Subgroups — C₁₃×#34433 #15720772

Order 3328.

2234 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2378	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2362	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2362	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2342	C₂	1	2	yes	maximal
9	C₁₃×#2342	C₂	1	2	yes	maximal
10	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic
17	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic
20	C₁₃×#543	C₄	1	16	yes	complemented
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#391	C₂²	1	2	yes	complemented
42	C₁₃×#391	C₂²	1	2	yes	complemented
43	C₁₃×#391	C₂²	1	2	yes	complemented
44	C₁₃×#391	C₂²	1	2	yes	complemented
45	C₁₃×#391	C₂²	1	2	yes	complemented
46	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#389	C₂²	1	2	yes	complemented
49	C₁₃×#389	C₂²	1	2	yes	complemented
50	C₁₃×#389	C₂²	1	2	yes	complemented
51	C₁₃×#389	C₂²	1	2	yes	complemented
52	C₁₃×#389	C₂²	1	2	yes	complemented
53	C₁₃×#388	C₂²	1	2	yes	—
54	C₁₃×#388	C₂²	1	2	yes	—
55	C₁₃×#388	C₂²	1	2	yes	—
56	C₁₃×#388	C₂²	1	2	yes	—
57	C₁₃×#388	C₂²	1	2	yes	—
58	C₁₃×#388	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	2	yes	—
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#387	C₂²	1	2	yes	complemented
70	C₁₃×#387	C₂²	1	2	yes	complemented
71	C₁₃×#387	C₂²	1	2	yes	complemented
72	C₁₃×#387	C₂²	1	2	yes	complemented
73	C₁₃×#387	C₂²	1	2	yes	complemented
74	C₁₃×#387	C₂²	1	2	yes	complemented
75	C₁₃×#387	C₂²	1	2	yes	complemented
76	C₁₃×#387	C₂²	1	2	yes	complemented
77	C₁₃×#387	C₂²	1	2	yes	complemented
78	C₁₃×#387	C₂²	1	2	yes	complemented
79	C₁₃×#387	C₂²	1	2	yes	complemented
80	C₁₃×#387	C₂²	1	2	yes	complemented
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#381	C₂²	1	2	yes	—
86	C₁₃×#381	C₂²	1	2	yes	—
87	C₁₃×#380	C₂²	1	1	yes	characteristic
88	C₁₃×#380	C₂²	1	1	yes	characteristic
89	C₁₃×#380	C₂²	1	2	yes	—
90	C₁₃×#380	C₂²	1	2	yes	—
91	C₁₃×#379	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
107	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
108	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
121	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
122	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
123	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
124	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
125	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
126	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
127	C₄×Q₈×C₁₃	—	4	2	no	—
128	C₄×Q₈×C₁₃	—	4	2	no	—
129	C₄×Q₈×C₁₃	—	4	4	no	—
130	C₁₃×#117	—	4	4	no	—
131	C₁₃×#117	—	4	4	no	—
132	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	—	4	2	no	—
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	#34433	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	—	2	2	no	—
215	C₂⁴×C₁₃	—	2	2	no	—
216	C₂⁴×C₁₃	—	4	1	no	—
217	C₂⁴×C₁₃	—	4	1	no	—
218	C₂⁴×C₁₃	—	4	1	no	—
219	C₂⁴×C₁₃	—	4	1	no	—
220	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
221	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
222	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂×Q₈×C₁₃	—	4	1	no	—
224	C₂×Q₈×C₁₃	—	4	1	no	—
225	C₂×Q₈×C₁₃	—	4	2	no	—
226	C₂×Q₈×C₁₃	—	4	2	no	—
227	C₂×Q₈×C₁₃	—	4	1	no	—
228	C₂×Q₈×C₁₃	—	4	1	no	—
229	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
230	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
231	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	2	no	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	2	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	4	1	no	—
239	C₂²×C₄×C₁₃	—	4	1	no	—
240	C₂²×C₄×C₁₃	—	4	1	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	4	1	no	—
244	C₂²×C₄×C₁₃	—	4	1	no	—
245	C₂²×C₄×C₁₃	—	4	2	no	—
246	C₂²×C₄×C₁₃	—	4	2	no	—
247	C₂²×C₄×C₁₃	—	4	1	no	—
248	C₂²×C₄×C₁₃	—	4	1	no	—
249	C₂²×C₄×C₁₃	—	4	1	no	—
250	C₂²×C₄×C₁₃	—	4	1	no	—
251	C₂²×C₄×C₁₃	—	4	1	no	—
252	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
253	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
254	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
255	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	4	1	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	1	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	—	4	2	no	—
283	C₁₃×C₄⋊C₄	—	4	2	no	—
284	C₁₃×C₄⋊C₄	—	4	1	no	—
285	C₁₃×C₄⋊C₄	—	4	1	no	—
286	C₁₃×C₄⋊C₄	—	4	2	no	—
287	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
288	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
289	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
290	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
