Subgroups — C₁₃×#62800 #15749139

Order 3328.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3522	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3519	C₂	1	6	yes	maximal, complemented
3	C₁₃×#3517	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3514	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3511	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3508	C₂	1	3	yes	maximal, complemented
7	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3494	C₂	1	6	yes	maximal, complemented
10	C₁₃×#3488	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3483	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3481	C₂	1	6	yes	maximal, complemented
13	C₁₃×#3480	C₂	1	2	yes	maximal, complemented
14	D₄×C₁₃×#41	C₂	1	6	yes	maximal, complemented
15	C₁₃×#3460	C₂	1	6	yes	maximal, complemented
16	C₁₃×#3444	C₂	1	3	yes	maximal, complemented
17	C₂×C₁₃×#532	C₂	1	3	yes	maximal, complemented
18	C₄×C₁₃×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
21	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×#41	C₂²	1	6	yes	complemented
23	C₁₃×#559	C₂²	1	6	yes	complemented
24	C₁₃×#559	C₂²	1	6	yes	complemented
25	Q₈²×C₁₃	C₂²	1	2	yes	complemented
26	C₁₃×#557	C₂²	1	2	yes	complemented
27	C₁₃×#556	C₂²	1	6	yes	complemented
28	C₁₃×#555	C₂²	1	6	yes	complemented
29	C₁₃×#555	C₂²	1	12	yes	complemented
30	C₁₃×#554	C₂²	1	6	yes	complemented
31	C₁₃×#554	C₂²	1	6	yes	complemented
32	C₁₃×#553	C₂²	1	12	yes	complemented
33	C₁₃×#553	C₂²	1	12	yes	complemented
34	C₁₃×#553	C₂²	1	12	yes	complemented
35	C₁₃×#551	C₂²	1	24	yes	complemented
36	C₁₃×#550	C₂²	1	6	yes	complemented
37	C₁₃×#550	C₂²	1	2	yes	complemented
38	C₁₃×#550	C₂²	1	6	yes	complemented
39	C₁₃×#550	C₂²	1	2	yes	complemented
40	C₁₃×#550	C₂²	1	4	yes	complemented
41	D₄×Q₈×C₁₃	C₂²	1	6	yes	complemented
42	C₁₃×#548	C₂²	1	4	yes	complemented
43	C₁₃×#548	C₂²	1	12	yes	complemented
44	C₁₃×#547	C₂²	1	12	yes	complemented
45	C₁₃×#547	C₂²	1	6	yes	complemented
46	C₁₃×#546	C₂²	1	24	yes	complemented
47	C₁₃×#546	C₂²	1	12	yes	complemented
48	C₁₃×#546	C₂²	1	12	yes	complemented
49	C₁₃×#546	C₂²	1	12	yes	complemented
50	D₄²×C₁₃	C₂²	1	12	yes	complemented
51	D₄²×C₁₃	C₂²	1	6	yes	complemented
52	D₄²×C₁₃	C₂²	1	6	yes	complemented
53	C₁₃×#544	C₂²	1	6	yes	complemented
54	C₁₃×#542	C₂²	1	12	yes	complemented
55	C₁₃×#542	C₂²	1	12	yes	complemented
56	C₁₃×#540	C₂²	1	12	yes	complemented
57	C₁₃×#540	C₂²	1	12	yes	complemented
58	C₁₃×#538	C₂²	1	24	yes	complemented
59	C₁₃×#537	C₂²	1	6	yes	complemented
60	C₁₃×#535	C₂²	1	6	yes	complemented
61	C₁₃×#535	C₂²	1	6	yes	complemented
62	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#533	C₂²	1	3	yes	complemented
64	C₁₃×#533	C₂²	1	3	yes	complemented
65	C₁₃×#532	C₂²	1	6	yes	complemented
66	C₁₃×#532	C₂²	1	3	yes	complemented
67	C₁₃×#532	C₂²	1	6	yes	complemented
68	C₁₃×#532	C₂²	1	6	yes	complemented
69	C₁₃×#532	C₂²	1	6	yes	complemented
70	C₁₃×#532	C₂²	1	6	yes	complemented
71	C₁₃×#532	C₂²	1	6	yes	complemented
72	C₁₃×#532	C₂²	1	6	yes	complemented
73	C₁₃×#532	C₂²	1	3	yes	complemented
74	C₁₃×#532	C₂²	1	3	yes	complemented
75	C₁₃×#532	C₂²	1	12	yes	complemented
76	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
77	C₂×C₁₃×#127	C₂²	1	3	yes	complemented
78	C₁₃×#529	C₂²	1	6	yes	complemented
79	C₁₃×#529	C₂²	1	6	yes	complemented
80	C₁₃×#529	C₂²	1	6	yes	complemented
81	C₁₃×#529	C₂²	1	6	yes	complemented
82	C₁₃×#529	C₂²	1	6	yes	complemented
83	C₁₃×#529	C₂²	1	6	yes	complemented
84	C₁₃×#529	C₂²	1	12	yes	complemented
85	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
86	C₁₃×#525	C₂²	1	6	yes	complemented
87	C₁₃×#525	C₂²	1	6	yes	complemented
88	C₁₃×#525	C₂²	1	6	yes	complemented
89	C₁₃×#525	C₂²	1	24	yes	complemented
90	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
91	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
92	C₁₃×#520	C₂²	1	2	yes	—
93	C₁₃×#520	C₂²	1	4	yes	complemented
94	C₁₃×#520	C₂²	1	6	yes	complemented
95	C₁₃×#518	C₂²	1	12	yes	complemented
96	C₁₃×#518	C₂²	1	6	yes	complemented
97	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
98	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
100	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
101	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
103	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
104	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₁₃×#41	C₂²	1	6	yes	complemented
106	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
107	C₄×C₁₃×#41	C₂²	1	6	yes	complemented
108	C₄×C₁₃×#41	C₂²	1	6	yes	complemented
109	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
112	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
113	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
114	C₂×C₄×D₄×C₁₃	C₂²	1	12	yes	complemented
115	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
116	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
117	C₂²×C₄²×C₁₃	C₂²	1	3	yes	complemented
118	C₁₃×H(5,𝔽₂)	—	2	16	no	—
119	C₂×C₁₃×#41	—	2	8	no	—
120	C₂×C₁₃×#41	—	4	24	no	—
121	C₂×C₁₃×#41	C₂³	1	3	yes	—
122	C₂×C₁₃×#41	C₂³	1	3	yes	—
123	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×#41	C₂³	1	6	yes	—
125	C₂×C₁₃×#41	C₂³	1	4	yes	—
126	C₂×C₁₃×#41	C₂³	1	6	yes	—
127	C₂×C₁₃×#41	C₂³	1	6	yes	—
128	C₂×C₁₃×#41	C₂³	1	12	yes	—
129	C₂×C₁₃×#41	C₂³	1	12	yes	—
130	C₂×C₁₃×#41	C₂³	1	12	yes	—
131	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
134	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
135	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
136	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
137	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
138	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
139	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
140	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
141	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
142	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
