Subgroups — C₂×C₁₃×#3559 #15749071

Order 3328.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3559	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#547	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#547	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#544	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#540	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#539	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#537	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	2	yes	—
18	C₂²×C₁₃×#41	C₂²	1	4	yes	—
19	C₁₃×#563	C₂²	1	32	yes	complemented
20	C₁₃×#562	C₂²	1	32	yes	complemented
21	C₁₃×#554	C₂²	1	32	yes	complemented
22	C₁₃×#553	C₂²	1	32	yes	complemented
23	C₁₃×#553	C₂²	1	32	yes	complemented
24	C₁₃×#547	C₂²	1	64	yes	complemented
25	C₁₃×#547	C₂²	1	32	yes	complemented
26	C₁₃×#544	C₂²	1	32	yes	complemented
27	C₁₃×#540	C₂²	1	32	yes	complemented
28	C₁₃×#539	C₂²	1	32	yes	complemented
29	C₁₃×#539	C₂²	1	64	yes	complemented
30	C₁₃×#537	C₂²	1	32	yes	complemented
31	C₁₃×#532	C₂²	1	16	yes	complemented
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
36	C₁₃×#529	C₂²	1	16	yes	complemented
37	C₂×C₁₃×#126	C₂²	1	4	yes	—
38	C₂×C₁₃×#126	C₂²	1	4	yes	—
39	C₂×C₁₃×#126	C₂²	1	2	yes	—
40	C₂×C₁₃×#125	C₂²	1	2	yes	—
41	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#125	C₂²	1	2	yes	—
43	C₂×C₁₃×#125	C₂²	1	2	yes	—
44	C₂×C₁₃×#125	C₂²	1	2	yes	—
45	C₂×C₁₃×#125	C₂²	1	4	yes	—
46	C₂×C₁₃×#125	C₂²	1	2	yes	—
47	C₂×C₁₃×#125	C₂²	1	16	yes	complemented
48	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#124	C₂²	1	2	yes	—
50	C₂×C₁₃×#123	C₂²	1	4	yes	—
51	C₂×C₁₃×#123	C₂²	1	4	yes	—
52	C₂×C₁₃×#123	C₂²	1	4	yes	—
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×C₂²⋊Q₈	C₂²	1	4	yes	—
58	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
63	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
64	C₂×C₁₃×#121	C₂²	1	4	yes	—
65	C₂×C₁₃×#121	C₂²	1	4	yes	—
66	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#121	C₂²	1	2	yes	—
68	C₂×C₁₃×#121	C₂²	1	2	yes	—
69	C₂×C₁₃×#121	C₂²	1	4	yes	—
70	C₂×C₁₃×#121	C₂²	1	4	yes	—
71	C₂×C₁₃×#121	C₂²	1	2	yes	—
72	C₂×C₁₃×#121	C₂²	1	2	yes	—
73	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
74	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
75	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
77	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
78	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
79	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
80	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
81	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
82	C₂×C₁₃×#117	C₂²	1	2	yes	—
83	C₂×C₁₃×#117	C₂²	1	2	yes	—
84	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
85	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
87	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
88	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
89	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
90	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
91	C₂×C₁₃×#41	—	4	8	no	—
92	C₂×C₁₃×#41	—	4	16	no	—
93	C₂×C₁₃×#41	C₂³	1	16	yes	—
94	C₂×C₁₃×#41	C₂³	1	32	yes	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
105	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
113	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
114	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	—
119	C₁₃×#127	C₂³	1	8	yes	—
120	C₁₃×#126	C₂³	1	16	yes	—
121	C₁₃×#126	C₂³	1	32	yes	—
122	C₁₃×#126	C₂³	1	32	yes	—
123	C₁₃×#125	C₂³	1	16	yes	—
124	C₁₃×#125	C₂³	1	16	yes	—
125	C₁₃×#125	C₂³	1	16	yes	—
126	C₁₃×#125	C₂³	1	16	yes	—
127	C₁₃×#125	C₂³	1	8	yes	—
128	C₁₃×#125	C₂³	1	32	yes	—
129	C₁₃×#125	C₂³	1	16	yes	—
130	C₁₃×#124	C₂³	1	8	yes	—
131	C₁₃×#124	C₂³	1	16	yes	—
132	C₁₃×#123	C₂³	1	16	yes	—
133	C₁₃×#123	C₂³	1	32	yes	—
134	C₁₃×#123	C₂³	1	32	yes	—
135	C₁₃×#123	C₂³	1	32	yes	—
136	C₁₃×#123	C₂³	1	32	yes	—
137	C₁₃×#123	C₂³	1	32	yes	—
138	C₁₃×#123	C₂³	1	32	yes	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
141	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
142	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
146	C₁₃×#121	C₂³	1	8	yes	—
147	C₁₃×#121	C₂³	1	16	yes	—
148	C₁₃×#121	C₂³	1	16	yes	—
149	C₁₃×#121	C₂³	1	32	yes	—
