Subgroups — C₂×#13115076 #15863816

Order 3328.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718785	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718779	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718897	C₂	1	1	yes	maximal, characteristic
4	C₂²×#88077	C₂	1	1	yes	maximal, characteristic
5	#13115076	C₂	1	8	yes	maximal, direct product factor
6	C₂×#11718148	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₁₃×#568	—	2	2	no	—
11	C₁₃×#568	—	2	2	no	—
12	C₁₃×#568	—	2	2	no	—
13	C₁₃×#568	C₂²	1	4	yes	—
14	C₂×C₁₃×#131	—	2	2	no	—
15	C₂×C₁₃×#131	—	2	2	no	—
16	C₂²×C₁₃×M₁₆	—	2	2	no	—
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×#88180	C₂²	1	1	yes	characteristic
20	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂²×#6099	C₂²	1	1	yes	characteristic
22	C₂²×#6099	C₂²	1	1	yes	characteristic
23	#11718897	—	2	2	no	—
24	#11718897	C₂²	1	4	yes	—
25	C₂×#88077	—	2	2	no	—
26	C₂×#88077	C₄	1	2	yes	complemented
27	C₂×#88077	C₄	1	4	yes	complemented
28	C₂×#88077	C₄	1	2	yes	complemented
29	C₂×#88077	C₂²	1	4	yes	—
30	#11718785	—	2	2	no	—
31	#11718785	C₂²	1	4	yes	complemented
32	C₂×#88062	—	2	2	no	—
33	#11718779	—	2	2	no	—
34	#11718779	C₂²	1	4	yes	complemented
35	C₂×#88054	—	2	2	no	—
36	#11718148	C₂²	1	4	yes	complemented
37	#11718147	C₂²	1	4	yes	complemented
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	—	2	1	no	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
45	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×#41	D₄	1	2	yes	—
47	C₂×C₁₃×#41	D₄	1	2	yes	—
48	C₂×C₁₃×#41	Q₈	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₃	Q₈	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×Dic₁₃	—	2	1	no	—
56	C₁₃×#131	—	2	8	no	—
57	C₁₃×#131	—	2	8	no	—
58	C₁₃×#131	—	2	8	no	—
59	C₁₃×#131	—	2	8	no	—
60	C₂×C₁₃×M₁₆	—	2	4	no	—
61	C₂×C₁₃×M₁₆	—	2	8	no	—
62	C₂×C₁₃×M₁₆	—	2	1	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂×C₁₃×M₁₆	—	2	1	no	—
67	C₂×C₁₃×M₁₆	—	2	1	no	—
68	C₂×C₁₃×M₁₆	—	2	1	no	—
69	C₂×C₁₃×M₁₆	—	2	8	no	—
70	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
71	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
72	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
73	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₃	—	2	4	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₂²×C₈×C₁₃	D₄	1	2	yes	—
78	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
79	#88180	—	2	1	no	—
80	#88180	—	2	1	no	—
81	#88180	—	2	1	no	—
82	#88180	C₂³	1	2	yes	—
83	C₂×C₄⋊Dic₁₃	—	2	1	no	—
84	C₂×C₄×Dic₁₃	—	2	1	no	—
85	C₂×C₄×Dic₁₃	—	2	1	no	—
86	C₂×C₄×Dic₁₃	—	2	1	no	—
87	C₂×C₄×Dic₁₃	—	2	1	no	—
88	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
90	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
92	C₂×#6099	—	2	1	no	—
93	C₂×#6099	—	2	1	no	—
94	C₂×#6099	—	2	1	no	—
95	C₂×#6099	—	2	1	no	—
96	C₂×#6099	—	2	1	no	—
97	C₂×#6099	—	2	1	no	—
98	C₂×#6099	—	2	1	no	—
99	C₂×#6099	—	2	1	no	—
100	C₂×#6099	C₂×C₄	1	2	yes	—
101	C₂×#6099	C₂×C₄	1	2	yes	—
102	C₂×#6099	C₂³	1	2	yes	—
103	C₂×#6099	C₂³	1	2	yes	—
104	C₂²×#1055	—	2	1	no	—
105	C₂²×#1055	—	2	1	no	—
106	#88077	—	2	8	no	—
107	#88077	C₂×C₄	1	8	yes	complemented
108	#88077	C₂×C₄	1	8	yes	complemented
109	#88062	—	2	8	no	—
110	#88054	—	2	8	no	—