143	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
144	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
145	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
146	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
147	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
148	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
149	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
151	C₁₃×#127	C₂³	1	3	yes	—
152	C₁₃×#127	C₂³	1	6	yes	—
153	C₁₃×#127	C₂³	1	6	yes	—
154	C₁₃×#127	C₂³	1	6	yes	—
155	C₁₃×#127	C₂³	1	12	yes	—
156	C₁₃×#126	C₂³	1	12	yes	—
157	C₁₃×#126	C₂³	1	12	yes	—
158	C₁₃×#126	C₂³	1	24	yes	—
159	C₁₃×#125	C₂³	1	2	yes	—
160	C₁₃×#125	C₂³	1	6	yes	—
161	C₁₃×#125	C₂³	1	6	yes	—
162	C₁₃×#125	C₂³	1	12	yes	—
163	C₁₃×#124	C₂³	1	6	yes	—
164	C₁₃×#124	C₂³	1	12	yes	—
165	C₁₃×#124	C₂³	1	12	yes	—
166	C₁₃×#124	C₂³	1	12	yes	—
167	C₁₃×#124	C₂³	1	6	yes	—
168	C₁₃×#124	C₂³	1	6	yes	—
169	C₁₃×#124	C₂³	1	12	yes	—
170	C₁₃×#124	C₂³	1	24	yes	—
171	C₁₃×#123	C₂³	1	12	yes	—
172	C₁₃×#123	C₂³	1	12	yes	—
173	C₁₃×#123	C₂³	1	12	yes	—
174	C₁₃×#123	C₂³	1	24	yes	—
175	C₁₃×#123	C₂³	1	24	yes	—
176	C₁₃×#123	C₂³	1	24	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
181	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
182	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
183	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
186	C₁₃×#121	C₂³	1	6	yes	—
187	C₁₃×#121	C₂³	1	6	yes	—
188	C₁₃×#121	C₂³	1	12	yes	—
189	C₁₃×#121	C₂³	1	12	yes	—
190	C₁₃×#121	C₂³	1	12	yes	—
191	C₁₃×#121	C₂³	1	12	yes	—
192	C₁₃×#121	C₂³	1	12	yes	—
193	C₁₃×#121	C₂³	1	12	yes	—
194	C₁₃×#121	C₂³	1	6	yes	—
195	C₁₃×#121	C₂³	1	6	yes	—
196	C₁₃×#121	C₂³	1	6	yes	—
197	C₁₃×#121	C₂³	1	6	yes	—
198	C₁₃×#121	C₂³	1	24	yes	—
199	C₁₃×#121	C₂³	1	24	yes	—
200	C₁₃×#121	C₂³	1	12	yes	—
201	C₁₃×#121	C₂³	1	12	yes	—
202	C₁₃×#121	C₂³	1	12	yes	—
203	C₁₃×#121	C₂³	1	24	yes	—
204	C₁₃×#120	C₂³	1	12	yes	—
205	C₁₃×#120	C₂³	1	24	yes	—
206	C₁₃×#120	C₂³	1	24	yes	—
207	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
221	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
222	C₄×D₄×C₁₃	C₂³	1	3	yes	—
223	C₄×D₄×C₁₃	C₂³	1	12	yes	—
224	C₄×D₄×C₁₃	C₂³	1	6	yes	—
225	C₄×D₄×C₁₃	C₂³	1	12	yes	—
226	C₄×D₄×C₁₃	C₂³	1	6	yes	—
227	C₄×D₄×C₁₃	C₂³	1	3	yes	—
228	C₄×D₄×C₁₃	C₂³	1	3	yes	—
229	C₄×D₄×C₁₃	C₂³	1	3	yes	—
230	C₄×D₄×C₁₃	C₂³	1	6	yes	—
231	C₄×D₄×C₁₃	C₂³	1	3	yes	—
232	C₄×D₄×C₁₃	C₂³	1	6	yes	—
233	C₄×D₄×C₁₃	C₂³	1	3	yes	—
234	C₄×D₄×C₁₃	C₂³	1	6	yes	—
235	C₄×D₄×C₁₃	C₂³	1	6	yes	—
236	C₄×D₄×C₁₃	C₂³	1	3	yes	—
237	C₄×D₄×C₁₃	C₂³	1	3	yes	—
238	C₄×D₄×C₁₃	C₂³	1	12	yes	—
239	C₄×D₄×C₁₃	C₂³	1	12	yes	—
240	C₄×D₄×C₁₃	C₂³	1	12	yes	—
241	C₄×D₄×C₁₃	C₂³	1	24	yes	—
242	C₄×D₄×C₁₃	C₂³	1	12	yes	—
243	C₄×D₄×C₁₃	C₂³	1	12	yes	—
244	C₄×D₄×C₁₃	C₂³	1	12	yes	—
245	C₄×D₄×C₁₃	C₂³	1	12	yes	—
246	C₄×D₄×C₁₃	C₂³	1	12	yes	—
247	C₄×D₄×C₁₃	C₂³	1	6	yes	—
248	C₄×D₄×C₁₃	C₂³	1	12	yes	—
249	C₄×D₄×C₁₃	C₂³	1	12	yes	—
250	C₄×D₄×C₁₃	C₂³	1	12	yes	—
251	C₄×D₄×C₁₃	C₂³	1	12	yes	—
252	C₄×D₄×C₁₃	C₂³	1	12	yes	—
253	C₄×D₄×C₁₃	C₂³	1	6	yes	—
254	C₄×D₄×C₁₃	C₂³	1	6	yes	—
255	C₄×D₄×C₁₃	C₂³	1	6	yes	—
256	C₁₃×#117	C₂³	1	3	yes	—
257	C₁₃×#117	C₂³	1	3	yes	—
258	C₁₃×#117	C₂³	1	6	yes	—
259	C₁₃×#117	C₂³	1	6	yes	—
260	C₁₃×#117	C₂³	1	3	yes	—
261	C₁₃×#117	C₂³	1	3	yes	—
262	C₁₃×#117	C₂³	1	2	yes	—
263	C₁₃×#117	C₂³	1	6	yes	—
264	C₁₃×#117	C₂³	1	12	yes	—
265	C₁₃×#117	C₂³	1	12	yes	—
266	C₁₃×#117	C₂³	1	12	yes	—
267	C₁₃×#117	C₂³	1	6	yes	—
268	C₁₃×#117	C₂³	1	12	yes	—
269	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
270	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
271	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
273	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
274	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
275	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
276	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
277	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
278	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
280	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
281	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
282	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
283	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
284	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
285	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
286	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
287	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
288	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
289	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
290	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
291	#62800	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
293	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
294	C₁₃×#41	—	2	4	no	—
295	C₁₃×#41	—	2	16	no	—
296	C₁₃×#41	—	2	12	no	—
297	C₁₃×#41	—	2	12	no	—
298	C₁₃×#41	—	2	24	no	—
299	C₁₃×#41	—	2	24	no	—
300	C₁₃×#41	—	4	24	no	—
301	C₁₃×#41	—	4	24	no	—
302	C₁₃×#41	—	4	24	no	—
303	C₁₃×#41	—	4	12	no	—
304	C₁₃×#41	#41	1	8	yes	complemented
305	C₂×Q₈×C₁₃	—	2	4	no	—
306	C₂×Q₈×C₁₃	—	4	12	no	—
307	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
308	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
309	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
310	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
311	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
312	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂×D₄×C₁₃	—	2	12	no	—
314	C₂×D₄×C₁₃	—	2	48	no	—
315	C₂×D₄×C₁₃	—	2	24	no	—
316	C₂×D₄×C₁₃	—	4	12	no	—
317	C₂×D₄×C₁₃	—	4	12	no	—
318	C₂×D₄×C₁₃	—	4	24	no	—
319	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
320	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
321	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
322	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
323	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
