Subgroups — C₂×C₁₃×#3515 #15749118

Order 3328.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3515	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#554	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	4	yes	maximal, complemented
8	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#547	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#541	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#125	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×#41	C₂²	1	2	yes	—
21	C₁₃×#557	C₂²	1	16	yes	complemented
22	C₁₃×#554	C₂²	1	16	yes	complemented
23	C₁₃×#554	C₂²	1	16	yes	complemented
24	C₁₃×#553	C₂²	1	32	yes	complemented
25	C₁₃×#552	C₂²	1	32	yes	complemented
26	C₁₃×#552	C₂²	1	64	yes	complemented
27	C₁₃×#552	C₂²	1	32	yes	complemented
28	C₁₃×#547	C₂²	1	16	yes	complemented
29	C₁₃×#547	C₂²	1	32	yes	complemented
30	C₁₃×#541	C₂²	1	32	yes	complemented
31	C₁₃×#539	C₂²	1	64	yes	complemented
32	C₁₃×#533	C₂²	1	16	yes	complemented
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
36	C₁₃×#529	C₂²	1	32	yes	complemented
37	C₁₃×#529	C₂²	1	16	yes	complemented
38	C₂×C₁₃×#126	C₂²	1	4	yes	—
39	C₂×C₁₃×#126	C₂²	1	2	yes	—
40	C₂×C₁₃×#126	C₂²	1	4	yes	—
41	C₂×C₁₃×#126	C₂²	1	4	yes	—
42	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#125	C₂²	1	2	yes	—
44	C₂×C₁₃×#125	C₂²	1	4	yes	—
45	C₂×C₁₃×#125	C₂²	1	4	yes	—
46	C₂×C₁₃×#125	C₂²	1	2	yes	—
47	C₂×C₁₃×#125	C₂²	1	2	yes	—
48	C₂×C₁₃×#125	C₂²	1	4	yes	—
49	C₂×C₁₃×#125	C₂²	1	4	yes	—
50	C₂×C₁₃×#125	C₂²	1	2	yes	—
51	C₂×C₁₃×#125	C₂²	1	32	yes	complemented
52	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#123	C₂²	1	2	yes	—
54	C₂×C₁₃×#123	C₂²	1	4	yes	—
55	C₂×C₁₃×#123	C₂²	1	4	yes	—
56	C₂×C₁₃×#123	C₂²	1	4	yes	—
57	C₂×C₁₃×#123	C₂²	1	4	yes	—
58	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
60	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
61	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
62	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
63	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
64	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
65	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
66	C₂×C₁₃×#121	C₂²	1	2	yes	—
67	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#121	C₂²	1	4	yes	—
69	C₁₃×#520	C₂²	1	32	yes	complemented
70	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
71	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
72	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
73	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
74	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
75	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
76	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
77	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
78	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
79	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
80	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
81	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
82	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
83	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
84	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
85	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
86	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
87	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
88	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
89	C₂×C₁₃×#117	C₂²	1	2	yes	—
90	C₂×C₁₃×#117	C₂²	1	2	yes	—
91	C₂×C₁₃×#117	C₂²	1	4	yes	—
92	C₂×C₁₃×#117	C₂²	1	4	yes	—
93	C₂×C₁₃×#117	C₂²	1	2	yes	—
94	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
95	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
97	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
98	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
100	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
101	C₂×C₁₃×#41	—	2	8	no	—
102	C₂×C₁₃×#41	—	2	16	no	—
103	C₂×C₁₃×#41	C₂³	1	8	yes	—
104	C₂×C₁₃×#41	C₂³	1	16	yes	—
105	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
123	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
126	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
127	C₁₃×#126	C₂³	1	32	yes	—
128	C₁₃×#126	C₂³	1	16	yes	—
129	C₁₃×#126	C₂³	1	32	yes	—
130	C₁₃×#126	C₂³	1	32	yes	—
131	C₁₃×#125	C₂³	1	8	yes	—
132	C₁₃×#125	C₂³	1	16	yes	—
133	C₁₃×#125	C₂³	1	32	yes	—
134	C₁₃×#125	C₂³	1	32	yes	—
135	C₁₃×#125	C₂³	1	16	yes	—
136	C₁₃×#125	C₂³	1	16	yes	—
137	C₁₃×#125	C₂³	1	32	yes	—
138	C₁₃×#125	C₂³	1	32	yes	—
139	C₁₃×#125	C₂³	1	16	yes	—
140	C₁₃×#124	C₂³	1	8	yes	—
141	C₁₃×#123	C₂³	1	16	yes	—
142	C₁₃×#123	C₂³	1	32	yes	—
