Subgroups — C₂×C₁₃×#3271 #15747368

Order 3328.

2826 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	C₂²×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3271	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#137	—	2	8	no	—
22	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#135	—	2	8	no	—
24	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
25	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#550	—	2	4	no	—
37	C₁₃×#550	C₂²	1	8	yes	complemented
38	C₁₃×#548	—	2	4	no	—
39	C₁₃×#548	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#127	—	2	1	no	—
41	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#124	—	2	1	no	—
43	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#121	—	2	1	no	—
47	C₂×C₁₃×#121	—	2	1	no	—
48	C₂×C₁₃×#121	—	2	1	no	—
49	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₁₃	—	2	1	no	—
55	C₂×C₄×D₄×C₁₃	—	2	1	no	—
56	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#496	C₂²	1	8	yes	complemented
58	C₁₃×#469	C₂²	1	8	yes	complemented
59	C₁₃×#465	C₂²	1	8	yes	complemented
60	C₁₃×#464	C₂²	1	8	yes	complemented
61	C₁₃×#460	C₂²	1	8	yes	complemented
62	C₁₃×#452	C₂²	1	8	yes	complemented
63	C₁₃×#449	C₂²	1	8	yes	complemented
64	C₁₃×#449	C₂²	1	8	yes	complemented
65	C₁₃×#448	C₂²	1	8	yes	complemented
66	C₁₃×#441	C₂²	1	8	yes	complemented
67	C₁₃×#435	C₂²	1	8	yes	complemented
68	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
78	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	2	2	no	—
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	—	2	4	no	—
83	C₂×C₁₃×#41	—	2	4	no	—
84	C₂×C₁₃×#41	—	2	4	no	—
85	C₂×C₁₃×#41	—	4	2	no	—
86	C₂×C₁₃×#41	—	4	2	no	—
87	C₂×C₁₃×#41	—	4	2	no	—
88	C₂×C₁₃×#41	C₂³	1	4	yes	—
89	C₂×C₁₃×#41	C₂³	1	4	yes	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂²×Q₈×C₁₃	—	2	1	no	—
92	C₂²×Q₈×C₁₃	—	2	2	no	—
93	C₂²×Q₈×C₁₃	—	2	4	no	—
94	C₂²×Q₈×C₁₃	—	4	2	no	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	—	2	1	no	—
103	C₂²×D₄×C₁₃	—	2	1	no	—
104	C₂²×D₄×C₁₃	—	2	1	no	—
105	C₂²×D₄×C₁₃	—	2	1	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
108	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	—	2	1	no	—
112	C₂³×C₄×C₁₃	—	2	1	no	—
113	C₂³×C₄×C₁₃	—	2	1	no	—
114	C₂³×C₄×C₁₃	—	2	1	no	—
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₁₃×#137	—	2	32	no	—
118	C₁₃×#135	—	2	32	no	—
119	C₂×C₁₃×Q₁₆	—	2	4	no	—
120	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
121	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
122	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
123	C₂×C₁₃×SD₁₆	—	2	4	no	—
124	C₂×C₁₃×SD₁₆	—	2	4	no	—
125	C₂×C₁₃×SD₁₆	—	2	4	no	—
126	C₂×C₁₃×SD₁₆	—	2	4	no	—
127	C₂×C₁₃×SD₁₆	—	4	2	no	—
128	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
132	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
133	C₂×C₁₃×D₈	—	2	4	no	—
134	C₂×C₁₃×D₈	—	4	2	no	—
135	C₂×C₁₃×D₈	C₂³	1	4	yes	—
136	C₂×C₁₃×D₈	C₂³	1	4	yes	—
137	C₂×C₁₃×M₁₆	—	2	4	no	—
138	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
139	C₂²×C₈×C₁₃	—	2	4	no	—
140	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
144	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	C₁₃×#127	—	2	8	no	—
146	C₁₃×#127	—	2	2	no	—
147	C₁₃×#127	C₂³	1	4	yes	—
148	C₁₃×#124	—	2	8	no	—
149	C₁₃×#124	—	2	2	no	—
150	C₁₃×#124	C₂³	1	4	yes	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	8	no	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₁₃×#121	—	2	8	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	8	no	—
159	C₁₃×#121	—	2	8	no	—
160	C₁₃×#121	C₂³	1	4	yes	—
161	C₁₃×#121	C₂³	1	4	yes	—
162	C₁₃×#121	C₂³	1	4	yes	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