324	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
325	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
326	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
327	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
328	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
329	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
330	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
331	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
332	C₂²×C₄×C₁₃	—	2	12	no	—
333	C₂²×C₄×C₁₃	—	2	12	no	—
334	C₂²×C₄×C₁₃	—	4	6	no	—
335	C₂²×C₄×C₁₃	—	4	24	no	—
336	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
339	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
340	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
341	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
342	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
343	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
344	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
345	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
346	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
347	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
348	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
349	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
350	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
352	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
353	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
354	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
355	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
356	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
357	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
358	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
360	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
370	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
371	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
372	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
373	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
374	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
375	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
376	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
377	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
378	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
379	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
380	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
381	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
382	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
383	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
384	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
385	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
386	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
387	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
388	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
389	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
390	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
391	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
392	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
393	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
394	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
396	C₄²×C₁₃	C₂⁴	1	3	yes	—
397	C₄²×C₁₃	C₂⁴	1	3	yes	—
398	C₄²×C₁₃	C₂⁴	1	3	yes	—
399	C₄²×C₁₃	C₂⁴	1	3	yes	—
400	C₄²×C₁₃	C₂⁴	1	3	yes	—
401	C₄²×C₁₃	C₂⁴	1	3	yes	—
402	C₄²×C₁₃	C₂⁴	1	3	yes	—
403	C₄²×C₁₃	C₂⁴	1	3	yes	—
404	C₄²×C₁₃	C₂⁴	1	3	yes	—
405	C₄²×C₁₃	C₂⁴	1	3	yes	—
406	C₄²×C₁₃	C₂⁴	1	12	yes	—
407	C₄²×C₁₃	C₂⁴	1	12	yes	—
408	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
409	C₄²×C₁₃	C₂⁴	1	3	yes	—
410	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
411	C₄²×C₁₃	C₂⁴	1	3	yes	—
412	C₄²×C₁₃	C₂⁴	1	4	yes	—
413	#3522	C₂×C₁₃	1	2	yes	complemented
414	#3519	C₂×C₁₃	1	6	yes	complemented
415	#3517	C₂×C₁₃	1	2	yes	complemented
416	#3514	C₂×C₁₃	1	6	yes	complemented
417	#3511	C₂×C₁₃	1	3	yes	complemented
418	#3508	C₂×C₁₃	1	3	yes	complemented
419	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
420	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
421	#3494	C₂×C₁₃	1	6	yes	complemented
422	#3488	C₂×C₁₃	1	2	yes	complemented
423	#3483	C₂×C₁₃	1	2	yes	complemented
424	#3481	C₂×C₁₃	1	6	yes	complemented
425	#3480	C₂×C₁₃	1	2	yes	complemented
426	D₄×#41	C₂×C₁₃	1	6	yes	complemented
427	#3460	C₂×C₁₃	1	6	yes	complemented
428	#3444	C₂×C₁₃	1	3	yes	complemented
429	C₂×#532	C₂×C₁₃	1	3	yes	complemented
430	C₄×H(5,𝔽₂)	C₂×C₁₃	1	2	yes	complemented
431	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
432	C₂³×C₁₃	—	2	6	no	—
433	C₂³×C₁₃	—	2	6	no	—
434	C₂³×C₁₃	—	2	24	no	—
435	C₂³×C₁₃	—	4	3	no	—
436	C₂³×C₁₃	—	4	12	no	—
437	C₂³×C₁₃	—	4	12	no	—
438	C₂³×C₁₃	C₂⁵	1	12	yes	—
439	C₂³×C₁₃	C₂⁵	1	3	yes	—
440	C₂³×C₁₃	C₂⁵	1	3	yes	—
441	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
442	Q₈×C₁₃	—	2	6	no	—
443	Q₈×C₁₃	—	2	4	no	—
444	Q₈×C₁₃	—	2	12	no	—
445	Q₈×C₁₃	—	2	4	no	—
446	Q₈×C₁₃	—	4	12	no	—
447	Q₈×C₁₃	C₂×#41	1	4	yes	complemented
448	D₄×C₁₃	—	2	24	no	—
449	D₄×C₁₃	—	2	12	no	—
450	D₄×C₁₃	—	2	24	no	—
451	D₄×C₁₃	—	2	24	no	—
452	D₄×C₁₃	—	2	12	no	—
453	D₄×C₁₃	—	2	6	no	—
454	D₄×C₁₃	—	2	12	no	—
455	D₄×C₁₃	—	2	12	no	—
456	D₄×C₁₃	—	4	12	no	—
457	D₄×C₁₃	—	4	12	no	—
458	D₄×C₁₃	—	4	24	no	—
459	D₄×C₁₃	—	4	12	no	—
460	D₄×C₁₃	C₂×#41	1	12	yes	complemented
461	C₂×C₄×C₁₃	—	2	6	no	—
462	C₂×C₄×C₁₃	—	2	6	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	6	no	—
465	C₂×C₄×C₁₃	—	2	6	no	—
466	C₂×C₄×C₁₃	—	2	6	no	—
467	C₂×C₄×C₁₃	—	2	24	no	—
468	C₂×C₄×C₁₃	—	2	6	no	—
469	C₂×C₄×C₁₃	—	2	6	no	—
470	C₂×C₄×C₁₃	—	2	6	no	—
471	C₂×C₄×C₁₃	—	2	6	no	—
472	C₂×C₄×C₁₃	—	2	24	no	—
473	C₂×C₄×C₁₃	—	2	2	no	—
474	C₂×C₄×C₁₃	—	2	6	no	—
475	C₂×C₄×C₁₃	—	2	6	no	—
476	C₂×C₄×C₁₃	—	4	3	no	—
477	C₂×C₄×C₁₃	—	4	3	no	—
478	C₂×C₄×C₁₃	—	4	3	no	—
479	C₂×C₄×C₁₃	—	4	12	no	—
480	C₂×C₄×C₁₃	—	4	24	no	—
