	semidirect
14. C₂×C₁₃×#525	C₂	semidirect
15. C₂²×C₁₃×#121	C₂	semidirect
16. C₂×C₁₃×#520	C₂	semidirect
17. C₂×C₁₃×#518	C₂	semidirect
18. C₂²×C₁₃×#117	C₂	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#553	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
27. C₁₃×#551	C₂²	semidirect
28. C₁₃×#547	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
30. C₁₃×#544	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
32. C₁₃×#540	C₂²	semidirect
33. C₁₃×#535	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
35. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₁₃×#127	C₂²	semidirect
38. C₁₃×#529	C₂²	semidirect
39. C₂×C₁₃×#126	C₂²	semidirect
40. C₂×C₁₃×#126	C₂²	semidirect
41. C₂×C₁₃×#125	C₂²	semidirect
42. C₂×C₁₃×#125	C₂²	semidirect
43. C₂×C₁₃×#124	C₂²	semidirect
44. C₂×C₁₃×#124	C₂²	semidirect
45. C₂×C₁₃×#124	C₂²	semidirect
46. C₁₃×#525	C₂²	semidirect
48. C₂×C₁₃×#123	C₂²	semidirect
49. C₂×C₁₃×#123	C₂²	semidirect
50. C₂×C₁₃×#123	C₂²	semidirect
51. C₂×C₁₃×#123	C₂²	semidirect
53. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₁₃×#121	C₂²	semidirect
61. C₂×C₁₃×#121	C₂²	semidirect
62. C₂×C₁₃×#121	C₂²	semidirect
63. C₂×C₁₃×#121	C₂²	semidirect
64. C₂×C₁₃×#121	C₂²	semidirect
65. C₂×C₁₃×#121	C₂²	semidirect
66. C₂×C₁₃×#121	C₂²	semidirect
67. C₂×C₁₃×#121	C₂²	semidirect
70. C₁₃×#520	C₂²	semidirect
71. C₁₃×#518	C₂²	semidirect
72. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
74. C₂×C₄×D₄×C₁₃	C₂²	semidirect
75. C₂×C₄×D₄×C₁₃	C₂²	semidirect
76. C₂×C₄×D₄×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
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
96. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
100. C₂²×C₄²×C₁₃	C₂²	semidirect
106. C₂×C₁₃×#41	C₂³	semidirect
138. C₁₃×C₄⋊Q₈	C₂³	semidirect
139. C₁₃×C₄⋊Q₈	C₂³	semidirect
140. C₁₃×#127	C₂³	semidirect
141. C₁₃×#126	C₂³	semidirect
142. C₁₃×#126	C₂³	semidirect
143. C₁₃×#125	C₂³	semidirect
144. C₁₃×#125	C₂³	semidirect
145. C₁₃×#124	C₂³	semidirect
146. C₁₃×#124	C₂³	semidirect
147. C₁₃×#124	C₂³	semidirect
149. C₁₃×#123	C₂³	semidirect
150. C₁₃×#123	C₂³	semidirect
151. C₁₃×#123	C₂³	semidirect
152. C₁₃×#123	C₂³	semidirect
154. C₁₃×C₂²⋊Q₈	C₂³	semidirect
155. C₁₃×C₂²⋊Q₈	C₂³	semidirect
156. C₁₃×C₂²⋊Q₈	C₂³	semidirect
161. C₁₃×#121	C₂³	semidirect
162. C₁₃×#121	C₂³	semidirect
163. C₁₃×#121	C₂³	semidirect
164. C₁₃×#121	C₂³	semidirect
165. C₁₃×#121	C₂³	semidirect
166. C₁₃×#121	C₂³	semidirect
167. C₁₃×#121	C₂³	semidirect
170. 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
177. C₄×D₄×C₁₃	C₂³	semidirect
178. C₄×D₄×C₁₃	C₂³	semidirect
179. C₄×D₄×C₁₃	C₂³	semidirect