167	C₄×D₄×C₁₃	—	2	8	no	—
168	C₄×D₄×C₁₃	—	2	8	no	—
169	C₄×D₄×C₁₃	D₄	1	4	yes	—
170	C₄×D₄×C₁₃	C₂³	1	4	yes	—
171	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
184	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	—	2	1	no	—
186	C₂×C₄²×C₁₃	—	2	1	no	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₁₃×#106	C₂³	1	4	yes	—
189	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
190	C₁₃×#103	C₂³	1	4	yes	—
191	C₁₃×#103	C₂³	1	4	yes	—
192	C₁₃×#103	C₂³	1	4	yes	—
193	C₁₃×#102	C₂³	1	4	yes	—
194	C₁₃×#102	C₂³	1	4	yes	—
195	C₁₃×#102	C₂³	1	4	yes	—
196	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₁₃×#97	C₂³	1	4	yes	—
199	C₂×#3271	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂⁴×C₁₃	—	2	1	no	—
201	C₂⁴×C₁₃	—	2	1	no	—
202	C₂⁴×C₁₃	—	2	1	no	—
203	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₁₃×#41	—	2	8	no	—
206	C₁₃×#41	—	2	8	no	—
207	C₁₃×#41	—	2	8	no	—
208	C₁₃×#41	—	4	4	no	—
209	C₁₃×#41	—	4	4	no	—
210	C₁₃×#41	—	4	4	no	—
211	C₁₃×#41	—	4	8	no	—
212	C₁₃×#41	—	4	8	no	—
213	C₁₃×#41	—	4	8	no	—
214	C₂×Q₈×C₁₃	—	2	1	no	—
215	C₂×Q₈×C₁₃	—	2	1	no	—
216	C₂×Q₈×C₁₃	—	2	4	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	2	no	—
219	C₂×Q₈×C₁₃	—	2	2	no	—
220	C₂×Q₈×C₁₃	—	2	8	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	2	no	—
223	C₂×Q₈×C₁₃	—	4	4	no	—
224	C₂×Q₈×C₁₃	—	4	4	no	—
225	C₂×Q₈×C₁₃	—	4	8	no	—
226	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
228	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
231	C₂×D₄×C₁₃	—	2	4	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	2	4	no	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	2	no	—
239	C₂×D₄×C₁₃	—	2	2	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	4	2	no	—
249	C₂×D₄×C₁₃	—	4	4	no	—
250	C₂×D₄×C₁₃	—	4	4	no	—
251	C₂×D₄×C₁₃	—	4	4	no	—
252	C₂×D₄×C₁₃	—	4	4	no	—
253	C₂×D₄×C₁₃	—	4	4	no	—
254	C₂×D₄×C₁₃	—	8	2	no	—
255	C₂×D₄×C₁₃	—	8	2	no	—
256	C₂×D₄×C₁₃	—	8	2	no	—
257	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	4	4	no	—
275	C₂²×C₄×C₁₃	—	4	4	no	—
276	C₂²×C₄×C₁₃	—	4	4	no	—
277	C₂²×C₄×C₁₃	—	4	4	no	—
278	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₁₃×Q₁₆	—	2	8	no	—
288	C₁₃×Q₁₆	C₂×D₄	1	16	yes	complemented
289	C₁₃×SD₁₆	—	2	8	no	—
290	C₁₃×SD₁₆	—	2	8	no	—
291	C₁₃×SD₁₆	—	2	8	no	—
292	C₁₃×SD₁₆	—	2	8	no	—
293	C₁₃×SD₁₆	—	4	4	no	—
294	C₁₃×D₈	—	2	8	no	—
295	C₁₃×D₈	—	4	4	no	—
296	C₁₃×M₁₆	—	2	8	no	—
297	C₂×C₈×C₁₃	—	2	2	no	—
298	C₂×C₈×C₁₃	—	2	2	no	—
299	C₂×C₈×C₁₃	—	2	2	no	—
300	C₂×C₈×C₁₃	—	2	8	no	—
301	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
302	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
303	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
304	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
305	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
306	C₁₃×C₄⋊C₄	—	2	4	no	—
307	C₁₃×C₄⋊C₄	—	2	4	no	—
308	C₁₃×C₄⋊C₄	—	2	4	no	—
309	C₁₃×C₄⋊C₄	—	2	1	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	C₂×D₄	1	2	yes	—
325	C₄²×C₁₃	C₂⁴	1	2	yes	—
326	C₂²×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
327	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
328	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
329	C₂×#548	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#3271	C₂×C₁₃	1	16	yes	direct product factor
331	C₂×#496	C₂×C₁₃	1	1	yes	characteristic, complemented
332	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
333	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
334	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
340	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	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	—	4	2	no	—