481	C₂×C₄×C₁₃	—	4	12	no	—
482	C₂×C₄×C₁₃	C₂×#41	1	12	yes	complemented
483	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
484	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
485	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
486	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
487	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
488	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
489	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
490	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
491	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
492	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
493	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
494	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
495	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
496	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
497	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
498	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
499	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
500	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
501	C₂²×#41	C₂²×C₁₃	1	6	yes	complemented
502	#559	C₂²×C₁₃	1	6	yes	complemented
503	#559	C₂²×C₁₃	1	6	yes	complemented
504	Q₈²	C₂²×C₁₃	1	2	yes	complemented
505	#557	C₂²×C₁₃	1	2	yes	complemented
506	#556	C₂²×C₁₃	1	6	yes	complemented
507	#555	C₂²×C₁₃	1	12	yes	complemented
508	#555	C₂²×C₁₃	1	6	yes	complemented
509	#554	C₂²×C₁₃	1	6	yes	complemented
510	#554	C₂²×C₁₃	1	6	yes	complemented
511	#553	C₂²×C₁₃	1	12	yes	complemented
512	#553	C₂²×C₁₃	1	12	yes	complemented
513	#553	C₂²×C₁₃	1	12	yes	complemented
514	#551	C₂²×C₁₃	1	24	yes	complemented
515	#550	C₂²×C₁₃	1	6	yes	complemented
516	#550	C₂²×C₁₃	1	2	yes	complemented
517	#550	C₂²×C₁₃	1	4	yes	complemented
518	#550	C₂²×C₁₃	1	2	yes	complemented
519	#550	C₂²×C₁₃	1	6	yes	complemented
520	D₄×Q₈	C₂²×C₁₃	1	6	yes	complemented
521	#548	C₂²×C₁₃	1	12	yes	complemented
522	#548	C₂²×C₁₃	1	4	yes	complemented
523	#547	C₂²×C₁₃	1	12	yes	complemented
524	#547	C₂²×C₁₃	1	6	yes	complemented
525	#546	C₂²×C₁₃	1	24	yes	complemented
526	#546	C₂²×C₁₃	1	12	yes	complemented
527	#546	C₂²×C₁₃	1	12	yes	complemented
528	#546	C₂²×C₁₃	1	12	yes	complemented
529	D₄²	C₂²×C₁₃	1	12	yes	complemented
530	D₄²	C₂²×C₁₃	1	6	yes	complemented
531	D₄²	C₂²×C₁₃	1	6	yes	complemented
532	#544	C₂²×C₁₃	1	6	yes	complemented
533	#542	C₂²×C₁₃	1	12	yes	complemented
534	#542	C₂²×C₁₃	1	12	yes	complemented
535	#540	C₂²×C₁₃	1	12	yes	complemented
536	#540	C₂²×C₁₃	1	12	yes	complemented
537	#538	C₂²×C₁₃	1	24	yes	complemented
538	#537	C₂²×C₁₃	1	6	yes	complemented
539	#535	C₂²×C₁₃	1	6	yes	complemented
540	#535	C₂²×C₁₃	1	6	yes	complemented
541	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
542	#533	C₂²×C₁₃	1	3	yes	complemented
543	#533	C₂²×C₁₃	1	3	yes	complemented
544	#532	C₂²×C₁₃	1	3	yes	complemented
545	#532	C₂²×C₁₃	1	6	yes	complemented
546	#532	C₂²×C₁₃	1	6	yes	complemented
547	#532	C₂²×C₁₃	1	6	yes	complemented
548	#532	C₂²×C₁₃	1	6	yes	complemented
549	#532	C₂²×C₁₃	1	6	yes	complemented
550	#532	C₂²×C₁₃	1	6	yes	complemented
551	#532	C₂²×C₁₃	1	6	yes	complemented
552	#532	C₂²×C₁₃	1	3	yes	complemented
553	#532	C₂²×C₁₃	1	3	yes	complemented
554	#532	C₂²×C₁₃	1	12	yes	complemented
555	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
556	C₂×#127	C₂²×C₁₃	1	3	yes	complemented
557	#529	C₂²×C₁₃	1	6	yes	complemented
558	#529	C₂²×C₁₃	1	6	yes	complemented
559	#529	C₂²×C₁₃	1	6	yes	complemented
560	#529	C₂²×C₁₃	1	6	yes	complemented
561	#529	C₂²×C₁₃	1	6	yes	complemented
562	#529	C₂²×C₁₃	1	6	yes	complemented
563	#529	C₂²×C₁₃	1	12	yes	complemented
564	C₂×#124	C₂²×C₁₃	1	6	yes	complemented
565	#525	C₂²×C₁₃	1	6	yes	complemented
566	#525	C₂²×C₁₃	1	6	yes	complemented
567	#525	C₂²×C₁₃	1	6	yes	complemented
568	#525	C₂²×C₁₃	1	24	yes	complemented
569	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
570	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
571	#520	C₂²×C₁₃	1	2	yes	—
572	#520	C₂²×C₁₃	1	6	yes	complemented
573	#520	C₂²×C₁₃	1	4	yes	complemented
574	#518	C₂²×C₁₃	1	6	yes	complemented
575	#518	C₂²×C₁₃	1	12	yes	complemented
576	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
577	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
578	C₄×#41	C₂²×C₁₃	1	3	yes	complemented
579	C₄×#41	C₂²×C₁₃	1	3	yes	complemented
580	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
581	C₄×#41	C₂²×C₁₃	1	3	yes	complemented
582	C₄×#41	C₂²×C₁₃	1	3	yes	complemented
583	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	C₄×#41	C₂²×C₁₃	1	6	yes	complemented
585	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
586	C₄×#41	C₂²×C₁₃	1	6	yes	complemented
587	C₄×#41	C₂²×C₁₃	1	6	yes	complemented
588	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
589	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
590	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	complemented
591	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	complemented
592	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
593	C₂×C₄×D₄	C₂²×C₁₃	1	12	yes	complemented
594	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
595	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
596	C₂²×C₄²	C₂²×C₁₃	1	3	yes	complemented
597	C₂²×C₁₃	—	2	1	no	—
598	C₂²×C₁₃	—	2	3	no	—
599	C₂²×C₁₃	—	2	1	no	—
600	C₂²×C₁₃	—	2	3	no	—
601	C₂²×C₁₃	—	2	3	no	—
602	C₂²×C₁₃	—	2	12	no	—
603	C₂²×C₁₃	—	2	3	no	—
604	C₂²×C₁₃	—	2	12	no	—
605	C₂²×C₁₃	—	2	3	no	—
606	C₂²×C₁₃	—	2	12	no	—
607	C₂²×C₁₃	—	4	12	no	—
608	C₂²×C₁₃	—	8	24	no	—
609	C₂²×C₁₃	C₂²×#41	1	6	yes	—
610	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
611	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
612	C₄×C₁₃	—	2	1	no	—
613	C₄×C₁₃	—	2	4	no	—
614	C₄×C₁₃	—	2	3	no	—
615	C₄×C₁₃	—	2	3	no	—
616	C₄×C₁₃	—	2	3	no	—
617	C₄×C₁₃	—	2	12	no	—
618	C₄×C₁₃	—	2	1	no	—
619	C₄×C₁₃	—	2	3	no	—
