Subgroups — C₂×#13116233 #15891635

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718786	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718785	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#88063	C₂	1	1	yes	maximal, characteristic
4	C₂²×#88063	C₂	1	1	yes	maximal, characteristic
5	C₂²×#88063	C₂	1	1	yes	maximal, characteristic
6	#13116233	C₂	1	8	yes	maximal, direct product factor
7	C₂×#11718152	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₅₂	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂²×#6099	C₂²	1	1	yes	characteristic
16	C₁₃×#430	—	2	2	no	—
17	C₁₃×#430	C₂²	1	4	yes	complemented
18	C₂×C₁₃×#108	—	2	2	no	—
19	C₂×#88063	—	2	2	no	—
20	C₂×#88063	—	2	2	no	—
21	C₂×#88063	—	2	2	no	—
22	C₂×#88063	—	2	2	no	—
23	C₂×#88063	—	2	2	no	—
24	C₂×#88063	—	2	2	no	—
25	C₂×#88063	C₂²	1	4	yes	—
26	C₂×#88063	C₂²	1	4	yes	—
27	C₂×#88063	C₂²	1	4	yes	—
28	#11718786	—	2	2	no	—
29	#11718786	C₂²	1	4	yes	complemented
30	#11718785	—	2	2	no	—
31	#11718785	C₂²	1	4	yes	complemented
32	C₂×#88062	—	2	2	no	—
33	C₂×#88059	—	2	2	no	—
34	#11718152	C₂²	1	4	yes	complemented
35	C₂⁴×D₁₃	Q₈	1	2	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×D₅₂	—	2	1	no	—
38	C₂²×D₅₂	—	2	1	no	—
39	C₂²×D₅₂	—	2	1	no	—
40	C₂²×D₅₂	—	2	1	no	—
41	C₂²×D₅₂	—	2	1	no	—
42	C₂²×D₅₂	—	2	1	no	—
43	C₂²×D₅₂	—	2	1	no	—
44	C₂²×D₅₂	—	2	1	no	—
45	C₂²×D₅₂	—	2	1	no	—
46	C₂²×D₅₂	—	2	1	no	—
47	C₂²×D₅₂	—	2	1	no	—
48	C₂²×D₅₂	—	2	1	no	—
49	C₂²×D₅₂	Q₈	1	2	yes	—
50	C₂²×D₅₂	C₂³	1	2	yes	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
63	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
64	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
65	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₂²×C₈×C₁₃	—	2	1	no	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂×#6099	—	2	1	no	—
73	C₂×#6099	—	2	1	no	—
74	C₂×#6099	—	2	1	no	—
75	C₂×#6099	—	2	1	no	—
76	C₂×#6099	—	2	1	no	—
77	C₂×#6099	—	2	1	no	—
78	C₂×#6099	—	2	1	no	—
79	C₂×#6099	—	2	1	no	—
80	C₂×#6099	—	2	1	no	—
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂×#6099	—	2	1	no	—
84	C₂×#6099	—	2	1	no	—
85	C₂×#6099	D₄	1	2	yes	—
86	C₂×#6099	D₄	1	2	yes	—
87	C₂×#6099	C₂³	1	2	yes	—
88	C₂×#6099	C₂³	1	2	yes	—
89	C₂×#6099	C₂³	1	2	yes	—
90	C₂²×#1055	—	2	1	no	—
91	C₂²×#1055	—	2	1	no	—
92	C₂²×#1055	—	2	1	no	—
93	C₁₃×#108	—	2	8	no	—
94	#88063	—	2	8	no	—
95	#88063	—	2	8	no	—
96	#88063	—	2	8	no	—