143	C₁₃×#123	C₂³	1	32	yes	—
144	C₁₃×#123	C₂³	1	32	yes	—
145	C₁₃×#123	C₂³	1	32	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
154	C₁₃×#121	C₂³	1	16	yes	—
155	C₁₃×#121	C₂³	1	8	yes	—
156	C₁₃×#121	C₂³	1	32	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
161	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
163	C₄×Q₈×C₁₃	C₂³	1	16	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	32	yes	—
169	C₄×D₄×C₁₃	C₂³	1	16	yes	—
170	C₄×D₄×C₁₃	C₂³	1	32	yes	—
171	C₄×D₄×C₁₃	C₂³	1	16	yes	—
172	C₄×D₄×C₁₃	C₂³	1	8	yes	—
173	C₄×D₄×C₁₃	C₂³	1	16	yes	—
174	C₁₃×#117	C₂³	1	8	yes	—
175	C₁₃×#117	C₂³	1	16	yes	—
176	C₁₃×#117	C₂³	1	16	yes	—
177	C₁₃×#117	C₂³	1	32	yes	—
178	C₁₃×#117	C₂³	1	32	yes	—
179	C₁₃×#117	C₂³	1	16	yes	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	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	4	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	2	yes	—
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
209	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	4	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	2	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	2	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
229	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
230	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
231	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
232	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
233	C₂×#3515	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
236	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
237	C₁₃×#41	—	2	32	no	—
238	C₁₃×#41	—	2	64	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	2	8	no	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	4	4	no	—
243	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
244	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
245	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
247	C₂×D₄×C₁₃	—	2	8	no	—
248	C₂×D₄×C₁₃	—	2	16	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	4	4	no	—
251	C₂×D₄×C₁₃	#41	1	8	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₁₃	—	2	8	no	—
258	C₂²×C₄×C₁₃	—	2	16	no	—
259	C₂²×C₄×C₁₃	—	2	4	no	—
260	C₂²×C₄×C₁₃	—	2	8	no	—
261	C₂²×C₄×C₁₃	—	2	8	no	—
262	C₂²×C₄×C₁₃	—	2	4	no	—
263	C₂²×C₄×C₁₃	—	4	4	no	—
264	C₂²×C₄×C₁₃	—	4	8	no	—
265	C₂²×C₄×C₁₃	—	4	2	no	—
266	C₂²×C₄×C₁₃	—	4	8	no	—
267	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
293	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
294	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
295	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
296	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
297	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
298	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	16	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×C₂²⋊C₄	C₂⁴	1	8	yes	—
316	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
317	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
319	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
320	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
321	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
323	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
324	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
325	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
326	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
327	C₄²×C₁₃	C₂⁴	1	4	yes	—
328	C₄²×C₁₃	C₂⁴	1	8	yes	—
329	C₄²×C₁₃	C₂⁴	1	4	yes	—
330	C₄²×C₁₃	C₂⁴	1	4	yes	—
331	C₄²×C₁₃	C₂⁴	1	8	yes	—
332	C₄²×C₁₃	C₂⁴	1	4	yes	—
333	C₄²×C₁₃	C₂⁴	1	8	yes	—
334	C₄²×C₁₃	C₂⁴	1	16	yes	—
335	C₄²×C₁₃	C₂⁴	1	16	yes	—
336	C₄²×C₁₃	C₂⁴	1	8	yes	—
337	#3515	C₂×C₁₃	1	32	yes	direct product factor
338	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
340	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#553	C₂×C₁₃	1	2	yes	complemented
342	C₂×#552	C₂×C₁₃	1	2	yes	complemented
343	C₂×#552	C₂×C₁₃	1	4	yes	complemented
344	C₂×#552	C₂×C₁₃	1	2	yes	complemented
345	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
346	C₂×#547	C₂×C₁₃	1	2	yes	complemented
347	C₂×#541	C₂×C₁₃	1	2	yes	complemented
348	C₂×#539	C₂×C₁₃	1	4	yes	complemented
349	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
351	C₂×#529	C₂×C₁₃	1	2	yes	complemented
352	C₂²×#125	C₂×C₁₃	1	2	yes	complemented
353	C₂×#520	C₂×C₁₃	1	2	yes	complemented
354	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₂³×C₁₃	—	2	4	no	—
356	C₂³×C₁₃	—	2	4	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	4	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	4	no	—