111	C₂×#1861	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	—	2	1	no	—
113	C₂⁴×C₁₃	#41	1	1	yes	characteristic
114	C₁₃×#41	—	2	2	no	—
115	C₁₃×#41	—	2	2	no	—
116	C₁₃×#41	—	2	2	no	—
117	C₁₃×#41	—	2	2	no	—
118	C₁₃×#41	—	2	2	no	—
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	C₄⋊C₄	1	4	yes	—
127	C₁₃×#41	C₄⋊C₄	1	4	yes	—
128	C₁₃×#41	C₂²×C₄	1	4	yes	—
129	C₁₃×#41	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	C₄⋊C₄	1	2	yes	—
134	C₂×Q₈×C₁₃	C₄⋊C₄	1	2	yes	—
135	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
146	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
147	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂²×Dic₁₃	—	2	1	no	—
170	C₂²×Dic₁₃	—	2	2	no	—
171	C₂²×Dic₁₃	—	2	1	no	—
172	C₂²×Dic₁₃	—	2	2	no	—
173	C₂²×Dic₁₃	—	4	4	no	—
174	C₂²×Dic₁₃	—	4	1	no	—
175	C₁₃×M₁₆	—	2	16	no	—
176	C₁₃×M₁₆	—	2	2	no	—
177	C₁₃×M₁₆	—	2	2	no	—
178	C₁₃×M₁₆	—	2	2	no	—
179	C₁₃×M₁₆	—	2	2	no	—
180	C₁₃×M₁₆	—	2	2	no	—
181	C₁₃×M₁₆	—	2	2	no	—
182	C₁₃×M₁₆	—	2	2	no	—
183	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
184	C₂×C₈×C₁₃	—	2	16	no	—
185	C₂×C₈×C₁₃	—	2	2	no	—
186	C₂×C₈×C₁₃	—	2	2	no	—
187	C₂×C₈×C₁₃	—	2	2	no	—
188	C₂×C₈×C₁₃	—	2	2	no	—
189	C₂×C₈×C₁₃	—	2	2	no	—
190	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
191	C₂²⋊Dic₁₃	—	2	2	no	—
192	C₂²⋊Dic₁₃	—	4	1	no	—
193	C₄⋊Dic₁₃	—	2	2	no	—
194	C₄⋊Dic₁₃	—	4	1	no	—
195	C₄×Dic₁₃	—	2	1	no	—
196	C₄×Dic₁₃	—	2	2	no	—
197	C₄×Dic₁₃	—	2	1	no	—
198	C₄×Dic₁₃	—	2	2	no	—
199	C₄×Dic₁₃	—	2	2	no	—
200	C₄×Dic₁₃	—	4	1	no	—
201	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
202	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
203	#6099	—	2	2	no	—
204	#6099	—	2	2	no	—
205	#6099	—	2	2	no	—
206	#6099	—	2	2	no	—
207	#6099	—	2	2	no	—
208	#6099	—	4	1	no	—
209	#6099	—	4	1	no	—
210	#6099	C₂²×C₄	1	4	yes	—
211	C₂×#1055	—	2	2	no	—
212	C₂×#1055	—	2	2	no	—
213	C₂×#1055	—	2	2	no	—
214	C₂×#1055	—	2	2	no	—
215	C₂×#1055	—	4	1	no	—
216	C₂×#1055	—	4	1	no	—
217	C₂×#568	D₁₃	1	1	yes	characteristic
218	C₂×#430	—	13	1	no	—
219	C₂×#423	—	13	1	no	—
220	C₂×#421	—	13	1	no	—
221	C₂²×#104	—	13	1	no	—
222	#1861	—	13	8	no	—
223	C₂×#344	—	13	1	no	—
224	C₂×#339	—	13	1	no	—
225	C₂³×C₁₃	—	2	2	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	4	2	no	—
229	C₂³×C₁₃	—	8	2	no	—
230	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
231	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
232	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
233	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂³×C₁₃	#123	1	1	yes	characteristic
235	C₂³×C₁₃	#123	1	1	yes	characteristic
236	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	2	2	no	—
240	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	2	2	no	—
246	D₄×C₁₃	—	2	2	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
267	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
268	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
269	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
276	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
277	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
284	C₂×Dic₁₃	—	2	4	no	—
285	C₂×Dic₁₃	—	2	2	no	—
286	C₂×Dic₁₃	—	2	2	no	—
287	C₂×Dic₁₃	—	4	4	no	—
288	C₂×Dic₁₃	—	4	4	no	—
289	C₂×Dic₁₃	—	4	2	no	—
290	C₂×Dic₁₃	—	4	2	no	—
