Subgroups — C₂×C₁₃×#3551 #15749078

Order 3328.

7354 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3551	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#560	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#555	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#551	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#546	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#540	C₂	1	4	yes	maximal, complemented
11	C₂×C₁₃×#538	C₂	1	4	yes	maximal, complemented
12	C₂×C₁₃×#537	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#563	C₂²	1	32	yes	complemented
23	C₁₃×#560	C₂²	1	32	yes	complemented
24	C₁₃×#555	C₂²	1	32	yes	complemented
25	C₁₃×#553	C₂²	1	32	yes	complemented
26	C₁₃×#552	C₂²	1	32	yes	complemented
27	C₁₃×#551	C₂²	1	32	yes	complemented
28	C₁₃×#548	C₂²	1	32	yes	complemented
29	C₁₃×#546	C₂²	1	32	yes	complemented
30	C₁₃×#540	C₂²	1	64	yes	complemented
31	C₁₃×#538	C₂²	1	64	yes	complemented
32	C₁₃×#537	C₂²	1	32	yes	complemented
33	C₁₃×#536	C₂²	1	16	yes	complemented
34	C₁₃×#535	C₂²	1	16	yes	complemented
35	C₁₃×#532	C₂²	1	16	yes	complemented
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#127	C₂²	1	2	yes	—
40	C₁₃×#529	C₂²	1	32	yes	complemented
41	C₂×C₁₃×#126	C₂²	1	4	yes	—
42	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
43	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
44	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
45	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
46	C₂×C₁₃×#124	C₂²	1	2	yes	—
47	C₂×C₁₃×#124	C₂²	1	2	yes	—
48	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#124	C₂²	1	2	yes	—
50	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
52	C₂×C₁₃×#123	C₂²	1	2	yes	—
53	C₂×C₁₃×#123	C₂²	1	4	yes	—
54	C₂×C₁₃×#123	C₂²	1	4	yes	—
55	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
56	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
57	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
58	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
61	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂×C₁₃×#121	C₂²	1	2	yes	—
64	C₂×C₁₃×#121	C₂²	1	2	yes	—
65	C₂×C₁₃×#121	C₂²	1	2	yes	—
66	C₂×C₁₃×#121	C₂²	1	2	yes	—
67	C₂×C₁₃×#121	C₂²	1	4	yes	—
68	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
69	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
70	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
71	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
72	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
73	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
74	C₂×C₁₃×#120	C₂²	1	2	yes	—
75	C₂×C₁₃×#120	C₂²	1	4	yes	—
76	C₂×C₁₃×#120	C₂²	1	2	yes	—
77	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
78	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
80	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
83	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
84	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
86	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
88	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
89	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
90	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
91	C₂⁵×C₁₃	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	—	4	4	no	—
93	C₂×C₁₃×#41	—	4	4	no	—
94	C₂×C₁₃×#41	—	4	8	no	—
95	C₂×C₁₃×#41	C₂³	1	8	yes	—
96	C₂×C₁₃×#41	C₂³	1	16	yes	—
97	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
98	C₂²×Q₈×C₁₃	—	4	4	no	—
99	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
104	C₂²×D₄×C₁₃	—	4	4	no	—
105	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
107	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
108	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
129	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
130	C₁₃×#127	C₂³	1	8	yes	—
131	C₁₃×#127	C₂³	1	16	yes	—
132	C₁₃×#126	C₂³	1	32	yes	—
133	C₁₃×#126	C₂³	1	32	yes	complemented
134	C₁₃×#126	C₂³	1	32	yes	complemented
135	C₁₃×#125	C₂³	1	16	yes	complemented
136	C₁₃×#125	C₂³	1	32	yes	complemented
137	C₁₃×#124	C₂³	1	16	yes	—
138	C₁₃×#124	C₂³	1	8	yes	—
139	C₁₃×#124	C₂³	1	16	yes	—
140	C₁₃×#124	C₂³	1	16	yes	—
141	C₁₃×#124	C₂³	1	8	yes	complemented