361	C₂³×C₁₃	—	2	4	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	C₂×#41	1	8	yes	—
364	C₂³×C₁₃	C₂⁵	1	2	yes	—
365	C₂³×C₁₃	C₂⁵	1	4	yes	—
366	C₂³×C₁₃	C₂⁵	1	4	yes	—
367	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
368	Q₈×C₁₃	—	2	8	no	—
369	Q₈×C₁₃	—	2	16	no	—
370	Q₈×C₁₃	—	2	8	no	—
371	Q₈×C₁₃	—	4	8	no	—
372	D₄×C₁₃	—	2	16	no	—
373	D₄×C₁₃	—	2	32	no	—
374	D₄×C₁₃	—	2	8	no	—
375	D₄×C₁₃	—	4	8	no	—
376	D₄×C₁₃	C₂×#41	1	16	yes	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	2	4	no	—
380	C₂×C₄×C₁₃	—	2	8	no	—
381	C₂×C₄×C₁₃	—	2	16	no	—
382	C₂×C₄×C₁₃	—	2	32	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	4	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	4	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	8	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	8	no	—
392	C₂×C₄×C₁₃	—	2	16	no	—
393	C₂×C₄×C₁₃	—	2	16	no	—
394	C₂×C₄×C₁₃	—	2	8	no	—
395	C₂×C₄×C₁₃	—	4	8	no	—
396	C₂×C₄×C₁₃	—	4	16	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	16	no	—
399	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
400	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
401	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
402	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
403	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
404	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
405	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
406	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
407	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
408	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
409	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
410	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
411	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
412	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
413	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
414	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
415	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×#41	C₂²×C₁₃	1	2	yes	—
417	#557	C₂²×C₁₃	1	16	yes	complemented
418	#554	C₂²×C₁₃	1	16	yes	complemented
419	#554	C₂²×C₁₃	1	16	yes	complemented
420	#553	C₂²×C₁₃	1	32	yes	complemented
421	#552	C₂²×C₁₃	1	32	yes	complemented
422	#552	C₂²×C₁₃	1	64	yes	complemented
423	#552	C₂²×C₁₃	1	32	yes	complemented
424	#547	C₂²×C₁₃	1	16	yes	complemented
425	#547	C₂²×C₁₃	1	32	yes	complemented
426	#541	C₂²×C₁₃	1	32	yes	complemented
427	#539	C₂²×C₁₃	1	64	yes	complemented
428	#533	C₂²×C₁₃	1	16	yes	complemented
429	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
432	#529	C₂²×C₁₃	1	32	yes	complemented
433	#529	C₂²×C₁₃	1	16	yes	complemented
434	C₂×#126	C₂²×C₁₃	1	4	yes	—
435	C₂×#126	C₂²×C₁₃	1	2	yes	—
436	C₂×#126	C₂²×C₁₃	1	4	yes	—
437	C₂×#126	C₂²×C₁₃	1	4	yes	—
438	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#125	C₂²×C₁₃	1	2	yes	—
440	C₂×#125	C₂²×C₁₃	1	4	yes	—
441	C₂×#125	C₂²×C₁₃	1	4	yes	—
442	C₂×#125	C₂²×C₁₃	1	2	yes	—
443	C₂×#125	C₂²×C₁₃	1	2	yes	—
444	C₂×#125	C₂²×C₁₃	1	4	yes	—
445	C₂×#125	C₂²×C₁₃	1	4	yes	—
446	C₂×#125	C₂²×C₁₃	1	2	yes	—
447	C₂×#125	C₂²×C₁₃	1	32	yes	complemented
448	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×#123	C₂²×C₁₃	1	2	yes	—
450	C₂×#123	C₂²×C₁₃	1	4	yes	—
451	C₂×#123	C₂²×C₁₃	1	4	yes	—
452	C₂×#123	C₂²×C₁₃	1	4	yes	—
453	C₂×#123	C₂²×C₁₃	1	4	yes	—
454	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
456	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
457	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
458	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
459	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
460	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
461	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
462	C₂×#121	C₂²×C₁₃	1	2	yes	—
463	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×#121	C₂²×C₁₃	1	4	yes	—
465	#520	C₂²×C₁₃	1	32	yes	complemented
466	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
467	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
470	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
471	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
472	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
474	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
476	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
477	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
478	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
479	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
480	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
481	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