620	C₄×C₁₃	—	2	3	no	—
621	C₄×C₁₃	—	2	4	no	—
622	C₄×C₁₃	C₂²×#41	1	6	yes	—
623	C₄×C₁₃	C₂²×#41	1	2	yes	—
624	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
625	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
626	C₄×C₁₃	#585	1	2	yes	—
627	H(5,𝔽₂)	—	2	16	no	—
628	C₂×#41	—	2	8	no	—
629	C₂×#41	—	4	24	no	—
630	C₂×#41	C₂³×C₁₃	1	3	yes	—
631	C₂×#41	C₂³×C₁₃	1	3	yes	—
632	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×#41	C₂³×C₁₃	1	6	yes	—
634	C₂×#41	C₂³×C₁₃	1	4	yes	—
635	C₂×#41	C₂³×C₁₃	1	6	yes	—
636	C₂×#41	C₂³×C₁₃	1	6	yes	—
637	C₂×#41	C₂³×C₁₃	1	12	yes	—
638	C₂×#41	C₂³×C₁₃	1	12	yes	—
639	C₂×#41	C₂³×C₁₃	1	12	yes	—
640	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
641	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
642	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
643	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
644	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
645	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
646	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
647	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
648	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
649	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
650	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
651	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
652	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
653	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
654	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
655	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
656	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
657	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
658	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
659	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
660	#127	C₂³×C₁₃	1	3	yes	—
661	#127	C₂³×C₁₃	1	6	yes	—
662	#127	C₂³×C₁₃	1	6	yes	—
663	#127	C₂³×C₁₃	1	6	yes	—
664	#127	C₂³×C₁₃	1	12	yes	—
665	#126	C₂³×C₁₃	1	12	yes	—
666	#126	C₂³×C₁₃	1	12	yes	—
667	#126	C₂³×C₁₃	1	24	yes	—
668	#125	C₂³×C₁₃	1	2	yes	—
669	#125	C₂³×C₁₃	1	6	yes	—
670	#125	C₂³×C₁₃	1	6	yes	—
671	#125	C₂³×C₁₃	1	12	yes	—
672	#124	C₂³×C₁₃	1	6	yes	—
673	#124	C₂³×C₁₃	1	12	yes	—
674	#124	C₂³×C₁₃	1	12	yes	—
675	#124	C₂³×C₁₃	1	12	yes	—
676	#124	C₂³×C₁₃	1	6	yes	—
677	#124	C₂³×C₁₃	1	6	yes	—
678	#124	C₂³×C₁₃	1	12	yes	—
679	#124	C₂³×C₁₃	1	24	yes	—
680	#123	C₂³×C₁₃	1	12	yes	—
681	#123	C₂³×C₁₃	1	12	yes	—
682	#123	C₂³×C₁₃	1	12	yes	—
683	#123	C₂³×C₁₃	1	24	yes	—
684	#123	C₂³×C₁₃	1	24	yes	—
685	#123	C₂³×C₁₃	1	24	yes	—
686	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
689	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
690	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
691	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
692	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
693	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
694	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
695	#121	C₂³×C₁₃	1	6	yes	—
696	#121	C₂³×C₁₃	1	6	yes	—
697	#121	C₂³×C₁₃	1	12	yes	—
698	#121	C₂³×C₁₃	1	12	yes	—
699	#121	C₂³×C₁₃	1	12	yes	—
700	#121	C₂³×C₁₃	1	12	yes	—
701	#121	C₂³×C₁₃	1	12	yes	—
702	#121	C₂³×C₁₃	1	12	yes	—
703	#121	C₂³×C₁₃	1	6	yes	—
704	#121	C₂³×C₁₃	1	6	yes	—
705	#121	C₂³×C₁₃	1	6	yes	—
706	#121	C₂³×C₁₃	1	6	yes	—
707	#121	C₂³×C₁₃	1	24	yes	—
708	#121	C₂³×C₁₃	1	24	yes	—
709	#121	C₂³×C₁₃	1	12	yes	—
710	#121	C₂³×C₁₃	1	12	yes	—
711	#121	C₂³×C₁₃	1	12	yes	—
712	#121	C₂³×C₁₃	1	24	yes	—
713	#120	C₂³×C₁₃	1	12	yes	—
714	#120	C₂³×C₁₃	1	24	yes	—
715	#120	C₂³×C₁₃	1	24	yes	—
716	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
717	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
720	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
721	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
722	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
723	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
724	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
725	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
726	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
727	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
728	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
729	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
730	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
731	C₄×D₄	C₂³×C₁₃	1	3	yes	—
732	C₄×D₄	C₂³×C₁₃	1	12	yes	—
733	C₄×D₄	C₂³×C₁₃	1	6	yes	—
734	C₄×D₄	C₂³×C₁₃	1	12	yes	—
735	C₄×D₄	C₂³×C₁₃	1	6	yes	—
736	C₄×D₄	C₂³×C₁₃	1	3	yes	—
737	C₄×D₄	C₂³×C₁₃	1	3	yes	—
738	C₄×D₄	C₂³×C₁₃	1	3	yes	—
739	C₄×D₄	C₂³×C₁₃	1	6	yes	—
740	C₄×D₄	C₂³×C₁₃	1	3	yes	—
741	C₄×D₄	C₂³×C₁₃	1	6	yes	—
742	C₄×D₄	C₂³×C₁₃	1	3	yes	—
743	C₄×D₄	C₂³×C₁₃	1	6	yes	—
744	C₄×D₄	C₂³×C₁₃	1	6	yes	—
745	C₄×D₄	C₂³×C₁₃	1	3	yes	—
746	C₄×D₄	C₂³×C₁₃	1	3	yes	—
747	C₄×D₄	C₂³×C₁₃	1	12	yes	—
748	C₄×D₄	C₂³×C₁₃	1	12	yes	—
749	C₄×D₄	C₂³×C₁₃	1	12	yes	—
750	C₄×D₄	C₂³×C₁₃	1	24	yes	—
751	C₄×D₄	C₂³×C₁₃	1	12	yes	—
752	C₄×D₄	C₂³×C₁₃	1	12	yes	—
753	C₄×D₄	C₂³×C₁₃	1	12	yes	—
754	C₄×D₄	C₂³×C₁₃	1	12	yes	—
755	C₄×D₄	C₂³×C₁₃	1	12	yes	—
756	C₄×D₄	C₂³×C₁₃	1	6	yes	—
757	C₄×D₄	C₂³×C₁₃	1	12	yes	—
758	C₄×D₄	C₂³×C₁₃	1	12	yes	—
759	C₄×D₄	C₂³×C₁₃	1	12	yes	—
760	C₄×D₄	C₂³×C₁₃	1	12	yes	—
761	C₄×D₄	C₂³×C₁₃	1	12	yes	—
762	C₄×D₄	C₂³×C₁₃	1	6	yes	—
763	C₄×D₄	C₂³×C₁₃	1	6	yes	—
764	C₄×D₄	C₂³×C₁₃	1	6	yes	—
765	#117	C₂³×C₁₃	1	3	yes	—
766	#117	C₂³×C₁₃	1	3	yes	—
767	#117	C₂³×C₁₃	1	6	yes	—
768	#117	C₂³×C₁₃	1	6	yes	—
769	#117	C₂³×C₁₃	1	3	yes	—
770	#117	C₂³×C₁₃	1	3	yes	—
771	#117	C₂³×C₁₃	1	2	yes	—
772	#117	C₂³×C₁₃	1	6	yes	—
773	#117	C₂³×C₁₃	1	12	yes	—
774	#117	C₂³×C₁₃	1	12	yes	—
775	#117	C₂³×C₁₃	1	12	yes	—
776	#117	C₂³×C₁₃	1	6	yes	—
777	#117	C₂³×C₁₃	1	12	yes	—
778	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
779	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
780	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
781	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