142	C₁₃×#124	C₂³	1	32	yes	complemented
143	C₁₃×#123	C₂³	1	16	yes	—
144	C₁₃×#123	C₂³	1	32	yes	—
145	C₁₃×#123	C₂³	1	32	yes	—
146	C₁₃×#123	C₂³	1	32	yes	complemented
147	C₁₃×#123	C₂³	1	16	yes	complemented
148	C₁₃×#123	C₂³	1	32	yes	complemented
149	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
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×C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₁₃×#121	C₂³	1	16	yes	—
155	C₁₃×#121	C₂³	1	16	yes	—
156	C₁₃×#121	C₂³	1	16	yes	—
157	C₁₃×#121	C₂³	1	16	yes	—
158	C₁₃×#121	C₂³	1	32	yes	—
159	C₁₃×#121	C₂³	1	16	yes	complemented
160	C₁₃×#121	C₂³	1	32	yes	complemented
161	C₁₃×#121	C₂³	1	32	yes	complemented
162	C₁₃×#121	C₂³	1	32	yes	complemented
163	C₁₃×#121	C₂³	1	32	yes	complemented
164	C₁₃×#121	C₂³	1	32	yes	complemented
165	C₁₃×#120	C₂³	1	16	yes	—
166	C₁₃×#120	C₂³	1	16	yes	—
167	C₁₃×#120	C₂³	1	32	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
169	C₄×D₄×C₁₃	C₂³	1	16	yes	—
170	C₄×D₄×C₁₃	C₂³	1	16	yes	—
171	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
172	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
173	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
174	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
175	C₁₃×#117	C₂³	1	8	yes	—
176	C₁₃×#117	C₂³	1	32	yes	complemented
177	C₁₃×#117	C₂³	1	8	yes	complemented
178	C₁₃×#117	C₂³	1	32	yes	complemented
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
191	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
196	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
199	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
200	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
202	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
205	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
206	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
212	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
214	C₂×#3551	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂⁴×C₁₃	—	4	4	no	—
216	C₂⁴×C₁₃	—	4	8	no	—
217	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
219	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
221	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
223	C₁₃×#41	—	4	16	no	—
224	C₁₃×#41	—	4	16	no	—
225	C₁₃×#41	—	4	32	no	—
226	C₂×Q₈×C₁₃	—	2	8	no	—
227	C₂×Q₈×C₁₃	—	4	4	no	—
228	C₂×Q₈×C₁₃	—	4	2	no	—
229	C₂×Q₈×C₁₃	—	4	2	no	—
230	C₂×Q₈×C₁₃	—	4	16	no	—
231	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
232	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
234	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
235	C₂×D₄×C₁₃	—	2	8	no	—
236	C₂×D₄×C₁₃	—	4	16	no	—
237	C₂×D₄×C₁₃	—	4	4	no	—
238	C₂×D₄×C₁₃	—	4	8	no	—
239	C₂×D₄×C₁₃	—	4	4	no	—
240	C₂×D₄×C₁₃	—	4	8	no	—
241	C₂×D₄×C₁₃	—	4	8	no	—
242	C₂×D₄×C₁₃	—	4	4	no	—
243	C₂×D₄×C₁₃	—	4	4	no	—
244	C₂×D₄×C₁₃	—	4	2	no	—
245	C₂×D₄×C₁₃	—	4	2	no	—
246	C₂×D₄×C₁₃	—	4	2	no	—
247	C₂×D₄×C₁₃	—	4	2	no	—
248	C₂×D₄×C₁₃	—	4	8	no	—
249	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
251	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
257	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
260	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
261	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
262	C₂²×C₄×C₁₃	—	2	4	no	—
263	C₂²×C₄×C₁₃	—	2	4	no	—
264	C₂²×C₄×C₁₃	—	2	8	no	—
265	C₂²×C₄×C₁₃	—	2	4	no	—
266	C₂²×C₄×C₁₃	—	4	8	no	—
267	C₂²×C₄×C₁₃	—	4	4	no	—
268	C₂²×C₄×C₁₃	—	4	8	no	—
269	C₂²×C₄×C₁₃	—	4	4	no	—
270	C₂²×C₄×C₁₃	—	4	8	no	—
271	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
291	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
293	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
294	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
295	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
296	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
297	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
298	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
301	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
302	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
303	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
304	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