291	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
292	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
293	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₁₃×C₂²⋊C₄	—	4	2	no	—
301	C₁₃×C₂²⋊C₄	—	4	2	no	—
302	C₁₃×C₂²⋊C₄	—	4	2	no	—
303	C₁₃×C₂²⋊C₄	—	4	2	no	—
304	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
305	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
306	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
307	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
308	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
309	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
310	C₄²×C₁₃	—	2	2	no	—
311	C₄²×C₁₃	—	2	2	no	—
312	C₄²×C₁₃	—	2	4	no	—
313	C₄²×C₁₃	—	2	4	no	—
314	C₄²×C₁₃	—	4	1	no	—
315	C₄²×C₁₃	—	4	1	no	—
316	C₄²×C₁₃	—	4	2	no	—
317	C₄²×C₁₃	—	4	2	no	—
318	C₄²×C₁₃	—	4	2	no	—
319	C₄²×C₁₃	—	4	2	no	—
320	C₄²×C₁₃	—	4	2	no	—
321	C₄²×C₁₃	—	4	2	no	—
322	C₄²×C₁₃	—	4	2	no	—
323	C₄²×C₁₃	—	4	2	no	—
324	C₂×#543	C₂×C₁₃	1	1	yes	characteristic
325	#2378	C₂×C₁₃	1	2	yes	complemented
326	#2378	C₂×C₁₃	1	2	yes	complemented
327	#2368	C₂×C₁₃	1	2	yes	complemented
328	#2362	C₂×C₁₃	1	2	yes	complemented
329	#2362	C₂×C₁₃	1	2	yes	complemented
330	#2360	C₂×C₁₃	1	2	yes	complemented
331	#2342	C₂×C₁₃	1	2	yes	—
332	#2342	C₂×C₁₃	1	2	yes	—
333	#2332	C₂×C₁₃	1	2	yes	complemented
334	#2332	C₂×C₁₃	1	2	yes	complemented
335	#2329	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#2329	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#2323	C₂×C₁₃	1	2	yes	complemented
338	#2323	C₂×C₁₃	1	2	yes	complemented
339	#2312	C₂×C₁₃	1	1	yes	characteristic
340	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
342	C₂×#388	C₂×C₁₃	1	1	yes	characteristic
343	C₂³×C₁₃	—	2	1	no	—
344	C₂³×C₁₃	—	2	1	no	—
345	C₂³×C₁₃	—	2	1	no	—
346	C₂³×C₁₃	—	2	1	no	—
347	C₂³×C₁₃	—	2	2	no	—
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	2	8	no	—
354	C₂³×C₁₃	—	4	4	no	—
355	C₂³×C₁₃	—	4	4	no	—
356	C₂³×C₁₃	—	8	2	no	—
357	C₂³×C₁₃	—	8	2	no	—
358	C₂³×C₁₃	—	8	2	no	—
359	C₂³×C₁₃	—	8	2	no	—
360	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
361	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
362	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
363	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
364	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
365	Q₈×C₁₃	—	4	4	no	—
366	Q₈×C₁₃	—	4	4	no	—
367	Q₈×C₁₃	—	4	8	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	4	4	no	—
411	C₂×C₄×C₁₃	—	4	4	no	—
412	C₂×C₄×C₁₃	—	4	8	no	—
413	C₂×C₄×C₁₃	—	4	8	no	—
414	C₂×C₄×C₁₃	—	4	4	no	—
415	C₂×C₄×C₁₃	—	4	4	no	—
416	C₂×C₄×C₁₃	—	8	2	no	—
417	C₂×C₄×C₁₃	—	8	2	no	—
418	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
419	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
420	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
421	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
422	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
424	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
425	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
426	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
427	#543	C₄×C₁₃	1	16	yes	complemented
428	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
431	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
432	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
433	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
434	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
435	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
437	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	C₂×#117	C₂²×C₁₃	1	2	yes	—
439	C₂×#117	C₂²×C₁₃	1	2	yes	—
440	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
441	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
442	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
443	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
444	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
445	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
446	#391	C₂²×C₁₃	1	2	yes	complemented
447	#391	C₂²×C₁₃	1	2	yes	complemented
448	#391	C₂²×C₁₃	1	2	yes	complemented
449	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#391	C₂²×C₁₃	1	2	yes	complemented
451	#391	C₂²×C₁₃	1	2	yes	complemented
452	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	#389	C₂²×C₁₃	1	2	yes	complemented
454	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#389	C₂²×C₁₃	1	2	yes	complemented
456	#389	C₂²×C₁₃	1	2	yes	complemented
457	#389	C₂²×C₁₃	1	2	yes	complemented
458	#389	C₂²×C₁₃	1	2	yes	complemented