150	C₁₃×#121	C₂³	1	32	yes	—
151	C₁₃×#121	C₂³	1	32	yes	—
152	C₁₃×#121	C₂³	1	16	yes	—
153	C₁₃×#121	C₂³	1	32	yes	—
154	C₁₃×#121	C₂³	1	16	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
156	C₄×D₄×C₁₃	C₂³	1	16	yes	—
157	C₄×D₄×C₁₃	C₂³	1	8	yes	—
158	C₄×D₄×C₁₃	C₂³	1	16	yes	—
159	C₄×D₄×C₁₃	C₂³	1	16	yes	—
160	C₄×D₄×C₁₃	C₂³	1	32	yes	—
161	C₄×D₄×C₁₃	C₂³	1	32	yes	—
162	C₄×D₄×C₁₃	C₂³	1	16	yes	—
163	C₄×D₄×C₁₃	C₂³	1	16	yes	—
164	C₁₃×#117	C₂³	1	16	yes	—
165	C₁₃×#117	C₂³	1	16	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	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	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	1	yes	characteristic
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
201	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
202	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
209	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
211	C₂×#3559	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
213	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
214	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₁₃×#41	—	4	32	no	—
216	C₁₃×#41	—	4	64	no	—
217	C₂×Q₈×C₁₃	—	4	2	no	—
218	C₂×Q₈×C₁₃	—	4	8	no	—
219	C₂×Q₈×C₁₃	—	4	4	no	—
220	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
221	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
222	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
223	C₂×D₄×C₁₃	—	2	8	no	—
224	C₂×D₄×C₁₃	—	2	16	no	—
225	C₂×D₄×C₁₃	—	2	8	no	—
226	C₂×D₄×C₁₃	—	4	8	no	—
227	C₂×D₄×C₁₃	—	4	4	no	—
228	C₂×D₄×C₁₃	—	4	2	no	—
229	C₂×D₄×C₁₃	—	4	8	no	—
230	C₂×D₄×C₁₃	—	4	4	no	—
231	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
232	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
233	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
234	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
235	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
236	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
237	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	2	8	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	2	8	no	—
243	C₂²×C₄×C₁₃	—	4	4	no	—
244	C₂²×C₄×C₁₃	—	4	8	no	—
245	C₂²×C₄×C₁₃	—	4	2	no	—
246	C₂²×C₄×C₁₃	—	4	8	no	—
247	C₂²×C₄×C₁₃	—	4	8	no	—
248	C₂²×C₄×C₁₃	—	4	8	no	—
249	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
272	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
273	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
274	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
275	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
276	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
291	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
292	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
294	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
295	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
296	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
297	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
298	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
299	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
300	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
301	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
302	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
303	C₄²×C₁₃	C₂⁴	1	4	yes	—
304	C₄²×C₁₃	C₂⁴	1	4	yes	—
305	C₄²×C₁₃	C₂⁴	1	4	yes	—
306	C₄²×C₁₃	C₂⁴	1	4	yes	—
307	C₄²×C₁₃	C₂⁴	1	8	yes	—
308	C₄²×C₁₃	C₂⁴	1	16	yes	—
309	#3559	C₂×C₁₃	1	32	yes	direct product factor
310	C₂×#563	C₂×C₁₃	1	2	yes	complemented
311	C₂×#562	C₂×C₁₃	1	2	yes	complemented
312	C₂×#554	C₂×C₁₃	1	2	yes	complemented
313	C₂×#553	C₂×C₁₃	1	2	yes	complemented
314	C₂×#553	C₂×C₁₃	1	2	yes	complemented
315	C₂×#547	C₂×C₁₃	1	4	yes	complemented
316	C₂×#547	C₂×C₁₃	1	2	yes	complemented
317	C₂×#544	C₂×C₁₃	1	2	yes	complemented
318	C₂×#540	C₂×C₁₃	1	2	yes	complemented
319	C₂×#539	C₂×C₁₃	1	2	yes	complemented
320	C₂×#539	C₂×C₁₃	1	4	yes	complemented
321	C₂×#537	C₂×C₁₃	1	2	yes	complemented
322	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
323	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
324	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	4	no	—
328	C₂³×C₁₃	—	2	8	no	—
329	C₂³×C₁₃	—	2	4	no	—
330	C₂³×C₁₃	—	2	8	no	—
331	C₂³×C₁₃	—	2	8	no	—