305	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
306	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
307	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
308	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
309	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
310	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
311	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
312	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
313	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
314	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
315	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
316	C₄²×C₁₃	C₂⁴	1	4	yes	—
317	C₄²×C₁₃	C₂⁴	1	8	yes	—
318	C₄²×C₁₃	C₂⁴	1	4	yes	—
319	C₄²×C₁₃	C₂⁴	1	8	yes	—
320	C₄²×C₁₃	C₂⁴	1	16	yes	—
321	C₄²×C₁₃	C₂⁴	1	8	yes	—
322	#3551	C₂×C₁₃	1	32	yes	direct product factor
323	C₂×#563	C₂×C₁₃	1	2	yes	complemented
324	C₂×#560	C₂×C₁₃	1	2	yes	complemented
325	C₂×#555	C₂×C₁₃	1	2	yes	complemented
326	C₂×#553	C₂×C₁₃	1	2	yes	complemented
327	C₂×#552	C₂×C₁₃	1	2	yes	complemented
328	C₂×#551	C₂×C₁₃	1	2	yes	complemented
329	C₂×#548	C₂×C₁₃	1	2	yes	complemented
330	C₂×#546	C₂×C₁₃	1	2	yes	complemented
331	C₂×#540	C₂×C₁₃	1	4	yes	complemented
332	C₂×#538	C₂×C₁₃	1	4	yes	complemented
333	C₂×#537	C₂×C₁₃	1	2	yes	complemented
334	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#529	C₂×C₁₃	1	2	yes	complemented
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	4	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	8	no	—
343	C₂³×C₁₃	—	2	4	no	—
344	C₂³×C₁₃	—	2	4	no	—
345	C₂³×C₁₃	—	2	8	no	—
346	C₂³×C₁₃	—	2	4	no	—
347	C₂³×C₁₃	—	2	4	no	—
348	C₂³×C₁₃	—	2	8	no	—
349	C₂³×C₁₃	—	2	4	no	—
350	C₂³×C₁₃	—	4	8	no	—
351	C₂³×C₁₃	—	4	16	no	—
352	C₂³×C₁₃	—	8	16	no	—
353	C₂³×C₁₃	C₂⁵	1	2	yes	—
354	C₂³×C₁₃	C₂⁵	1	8	yes	—
355	C₂³×C₁₃	C₂⁵	1	2	yes	—
356	C₂³×C₁₃	C₂⁵	1	4	yes	—
357	C₂³×C₁₃	C₂⁵	1	2	yes	—
358	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
359	Q₈×C₁₃	—	2	16	no	—
360	Q₈×C₁₃	—	4	8	no	—
361	Q₈×C₁₃	—	4	4	no	—
362	Q₈×C₁₃	—	4	4	no	—
363	D₄×C₁₃	—	2	16	no	—
364	D₄×C₁₃	—	4	8	no	—
365	D₄×C₁₃	—	4	16	no	—
366	D₄×C₁₃	—	4	8	no	—
367	D₄×C₁₃	—	4	16	no	—
368	D₄×C₁₃	—	4	16	no	—
369	D₄×C₁₃	—	4	8	no	—
370	D₄×C₁₃	—	4	8	no	—
371	D₄×C₁₃	—	4	4	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	4	no	—
374	D₄×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	4	16	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	8	no	—
381	C₂×C₄×C₁₃	—	2	4	no	—
382	C₂×C₄×C₁₃	—	2	8	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	8	no	—
385	C₂×C₄×C₁₃	—	2	8	no	—
386	C₂×C₄×C₁₃	—	2	8	no	—
387	C₂×C₄×C₁₃	—	2	16	no	—
388	C₂×C₄×C₁₃	—	2	8	no	—
389	C₂×C₄×C₁₃	—	4	16	no	—
390	C₂×C₄×C₁₃	—	4	8	no	—
391	C₂×C₄×C₁₃	—	4	16	no	—
392	C₂×C₄×C₁₃	—	4	8	no	—
393	C₂×C₄×C₁₃	—	4	16	no	—
394	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
395	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
396	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
397	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
398	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
399	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
400	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
401	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
402	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
403	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
404	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
405	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
406	C₂²×#41	C₂²×C₁₃	1	2	yes	—
407	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
410	#563	C₂²×C₁₃	1	32	yes	complemented
411	#560	C₂²×C₁₃	1	32	yes	complemented
412	#555	C₂²×C₁₃	1	32	yes	complemented
413	#553	C₂²×C₁₃	1	32	yes	complemented
414	#552	C₂²×C₁₃	1	32	yes	complemented
415	#551	C₂²×C₁₃	1	32	yes	complemented
416	#548	C₂²×C₁₃	1	32	yes	complemented
417	#546	C₂²×C₁₃	1	32	yes	complemented
418	#540	C₂²×C₁₃	1	64	yes	complemented
419	#538	C₂²×C₁₃	1	64	yes	complemented
420	#537	C₂²×C₁₃	1	32	yes	complemented
421	#536	C₂²×C₁₃	1	16	yes	complemented
422	#535	C₂²×C₁₃	1	16	yes	complemented
423	#532	C₂²×C₁₃	1	16	yes	complemented
424	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