180. C₄×D₄×C₁₃	C₂³	semidirect
185. C₁₃×#117	C₂³	semidirect
186. C₁₃×#117	C₂³	semidirect
187. C₁₃×#117	C₂³	semidirect
188. C₁₃×#117	C₂³	semidirect
189. C₁₃×#117	C₂³	semidirect
207. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
208. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
209. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
235. C₂×C₄²×C₁₃	C₂³	semidirect
236. C₂×#3494	C₁₃	direct (N × H)
291. C₂²×C₄×C₁₃	#41	semidirect
355. #3494	C₂×C₁₃	direct (N × H)
356. C₂×#555	C₂×C₁₃	semidirect
357. C₂×#553	C₂×C₁₃	semidirect
358. C₂×#553	C₂×C₁₃	semidirect
359. C₂×#551	C₂×C₁₃	semidirect
360. C₂×#547	C₂×C₁₃	semidirect
361. C₂×#546	C₂×C₁₃	semidirect
362. C₂×#544	C₂×C₁₃	semidirect
363. C₂×#542	C₂×C₁₃	semidirect
364. C₂×#540	C₂×C₁₃	semidirect
365. C₂×#535	C₂×C₁₃	semidirect
366. C₂×#532	C₂×C₁₃	semidirect
367. C₂×#529	C₂×C₁₃	semidirect
368. C₂×#525	C₂×C₁₃	semidirect
369. C₂²×#121	C₂×C₁₃	semidirect
370. C₂×#520	C₂×C₁₃	semidirect
371. C₂×#518	C₂×C₁₃	semidirect
372. C₂²×#117	C₂×C₁₃	semidirect
438. C₂×C₄×C₁₃	C₂×#41	semidirect
452. C₂²×#41	C₂²×C₁₃	semidirect
456. #555	C₂²×C₁₃	semidirect
457. #553	C₂²×C₁₃	semidirect
458. #553	C₂²×C₁₃	semidirect
459. #551	C₂²×C₁₃	semidirect
460. #547	C₂²×C₁₃	semidirect
461. #546	C₂²×C₁₃	semidirect
462. #544	C₂²×C₁₃	semidirect
463. #542	C₂²×C₁₃	semidirect
464. #540	C₂²×C₁₃	semidirect
465. #535	C₂²×C₁₃	semidirect
466. #532	C₂²×C₁₃	semidirect
467. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
468. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
469. C₂×#127	C₂²×C₁₃	semidirect
470. #529	C₂²×C₁₃	semidirect
471. C₂×#126	C₂²×C₁₃	semidirect
472. C₂×#126	C₂²×C₁₃	semidirect
473. C₂×#125	C₂²×C₁₃	semidirect
474. C₂×#125	C₂²×C₁₃	semidirect
475. C₂×#124	C₂²×C₁₃	semidirect
476. C₂×#124	C₂²×C₁₃	semidirect
477. C₂×#124	C₂²×C₁₃	semidirect
478. #525	C₂²×C₁₃	semidirect
480. C₂×#123	C₂²×C₁₃	semidirect
481. C₂×#123	C₂²×C₁₃	semidirect
482. C₂×#123	C₂²×C₁₃	semidirect
483. C₂×#123	C₂²×C₁₃	semidirect
485. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
486. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
487. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
492. C₂×#121	C₂²×C₁₃	semidirect
493. C₂×#121	C₂²×C₁₃	semidirect
494. C₂×#121	C₂²×C₁₃	semidirect
495. C₂×#121	C₂²×C₁₃	semidirect
496. C₂×#121	C₂²×C₁₃	semidirect
497. C₂×#121	C₂²×C₁₃	semidirect
498. C₂×#121	C₂²×C₁₃	semidirect
499. C₂×#121	C₂²×C₁₃	semidirect
502. #520	C₂²×C₁₃	semidirect
503. #518	C₂²×C₁₃	semidirect
504. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
506. C₂×C₄×D₄	C₂²×C₁₃	semidirect
507. C₂×C₄×D₄	C₂²×C₁₃	semidirect