291	C₂×Dic₁₃	—	8	2	no	—
292	C₈×C₁₃	—	2	4	no	—
293	C₈×C₁₃	—	2	4	no	—
294	#1055	—	2	4	no	—
295	#1055	—	4	2	no	—
296	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
297	#568	—	2	2	no	—
298	#568	—	2	2	no	—
299	#568	—	2	2	no	—
300	#568	C₂×D₁₃	1	4	yes	—
301	C₂×#131	—	2	2	no	—
302	C₂×#131	—	2	2	no	—
303	C₂²×M₁₆	—	2	2	no	—
304	C₂²×M₁₆	—	13	1	no	—
305	C₂²×M₁₆	—	13	1	no	—
306	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
307	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
308	C₂×#117	—	13	1	no	—
309	C₂²×C₄²	—	13	1	no	—
310	#430	—	13	4	no	—
311	#430	—	26	2	no	—
312	C₂×#108	—	26	2	no	—
313	#423	—	13	4	no	—
314	#423	—	26	2	no	—
315	C₂×C₄⋊C₈	—	26	2	no	—
316	#421	—	13	4	no	—
317	#421	—	26	2	no	—
318	C₂×#104	—	13	2	no	—
319	C₂×#104	—	13	4	no	—
320	C₂×#104	—	13	2	no	—
321	C₂×#104	—	13	4	no	—
322	C₂×#104	—	26	2	no	—
323	#344	—	13	4	no	—
324	#339	—	13	4	no	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	4	no	—
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	—	8	2	no	—
335	C₂²×C₁₃	—	8	2	no	—
336	C₂²×C₁₃	#385	1	1	yes	characteristic
337	C₂²×C₁₃	#385	1	1	yes	characteristic
338	C₂²×C₁₃	#385	1	1	yes	characteristic
339	C₂²×C₁₃	#385	1	1	yes	characteristic
340	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
341	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
342	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
343	C₄×C₁₃	—	2	4	no	—
344	C₄×C₁₃	#385	1	1	yes	characteristic
345	C₄×C₁₃	#385	1	1	yes	characteristic
346	C₄×C₁₃	#385	1	1	yes	characteristic
347	C₄×C₁₃	#385	1	1	yes	characteristic
348	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
349	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
350	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
351	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
352	Dic₁₃	—	2	4	no	—
353	Dic₁₃	—	4	2	no	—
354	Dic₁₃	—	8	2	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	Dic₂₆	1	2	yes	—
362	C₂×#41	C₄×D₁₃	1	2	yes	—
363	C₂×#41	C₄×D₁₃	1	2	yes	—
364	C₂×#41	C₂²⋊D₁₃	1	2	yes	—
365	C₂×#41	C₂²⋊D₁₃	1	2	yes	—
366	C₂×#41	C₂²×D₁₃	1	2	yes	—
367	C₂²×Q₈	Dic₂₆	1	1	yes	characteristic
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	Dic₂₆	1	1	yes	characteristic
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	26	1	no	—
372	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
373	#131	—	2	8	no	—
374	#131	—	2	8	no	—
375	#131	—	2	8	no	—
376	#131	—	2	8	no	—
377	C₂×M₁₆	—	2	4	no	—
378	C₂×M₁₆	—	2	8	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	8	no	—
387	C₂×M₁₆	—	13	2	no	—
388	C₂×M₁₆	—	13	2	no	—
389	C₂×M₁₆	—	13	2	no	—
390	C₂×M₁₆	—	13	2	no	—
391	C₂×M₁₆	—	26	1	no	—
392	C₂×M₁₆	—	26	1	no	—
393	C₂×M₁₆	—	26	1	no	—
394	C₂×M₁₆	—	26	1	no	—
395	C₂×M₁₆	—	26	1	no	—
396	C₂×M₁₆	—	26	1	no	—
397	C₂×M₁₆	—	26	1	no	—
398	C₂×M₁₆	—	26	1	no	—
399	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
400	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
401	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
402	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
403	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
404	C₂²×C₈	—	2	4	no	—
405	C₂²×C₈	—	2	1	no	—
406	C₂²×C₈	—	26	1	no	—
407	C₂²×C₈	—	26	1	no	—
408	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
409	#117	—	13	2	no	—