426	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#127	C₂²×C₁₃	1	2	yes	—
428	#529	C₂²×C₁₃	1	32	yes	complemented
429	C₂×#126	C₂²×C₁₃	1	4	yes	—
430	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
431	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
432	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
433	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
434	C₂×#124	C₂²×C₁₃	1	2	yes	—
435	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#124	C₂²×C₁₃	1	2	yes	—
437	C₂×#124	C₂²×C₁₃	1	2	yes	—
438	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
440	C₂×#123	C₂²×C₁₃	1	2	yes	—
441	C₂×#123	C₂²×C₁₃	1	4	yes	—
442	C₂×#123	C₂²×C₁₃	1	4	yes	—
443	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
444	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
445	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
446	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
447	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
448	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
449	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
450	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
451	C₂×#121	C₂²×C₁₃	1	2	yes	—
452	C₂×#121	C₂²×C₁₃	1	2	yes	—
453	C₂×#121	C₂²×C₁₃	1	2	yes	—
454	C₂×#121	C₂²×C₁₃	1	2	yes	—
455	C₂×#121	C₂²×C₁₃	1	4	yes	—
456	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
457	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
458	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
459	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
460	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
461	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
462	C₂×#120	C₂²×C₁₃	1	2	yes	—
463	C₂×#120	C₂²×C₁₃	1	2	yes	—
464	C₂×#120	C₂²×C₁₃	1	4	yes	—
465	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
466	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
467	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
468	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
469	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
470	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
471	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
472	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
474	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
476	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
477	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
478	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	C₂²×C₁₃	—	2	2	no	—
480	C₂²×C₁₃	—	2	4	no	—
481	C₂²×C₁₃	—	2	2	no	—
482	C₂²×C₁₃	—	2	2	no	—
483	C₂²×C₁₃	—	2	8	no	—
484	C₂²×C₁₃	—	2	4	no	—
485	C₂²×C₁₃	—	2	4	no	—
486	C₂²×C₁₃	—	2	8	no	—
487	C₂²×C₁₃	—	2	4	no	—
488	C₂²×C₁₃	—	2	4	no	—
489	C₂²×C₁₃	—	2	8	no	—
490	C₂²×C₁₃	—	2	4	no	—
491	C₂²×C₁₃	—	4	4	no	—
492	C₂²×C₁₃	—	4	8	no	—
493	C₂²×C₁₃	—	4	4	no	—
494	C₂²×C₁₃	—	4	16	no	—
495	C₂²×C₁₃	—	4	4	no	—
496	C₂²×C₁₃	—	8	16	no	—
497	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
498	C₂²×C₁₃	#585	1	4	yes	—
499	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
500	C₄×C₁₃	—	2	4	no	—
501	C₄×C₁₃	—	2	2	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	2	no	—
504	C₄×C₁₃	—	2	8	no	—
505	C₄×C₁₃	—	2	4	no	—
506	C₄×C₁₃	—	2	8	no	—
507	C₄×C₁₃	—	2	4	no	—
508	C₄×C₁₃	—	2	8	no	—
509	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
510	C₂⁵	C₂³×C₁₃	1	2	yes	—
511	C₂×#41	—	4	4	no	—
512	C₂×#41	—	4	4	no	—
513	C₂×#41	—	4	8	no	—
514	C₂×#41	C₂³×C₁₃	1	8	yes	—
515	C₂×#41	C₂³×C₁₃	1	16	yes	—
516	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
517	C₂²×Q₈	—	4	4	no	—
518	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
519	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
520	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
521	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
522	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
523	C₂²×D₄	—	4	4	no	—
524	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
525	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
526	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
527	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
528	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