332	C₂³×C₁₃	—	2	4	no	—
333	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
334	C₂³×C₁₃	C₂⁵	1	4	yes	—
335	C₂³×C₁₃	C₂⁵	1	8	yes	—
336	C₂³×C₁₃	C₂⁵	1	2	yes	—
337	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
338	Q₈×C₁₃	—	4	4	no	—
339	Q₈×C₁₃	—	4	16	no	—
340	Q₈×C₁₃	—	4	8	no	—
341	D₄×C₁₃	—	2	16	no	—
342	D₄×C₁₃	—	2	32	no	—
343	D₄×C₁₃	—	2	16	no	—
344	D₄×C₁₃	—	4	16	no	—
345	D₄×C₁₃	—	4	8	no	—
346	D₄×C₁₃	—	4	4	no	—
347	D₄×C₁₃	—	4	16	no	—
348	D₄×C₁₃	—	4	8	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	8	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	8	no	—
353	C₂×C₄×C₁₃	—	2	16	no	—
354	C₂×C₄×C₁₃	—	2	8	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	4	no	—
358	C₂×C₄×C₁₃	—	2	8	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	8	no	—
363	C₂×C₄×C₁₃	—	2	16	no	—
364	C₂×C₄×C₁₃	—	4	8	no	—
365	C₂×C₄×C₁₃	—	4	16	no	—
366	C₂×C₄×C₁₃	—	4	4	no	—
367	C₂×C₄×C₁₃	—	4	16	no	—
368	C₂×C₄×C₁₃	—	4	16	no	—
369	C₂×C₄×C₁₃	—	4	16	no	—
370	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
371	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
372	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
373	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
374	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
375	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
376	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
377	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
378	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
379	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
380	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
381	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
382	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
383	C₂²×#41	C₂²×C₁₃	1	2	yes	—
384	C₂²×#41	C₂²×C₁₃	1	4	yes	—
385	#563	C₂²×C₁₃	1	32	yes	complemented
386	#562	C₂²×C₁₃	1	32	yes	complemented
387	#554	C₂²×C₁₃	1	32	yes	complemented
388	#553	C₂²×C₁₃	1	32	yes	complemented
389	#553	C₂²×C₁₃	1	32	yes	complemented
390	#547	C₂²×C₁₃	1	64	yes	complemented
391	#547	C₂²×C₁₃	1	32	yes	complemented
392	#544	C₂²×C₁₃	1	32	yes	complemented
393	#540	C₂²×C₁₃	1	32	yes	complemented
394	#539	C₂²×C₁₃	1	32	yes	complemented
395	#539	C₂²×C₁₃	1	64	yes	complemented
396	#537	C₂²×C₁₃	1	32	yes	complemented
397	#532	C₂²×C₁₃	1	16	yes	complemented
398	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
400	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
401	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
402	#529	C₂²×C₁₃	1	16	yes	complemented
403	C₂×#126	C₂²×C₁₃	1	2	yes	—
404	C₂×#126	C₂²×C₁₃	1	4	yes	—
405	C₂×#126	C₂²×C₁₃	1	4	yes	—
406	C₂×#125	C₂²×C₁₃	1	2	yes	—
407	C₂×#125	C₂²×C₁₃	1	2	yes	—
408	C₂×#125	C₂²×C₁₃	1	2	yes	—
409	C₂×#125	C₂²×C₁₃	1	2	yes	—
410	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#125	C₂²×C₁₃	1	4	yes	—
412	C₂×#125	C₂²×C₁₃	1	2	yes	—
413	C₂×#125	C₂²×C₁₃	1	16	yes	complemented
414	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#124	C₂²×C₁₃	1	2	yes	—
416	C₂×#123	C₂²×C₁₃	1	2	yes	—
417	C₂×#123	C₂²×C₁₃	1	4	yes	—
418	C₂×#123	C₂²×C₁₃	1	4	yes	—
419	C₂×#123	C₂²×C₁₃	1	4	yes	—
420	C₂×#123	C₂²×C₁₃	1	4	yes	—
421	C₂×#123	C₂²×C₁₃	1	4	yes	—
422	C₂×#123	C₂²×C₁₃	1	4	yes	—
423	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
425	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
426	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
427	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
428	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
429	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
430	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#121	C₂²×C₁₃	1	2	yes	—
432	C₂×#121	C₂²×C₁₃	1	2	yes	—
433	C₂×#121	C₂²×C₁₃	1	4	yes	—
434	C₂×#121	C₂²×C₁₃	1	4	yes	—
435	C₂×#121	C₂²×C₁₃	1	4	yes	—
436	C₂×#121	C₂²×C₁₃	1	2	yes	—
437	C₂×#121	C₂²×C₁₃	1	4	yes	—
438	C₂×#121	C₂²×C₁₃	1	2	yes	—
439	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
443	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
444	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
445	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
446	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
448	C₂×#117	C₂²×C₁₃	1	2	yes	—
449	C₂×#117	C₂²×C₁₃	1	2	yes	—