459	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#388	C₂²×C₁₃	1	2	yes	—
461	#388	C₂²×C₁₃	1	2	yes	—
462	#388	C₂²×C₁₃	1	2	yes	—
463	#388	C₂²×C₁₃	1	2	yes	—
464	#388	C₂²×C₁₃	1	2	yes	—
465	#388	C₂²×C₁₃	1	2	yes	—
466	#388	C₂²×C₁₃	1	2	yes	—
467	#388	C₂²×C₁₃	1	2	yes	—
468	#388	C₂²×C₁₃	1	2	yes	—
469	#388	C₂²×C₁₃	1	2	yes	—
470	#388	C₂²×C₁₃	1	2	yes	—
471	#388	C₂²×C₁₃	1	2	yes	—
472	#388	C₂²×C₁₃	1	2	yes	—
473	#388	C₂²×C₁₃	1	2	yes	—
474	#388	C₂²×C₁₃	1	2	yes	—
475	#388	C₂²×C₁₃	1	2	yes	—
476	#387	C₂²×C₁₃	1	2	yes	complemented
477	#387	C₂²×C₁₃	1	2	yes	complemented
478	#387	C₂²×C₁₃	1	2	yes	complemented
479	#387	C₂²×C₁₃	1	2	yes	complemented
480	#387	C₂²×C₁₃	1	2	yes	complemented
481	#387	C₂²×C₁₃	1	2	yes	complemented
482	#387	C₂²×C₁₃	1	2	yes	complemented
483	#387	C₂²×C₁₃	1	2	yes	complemented
484	#387	C₂²×C₁₃	1	2	yes	complemented
485	#387	C₂²×C₁₃	1	2	yes	complemented
486	#387	C₂²×C₁₃	1	2	yes	complemented
487	#387	C₂²×C₁₃	1	2	yes	complemented
488	#385	C₂²×C₁₃	1	2	yes	—
489	#385	C₂²×C₁₃	1	2	yes	—
490	#385	C₂²×C₁₃	1	2	yes	—
491	#385	C₂²×C₁₃	1	2	yes	—
492	#381	C₂²×C₁₃	1	2	yes	—
493	#381	C₂²×C₁₃	1	2	yes	—
494	#380	C₂²×C₁₃	1	1	yes	characteristic
495	#380	C₂²×C₁₃	1	1	yes	characteristic
496	#380	C₂²×C₁₃	1	2	yes	—
497	#380	C₂²×C₁₃	1	2	yes	—
498	#379	C₂²×C₁₃	1	2	yes	—
499	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
500	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
501	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
503	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
504	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
505	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
506	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
509	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
510	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
511	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
512	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
513	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
514	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
515	C₂²×C₁₃	—	2	2	no	—
516	C₂²×C₁₃	—	2	2	no	—
517	C₂²×C₁₃	—	2	2	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	4	no	—
522	C₂²×C₁₃	—	2	4	no	—
523	C₂²×C₁₃	—	2	4	no	—
524	C₂²×C₁₃	—	4	2	no	—
525	C₂²×C₁₃	—	4	2	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	8	8	no	—
529	C₂²×C₁₃	#519	1	4	yes	—
530	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
531	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	C₂²×C₁₃	#585	1	1	yes	characteristic
536	C₂²×C₁₃	#585	1	1	yes	characteristic
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	—	2	2	no	—
539	C₄×C₁₃	—	2	4	no	—
540	C₄×C₁₃	—	2	4	no	—
541	C₄×C₁₃	—	2	4	no	—
542	C₄×C₁₃	—	2	4	no	—
543	C₄×C₁₃	—	2	4	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	—	2	2	no	—
546	C₄×C₁₃	—	4	2	no	—
547	C₄×C₁₃	—	4	1	no	—
548	C₄×C₁₃	—	4	2	no	—
549	C₄×C₁₃	—	4	1	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	2	no	—
552	C₄×C₁₃	—	4	2	no	—
553	C₄×C₁₃	—	4	2	no	—
554	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
557	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
564	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
565	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
567	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
568	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
569	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
570	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
571	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
572	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
573	C₄×Q₈	—	4	2	no	—
574	C₄×Q₈	—	4	2	no	—
575	C₄×Q₈	—	4	4	no	—
576	#117	—	4	4	no	—
577	#117	—	4	4	no	—
578	C₂×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₂²⋊C₄	—	4	2	no	—
601	C₂×C₂²⋊C₄	—	4	2	no	—
602	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
603	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	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	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₄²	—	4	2	no	—
621	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
626	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
628	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
635	#95	C₂³×C₁₃	1	2	yes	—
636	#95	C₂³×C₁₃	1	2	yes	—
637	#95	C₂³×C₁₃	1	2	yes	—
638	#95	C₂³×C₁₃	1	2	yes	—
639	#95	C₂³×C₁₃	1	2	yes	—
640	#95	C₂³×C₁₃	1	2	yes	—
641	#95	C₂³×C₁₃	1	2	yes	—
642	#95	C₂³×C₁₃	1	2	yes	—
643	#95	C₂³×C₁₃	1	2	yes	—
644	#95	C₂³×C₁₃	1	2	yes	—
645	#95	C₂³×C₁₃	1	2	yes	—