529	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
530	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
533	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
534	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
535	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
538	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
539	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
543	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
544	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
545	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
546	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
548	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
549	#127	C₂³×C₁₃	1	8	yes	—
550	#127	C₂³×C₁₃	1	16	yes	—
551	#126	C₂³×C₁₃	1	32	yes	—
552	#126	C₂³×C₁₃	1	32	yes	complemented
553	#126	C₂³×C₁₃	1	32	yes	complemented
554	#125	C₂³×C₁₃	1	16	yes	complemented
555	#125	C₂³×C₁₃	1	32	yes	complemented
556	#124	C₂³×C₁₃	1	16	yes	—
557	#124	C₂³×C₁₃	1	8	yes	—
558	#124	C₂³×C₁₃	1	16	yes	—
559	#124	C₂³×C₁₃	1	16	yes	—
560	#124	C₂³×C₁₃	1	8	yes	complemented
561	#124	C₂³×C₁₃	1	32	yes	complemented
562	#123	C₂³×C₁₃	1	16	yes	—
563	#123	C₂³×C₁₃	1	32	yes	—
564	#123	C₂³×C₁₃	1	32	yes	—
565	#123	C₂³×C₁₃	1	32	yes	complemented
566	#123	C₂³×C₁₃	1	16	yes	complemented
567	#123	C₂³×C₁₃	1	32	yes	complemented
568	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
569	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
570	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
571	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
572	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
573	#121	C₂³×C₁₃	1	16	yes	—
574	#121	C₂³×C₁₃	1	16	yes	—
575	#121	C₂³×C₁₃	1	16	yes	—
576	#121	C₂³×C₁₃	1	16	yes	—
577	#121	C₂³×C₁₃	1	32	yes	—
578	#121	C₂³×C₁₃	1	16	yes	complemented
579	#121	C₂³×C₁₃	1	32	yes	complemented
580	#121	C₂³×C₁₃	1	32	yes	complemented
581	#121	C₂³×C₁₃	1	32	yes	complemented
582	#121	C₂³×C₁₃	1	32	yes	complemented
583	#121	C₂³×C₁₃	1	32	yes	complemented
584	#120	C₂³×C₁₃	1	16	yes	—
585	#120	C₂³×C₁₃	1	16	yes	—
586	#120	C₂³×C₁₃	1	32	yes	—
587	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
588	C₄×D₄	C₂³×C₁₃	1	16	yes	—
589	C₄×D₄	C₂³×C₁₃	1	16	yes	—
590	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
591	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
592	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
593	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
594	#117	C₂³×C₁₃	1	8	yes	—
595	#117	C₂³×C₁₃	1	32	yes	complemented
596	#117	C₂³×C₁₃	1	8	yes	complemented
597	#117	C₂³×C₁₃	1	32	yes	complemented
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
610	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
626	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
629	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
633	C₂×C₁₃	—	4	2	no	—
634	C₂×C₁₃	—	4	4	no	—
635	C₂×C₁₃	—	4	2	no	—
636	C₂×C₁₃	—	4	8	no	—
637	C₂×C₁₃	—	4	2	no	—
638	C₂×C₁₃	#3551	1	4	yes	direct product factor
639	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₁₃	C₂×#585	1	2	yes	—
641	C₂⁴	—	4	4	no	—
642	C₂⁴	—	4	8	no	—
643	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
644	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
645	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
646	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
647	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
648	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
649	#41	—	4	16	no	—
650	#41	—	4	16	no	—
651	#41	—	4	32	no	—
652	C₂×Q₈	—	2	8	no	—
653	C₂×Q₈	—	4	4	no	—
654	C₂×Q₈	—	4	2	no	—
655	C₂×Q₈	—	4	2	no	—
656	C₂×Q₈	—	4	16	no	—
657	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
658	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
659	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
660	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
661	C₂×D₄	—	2	8	no	—
662	C₂×D₄	—	4	16	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	8	no	—
670	C₂×D₄	—	4	8	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	8	no	—
673	C₂×D₄	—	4	8	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