782	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
787	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
788	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
789	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
790	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
791	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
792	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
793	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
794	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
795	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
796	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
797	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
798	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
799	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
800	C₂×C₁₃	—	2	2	no	—
801	C₂×C₁₃	—	2	6	no	—
802	C₂×C₁₃	—	4	3	no	—
803	C₂×C₁₃	—	4	12	no	—
804	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
805	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
806	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
807	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
808	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
809	#41	—	2	4	no	—
810	#41	—	2	16	no	—
811	#41	—	2	12	no	—
812	#41	—	2	12	no	—
813	#41	—	2	24	no	—
814	#41	—	2	24	no	—
815	#41	—	4	24	no	—
816	#41	—	4	24	no	—
817	#41	—	4	24	no	—
818	#41	—	4	12	no	—
819	#41	C₁₃×#41	1	8	yes	complemented
820	C₂×Q₈	—	2	4	no	—
821	C₂×Q₈	—	4	12	no	—
822	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
823	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
824	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
825	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
826	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
827	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
828	C₂×D₄	—	2	12	no	—
829	C₂×D₄	—	2	48	no	—
830	C₂×D₄	—	2	24	no	—
831	C₂×D₄	—	4	12	no	—
832	C₂×D₄	—	4	12	no	—
833	C₂×D₄	—	4	24	no	—
834	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
835	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
836	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
837	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
838	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
839	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
840	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
841	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
842	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
843	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
844	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
845	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
846	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
847	C₂²×C₄	—	2	12	no	—
848	C₂²×C₄	—	2	12	no	—
849	C₂²×C₄	—	4	24	no	—
850	C₂²×C₄	—	4	6	no	—
851	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
854	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
855	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
856	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
857	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
858	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
859	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
860	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
861	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
862	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
863	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
864	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
865	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
866	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
867	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
868	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
869	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
870	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
871	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
872	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
873	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
874	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
875	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
876	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
877	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
878	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
879	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
880	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
881	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
882	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
883	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
884	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
885	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
887	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
888	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
889	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
890	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
891	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
892	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
893	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
894	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
895	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
896	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
897	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
898	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
899	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
900	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
901	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
902	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
903	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
904	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