482	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
484	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
485	C₂×#117	C₂²×C₁₃	1	2	yes	—
486	C₂×#117	C₂²×C₁₃	1	2	yes	—
487	C₂×#117	C₂²×C₁₃	1	4	yes	—
488	C₂×#117	C₂²×C₁₃	1	4	yes	—
489	C₂×#117	C₂²×C₁₃	1	2	yes	—
490	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
491	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
492	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
493	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
494	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
495	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
496	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
497	C₂²×C₁₃	—	2	4	no	—
498	C₂²×C₁₃	—	2	4	no	—
499	C₂²×C₁₃	—	2	16	no	—
500	C₂²×C₁₃	—	2	2	no	—
501	C₂²×C₁₃	—	2	4	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	4	no	—
504	C₂²×C₁₃	—	2	4	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	4	4	no	—
507	C₂²×C₁₃	—	4	8	no	—
508	C₂²×C₁₃	C₂²×#41	1	8	yes	—
509	C₂²×C₁₃	C₂²×#41	1	2	yes	—
510	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
511	C₂²×C₁₃	#585	1	2	yes	—
512	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	—	2	4	no	—
515	C₄×C₁₃	—	2	4	no	—
516	C₄×C₁₃	—	2	8	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	4	no	—
519	C₄×C₁₃	—	2	4	no	—
520	C₄×C₁₃	—	2	2	no	—
521	C₄×C₁₃	—	2	4	no	—
522	C₄×C₁₃	—	2	4	no	—
523	C₄×C₁₃	—	2	8	no	—
524	C₄×C₁₃	—	2	2	no	—
525	C₄×C₁₃	C₂²×#41	1	4	yes	—
526	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
527	C₂×#41	—	2	8	no	—
528	C₂×#41	—	2	16	no	—
529	C₂×#41	C₂³×C₁₃	1	8	yes	—
530	C₂×#41	C₂³×C₁₃	1	16	yes	—
531	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
534	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
535	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
537	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
538	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
539	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
541	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
542	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
543	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
544	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
547	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
548	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
549	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
551	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
552	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
553	#126	C₂³×C₁₃	1	32	yes	—
554	#126	C₂³×C₁₃	1	16	yes	—
555	#126	C₂³×C₁₃	1	32	yes	—
556	#126	C₂³×C₁₃	1	32	yes	—
557	#125	C₂³×C₁₃	1	8	yes	—
558	#125	C₂³×C₁₃	1	16	yes	—
559	#125	C₂³×C₁₃	1	32	yes	—
560	#125	C₂³×C₁₃	1	32	yes	—
561	#125	C₂³×C₁₃	1	16	yes	—
562	#125	C₂³×C₁₃	1	16	yes	—
563	#125	C₂³×C₁₃	1	32	yes	—
564	#125	C₂³×C₁₃	1	32	yes	—
565	#125	C₂³×C₁₃	1	16	yes	—
566	#124	C₂³×C₁₃	1	8	yes	—
567	#123	C₂³×C₁₃	1	16	yes	—
568	#123	C₂³×C₁₃	1	32	yes	—
569	#123	C₂³×C₁₃	1	32	yes	—
570	#123	C₂³×C₁₃	1	32	yes	—
571	#123	C₂³×C₁₃	1	32	yes	—
572	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
573	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
574	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
575	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
576	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
577	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
578	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
579	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
580	#121	C₂³×C₁₃	1	16	yes	—
581	#121	C₂³×C₁₃	1	8	yes	—
582	#121	C₂³×C₁₃	1	32	yes	—
583	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
584	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
585	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
586	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
587	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
588	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
589	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
590	C₄×D₄	C₂³×C₁₃	1	8	yes	—
591	C₄×D₄	C₂³×C₁₃	1	16	yes	—
592	C₄×D₄	C₂³×C₁₃	1	8	yes	—
593	C₄×D₄	C₂³×C₁₃	1	16	yes	—
594	C₄×D₄	C₂³×C₁₃	1	32	yes	—
595	C₄×D₄	C₂³×C₁₃	1	16	yes	—
596	C₄×D₄	C₂³×C₁₃	1	32	yes	—
597	C₄×D₄	C₂³×C₁₃	1	16	yes	—
598	C₄×D₄	C₂³×C₁₃	1	8	yes	—
599	C₄×D₄	C₂³×C₁₃	1	16	yes	—
600	#117	C₂³×C₁₃	1	8	yes	—
601	#117	C₂³×C₁₃	1	16	yes	—
602	#117	C₂³×C₁₃	1	16	yes	—
603	#117	C₂³×C₁₃	1	32	yes	—
604	#117	C₂³×C₁₃	1	32	yes	—
605	#117	C₂³×C₁₃	1	16	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
650	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