676	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
677	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
678	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
679	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
680	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
681	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
682	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
683	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
684	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
685	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
686	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
687	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	8	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	4	4	no	—
693	C₂²×C₄	—	4	8	no	—
694	C₂²×C₄	—	4	8	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	—	4	8	no	—
697	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
700	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
704	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
706	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
708	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
709	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
710	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
711	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
712	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
717	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
718	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
719	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
720	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
721	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
722	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
723	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
727	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
728	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
729	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
730	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
731	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
732	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
733	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
734	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
735	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
736	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
737	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
738	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
739	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
740	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
741	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
742	C₄²	C₂⁴×C₁₃	1	4	yes	—
743	C₄²	C₂⁴×C₁₃	1	8	yes	—
744	C₄²	C₂⁴×C₁₃	1	4	yes	—
745	C₄²	C₂⁴×C₁₃	1	8	yes	—
746	C₄²	C₂⁴×C₁₃	1	16	yes	—
747	C₄²	C₂⁴×C₁₃	1	8	yes	—
748	C₁₃	C₂×#3551	1	1	yes	characteristic, direct product factor, Sylow
749	C₂³	—	2	2	no	—
750	C₂³	—	2	4	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	8	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	8	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	8	no	—
760	C₂³	—	2	4	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	16	no	—
763	C₂³	—	8	16	no	—
764	C₂³	C₂⁵×C₁₃	1	2	yes	—
765	C₂³	C₂⁵×C₁₃	1	8	yes	—
766	C₂³	C₂⁵×C₁₃	1	2	yes	—
767	C₂³	C₂⁵×C₁₃	1	4	yes	—
768	C₂³	C₂⁵×C₁₃	1	2	yes	—
769	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
770	Q₈	—	2	16	no	—
771	Q₈	—	4	8	no	—
772	Q₈	—	4	4	no	—
773	Q₈	—	4	4	no	—
774	D₄	—	2	16	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	16	no	—
777	D₄	—	4	8	no	—
778	D₄	—	4	16	no	—
779	D₄	—	4	16	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	4	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	16	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	8	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	16	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	4	16	no	—
801	C₂×C₄	—	4	8	no	—
802	C₂×C₄	—	4	16	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	4	16	no	—
805	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
806	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