450	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
451	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
452	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
453	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
454	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
455	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
456	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	2	8	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	8	no	—
462	C₂²×C₁₃	—	2	4	no	—
463	C₂²×C₁₃	—	2	8	no	—
464	C₂²×C₁₃	—	2	8	no	—
465	C₂²×C₁₃	—	2	4	no	—
466	C₂²×C₁₃	—	4	8	no	—
467	C₂²×C₁₃	—	4	16	no	—
468	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
469	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
470	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
471	C₂²×C₁₃	#585	1	2	yes	—
472	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
473	C₄×C₁₃	—	2	2	no	—
474	C₄×C₁₃	—	2	8	no	—
475	C₄×C₁₃	—	2	2	no	—
476	C₄×C₁₃	—	2	8	no	—
477	C₄×C₁₃	—	2	4	no	—
478	C₄×C₁₃	—	2	2	no	—
479	C₄×C₁₃	—	2	4	no	—
480	C₄×C₁₃	—	2	8	no	—
481	C₄×C₁₃	—	2	4	no	—
482	C₄×C₁₃	—	2	2	no	—
483	C₄×C₁₃	—	2	2	no	—
484	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
485	C₂×#41	—	4	8	no	—
486	C₂×#41	—	4	16	no	—
487	C₂×#41	C₂³×C₁₃	1	16	yes	—
488	C₂×#41	C₂³×C₁₃	1	32	yes	—
489	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
491	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
492	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
493	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
494	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
495	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
496	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
498	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
499	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
501	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
504	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
507	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
508	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
509	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
510	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
511	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
512	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	—
513	#127	C₂³×C₁₃	1	8	yes	—
514	#126	C₂³×C₁₃	1	16	yes	—
515	#126	C₂³×C₁₃	1	32	yes	—
516	#126	C₂³×C₁₃	1	32	yes	—
517	#125	C₂³×C₁₃	1	16	yes	—
518	#125	C₂³×C₁₃	1	16	yes	—
519	#125	C₂³×C₁₃	1	16	yes	—
520	#125	C₂³×C₁₃	1	16	yes	—
521	#125	C₂³×C₁₃	1	8	yes	—
522	#125	C₂³×C₁₃	1	32	yes	—
523	#125	C₂³×C₁₃	1	16	yes	—
524	#124	C₂³×C₁₃	1	8	yes	—
525	#124	C₂³×C₁₃	1	16	yes	—
526	#123	C₂³×C₁₃	1	16	yes	—
527	#123	C₂³×C₁₃	1	32	yes	—
528	#123	C₂³×C₁₃	1	32	yes	—
529	#123	C₂³×C₁₃	1	32	yes	—
530	#123	C₂³×C₁₃	1	32	yes	—
531	#123	C₂³×C₁₃	1	32	yes	—
532	#123	C₂³×C₁₃	1	32	yes	—
533	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
534	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
535	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
536	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
537	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
538	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
539	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
540	#121	C₂³×C₁₃	1	8	yes	—
541	#121	C₂³×C₁₃	1	16	yes	—
542	#121	C₂³×C₁₃	1	16	yes	—
543	#121	C₂³×C₁₃	1	32	yes	—
544	#121	C₂³×C₁₃	1	32	yes	—
545	#121	C₂³×C₁₃	1	32	yes	—
546	#121	C₂³×C₁₃	1	16	yes	—
547	#121	C₂³×C₁₃	1	32	yes	—
548	#121	C₂³×C₁₃	1	16	yes	—
549	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
550	C₄×D₄	C₂³×C₁₃	1	16	yes	—
551	C₄×D₄	C₂³×C₁₃	1	8	yes	—
552	C₄×D₄	C₂³×C₁₃	1	16	yes	—
553	C₄×D₄	C₂³×C₁₃	1	16	yes	—
554	C₄×D₄	C₂³×C₁₃	1	32	yes	—
555	C₄×D₄	C₂³×C₁₃	1	32	yes	—
556	C₄×D₄	C₂³×C₁₃	1	16	yes	—
557	C₄×D₄	C₂³×C₁₃	1	16	yes	—
558	#117	C₂³×C₁₃	1	16	yes	—
559	#117	C₂³×C₁₃	1	16	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
601	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
605	C₂×C₁₃	—	2	4	no	—
606	C₂×C₁₃	—	4	4	no	—
607	C₂×C₁₃	—	4	8	no	—
608	C₂×C₁₃	#3559	1	4	yes	direct product factor
609	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
611	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