352	C₂³×C₁₃	—	4	2	no	—
353	C₂³×C₁₃	—	4	2	no	—
354	C₂³×C₁₃	—	4	2	no	—
355	C₂³×C₁₃	—	4	2	no	—
356	C₂³×C₁₃	—	4	2	no	—
357	C₂³×C₁₃	—	4	2	no	—
358	C₂³×C₁₃	—	4	2	no	—
359	C₂³×C₁₃	—	4	2	no	—
360	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
361	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
362	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₁₃	—	2	4	no	—
364	Q₈×C₁₃	—	2	4	no	—
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	2	no	—
369	Q₈×C₁₃	—	4	8	no	—
370	Q₈×C₁₃	—	4	2	no	—
371	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
372	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
373	D₄×C₁₃	—	2	2	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	2	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	2	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	4	4	no	—
380	D₄×C₁₃	—	4	8	no	—
381	D₄×C₁₃	—	4	8	no	—
382	D₄×C₁₃	—	4	8	no	—
383	D₄×C₁₃	—	4	8	no	—
384	D₄×C₁₃	—	4	8	no	—
385	D₄×C₁₃	—	4	2	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	4	2	no	—
388	D₄×C₁₃	—	8	4	no	—
389	D₄×C₁₃	—	8	4	no	—
390	D₄×C₁₃	—	8	4	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	4	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	2	2	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	4	no	—
400	C₂×C₄×C₁₃	—	2	4	no	—
401	C₂×C₄×C₁₃	—	2	2	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	—	4	8	no	—
409	C₂×C₄×C₁₃	—	4	8	no	—
410	C₂×C₄×C₁₃	—	4	8	no	—
411	C₂×C₄×C₁₃	—	4	8	no	—
412	C₂×C₄×C₁₃	—	4	2	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	2	no	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
423	C₈×C₁₃	—	2	2	no	—
424	C₈×C₁₃	—	2	2	no	—
425	C₈×C₁₃	—	2	2	no	—
426	C₈×C₁₃	C₂²×D₄	1	4	yes	—
427	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
429	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
430	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#137	—	2	8	no	—
432	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
433	C₂×#135	—	2	8	no	—
434	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
435	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
436	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
438	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
440	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
441	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
442	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
443	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
445	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
446	#550	—	2	4	no	—
447	#550	C₂²×C₁₃	1	8	yes	complemented
448	#548	—	2	4	no	—
449	#548	C₂²×C₁₃	1	8	yes	complemented
450	C₂×#127	—	2	1	no	—
451	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×#124	—	2	1	no	—
453	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₂²⋊Q₈	—	2	1	no	—
455	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×#121	—	2	1	no	—
457	C₂×#121	—	2	1	no	—
458	C₂×#121	—	2	1	no	—
459	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
461	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×C₄×D₄	—	2	1	no	—
465	C₂×C₄×D₄	—	2	1	no	—
466	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
467	#496	C₂²×C₁₃	1	8	yes	complemented
468	#469	C₂²×C₁₃	1	8	yes	complemented
469	#465	C₂²×C₁₃	1	8	yes	complemented
470	#464	C₂²×C₁₃	1	8	yes	complemented
471	#460	C₂²×C₁₃	1	8	yes	complemented
472	#452	C₂²×C₁₃	1	8	yes	complemented
473	#449	C₂²×C₁₃	1	8	yes	complemented
474	#449	C₂²×C₁₃	1	8	yes	complemented
475	#448	C₂²×C₁₃	1	8	yes	complemented
476	#441	C₂²×C₁₃	1	8	yes	complemented
477	#435	C₂²×C₁₃	1	8	yes	complemented