651	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
657	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
658	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₁₃	—	2	8	no	—
660	C₂×C₁₃	—	4	2	no	—
661	C₂×C₁₃	—	4	4	no	—
662	C₂×C₁₃	#3515	1	4	yes	direct product factor
663	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
664	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
665	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
666	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
668	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
669	#41	—	2	32	no	—
670	#41	—	2	64	no	—
671	C₂×Q₈	—	2	4	no	—
672	C₂×Q₈	—	2	8	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
676	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
677	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
678	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	16	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	4	4	no	—
683	C₂×D₄	C₁₃×#41	1	8	yes	—
684	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
685	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
686	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
687	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
688	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
689	C₂²×C₄	—	2	16	no	—
690	C₂²×C₄	—	2	8	no	—
691	C₂²×C₄	—	2	8	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	8	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	—	4	8	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	8	no	—
699	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
707	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
709	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
710	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
711	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
716	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
717	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
718	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
720	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
727	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
728	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
729	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
730	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
731	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
732	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
733	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
734	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
735	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
738	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
739	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
740	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
741	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
742	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
743	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
744	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
745	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
746	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
747	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
748	C₂²⋊C₄	C₂⁴×C₁₃	1	8	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	8	yes	—
754	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
755	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
756	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
757	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
758	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
759	C₄²	C₂⁴×C₁₃	1	4	yes	—
760	C₄²	C₂⁴×C₁₃	1	8	yes	—
761	C₄²	C₂⁴×C₁₃	1	4	yes	—
762	C₄²	C₂⁴×C₁₃	1	4	yes	—
763	C₄²	C₂⁴×C₁₃	1	8	yes	—
764	C₄²	C₂⁴×C₁₃	1	4	yes	—
765	C₄²	C₂⁴×C₁₃	1	8	yes	—
766	C₄²	C₂⁴×C₁₃	1	16	yes	—
767	C₄²	C₂⁴×C₁₃	1	16	yes	—
768	C₄²	C₂⁴×C₁₃	1	8	yes	—
769	C₁₃	C₂×#3515	1	1	yes	characteristic, direct product factor, Sylow
770	C₂³	—	2	4	no	—
771	C₂³	—	2	4	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	4	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	4	no	—
776	C₂³	—	2	4	no	—
777	C₂³	—	2	2	no	—
778	C₂³	C₂×C₁₃×#41	1	8	yes	—
779	C₂³	C₂⁵×C₁₃	1	2	yes	—
780	C₂³	C₂⁵×C₁₃	1	4	yes	—
781	C₂³	C₂⁵×C₁₃	1	4	yes	—
782	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
783	Q₈	—	2	8	no	—
784	Q₈	—	2	16	no	—
785	Q₈	—	2	8	no	—
786	Q₈	—	4	8	no	—
787	D₄	—	2	16	no	—
788	D₄	—	2	32	no	—
789	D₄	—	2	8	no	—
790	D₄	—	4	8	no	—
791	D₄	C₂×C₁₃×#41	1	16	yes	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	16	no	—