97	#88062	—	2	8	no	—
98	#88059	—	2	8	no	—
99	C₂×#2069	—	13	1	no	maximal, Sylow
100	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
101	C₂³×D₁₃	—	2	2	no	—
102	C₂³×D₁₃	—	2	2	no	—
103	C₂³×D₁₃	—	2	2	no	—
104	C₂³×D₁₃	—	2	2	no	—
105	C₂³×D₁₃	—	2	2	no	—
106	C₂³×D₁₃	—	2	2	no	—
107	C₂³×D₁₃	—	8	4	no	—
108	C₂³×D₁₃	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂×D₅₂	—	2	2	no	—
124	C₂×D₅₂	—	2	2	no	—
125	C₂×D₅₂	—	2	2	no	—
126	C₂×D₅₂	—	2	2	no	—
127	C₂×D₅₂	—	2	2	no	—
128	C₂×D₅₂	—	2	2	no	—
129	C₂×D₅₂	—	2	2	no	—
130	C₂×D₅₂	—	2	2	no	—
131	C₂×D₅₂	—	2	2	no	—
132	C₂×D₅₂	—	2	2	no	—
133	C₂×D₅₂	—	2	2	no	—
134	C₂×D₅₂	—	2	2	no	—
135	C₂×D₅₂	—	4	1	no	—
136	C₂×D₅₂	—	4	1	no	—
137	C₂×D₅₂	—	4	1	no	—
138	C₂×D₅₂	—	4	1	no	—
139	C₂×D₅₂	—	4	1	no	—
140	C₂×D₅₂	—	4	1	no	—
141	C₂×D₅₂	—	4	1	no	—
142	C₂×D₅₂	—	4	1	no	—
143	C₂×D₅₂	—	4	1	no	—
144	C₂×D₅₂	—	4	1	no	—
145	C₂×D₅₂	—	4	1	no	—
146	C₂×D₅₂	—	4	1	no	—
147	C₂×D₅₂	—	4	1	no	—
148	C₂×D₅₂	—	4	1	no	—
149	C₂×D₅₂	—	4	1	no	—
150	C₂×D₅₂	—	4	1	no	—
151	C₁₃×M₁₆	—	2	2	no	—
152	C₁₃×M₁₆	—	2	2	no	—
153	C₁₃×M₁₆	—	2	2	no	—
154	C₁₃×M₁₆	—	2	2	no	—
155	C₁₃×M₁₆	—	2	2	no	—
156	C₁₃×M₁₆	—	2	2	no	—
157	C₁₃×M₁₆	—	2	2	no	—
158	C₁₃×M₁₆	—	2	2	no	—
159	C₁₃×M₁₆	—	4	1	no	—
160	C₁₃×M₁₆	—	4	1	no	—
161	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
162	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	4	1	no	—
171	C₂×C₈×C₁₃	—	4	1	no	—
172	#6099	—	2	2	no	—
173	#6099	—	2	2	no	—
174	#6099	—	2	2	no	—
175	#6099	—	2	2	no	—
176	#6099	—	2	2	no	—
177	#6099	—	2	2	no	—
178	#6099	—	2	2	no	—
179	#6099	—	4	1	no	—
180	#6099	—	4	1	no	—
181	#6099	—	4	1	no	—
182	#6099	—	4	1	no	—
183	#6099	C₂×D₄	1	4	yes	—
184	C₂×#1055	—	2	2	no	—
185	C₂×#1055	—	2	2	no	—
186	C₂×#1055	—	2	2	no	—
187	C₂×#1055	—	2	2	no	—
188	C₂×#1055	—	2	2	no	—
189	C₂×#1055	—	4	1	no	—
190	C₂×#1055	—	4	1	no	—
191	C₂×#1055	—	4	1	no	—
192	C₂×#1055	—	4	1	no	—
193	C₂×#430	—	13	1	no	—
194	C₂×#430	—	13	1	no	—
195	C₂×#430	D₁₃	1	1	yes	characteristic, complemented
196	C₂²×#100	—	13	1	no	—
197	C₂²×#100	—	13	1	no	—
198	C₂²×#100	—	13	1	no	—
199	#2069	—	13	8	no	—
200	C₂×#338	—	13	1	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
207	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
209	C₂²×D₁₃	—	2	4	no	—
210	C₂²×D₁₃	—	2	4	no	—
211	C₂²×D₁₃	—	2	4	no	—
212	C₂²×D₁₃	—	4	2	no	—
213	C₂²×D₁₃	—	4	2	no	—
214	C₂²×D₁₃	—	4	2	no	—
215	C₂²×D₁₃	—	4	2	no	—