478	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
485	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
486	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
488	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	2	2	no	—
491	C₂²×C₁₃	—	2	2	no	—
492	C₂²×C₁₃	—	2	2	no	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	2	2	no	—
495	C₂²×C₁₃	—	4	4	no	—
496	C₂²×C₁₃	—	4	4	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	8	4	no	—
507	C₂²×C₁₃	—	8	4	no	—
508	C₂²×C₁₃	—	8	4	no	—
509	C₂²×C₁₃	D₄²	1	2	yes	—
510	C₂²×C₁₃	#575	1	2	yes	—
511	C₂²×C₁₃	#577	1	2	yes	—
512	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	4	no	—
516	C₄×C₁₃	—	2	4	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	2	no	—
519	C₄×C₁₃	—	4	2	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	D₄²	1	2	yes	—
523	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂×#41	—	2	2	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	—	2	2	no	—
528	C₂×#41	—	2	4	no	—
529	C₂×#41	—	2	4	no	—
530	C₂×#41	—	2	4	no	—
531	C₂×#41	—	4	2	no	—
532	C₂×#41	—	4	2	no	—
533	C₂×#41	—	4	2	no	—
534	C₂×#41	C₂³×C₁₃	1	4	yes	—
535	C₂×#41	C₂³×C₁₃	1	4	yes	—
536	C₂×#41	C₂³×C₁₃	1	4	yes	—
537	C₂²×Q₈	—	2	1	no	—
538	C₂²×Q₈	—	2	2	no	—
539	C₂²×Q₈	—	2	4	no	—
540	C₂²×Q₈	—	4	2	no	—
541	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
543	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂³×C₄	—	2	1	no	—
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	—	2	1	no	—
561	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
563	#137	—	2	32	no	—
564	#135	—	2	32	no	—
565	C₂×Q₁₆	—	2	4	no	—
566	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
567	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
568	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
569	C₂×SD₁₆	—	2	4	no	—
570	C₂×SD₁₆	—	2	4	no	—
571	C₂×SD₁₆	—	2	4	no	—
572	C₂×SD₁₆	—	2	4	no	—
573	C₂×SD₁₆	—	4	2	no	—
574	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
575	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
576	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
577	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
578	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
579	C₂×D₈	—	2	4	no	—
580	C₂×D₈	—	4	2	no	—
581	C₂×D₈	C₂³×C₁₃	1	4	yes	—
582	C₂×D₈	C₂³×C₁₃	1	4	yes	—
583	C₂×M₁₆	—	2	4	no	—
584	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
585	C₂²×C₈	—	2	4	no	—
586	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
587	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
588	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
589	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
590	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
591	#127	—	2	8	no	—
592	#127	—	2	2	no	—
593	#127	C₂³×C₁₃	1	4	yes	—
594	#124	—	2	8	no	—
595	#124	—	2	2	no	—
596	#124	C₂³×C₁₃	1	4	yes	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	8	no	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
600	#121	—	2	8	no	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	8	no	—
605	#121	—	2	8	no	—
606	#121	C₂³×C₁₃	1	4	yes	—
607	#121	C₂³×C₁₃	1	4	yes	—
608	#121	C₂³×C₁₃	1	4	yes	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
612	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
613	C₄×D₄	—	2	8	no	—
614	C₄×D₄	—	2	8	no	—
615	C₄×D₄	D₄×C₁₃	1	4	yes	—
616	C₄×D₄	C₂³×C₁₃	1	4	yes	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
634	#106	C₂³×C₁₃	1	4	yes	—
635	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
636	#103	C₂³×C₁₃	1	4	yes	—
637	#103	C₂³×C₁₃	1	4	yes	—
638	#103	C₂³×C₁₃	1	4	yes	—
639	#102	C₂³×C₁₃	1	4	yes	—
640	#102	C₂³×C₁₃	1	4	yes	—
641	#102	C₂³×C₁₃	1	4	yes	—