797	C₂×C₄	—	2	32	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	8	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	8	no	—
807	C₂×C₄	—	2	16	no	—
808	C₂×C₄	—	2	16	no	—
809	C₂×C₄	—	2	8	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	16	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	16	no	—
814	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
815	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
816	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
817	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
818	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
819	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
820	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
821	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
822	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
823	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
824	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
825	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
826	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
827	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
828	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
829	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	16	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	4	8	no	—
841	C₂²	C₂²×C₁₃×#41	1	8	yes	—
842	C₂²	C₂²×C₁₃×#41	1	2	yes	—
843	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
844	C₂²	C₁₃×#585	1	2	yes	—
845	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	4	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	8	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	4	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	2	2	no	—
858	C₄	C₂²×C₁₃×#41	1	4	yes	—
859	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
860	C₂	—	2	8	no	—
861	C₂	—	4	2	no	—
862	C₂	—	4	4	no	—
863	C₂	C₁₃×#3515	1	4	yes	direct product factor
864	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
865	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
866	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×#3515	C₂	direct (N × H)
2. C₂×C₁₃×#557	C₂	semidirect
3. C₂×C₁₃×#554	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×#552	C₂	semidirect
9. C₂×C₁₃×#547	C₂	semidirect
10. C₂×C₁₃×#547	C₂	semidirect
11. C₂×C₁₃×#541	C₂	semidirect
12. C₂×C₁₃×#539	C₂	semidirect
13. C₂×C₁₃×#533	C₂	semidirect
14. C₂×C₁₃×#529	C₂	semidirect
15. C₂×C₁₃×#529	C₂	semidirect
16. C₂²×C₁₃×#125	C₂	semidirect
17. C₂×C₁₃×#520	C₂	semidirect
18. C₂×C₄×C₁₃×#41	C₂	semidirect
21. C₁₃×#557	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
24. C₁₃×#553	C₂²	semidirect
25. C₁₃×#552	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
27. C₁₃×#552	C₂²	semidirect
28. C₁₃×#547	C₂²	semidirect
29. C₁₃×#547	C₂²	semidirect
30. C₁₃×#541	C₂²	semidirect
31. C₁₃×#539	C₂²	semidirect
32. C₁₃×#533	C₂²	semidirect
36. C₁₃×#529	C₂²	semidirect
37. C₁₃×#529	C₂²	semidirect
51. C₂×C₁₃×#125	C₂²	semidirect
69. C₁₃×#520	C₂²	semidirect
70. C₄×C₁₃×#41	C₂²	semidirect
233. C₂×#3515	C₁₃	direct (N × H)
337. #3515	C₂×C₁₃	direct (N × H)
338. C₂×#557	C₂×C₁₃	semidirect
339. C₂×#554	C₂×C₁₃	semidirect
340. C₂×#554	C₂×C₁₃	semidirect
341. C₂×#553	C₂×C₁₃	semidirect
342. C₂×#552	C₂×C₁₃	semidirect
343. C₂×#552	C₂×C₁₃	semidirect
344. C₂×#552	C₂×C₁₃	semidirect
345. C₂×#547	C₂×C₁₃	semidirect
346. C₂×#547	C₂×C₁₃	semidirect
347. C₂×#541	C₂×C₁₃	semidirect
348. C₂×#539	C₂×C₁₃	semidirect
349. C₂×#533	C₂×C₁₃	semidirect
350. C₂×#529	C₂×C₁₃	semidirect
351. C₂×#529	C₂×C₁₃	semidirect
352. C₂²×#125	C₂×C₁₃	semidirect
353. C₂×#520	C₂×C₁₃	semidirect
354. C₂×C₄×#41	C₂×C₁₃	semidirect
417. #557	C₂²×C₁₃	semidirect
418. #554	C₂²×C₁₃	semidirect
419. #554	C₂²×C₁₃	semidirect
420. #553	C₂²×C₁₃	semidirect
421. #552	C₂²×C₁₃	semidirect
422. #552	C₂²×C₁₃	semidirect
423. #552	C₂²×C₁₃	semidirect
424. #547	C₂²×C₁₃	semidirect
425. #547	C₂²×C₁₃	semidirect
426. #541	C₂²×C₁₃	semidirect
427. #539	C₂²×C₁₃	semidirect
428. #533	C₂²×C₁₃	semidirect
432. #529	C₂²×C₁₃	semidirect
433. #529	C₂²×C₁₃	semidirect
447. C₂×#125	C₂²×C₁₃	semidirect
465. #520	C₂²×C₁₃	semidirect
466. C₄×#41	C₂²×C₁₃	semidirect
662. C₂×C₁₃	#3515	direct (N × H)
769. C₁₃	C₂×#3515	direct (N × H)
863. C₂	C₁₃×#3515	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×#3515	2
C₂×C₁₃×#557	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#552	2
C₂×C₁₃×#547	2
C₂×C₁₃×#541	2
C₂×C₁₃×#539	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂²×C₁₃×#125	2
C₂×C₁₃×#520	2
C₂×C₄×C₁₃×#41	2
C₂×#3515	13

Subgroups — C2×C13×#3515 #15749118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3515 #15749118