646	#95	C₂³×C₁₃	1	2	yes	—
647	#95	C₂³×C₁₃	1	2	yes	—
648	#95	C₂³×C₁₃	1	2	yes	—
649	#95	C₂³×C₁₃	1	2	yes	—
650	#95	C₂³×C₁₃	1	2	yes	—
651	#95	C₂³×C₁₃	1	2	yes	—
652	#95	C₂³×C₁₃	1	2	yes	—
653	#95	C₂³×C₁₃	1	2	yes	—
654	#95	C₂³×C₁₃	1	2	yes	—
655	#95	C₂³×C₁₃	1	2	yes	—
656	#95	C₂³×C₁₃	1	2	yes	—
657	#95	C₂³×C₁₃	1	2	yes	—
658	#95	C₂³×C₁₃	1	2	yes	—
659	C₂×C₁₃	—	2	4	no	—
660	C₂×C₁₃	—	4	4	no	—
661	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
662	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂×C₁₃	#3535	1	1	yes	characteristic
665	C₂×C₁₃	#3536	1	1	yes	characteristic
666	C₂×C₁₃	#3561	1	1	yes	characteristic
667	C₂×C₁₃	#3564	1	1	yes	characteristic
668	C₂⁴	—	2	2	no	—
669	C₂⁴	—	2	2	no	—
670	C₂⁴	—	4	1	no	—
671	C₂⁴	—	4	1	no	—
672	C₂⁴	—	4	1	no	—
673	C₂⁴	—	4	1	no	—
674	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
675	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
676	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂×Q₈	—	4	1	no	—
678	C₂×Q₈	—	4	1	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	1	no	—
682	C₂×Q₈	—	4	1	no	—
683	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
684	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
685	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	4	1	no	—
693	C₂²×C₄	—	4	1	no	—
694	C₂²×C₄	—	4	1	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	1	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	1	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
707	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
708	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
709	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
710	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
742	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
743	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
744	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
745	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
746	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
747	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
759	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
760	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
761	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
762	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
763	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	2	4	no	—
768	C₄²	—	4	1	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	2	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₁₃	#34433	1	1	yes	characteristic, direct product factor, Sylow
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	8	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	4	4	no	—
792	C₂³	—	8	2	no	—
793	C₂³	—	8	2	no	—
794	C₂³	—	8	2	no	—
795	C₂³	—	8	2	no	—
796	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
797	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
798	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
799	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
800	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
801	Q₈	—	4	4	no	—
802	Q₈	—	4	4	no	—
803	Q₈	—	4	8	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	8	2	no	—
853	C₂×C₄	—	8	2	no	—
854	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
855	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
856	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
857	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
858	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
859	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
860	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
861	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
862	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	8	8	no	—
877	C₂²	C₁₃×#519	1	4	yes	—
878	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
879	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
880	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
881	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
882	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
883	C₂²	C₁₃×#585	1	1	yes	characteristic
884	C₂²	C₁₃×#585	1	1	yes	characteristic
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₂	—	2	4	no	—
903	C₂	—	4	4	no	—
904	C₂	C₂×C₁₃×#519	1	1	yes	characteristic
905	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
906	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
907	C₂	C₁₃×#3535	1	1	yes	characteristic
908	C₂	C₁₃×#3536	1	1	yes	characteristic
909	C₂	C₁₃×#3561	1	1	yes	characteristic