642	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
643	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
644	#97	C₂³×C₁₃	1	4	yes	—
645	C₂×C₁₃	—	4	2	no	—
646	C₂×C₁₃	—	4	2	no	—
647	C₂×C₁₃	—	8	2	no	—
648	C₂×C₁₃	—	8	2	no	—
649	C₂×C₁₃	—	8	2	no	—
650	C₂×C₁₃	#3271	1	4	yes	direct product factor
651	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
652	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
653	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
654	C₂⁴	—	2	1	no	—
655	C₂⁴	—	2	1	no	—
656	C₂⁴	—	2	1	no	—
657	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
659	#41	—	2	8	no	—
660	#41	—	2	8	no	—
661	#41	—	2	8	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	#41	—	4	4	no	—
665	#41	—	4	8	no	—
666	#41	—	4	8	no	—
667	#41	—	4	8	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	4	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	8	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	4	4	no	—
678	C₂×Q₈	—	4	4	no	—
679	C₂×Q₈	—	4	8	no	—
680	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
681	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
682	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	8	2	no	—
709	C₂×D₄	—	8	2	no	—
710	C₂×D₄	—	8	2	no	—
711	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
712	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	4	4	no	—
729	C₂²×C₄	—	4	4	no	—
730	C₂²×C₄	—	4	4	no	—
731	C₂²×C₄	—	4	4	no	—
732	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
737	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
741	Q₁₆	—	2	8	no	—
742	Q₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
743	SD₁₆	—	2	8	no	—
744	SD₁₆	—	2	8	no	—
745	SD₁₆	—	2	8	no	—
746	SD₁₆	—	2	8	no	—
747	SD₁₆	—	4	4	no	—
748	D₈	—	2	8	no	—
749	D₈	—	4	4	no	—
750	M₁₆	—	2	8	no	—
751	C₂×C₈	—	2	2	no	—
752	C₂×C₈	—	2	2	no	—
753	C₂×C₈	—	2	2	no	—
754	C₂×C₈	—	2	8	no	—
755	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
756	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
757	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
758	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
759	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
775	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	C₂×D₄×C₁₃	1	2	yes	—
779	C₄²	C₂⁴×C₁₃	1	2	yes	—
780	C₁₃	C₂×#3271	1	1	yes	characteristic, direct product factor, Sylow
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	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	2	no	—
790	C₂³	—	4	2	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	2	no	—
794	C₂³	—	4	2	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
800	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
801	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	Q₈	—	2	4	no	—
803	Q₈	—	2	4	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	2	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	4	8	no	—
809	Q₈	—	4	2	no	—
810	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
811	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	2	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	8	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	8	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	2	no	—
826	D₄	—	4	2	no	—
827	D₄	—	8	4	no	—
828	D₄	—	8	4	no	—
829	D₄	—	8	4	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	4	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	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	4	8	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	8	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
858	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