807	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
808	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
809	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
810	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
811	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
812	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
813	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
814	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
815	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	8	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	8	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	4	4	no	—
829	C₂²	—	4	8	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	16	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	8	16	no	—
834	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
835	C₂²	C₁₃×#585	1	4	yes	—
836	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
837	C₄	—	2	4	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	8	no	—
842	C₄	—	2	4	no	—
843	C₄	—	2	8	no	—
844	C₄	—	2	4	no	—
845	C₄	—	2	8	no	—
846	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
847	C₂	—	4	2	no	—
848	C₂	—	4	8	no	—
849	C₂	—	4	2	no	—
850	C₂	—	4	4	no	—
851	C₂	—	4	2	no	—
852	C₂	C₁₃×#3551	1	4	yes	direct product factor
853	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
854	C₂	C₂×C₁₃×#585	1	2	yes	—

	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×#3551	C₂	direct (N × H)
2. C₂×C₁₃×#563	C₂	semidirect
3. C₂×C₁₃×#560	C₂	semidirect
4. C₂×C₁₃×#555	C₂	semidirect
5. C₂×C₁₃×#553	C₂	semidirect
6. C₂×C₁₃×#552	C₂	semidirect
7. C₂×C₁₃×#551	C₂	semidirect
8. C₂×C₁₃×#548	C₂	semidirect
9. C₂×C₁₃×#546	C₂	semidirect
10. C₂×C₁₃×#540	C₂	semidirect
11. C₂×C₁₃×#538	C₂	semidirect
12. C₂×C₁₃×#537	C₂	semidirect
13. C₂×C₁₃×#536	C₂	semidirect
14. C₂×C₁₃×#535	C₂	semidirect
15. C₂×C₁₃×#532	C₂	semidirect
16. C₂×C₁₃×#529	C₂	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂³×Q₈×C₁₃	C₂²	semidirect
22. C₁₃×#563	C₂²	semidirect
23. C₁₃×#560	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#553	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
27. C₁₃×#551	C₂²	semidirect
28. C₁₃×#548	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
30. C₁₃×#540	C₂²	semidirect
31. C₁₃×#538	C₂²	semidirect
32. C₁₃×#537	C₂²	semidirect
33. C₁₃×#536	C₂²	semidirect
34. C₁₃×#535	C₂²	semidirect
35. C₁₃×#532	C₂²	semidirect
36. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
40. C₁₃×#529	C₂²	semidirect
42. C₂×C₁₃×#126	C₂²	semidirect
43. C₂×C₁₃×#126	C₂²	semidirect
44. C₂×C₁₃×#125	C₂²	semidirect
45. C₂×C₁₃×#125	C₂²	semidirect
50. C₂×C₁₃×#124	C₂²	semidirect
51. C₂×C₁₃×#124	C₂²	semidirect
55. C₂×C₁₃×#123	C₂²	semidirect
56. C₂×C₁₃×#123	C₂²	semidirect
57. C₂×C₁₃×#123	C₂²	semidirect
59. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
61. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
68. C₂×C₁₃×#121	C₂²	semidirect
69. C₂×C₁₃×#121	C₂²	semidirect
70. C₂×C₁₃×#121	C₂²	semidirect
71. C₂×C₁₃×#121	C₂²	semidirect
72. C₂×C₁₃×#121	C₂²	semidirect
73. C₂×C₁₃×#121	C₂²	semidirect
77. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
80. C₂×C₄×D₄×C₁₃	C₂²	semidirect
81. C₂×C₄×D₄×C₁₃	C₂²	semidirect
82. C₂×C₄×D₄×C₁₃	C₂²	semidirect
83. C₂×C₄×D₄×C₁₃	C₂²	semidirect
85. C₂×C₁₃×#117	C₂²	semidirect
86. C₂×C₁₃×#117	C₂²	semidirect
87. C₂×C₁₃×#117	C₂²	semidirect
88. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
90. C₂²×C₄²×C₁₃	C₂²	semidirect
97. C₂×C₁₃×#41	C₂³	semidirect
103. C₂²×Q₈×C₁₃	C₂³	semidirect
128. C₁₃×C₄⋊Q₈	C₂³	semidirect
129. C₁₃×C₄⋊Q₈	C₂³	semidirect
133. C₁₃×#126	C₂³	semidirect
134. C₁₃×#126	C₂³	semidirect
135. C₁₃×#125	C₂³	semidirect
136. C₁₃×#125	C₂³	semidirect
141. C₁₃×#124	C₂³	semidirect
142. C₁₃×#124	C₂³	semidirect
146. C₁₃×#123	C₂³	semidirect
147. C₁₃×#123	C₂³	semidirect
148. C₁₃×#123	C₂³	semidirect
150. C₁₃×C₂²⋊Q₈	C₂³	semidirect
151. C₁₃×C₂²⋊Q₈	C₂³	semidirect
152. C₁₃×C₂²⋊Q₈	C₂³	semidirect
153. C₁₃×C₂²⋊Q₈	C₂³	semidirect
159. C₁₃×#121	C₂³	semidirect
160. C₁₃×#121	C₂³	semidirect
161. C₁₃×#121	C₂³	semidirect
162. C₁₃×#121	C₂³	semidirect
163. C₁₃×#121	C₂³	semidirect