910	C₂	C₁₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
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
2. C₁₃×#2378	C₂	semidirect
3. C₁₃×#2378	C₂	semidirect
4. C₁₃×#2368	C₂	semidirect
5. C₁₃×#2362	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
7. C₁₃×#2360	C₂	semidirect
10. C₁₃×#2332	C₂	semidirect
11. C₁₃×#2332	C₂	semidirect
12. C₁₃×#2329	C₂	semidirect
13. C₁₃×#2329	C₂	semidirect
14. C₁₃×#2323	C₂	semidirect
15. C₁₃×#2323	C₂	semidirect
17. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
20. C₁₃×#543	C₄	semidirect
28. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
29. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
39. C₁₃×#391	C₂²	semidirect
40. C₁₃×#391	C₂²	semidirect
41. C₁₃×#391	C₂²	semidirect
42. C₁₃×#391	C₂²	semidirect
43. C₁₃×#391	C₂²	semidirect
44. C₁₃×#391	C₂²	semidirect
45. C₁₃×#391	C₂²	semidirect
46. C₁₃×#389	C₂²	semidirect
47. C₁₃×#389	C₂²	semidirect
48. C₁₃×#389	C₂²	semidirect
49. C₁₃×#389	C₂²	semidirect
50. C₁₃×#389	C₂²	semidirect
51. C₁₃×#389	C₂²	semidirect
52. C₁₃×#389	C₂²	semidirect
69. C₁₃×#387	C₂²	semidirect
70. C₁₃×#387	C₂²	semidirect
71. C₁₃×#387	C₂²	semidirect
72. C₁₃×#387	C₂²	semidirect
73. C₁₃×#387	C₂²	semidirect
74. C₁₃×#387	C₂²	semidirect
75. C₁₃×#387	C₂²	semidirect
76. C₁₃×#387	C₂²	semidirect
77. C₁₃×#387	C₂²	semidirect
78. C₁₃×#387	C₂²	semidirect
79. C₁₃×#387	C₂²	semidirect
80. C₁₃×#387	C₂²	semidirect
92. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
93. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
94. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
95. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
96. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
97. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
98. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
123. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
124. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
125. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
126. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
213. #34433	C₁₃	direct (N × H)
325. #2378	C₂×C₁₃	semidirect
326. #2378	C₂×C₁₃	semidirect
327. #2368	C₂×C₁₃	semidirect
328. #2362	C₂×C₁₃	semidirect
329. #2362	C₂×C₁₃	semidirect
330. #2360	C₂×C₁₃	semidirect
333. #2332	C₂×C₁₃	semidirect
334. #2332	C₂×C₁₃	semidirect
335. #2329	C₂×C₁₃	semidirect
336. #2329	C₂×C₁₃	semidirect
337. #2323	C₂×C₁₃	semidirect
338. #2323	C₂×C₁₃	semidirect
340. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
341. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
427. #543	C₄×C₁₃	semidirect
435. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
436. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
437. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
446. #391	C₂²×C₁₃	semidirect
447. #391	C₂²×C₁₃	semidirect
448. #391	C₂²×C₁₃	semidirect
449. #391	C₂²×C₁₃	semidirect
450. #391	C₂²×C₁₃	semidirect
451. #391	C₂²×C₁₃	semidirect
452. #391	C₂²×C₁₃	semidirect
453. #389	C₂²×C₁₃	semidirect
454. #389	C₂²×C₁₃	semidirect
455. #389	C₂²×C₁₃	semidirect
456. #389	C₂²×C₁₃	semidirect
457. #389	C₂²×C₁₃	semidirect
458. #389	C₂²×C₁₃	semidirect
459. #389	C₂²×C₁₃	semidirect
476. #387	C₂²×C₁₃	semidirect
477. #387	C₂²×C₁₃	semidirect
478. #387	C₂²×C₁₃	semidirect
479. #387	C₂²×C₁₃	semidirect
480. #387	C₂²×C₁₃	semidirect
481. #387	C₂²×C₁₃	semidirect
482. #387	C₂²×C₁₃	semidirect
483. #387	C₂²×C₁₃	semidirect
484. #387	C₂²×C₁₃	semidirect
485. #387	C₂²×C₁₃	semidirect
486. #387	C₂²×C₁₃	semidirect
487. #387	C₂²×C₁₃	semidirect
499. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
500. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
501. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
502. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
503. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
504. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
505. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
569. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
570. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
571. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
572. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
778. C₁₃	#34433	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#543	2
C₁₃×#2378	2
C₁₃×#2368	2
C₁₃×#2362	2
C₁₃×#2360	2
C₁₃×#2342	2
C₁₃×#2332	2
C₁₃×#2329	2
C₁₃×#2323	2
C₁₃×#2312	2
C₄×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#388	2
#34433	13

Subgroups — C13×#34433 #15720772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34433 #15720772