410	#117	—	26	1	no	—
411	#117	—	26	1	no	—
412	#117	—	26	1	no	—
413	C₂×C₄⋊C₄	—	26	1	no	—
414	C₂×C₂²⋊C₄	—	26	1	no	—
415	C₂×C₄²	—	13	1	no	—
416	C₂×C₄²	—	13	2	no	—
417	C₂×C₄²	—	13	1	no	—
418	C₂×C₄²	—	13	2	no	—
419	C₂×C₄²	—	26	1	no	—
420	C₂×C₄²	—	26	1	no	—
421	C₂×C₄²	—	26	1	no	—
422	C₂×C₄²	—	26	1	no	—
423	#108	—	26	8	no	—
424	C₄⋊C₈	—	26	8	no	—
425	#104	—	13	8	no	—
426	#104	—	13	8	no	—
427	#104	—	26	8	no	—
428	C₂×C₁₃	—	2	1	no	—
429	C₂×C₁₃	—	2	1	no	—
430	C₂×C₁₃	—	2	1	no	—
431	C₂×C₁₃	—	2	1	no	—
432	C₂×C₁₃	—	2	1	no	—
433	C₂×C₁₃	—	2	1	no	—
434	C₂×C₁₃	—	4	4	no	—
435	C₂×C₁₃	#1861	1	2	yes	complemented
436	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
437	C₂⁴	—	2	1	no	—
438	C₂⁴	#6127	1	1	yes	characteristic
439	#41	—	2	2	no	—
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	#6101	1	4	yes	—
452	#41	#6101	1	4	yes	—
453	#41	C₂×C₄×D₁₃	1	4	yes	—
454	#41	C₂×C₂²⋊D₁₃	1	4	yes	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	#6101	1	2	yes	—
459	C₂×Q₈	#6101	1	2	yes	—
460	C₂×Q₈	C₂×Dic₂₆	1	2	yes	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	#6101	1	2	yes	—
471	C₂×D₄	#6101	1	2	yes	—
472	C₂×D₄	C₂×Dic₂₆	1	2	yes	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	26	1	no	—
481	C₂²×C₄	—	26	2	no	—
482	C₂²×C₄	—	26	1	no	—
483	C₂²×C₄	—	26	2	no	—
484	C₂²×C₄	—	52	4	no	—
485	C₂²×C₄	—	52	1	no	—
486	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
487	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
490	C₂²×C₄	#6127	1	1	yes	characteristic
491	C₂²×C₄	#6127	1	1	yes	characteristic
492	C₂²×C₄	#6127	1	1	yes	characteristic
493	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
500	M₁₆	—	2	16	no	—
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	2	2	no	—
505	M₁₆	—	2	2	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	13	4	no	—
509	M₁₆	—	26	2	no	—
510	M₁₆	—	26	2	no	—
511	M₁₆	—	26	2	no	—
512	M₁₆	—	26	2	no	—
513	M₁₆	—	26	2	no	—
514	M₁₆	—	52	1	no	—
515	M₁₆	—	52	1	no	—
516	M₁₆	C₂×C₂²⋊D₁₃	1	4	yes	—
517	C₂×C₈	—	2	16	no	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	26	2	no	—
524	C₂×C₈	—	26	2	no	—
525	C₂×C₈	—	26	2	no	—
526	C₂×C₈	—	26	2	no	—
527	C₂×C₈	—	52	1	no	—
528	C₂×C₈	—	52	1	no	—
529	C₂×C₈	C₂×C₂²⋊D₁₃	1	4	yes	—
530	C₄⋊C₄	—	26	2	no	—
531	C₄⋊C₄	—	52	1	no	—
532	C₂²⋊C₄	—	26	2	no	—
533	C₂²⋊C₄	—	52	1	no	—
534	C₄²	—	13	2	no	—
535	C₄²	—	13	2	no	—
536	C₄²	—	26	1	no	—
537	C₄²	—	26	2	no	—
538	C₄²	—	26	1	no	—
539	C₄²	—	26	2	no	—
540	C₄²	—	26	2	no	—
541	C₄²	—	52	1	no	—
542	C₁₃	C₂×#1861	1	1	yes	characteristic, complemented, Sylow
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	#88178	1	1	yes	characteristic
549	C₂³	#88178	1	1	yes	characteristic
550	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
551	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
552	C₂³	#88183	1	1	yes	characteristic
553	C₂³	#88183	1	1	yes	characteristic
554	C₂³	C₂×#6127	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	C₂×#6101	1	4	yes	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	C₂×#6101	1	4	yes	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	26	4	no	—
575	C₂×C₄	—	26	2	no	—
576	C₂×C₄	—	26	2	no	—
577	C₂×C₄	—	52	4	no	—
578	C₂×C₄	—	52	4	no	—
579	C₂×C₄	—	52	2	no	—
580	C₂×C₄	—	52	2	no	—
581	C₂×C₄	—	104	2	no	—