164. C₁₃×#121	C₂³	semidirect
168. C₄×Q₈×C₁₃	C₂³	semidirect
171. C₄×D₄×C₁₃	C₂³	semidirect
172. C₄×D₄×C₁₃	C₂³	semidirect
173. C₄×D₄×C₁₃	C₂³	semidirect
174. C₄×D₄×C₁₃	C₂³	semidirect
176. C₁₃×#117	C₂³	semidirect
177. C₁₃×#117	C₂³	semidirect
178. C₁₃×#117	C₂³	semidirect
190. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
213. C₂×C₄²×C₁₃	C₂³	semidirect
214. C₂×#3551	C₁₃	direct (N × H)
322. #3551	C₂×C₁₃	direct (N × H)
323. C₂×#563	C₂×C₁₃	semidirect
324. C₂×#560	C₂×C₁₃	semidirect
325. C₂×#555	C₂×C₁₃	semidirect
326. C₂×#553	C₂×C₁₃	semidirect
327. C₂×#552	C₂×C₁₃	semidirect
328. C₂×#551	C₂×C₁₃	semidirect
329. C₂×#548	C₂×C₁₃	semidirect
330. C₂×#546	C₂×C₁₃	semidirect
331. C₂×#540	C₂×C₁₃	semidirect
332. C₂×#538	C₂×C₁₃	semidirect
333. C₂×#537	C₂×C₁₃	semidirect
334. C₂×#536	C₂×C₁₃	semidirect
335. C₂×#535	C₂×C₁₃	semidirect
336. C₂×#532	C₂×C₁₃	semidirect
337. C₂×#529	C₂×C₁₃	semidirect
407. C₂²×#41	C₂²×C₁₃	semidirect
408. C₂³×Q₈	C₂²×C₁₃	semidirect
410. #563	C₂²×C₁₃	semidirect
411. #560	C₂²×C₁₃	semidirect
412. #555	C₂²×C₁₃	semidirect
413. #553	C₂²×C₁₃	semidirect
414. #552	C₂²×C₁₃	semidirect
415. #551	C₂²×C₁₃	semidirect
416. #548	C₂²×C₁₃	semidirect
417. #546	C₂²×C₁₃	semidirect
418. #540	C₂²×C₁₃	semidirect
419. #538	C₂²×C₁₃	semidirect
420. #537	C₂²×C₁₃	semidirect
421. #536	C₂²×C₁₃	semidirect
422. #535	C₂²×C₁₃	semidirect
423. #532	C₂²×C₁₃	semidirect
424. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
425. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
428. #529	C₂²×C₁₃	semidirect
430. C₂×#126	C₂²×C₁₃	semidirect
431. C₂×#126	C₂²×C₁₃	semidirect
432. C₂×#125	C₂²×C₁₃	semidirect
433. C₂×#125	C₂²×C₁₃	semidirect
438. C₂×#124	C₂²×C₁₃	semidirect
439. C₂×#124	C₂²×C₁₃	semidirect
443. C₂×#123	C₂²×C₁₃	semidirect
444. C₂×#123	C₂²×C₁₃	semidirect
445. C₂×#123	C₂²×C₁₃	semidirect
447. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
448. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
449. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
450. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
456. C₂×#121	C₂²×C₁₃	semidirect
457. C₂×#121	C₂²×C₁₃	semidirect
458. C₂×#121	C₂²×C₁₃	semidirect
459. C₂×#121	C₂²×C₁₃	semidirect
460. C₂×#121	C₂²×C₁₃	semidirect
461. C₂×#121	C₂²×C₁₃	semidirect
465. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
468. C₂×C₄×D₄	C₂²×C₁₃	semidirect
469. C₂×C₄×D₄	C₂²×C₁₃	semidirect
470. C₂×C₄×D₄	C₂²×C₁₃	semidirect
471. C₂×C₄×D₄	C₂²×C₁₃	semidirect
473. C₂×#117	C₂²×C₁₃	semidirect
474. C₂×#117	C₂²×C₁₃	semidirect
475. C₂×#117	C₂²×C₁₃	semidirect
476. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
478. C₂²×C₄²	C₂²×C₁₃	semidirect
516. C₂×#41	C₂³×C₁₃	semidirect
522. C₂²×Q₈	C₂³×C₁₃	semidirect
547. C₄⋊Q₈	C₂³×C₁₃	semidirect
548. C₄⋊Q₈	C₂³×C₁₃	semidirect
552. #126	C₂³×C₁₃	semidirect
553. #126	C₂³×C₁₃	semidirect
554. #125	C₂³×C₁₃	semidirect
555. #125	C₂³×C₁₃	semidirect
560. #124	C₂³×C₁₃	semidirect
561. #124	C₂³×C₁₃	semidirect
565. #123	C₂³×C₁₃	semidirect
566. #123	C₂³×C₁₃	semidirect
567. #123	C₂³×C₁₃	semidirect
569. C₂²⋊Q₈	C₂³×C₁₃	semidirect
570. C₂²⋊Q₈	C₂³×C₁₃	semidirect
571. C₂²⋊Q₈	C₂³×C₁₃	semidirect
572. C₂²⋊Q₈	C₂³×C₁₃	semidirect
578. #121	C₂³×C₁₃	semidirect
579. #121	C₂³×C₁₃	semidirect
580. #121	C₂³×C₁₃	semidirect
581. #121	C₂³×C₁₃	semidirect
582. #121	C₂³×C₁₃	semidirect
583. #121	C₂³×C₁₃	semidirect
587. C₄×Q₈	C₂³×C₁₃	semidirect
590. C₄×D₄	C₂³×C₁₃	semidirect
591. C₄×D₄	C₂³×C₁₃	semidirect
592. C₄×D₄	C₂³×C₁₃	semidirect
593. C₄×D₄	C₂³×C₁₃	semidirect
595. #117	C₂³×C₁₃	semidirect
596. #117	C₂³×C₁₃	semidirect
597. #117	C₂³×C₁₃	semidirect
609. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
632. C₂×C₄²	C₂³×C₁₃	semidirect
638. C₂×C₁₃	#3551	direct (N × H)
748. C₁₃	C₂×#3551	direct (N × H)
852. C₂	C₁₃×#3551	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×#3551	2
C₂×C₁₃×#563	2
C₂×C₁₃×#560	2
C₂×C₁₃×#555	2
C₂×C₁₃×#553	2
C₂×C₁₃×#552	2
C₂×C₁₃×#551	2
C₂×C₁₃×#548	2
C₂×C₁₃×#546	2
C₂×C₁₃×#540	2
C₂×C₁₃×#538	2
C₂×C₁₃×#537	2
C₂×C₁₃×#536	2
C₂×C₁₃×#535	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×#3551	13

Subgroups — C2×C13×#3551 #15749078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3551 #15749078