216	C₂²×D₁₃	—	8	4	no	—
217	C₂²×D₁₃	—	8	4	no	—
218	C₂²×D₁₃	—	8	4	no	—
219	C₂²×D₁₃	—	8	4	no	—
220	C₂²×D₁₃	—	8	4	no	—
221	C₂²×D₁₃	—	8	4	no	—
222	C₂²×D₁₃	—	8	4	no	—
223	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
234	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
251	D₅₂	—	4	2	no	—
252	D₅₂	—	4	2	no	—
253	D₅₂	—	4	2	no	—
254	D₅₂	—	4	2	no	—
255	D₅₂	—	4	2	no	—
256	D₅₂	—	4	2	no	—
257	D₅₂	—	4	2	no	—
258	D₅₂	—	4	2	no	—
259	C₈×C₁₃	—	2	4	no	—
260	C₈×C₁₃	—	2	4	no	—
261	C₈×C₁₃	—	4	2	no	—
262	#1055	—	2	4	no	—
263	#1055	—	4	2	no	—
264	#1055	—	4	2	no	—
265	C₂³×D₄	—	13	1	no	—
266	C₂²×M₁₆	—	13	1	no	—
267	C₂²×M₁₆	—	13	1	no	—
268	C₂²×M₁₆	—	13	1	no	—
269	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
270	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
271	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
272	#430	—	2	2	no	—
273	#430	—	13	4	no	—
274	#430	—	13	4	no	—
275	#430	—	26	2	no	—
276	#430	—	26	2	no	—
277	#430	C₂×D₁₃	1	4	yes	complemented
278	C₂×#108	—	2	2	no	—
279	C₂×#108	—	26	2	no	—
280	C₂×#108	—	26	2	no	—
281	C₂×#100	—	13	4	no	—
282	C₂×#100	—	13	4	no	—
283	C₂×#100	—	13	4	no	—
284	C₂×#100	—	26	2	no	—
285	C₂×#100	—	26	2	no	—
286	C₂×#100	—	26	2	no	—
287	C₂×#100	—	26	2	no	—
288	C₂×#100	—	26	2	no	—
289	C₂×#100	—	26	2	no	—
290	#338	—	13	4	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	4	1	no	—
295	C₂²×C₁₃	—	4	1	no	—
296	C₂²×C₁₃	—	4	1	no	—
297	C₂²×C₁₃	—	4	1	no	—
298	C₂²×C₁₃	#396	1	1	yes	characteristic
299	C₂²×C₁₃	#396	1	1	yes	characteristic
300	C₂²×C₁₃	#396	1	1	yes	characteristic
301	C₂²×C₁₃	#396	1	1	yes	characteristic
302	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
303	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
304	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	C₂×D₁₃	—	4	4	no	—
306	C₂×D₁₃	—	8	4	no	—
307	C₂×D₁₃	—	8	4	no	—
308	C₂×D₁₃	—	8	4	no	—
309	C₂×D₁₃	—	8	4	no	—
310	C₂×D₁₃	—	8	4	no	—
311	C₂×D₁₃	—	8	4	no	—
312	C₂×D₁₃	—	8	4	no	—
313	C₄×C₁₃	#396	1	1	yes	characteristic
314	C₄×C₁₃	#396	1	1	yes	characteristic
315	C₄×C₁₃	#396	1	1	yes	characteristic
316	C₄×C₁₃	#396	1	1	yes	characteristic
317	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
318	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
319	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
320	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
321	C₂⁵	—	13	2	no	—
322	C₂²×D₄	—	13	2	no	—