612	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
613	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
614	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
615	#41	—	4	32	no	—
616	#41	—	4	64	no	—
617	C₂×Q₈	—	4	8	no	—
618	C₂×Q₈	—	4	4	no	—
619	C₂×Q₈	—	4	2	no	—
620	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
621	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
622	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
623	C₂×D₄	—	2	8	no	—
624	C₂×D₄	—	2	16	no	—
625	C₂×D₄	—	2	8	no	—
626	C₂×D₄	—	4	8	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	8	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
632	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
633	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
634	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
635	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
636	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
637	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
638	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	8	no	—
643	C₂²×C₄	—	4	8	no	—
644	C₂²×C₄	—	4	8	no	—
645	C₂²×C₄	—	4	8	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	—	4	8	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
657	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
659	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
667	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
668	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
672	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
673	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
674	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
675	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
676	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
677	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
678	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
679	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
681	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
682	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
683	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
684	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
685	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
686	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
687	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
688	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
689	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
691	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
692	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
693	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
694	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
695	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
696	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
697	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
698	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
699	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
700	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
701	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
702	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
703	C₄²	C₂⁴×C₁₃	1	4	yes	—
704	C₄²	C₂⁴×C₁₃	1	4	yes	—
705	C₄²	C₂⁴×C₁₃	1	4	yes	—
706	C₄²	C₂⁴×C₁₃	1	4	yes	—
707	C₄²	C₂⁴×C₁₃	1	8	yes	—
708	C₄²	C₂⁴×C₁₃	1	16	yes	—
709	C₁₃	C₂×#3559	1	1	yes	characteristic, direct product factor, Sylow
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	8	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	4	no	—
718	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
719	C₂³	C₂⁵×C₁₃	1	4	yes	—
720	C₂³	C₂⁵×C₁₃	1	8	yes	—
721	C₂³	C₂⁵×C₁₃	1	2	yes	—
722	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
723	Q₈	—	4	16	no	—
724	Q₈	—	4	8	no	—
725	Q₈	—	4	4	no	—
726	D₄	—	2	16	no	—
727	D₄	—	2	32	no	—
728	D₄	—	2	16	no	—
729	D₄	—	4	16	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	16	no	—
733	D₄	—	4	8	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	8	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	8	no	—
738	C₂×C₄	—	2	16	no	—
739	C₂×C₄	—	2	8	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	8	no	—