905	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
906	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
907	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
908	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
909	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
910	C₄²	C₂⁴×C₁₃	1	3	yes	—
911	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
912	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
913	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
914	C₄²	C₂⁴×C₁₃	1	3	yes	—
915	C₄²	C₂⁴×C₁₃	1	3	yes	—
916	C₄²	C₂⁴×C₁₃	1	3	yes	—
917	C₄²	C₂⁴×C₁₃	1	3	yes	—
918	C₄²	C₂⁴×C₁₃	1	4	yes	—
919	C₄²	C₂⁴×C₁₃	1	3	yes	—
920	C₄²	C₂⁴×C₁₃	1	3	yes	—
921	C₄²	C₂⁴×C₁₃	1	3	yes	—
922	C₄²	C₂⁴×C₁₃	1	3	yes	—
923	C₄²	C₂⁴×C₁₃	1	3	yes	—
924	C₄²	C₂⁴×C₁₃	1	3	yes	—
925	C₄²	C₂⁴×C₁₃	1	3	yes	—
926	C₄²	C₂⁴×C₁₃	1	12	yes	—
927	C₄²	C₂⁴×C₁₃	1	12	yes	—
928	C₁₃	#62800	1	1	yes	characteristic, direct product factor, Sylow
929	C₂³	—	2	6	no	—
930	C₂³	—	2	6	no	—
931	C₂³	—	2	24	no	—
932	C₂³	—	4	3	no	—
933	C₂³	—	4	12	no	—
934	C₂³	—	4	12	no	—
935	C₂³	C₂⁵×C₁₃	1	12	yes	—
936	C₂³	C₂⁵×C₁₃	1	3	yes	—
937	C₂³	C₂⁵×C₁₃	1	3	yes	—
938	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
939	Q₈	—	2	6	no	—
940	Q₈	—	2	4	no	—
941	Q₈	—	2	12	no	—
942	Q₈	—	2	4	no	—
943	Q₈	—	4	12	no	—
944	Q₈	C₂×C₁₃×#41	1	4	yes	complemented
945	D₄	—	2	24	no	—
946	D₄	—	2	12	no	—
947	D₄	—	2	24	no	—
948	D₄	—	2	24	no	—
949	D₄	—	2	12	no	—
950	D₄	—	2	6	no	—
951	D₄	—	2	12	no	—
952	D₄	—	2	12	no	—
953	D₄	—	4	12	no	—
954	D₄	—	4	12	no	—
955	D₄	—	4	24	no	—
956	D₄	—	4	12	no	—
957	D₄	C₂×C₁₃×#41	1	12	yes	complemented
958	C₂×C₄	—	2	6	no	—
959	C₂×C₄	—	2	6	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	6	no	—
962	C₂×C₄	—	2	6	no	—
963	C₂×C₄	—	2	6	no	—
964	C₂×C₄	—	2	24	no	—
965	C₂×C₄	—	2	6	no	—
966	C₂×C₄	—	2	6	no	—
967	C₂×C₄	—	2	6	no	—
968	C₂×C₄	—	2	6	no	—
969	C₂×C₄	—	2	24	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	6	no	—
972	C₂×C₄	—	2	6	no	—
973	C₂×C₄	—	4	12	no	—
974	C₂×C₄	—	4	3	no	—
975	C₂×C₄	—	4	3	no	—
976	C₂×C₄	—	4	3	no	—
977	C₂×C₄	—	4	24	no	—
978	C₂×C₄	—	4	12	no	—
979	C₂×C₄	C₂×C₁₃×#41	1	12	yes	complemented
980	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
981	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
982	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
983	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
984	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
985	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
986	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
987	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
988	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
989	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
990	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
991	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
992	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
993	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
994	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
996	C₂²	—	2	1	no	—
997	C₂²	—	2	3	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	3	no	—
1000	C₂²	—	2	3	no	—
1001	C₂²	—	2	12	no	—
1002	C₂²	—	2	3	no	—
1003	C₂²	—	2	12	no	—
1004	C₂²	—	2	3	no	—
1005	C₂²	—	2	12	no	—
1006	C₂²	—	4	12	no	—
1007	C₂²	—	8	24	no	—
1008	C₂²	C₂²×C₁₃×#41	1	6	yes	—
1009	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1010	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1011	C₄	—	2	1	no	—
1012	C₄	—	2	4	no	—
1013	C₄	—	2	3	no	—
1014	C₄	—	2	3	no	—
1015	C₄	—	2	3	no	—
1016	C₄	—	2	12	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	3	no	—
1019	C₄	—	2	3	no	—
1020	C₄	—	2	4	no	—
1021	C₄	C₂²×C₁₃×#41	1	6	yes	—
1022	C₄	C₂²×C₁₃×#41	1	2	yes	—
1023	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1024	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1025	C₄	C₁₃×#585	1	2	yes	—
1026	C₂	—	2	2	no	—
1027	C₂	—	2	6	no	—
1028	C₂	—	4	3	no	—
1029	C₂	—	4	12	no	—
1030	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
1031	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂²×C₁₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3522	C₂	semidirect
2. C₁₃×#3519	C₂	semidirect
3. C₁₃×#3517	C₂	semidirect
4. C₁₃×#3514	C₂	semidirect
5. C₁₃×#3511	C₂	semidirect
6. C₁₃×#3508	C₂	semidirect
7. C₁₃×#3503	C₂	semidirect
8. C₁₃×#3498	C₂	semidirect
9. C₁₃×#3494	C₂	semidirect
10. C₁₃×#3488	C₂	semidirect
11. C₁₃×#3483	C₂	semidirect
12. C₁₃×#3481	C₂	semidirect
13. C₁₃×#3480	C₂	semidirect
14. D₄×C₁₃×#41	C₂	semidirect
15. C₁₃×#3460	C₂	semidirect
16. C₁₃×#3444	C₂	semidirect
17. C₂×C₁₃×#532	C₂	semidirect
18. C₄×C₁₃×H(5,𝔽₂)	C₂	semidirect
19. C₂×C₄×C₁₃×#41	C₂	semidirect
22. C₂²×C₁₃×#41	C₂²	semidirect
23. C₁₃×#559	C₂²	semidirect
24. C₁₃×#559	C₂²	semidirect
25. Q₈²×C₁₃	C₂²	semidirect
26. C₁₃×#557	C₂²	semidirect
27. C₁₃×#556	C₂²	semidirect
28. C₁₃×#555	C₂²	semidirect
29. C₁₃×#555	C₂²	semidirect
30. C₁₃×#554	C₂²	semidirect
31. C₁₃×#554	C₂²	semidirect
32. C₁₃×#553	C₂²	semidirect
33. C₁₃×#553	C₂²	semidirect
34. C₁₃×#553	C₂²	semidirect
35. C₁₃×#551	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
37. C₁₃×#550	C₂²	semidirect
38. C₁₃×#550	C₂²	semidirect
39. C₁₃×#550	C₂²	semidirect
40. C₁₃×#550	C₂²	semidirect
41. D₄×Q₈×C₁₃	C₂²	semidirect
42. C₁₃×#548	C₂²	semidirect
43. C₁₃×#548	C₂²	semidirect
44. C₁₃×#547	C₂²	semidirect
45. C₁₃×#547	C₂²	semidirect
46. C₁₃×#546	C₂²	semidirect
47. C₁₃×#546	C₂²	semidirect
48. C₁₃×#546	C₂²	semidirect
49. C₁₃×#546	C₂²	semidirect
50. D₄²×C₁₃	C₂²	semidirect
51. D₄²×C₁₃	C₂²	semidirect
52. D₄²×C₁₃	C₂²	semidirect
53. C₁₃×#544	C₂²	semidirect
54. C₁₃×#542	C₂²	semidirect
55. C₁₃×#542	C₂²	semidirect
56. C₁₃×#540	C₂²	semidirect
57. C₁₃×#540	C₂²	semidirect
58. C₁₃×#538	C₂²	semidirect
59. C₁₃×#537	C₂²	semidirect
60. C₁₃×#535	C₂²	semidirect
61. C₁₃×#535	C₂²	semidirect
62. C₁₃×#533	C₂²	semidirect
63. C₁₃×#533	C₂²	semidirect