508. C₂×C₄×D₄	C₂²×C₁₃	semidirect
509. C₂×C₄×D₄	C₂²×C₁₃	semidirect
510. C₂×C₄×D₄	C₂²×C₁₃	semidirect
511. C₂×C₄×D₄	C₂²×C₁₃	semidirect
512. C₂×C₄×D₄	C₂²×C₁₃	semidirect
513. C₂×C₄×D₄	C₂²×C₁₃	semidirect
514. C₂×C₄×D₄	C₂²×C₁₃	semidirect
519. C₂×#117	C₂²×C₁₃	semidirect
520. C₂×#117	C₂²×C₁₃	semidirect
521. C₂×#117	C₂²×C₁₃	semidirect
522. C₂×#117	C₂²×C₁₃	semidirect
523. C₂×#117	C₂²×C₁₃	semidirect
524. C₂×#117	C₂²×C₁₃	semidirect
526. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
527. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
528. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
532. C₂²×C₄²	C₂²×C₁₃	semidirect
576. C₂×#41	C₂³×C₁₃	semidirect
608. C₄⋊Q₈	C₂³×C₁₃	semidirect
609. C₄⋊Q₈	C₂³×C₁₃	semidirect
610. #127	C₂³×C₁₃	semidirect
611. #126	C₂³×C₁₃	semidirect
612. #126	C₂³×C₁₃	semidirect
613. #125	C₂³×C₁₃	semidirect
614. #125	C₂³×C₁₃	semidirect
615. #124	C₂³×C₁₃	semidirect
616. #124	C₂³×C₁₃	semidirect
617. #124	C₂³×C₁₃	semidirect
619. #123	C₂³×C₁₃	semidirect
620. #123	C₂³×C₁₃	semidirect
621. #123	C₂³×C₁₃	semidirect
622. #123	C₂³×C₁₃	semidirect
624. C₂²⋊Q₈	C₂³×C₁₃	semidirect
625. C₂²⋊Q₈	C₂³×C₁₃	semidirect
626. C₂²⋊Q₈	C₂³×C₁₃	semidirect
631. #121	C₂³×C₁₃	semidirect
632. #121	C₂³×C₁₃	semidirect
633. #121	C₂³×C₁₃	semidirect
634. #121	C₂³×C₁₃	semidirect
635. #121	C₂³×C₁₃	semidirect
636. #121	C₂³×C₁₃	semidirect
637. #121	C₂³×C₁₃	semidirect
640. C₄×Q₈	C₂³×C₁₃	semidirect
642. C₄×D₄	C₂³×C₁₃	semidirect
643. C₄×D₄	C₂³×C₁₃	semidirect
644. C₄×D₄	C₂³×C₁₃	semidirect
645. C₄×D₄	C₂³×C₁₃	semidirect
646. C₄×D₄	C₂³×C₁₃	semidirect
647. C₄×D₄	C₂³×C₁₃	semidirect
648. C₄×D₄	C₂³×C₁₃	semidirect
649. C₄×D₄	C₂³×C₁₃	semidirect
650. C₄×D₄	C₂³×C₁₃	semidirect
655. #117	C₂³×C₁₃	semidirect
656. #117	C₂³×C₁₃	semidirect
657. #117	C₂³×C₁₃	semidirect
658. #117	C₂³×C₁₃	semidirect
659. #117	C₂³×C₁₃	semidirect
677. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
678. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
679. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
705. C₂×C₄²	C₂³×C₁₃	semidirect
711. C₂×C₁₃	#3494	direct (N × H)
769. C₂²×C₄	C₁₃×#41	semidirect
833. C₁₃	C₂×#3494	direct (N × H)
899. C₂×C₄	C₂×C₁₃×#41	semidirect
955. C₂	C₁₃×#3494	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×#3494	2
C₂×C₁₃×#555	2
C₂×C₁₃×#553	2
C₂×C₁₃×#551	2
C₂×C₁₃×#547	2
C₂×C₁₃×#546	2
C₂×C₁₃×#544	2
C₂×C₁₃×#542	2
C₂×C₁₃×#540	2
C₂×C₁₃×#535	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂²×C₁₃×#121	2
C₂×C₁₃×#520	2
C₂×C₁₃×#518	2
C₂²×C₁₃×#117	2
C₂×#3494	13

Subgroups — C2×C13×#3494 #15749136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3494 #15749136