748	C₂×C₄	—	2	16	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	16	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	16	no	—
753	C₂×C₄	—	4	16	no	—
754	C₂×C₄	—	4	16	no	—
755	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
756	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
757	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
758	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
759	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
760	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
761	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
762	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
763	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
764	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
765	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
766	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
767	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
768	C₂²	—	2	8	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	8	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	8	no	—
775	C₂²	—	2	8	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	4	8	no	—
778	C₂²	—	4	16	no	—
779	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
780	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
781	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
782	C₂²	C₁₃×#585	1	2	yes	—
783	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
784	C₄	—	2	2	no	—
785	C₄	—	2	8	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	8	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	8	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
796	C₂	—	2	4	no	—
797	C₂	—	4	4	no	—
798	C₂	—	4	8	no	—
799	C₂	C₁₃×#3559	1	4	yes	direct product factor
800	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
802	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×#3559	C₂	direct (N × H)
2. C₂×C₁₃×#563	C₂	semidirect
3. C₂×C₁₃×#562	C₂	semidirect
4. C₂×C₁₃×#554	C₂	semidirect
5. C₂×C₁₃×#553	C₂	semidirect
6. C₂×C₁₃×#553	C₂	semidirect
7. C₂×C₁₃×#547	C₂	semidirect
8. C₂×C₁₃×#547	C₂	semidirect
9. C₂×C₁₃×#544	C₂	semidirect
10. C₂×C₁₃×#540	C₂	semidirect
11. C₂×C₁₃×#539	C₂	semidirect
12. C₂×C₁₃×#539	C₂	semidirect
13. C₂×C₁₃×#537	C₂	semidirect
14. C₂×C₁₃×#532	C₂	semidirect
15. C₂×C₁₃×#529	C₂	semidirect
16. C₂²×C₁₃×#125	C₂	semidirect
19. C₁₃×#563	C₂²	semidirect
20. C₁₃×#562	C₂²	semidirect
21. C₁₃×#554	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#553	C₂²	semidirect
24. C₁₃×#547	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
26. C₁₃×#544	C₂²	semidirect
27. C₁₃×#540	C₂²	semidirect
28. C₁₃×#539	C₂²	semidirect
29. C₁₃×#539	C₂²	semidirect
30. C₁₃×#537	C₂²	semidirect
31. C₁₃×#532	C₂²	semidirect
36. C₁₃×#529	C₂²	semidirect
47. C₂×C₁₃×#125	C₂²	semidirect
211. C₂×#3559	C₁₃	direct (N × H)
309. #3559	C₂×C₁₃	direct (N × H)
310. C₂×#563	C₂×C₁₃	semidirect
311. C₂×#562	C₂×C₁₃	semidirect
312. C₂×#554	C₂×C₁₃	semidirect
313. C₂×#553	C₂×C₁₃	semidirect
314. C₂×#553	C₂×C₁₃	semidirect
315. C₂×#547	C₂×C₁₃	semidirect
316. C₂×#547	C₂×C₁₃	semidirect
317. C₂×#544	C₂×C₁₃	semidirect
318. C₂×#540	C₂×C₁₃	semidirect
319. C₂×#539	C₂×C₁₃	semidirect
320. C₂×#539	C₂×C₁₃	semidirect
321. C₂×#537	C₂×C₁₃	semidirect
322. C₂×#532	C₂×C₁₃	semidirect
323. C₂×#529	C₂×C₁₃	semidirect
324. C₂²×#125	C₂×C₁₃	semidirect
385. #563	C₂²×C₁₃	semidirect
386. #562	C₂²×C₁₃	semidirect
387. #554	C₂²×C₁₃	semidirect
388. #553	C₂²×C₁₃	semidirect
389. #553	C₂²×C₁₃	semidirect
390. #547	C₂²×C₁₃	semidirect
391. #547	C₂²×C₁₃	semidirect
392. #544	C₂²×C₁₃	semidirect
393. #540	C₂²×C₁₃	semidirect
394. #539	C₂²×C₁₃	semidirect
395. #539	C₂²×C₁₃	semidirect
396. #537	C₂²×C₁₃	semidirect
397. #532	C₂²×C₁₃	semidirect
402. #529	C₂²×C₁₃	semidirect
413. C₂×#125	C₂²×C₁₃	semidirect
608. C₂×C₁₃	#3559	direct (N × H)
709. C₁₃	C₂×#3559	direct (N × H)
799. C₂	C₁₃×#3559	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×#3559	2
C₂×C₁₃×#563	2
C₂×C₁₃×#562	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#547	2
C₂×C₁₃×#544	2
C₂×C₁₃×#540	2
C₂×C₁₃×#539	2
C₂×C₁₃×#537	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂²×C₁₃×#125	2
C₂×#3559	13

Subgroups — C2×C13×#3559 #15749071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3559 #15749071