64. C₁₃×#533	C₂²	semidirect
65. C₁₃×#532	C₂²	semidirect
66. C₁₃×#532	C₂²	semidirect
67. C₁₃×#532	C₂²	semidirect
68. C₁₃×#532	C₂²	semidirect
69. C₁₃×#532	C₂²	semidirect
70. C₁₃×#532	C₂²	semidirect
71. C₁₃×#532	C₂²	semidirect
72. C₁₃×#532	C₂²	semidirect
73. C₁₃×#532	C₂²	semidirect
74. C₁₃×#532	C₂²	semidirect
75. C₁₃×#532	C₂²	semidirect
76. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
77. C₂×C₁₃×#127	C₂²	semidirect
78. C₁₃×#529	C₂²	semidirect
79. C₁₃×#529	C₂²	semidirect
80. C₁₃×#529	C₂²	semidirect
81. C₁₃×#529	C₂²	semidirect
82. C₁₃×#529	C₂²	semidirect
83. C₁₃×#529	C₂²	semidirect
84. C₁₃×#529	C₂²	semidirect
85. C₂×C₁₃×#124	C₂²	semidirect
86. C₁₃×#525	C₂²	semidirect
87. C₁₃×#525	C₂²	semidirect
88. C₁₃×#525	C₂²	semidirect
89. C₁₃×#525	C₂²	semidirect
90. C₂×C₁₃×#121	C₂²	semidirect
91. C₂×C₁₃×#121	C₂²	semidirect
93. C₁₃×#520	C₂²	semidirect
94. C₁₃×#520	C₂²	semidirect
95. C₁₃×#518	C₂²	semidirect
96. C₁₃×#518	C₂²	semidirect
99. C₄×C₁₃×#41	C₂²	semidirect
100. C₄×C₁₃×#41	C₂²	semidirect
101. C₄×C₁₃×#41	C₂²	semidirect
102. C₄×C₁₃×#41	C₂²	semidirect
103. C₄×C₁₃×#41	C₂²	semidirect
104. C₄×C₁₃×#41	C₂²	semidirect
105. C₄×C₁₃×#41	C₂²	semidirect
106. C₄×C₁₃×#41	C₂²	semidirect
107. C₄×C₁₃×#41	C₂²	semidirect
108. C₄×C₁₃×#41	C₂²	semidirect
109. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
110. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
111. C₂×C₄×D₄×C₁₃	C₂²	semidirect
112. C₂×C₄×D₄×C₁₃	C₂²	semidirect
113. C₂×C₄×D₄×C₁₃	C₂²	semidirect
114. C₂×C₄×D₄×C₁₃	C₂²	semidirect
115. C₂×C₄×D₄×C₁₃	C₂²	semidirect
116. C₂×C₁₃×#117	C₂²	semidirect
117. C₂²×C₄²×C₁₃	C₂²	semidirect
291. #62800	C₁₃	direct (N × H)
304. C₁₃×#41	#41	semidirect
413. #3522	C₂×C₁₃	semidirect
414. #3519	C₂×C₁₃	semidirect
415. #3517	C₂×C₁₃	semidirect
416. #3514	C₂×C₁₃	semidirect
417. #3511	C₂×C₁₃	semidirect
418. #3508	C₂×C₁₃	semidirect
419. #3503	C₂×C₁₃	semidirect
420. #3498	C₂×C₁₃	semidirect
421. #3494	C₂×C₁₃	semidirect
422. #3488	C₂×C₁₃	semidirect
423. #3483	C₂×C₁₃	semidirect
424. #3481	C₂×C₁₃	semidirect
425. #3480	C₂×C₁₃	semidirect
426. D₄×#41	C₂×C₁₃	semidirect
427. #3460	C₂×C₁₃	semidirect
428. #3444	C₂×C₁₃	semidirect
429. C₂×#532	C₂×C₁₃	semidirect
430. C₄×H(5,𝔽₂)	C₂×C₁₃	semidirect
431. C₂×C₄×#41	C₂×C₁₃	semidirect
447. Q₈×C₁₃	C₂×#41	semidirect
460. D₄×C₁₃	C₂×#41	semidirect
482. C₂×C₄×C₁₃	C₂×#41	semidirect
483. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
501. C₂²×#41	C₂²×C₁₃	semidirect
502. #559	C₂²×C₁₃	semidirect
503. #559	C₂²×C₁₃	semidirect
504. Q₈²	C₂²×C₁₃	semidirect
505. #557	C₂²×C₁₃	semidirect
506. #556	C₂²×C₁₃	semidirect
507. #555	C₂²×C₁₃	semidirect
508. #555	C₂²×C₁₃	semidirect
509. #554	C₂²×C₁₃	semidirect
510. #554	C₂²×C₁₃	semidirect
511. #553	C₂²×C₁₃	semidirect
512. #553	C₂²×C₁₃	semidirect
513. #553	C₂²×C₁₃	semidirect
514. #551	C₂²×C₁₃	semidirect
515. #550	C₂²×C₁₃	semidirect
516. #550	C₂²×C₁₃	semidirect
517. #550	C₂²×C₁₃	semidirect
518. #550	C₂²×C₁₃	semidirect
519. #550	C₂²×C₁₃	semidirect
520. D₄×Q₈	C₂²×C₁₃	semidirect
521. #548	C₂²×C₁₃	semidirect
522. #548	C₂²×C₁₃	semidirect
523. #547	C₂²×C₁₃	semidirect
524. #547	C₂²×C₁₃	semidirect
525. #546	C₂²×C₁₃	semidirect
526. #546	C₂²×C₁₃	semidirect
527. #546	C₂²×C₁₃	semidirect
528. #546	C₂²×C₁₃	semidirect
529. D₄²	C₂²×C₁₃	semidirect
530. D₄²	C₂²×C₁₃	semidirect
531. D₄²	C₂²×C₁₃	semidirect
532. #544	C₂²×C₁₃	semidirect
533. #542	C₂²×C₁₃	semidirect
534. #542	C₂²×C₁₃	semidirect
535. #540	C₂²×C₁₃	semidirect
536. #540	C₂²×C₁₃	semidirect
537. #538	C₂²×C₁₃	semidirect
538. #537	C₂²×C₁₃	semidirect
539. #535	C₂²×C₁₃	semidirect
540. #535	C₂²×C₁₃	semidirect
541. #533	C₂²×C₁₃	semidirect
542. #533	C₂²×C₁₃	semidirect
543. #533	C₂²×C₁₃	semidirect
544. #532	C₂²×C₁₃	semidirect
545. #532	C₂²×C₁₃	semidirect
546. #532	C₂²×C₁₃	semidirect
547. #532	C₂²×C₁₃	semidirect
548. #532	C₂²×C₁₃	semidirect
549. #532	C₂²×C₁₃	semidirect
550. #532	C₂²×C₁₃	semidirect
551. #532	C₂²×C₁₃	semidirect
552. #532	C₂²×C₁₃	semidirect
553. #532	C₂²×C₁₃	semidirect
554. #532	C₂²×C₁₃	semidirect
555. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
556. C₂×#127	C₂²×C₁₃	semidirect
557. #529	C₂²×C₁₃	semidirect
558. #529	C₂²×C₁₃	semidirect
559. #529	C₂²×C₁₃	semidirect
560. #529	C₂²×C₁₃	semidirect
561. #529	C₂²×C₁₃	semidirect
562. #529	C₂²×C₁₃	semidirect
563. #529	C₂²×C₁₃	semidirect
564. C₂×#124	C₂²×C₁₃	semidirect
565. #525	C₂²×C₁₃	semidirect
566. #525	C₂²×C₁₃	semidirect
567. #525	C₂²×C₁₃	semidirect
568. #525	C₂²×C₁₃	semidirect
569. C₂×#121	C₂²×C₁₃	semidirect
570. C₂×#121	C₂²×C₁₃	semidirect
572. #520	C₂²×C₁₃	semidirect
573. #520	C₂²×C₁₃	semidirect
574. #518	C₂²×C₁₃	semidirect
575. #518	C₂²×C₁₃	semidirect
578. C₄×#41	C₂²×C₁₃	semidirect
579. C₄×#41	C₂²×C₁₃	semidirect
580. C₄×#41	C₂²×C₁₃	semidirect
581. C₄×#41	C₂²×C₁₃	semidirect
582. C₄×#41	C₂²×C₁₃	semidirect
583. C₄×#41	C₂²×C₁₃	semidirect
584. C₄×#41	C₂²×C₁₃	semidirect
585. C₄×#41	C₂²×C₁₃	semidirect
586. C₄×#41	C₂²×C₁₃	semidirect
587. C₄×#41	C₂²×C₁₃	semidirect
588. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
589. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
590. C₂×C₄×D₄	C₂²×C₁₃	semidirect
591. C₂×C₄×D₄	C₂²×C₁₃	semidirect
592. C₂×C₄×D₄	C₂²×C₁₃	semidirect
593. C₂×C₄×D₄	C₂²×C₁₃	semidirect
594. C₂×C₄×D₄	C₂²×C₁₃	semidirect
595. C₂×#117	C₂²×C₁₃	semidirect
596. C₂²×C₄²	C₂²×C₁₃	semidirect
819. #41	C₁₃×#41	semidirect
928. C₁₃	#62800	direct (N × H)
944. Q₈	C₂×C₁₃×#41	semidirect
957. D₄	C₂×C₁₃×#41	semidirect
979. C₂×C₄	C₂×C₁₃×#41	semidirect
980. C₂×C₄	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3522	2
C₁₃×#3519	2
C₁₃×#3517	2
C₁₃×#3514	2
C₁₃×#3511	2
C₁₃×#3508	2
C₁₃×#3503	2
C₁₃×#3498	2
C₁₃×#3494	2
C₁₃×#3488	2
C₁₃×#3483	2
C₁₃×#3481	2
C₁₃×#3480	2
D₄×C₁₃×#41	2
C₁₃×#3460	2
C₁₃×#3444	2
C₂×C₁₃×#532	2
C₄×C₁₃×H(5,𝔽₂)	2
C₂×C₄×C₁₃×#41	2
#62800	13

Subgroups — C13×#62800 #15749139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62800 #15749139