582	C₂×C₄	C₂×#6101	1	1	yes	characteristic
583	C₂×C₄	C₂×#6101	1	1	yes	characteristic
584	C₂×C₄	C₂×#6101	1	1	yes	characteristic
585	C₂×C₄	C₂×#6101	1	1	yes	characteristic
586	C₂×C₄	#88178	1	1	yes	characteristic
587	C₂×C₄	#88178	1	1	yes	characteristic
588	C₂×C₄	#88178	1	1	yes	characteristic
589	C₂×C₄	#88178	1	1	yes	characteristic
590	C₂×C₄	#88178	1	1	yes	characteristic
591	C₂×C₄	#88178	1	1	yes	characteristic
592	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
593	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
594	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
595	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
596	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
597	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
598	C₂×C₄	#88183	1	1	yes	characteristic
599	C₂×C₄	#88183	1	1	yes	characteristic
600	C₂×C₄	#88207	1	1	yes	characteristic
601	C₂×C₄	#88207	1	1	yes	characteristic
602	C₂×C₄	#88207	1	1	yes	characteristic
603	C₂×C₄	#88207	1	1	yes	characteristic
604	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
605	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂×#6127	1	1	yes	characteristic
607	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	2	4	no	—
612	C₈	—	26	4	no	—
613	C₈	—	52	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	#11718871	1	1	yes	characteristic
626	C₂²	#11718871	1	1	yes	characteristic
627	C₂²	#11718871	1	1	yes	characteristic
628	C₂²	#11718871	1	1	yes	characteristic
629	C₂²	C₂×#88178	1	1	yes	characteristic
630	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
631	C₂²	C₂×#88183	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	26	4	no	—
634	C₄	—	52	2	no	—
635	C₄	—	104	2	no	—
636	C₄	#11718871	1	1	yes	characteristic
637	C₄	#11718871	1	1	yes	characteristic
638	C₄	#11718871	1	1	yes	characteristic
639	C₄	#11718871	1	1	yes	characteristic
640	C₄	C₂²×#6101	1	1	yes	characteristic
641	C₄	C₂×#88178	1	1	yes	characteristic
642	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
643	C₄	C₂×#88207	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	4	4	no	—
651	C₂	#13115076	1	2	yes	direct product factor
652	C₂	C₂×#11718871	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88207
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#568	C₂
socle	C₂²×C₁₃	#385
prime radical	C₂²×C₁₃×#41	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#568	D₁₃
hypocenter	C₁₃	C₂×#1861
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
1. C₂×#11718785	C₂	semidirect
2. C₂×#11718779	C₂	semidirect
5. #13115076	C₂	direct (N × H)
6. C₂×#11718148	C₂	semidirect
7. C₂×#11718147	C₂	semidirect
26. C₂×#88077	C₄	semidirect
27. C₂×#88077	C₄	semidirect
28. C₂×#88077	C₄	semidirect
31. #11718785	C₂²	semidirect
34. #11718779	C₂²	semidirect
36. #11718148	C₂²	semidirect
37. #11718147	C₂²	semidirect
107. #88077	C₂×C₄	semidirect
108. #88077	C₂×C₄	semidirect
435. C₂×C₁₃	#1861	semidirect
542. C₁₃	C₂×#1861	semidirect
651. C₂	#13115076	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×#11718785	2
C₂×#11718779	2
C₂×#11718897	2
C₂²×#88077	2
#13115076	2
C₂×#11718148	2
C₂×#11718147	2
C₂×C₁₃×#568	2
C₂×#1861	13

Subgroups — C2×#13115076 #15863816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115076 #15863816