859	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
860	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
861	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
862	C₈	—	2	2	no	—
863	C₈	—	2	2	no	—
864	C₈	—	2	2	no	—
865	C₈	C₂²×D₄×C₁₃	1	4	yes	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	4	4	no	—
873	C₂²	—	4	4	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	8	4	no	—
884	C₂²	—	8	4	no	—
885	C₂²	—	8	4	no	—
886	C₂²	D₄²×C₁₃	1	2	yes	—
887	C₂²	C₁₃×#575	1	2	yes	—
888	C₂²	C₁₃×#577	1	2	yes	—
889	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	4	no	—
895	C₄	—	2	4	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	D₄²×C₁₃	1	2	yes	—
900	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
901	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂	—	4	2	no	—
903	C₂	—	4	2	no	—
904	C₂	—	8	2	no	—
905	C₂	—	8	2	no	—
906	C₂	—	8	2	no	—
907	C₂	C₁₃×#3271	1	4	yes	direct product factor
908	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
909	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
910	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#137	C₂	semidirect
2. C₂²×C₁₃×#135	C₂	semidirect
3. C₂×C₁₃×#550	C₂	semidirect
4. C₂×C₁₃×#548	C₂	semidirect
5. C₁₃×#3271	C₂	direct (N × H)
6. C₂×C₁₃×#496	C₂	semidirect
7. C₂×C₁₃×#469	C₂	semidirect
8. C₂×C₁₃×#465	C₂	semidirect
9. C₂×C₁₃×#464	C₂	semidirect
10. C₂×C₁₃×#460	C₂	semidirect
11. C₂×C₁₃×#452	C₂	semidirect
12. C₂×C₁₃×#449	C₂	semidirect
13. C₂×C₁₃×#449	C₂	semidirect
14. C₂×C₁₃×#448	C₂	semidirect
15. C₂×C₁₃×#441	C₂	semidirect
16. C₂×C₁₃×#435	C₂	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
24. C₂×C₁₃×#135	C₂²	semidirect
37. C₁₃×#550	C₂²	semidirect
39. C₁₃×#548	C₂²	semidirect
57. C₁₃×#496	C₂²	semidirect
58. C₁₃×#469	C₂²	semidirect
59. C₁₃×#465	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#460	C₂²	semidirect
62. C₁₃×#452	C₂²	semidirect
63. C₁₃×#449	C₂²	semidirect
64. C₁₃×#449	C₂²	semidirect
65. C₁₃×#448	C₂²	semidirect
66. C₁₃×#441	C₂²	semidirect
67. C₁₃×#435	C₂²	semidirect
120. C₂×C₁₃×Q₁₆	D₄	semidirect
199. C₂×#3271	C₁₃	direct (N × H)
288. C₁₃×Q₁₆	C₂×D₄	semidirect
326. C₂²×#137	C₂×C₁₃	semidirect
327. C₂²×#135	C₂×C₁₃	semidirect
328. C₂×#550	C₂×C₁₃	semidirect
329. C₂×#548	C₂×C₁₃	semidirect
330. #3271	C₂×C₁₃	direct (N × H)
331. C₂×#496	C₂×C₁₃	semidirect
332. C₂×#469	C₂×C₁₃	semidirect
333. C₂×#465	C₂×C₁₃	semidirect
334. C₂×#464	C₂×C₁₃	semidirect
335. C₂×#460	C₂×C₁₃	semidirect
336. C₂×#452	C₂×C₁₃	semidirect
337. C₂×#449	C₂×C₁₃	semidirect
338. C₂×#449	C₂×C₁₃	semidirect
339. C₂×#448	C₂×C₁₃	semidirect
340. C₂×#441	C₂×C₁₃	semidirect
341. C₂×#435	C₂×C₁₃	semidirect
432. C₂×#137	C₂²×C₁₃	semidirect
434. C₂×#135	C₂²×C₁₃	semidirect
447. #550	C₂²×C₁₃	semidirect
449. #548	C₂²×C₁₃	semidirect
467. #496	C₂²×C₁₃	semidirect
468. #469	C₂²×C₁₃	semidirect
469. #465	C₂²×C₁₃	semidirect
470. #464	C₂²×C₁₃	semidirect
471. #460	C₂²×C₁₃	semidirect
472. #452	C₂²×C₁₃	semidirect
473. #449	C₂²×C₁₃	semidirect
474. #449	C₂²×C₁₃	semidirect
475. #448	C₂²×C₁₃	semidirect
476. #441	C₂²×C₁₃	semidirect
477. #435	C₂²×C₁₃	semidirect
566. C₂×Q₁₆	D₄×C₁₃	semidirect
650. C₂×C₁₃	#3271	direct (N × H)
742. Q₁₆	C₂×D₄×C₁₃	semidirect
780. C₁₃	C₂×#3271	direct (N × H)
907. C₂	C₁₃×#3271	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#137	2
C₂²×C₁₃×#135	2
C₂×C₁₃×#550	2
C₂×C₁₃×#548	2
C₁₃×#3271	2
C₂×C₁₃×#496	2
C₂×C₁₃×#469	2
C₂×C₁₃×#465	2
C₂×C₁₃×#464	2
C₂×C₁₃×#460	2
C₂×C₁₃×#452	2
C₂×C₁₃×#449	2
C₂×C₁₃×#448	2
C₂×C₁₃×#441	2
C₂×C₁₃×#435	2
C₂×#3271	13

Subgroups — C2×C13×#3271 #15747368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3271 #15747368