323	C₂²×D₄	—	13	2	no	—
324	C₂²×D₄	—	26	1	no	—
325	C₂²×D₄	—	26	1	no	—
326	C₂²×D₄	—	26	1	no	—
327	C₂²×D₄	—	26	1	no	—
328	C₂²×D₄	—	26	1	no	—
329	C₂²×D₄	—	26	1	no	—
330	C₂²×D₄	—	26	1	no	—
331	C₂²×D₄	—	26	1	no	—
332	C₂²×D₄	—	26	1	no	—
333	C₂²×D₄	—	26	1	no	—
334	C₂²×D₄	—	26	1	no	—
335	C₂²×D₄	—	26	1	no	—
336	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	13	2	no	—
349	C₂×M₁₆	—	13	2	no	—
350	C₂×M₁₆	—	13	2	no	—
351	C₂×M₁₆	—	13	2	no	—
352	C₂×M₁₆	—	13	2	no	—
353	C₂×M₁₆	—	26	1	no	—
354	C₂×M₁₆	—	26	1	no	—
355	C₂×M₁₆	—	26	1	no	—
356	C₂×M₁₆	—	26	1	no	—
357	C₂×M₁₆	—	26	1	no	—
358	C₂×M₁₆	—	26	1	no	—
359	C₂×M₁₆	—	26	1	no	—
360	C₂×M₁₆	—	26	1	no	—
361	C₂×M₁₆	—	26	1	no	—
362	C₂×M₁₆	—	26	1	no	—
363	C₂×M₁₆	—	26	1	no	—
364	C₂×M₁₆	—	26	1	no	—
365	C₂×M₁₆	—	26	1	no	—
366	C₂×M₁₆	D₅₂	1	2	yes	—
367	C₂×M₁₆	D₅₂	1	2	yes	—
368	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
369	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
370	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
371	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
372	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	26	1	no	—
377	C₂²×C₈	—	26	1	no	—
378	C₂²×C₈	—	26	1	no	—
379	#108	—	2	8	no	—
380	#108	—	26	8	no	—
381	#108	—	26	8	no	—
382	#100	—	26	8	no	—
383	#100	—	26	8	no	—
384	#100	—	26	8	no	—
385	C₂×C₁₃	—	2	1	no	—
386	C₂×C₁₃	—	2	1	no	—
387	C₂×C₁₃	—	2	1	no	—
388	C₂×C₁₃	—	2	1	no	—
389	C₂×C₁₃	—	2	1	no	—
390	C₂×C₁₃	—	2	1	no	—
391	C₂×C₁₃	#2069	1	2	yes	complemented
392	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
393	D₁₃	—	8	4	no	—
394	C₂⁴	—	13	4	no	—
395	C₂⁴	—	26	2	no	—
396	C₂⁴	—	26	2	no	—
397	C₂⁴	—	26	2	no	—
398	C₂⁴	—	26	2	no	—
399	C₂⁴	—	26	2	no	—
400	C₂⁴	—	26	2	no	—
401	C₂⁴	—	104	4	no	—
402	C₂⁴	Q₈×D₁₃	1	1	yes	characteristic
403	C₂×D₄	—	26	2	no	—
404	C₂×D₄	—	26	2	no	—
405	C₂×D₄	—	26	2	no	—
406	C₂×D₄	—	26	2	no	—
407	C₂×D₄	—	26	2	no	—
408	C₂×D₄	—	26	2	no	—
409	C₂×D₄	—	26	2	no	—
410	C₂×D₄	—	26	2	no	—
411	C₂×D₄	—	26	2	no	—
412	C₂×D₄	—	26	2	no	—
413	C₂×D₄	—	26	2	no	—
414	C₂×D₄	—	26	2	no	—
415	C₂×D₄	—	52	1	no	—
416	C₂×D₄	—	52	1	no	—
417	C₂×D₄	—	52	1	no	—
418	C₂×D₄	—	52	1	no	—
419	C₂×D₄	—	52	1	no	—
420	C₂×D₄	—	52	1	no	—
421	C₂×D₄	—	52	1	no	—
422	C₂×D₄	—	52	1	no	—
423	C₂×D₄	—	52	1	no	—
424	C₂×D₄	—	52	1	no	—
425	C₂×D₄	—	52	1	no	—
426	C₂×D₄	—	52	1	no	—
427	C₂×D₄	—	52	1	no	—
428	C₂×D₄	—	52	1	no	—
429	C₂×D₄	—	52	1	no	—
430	C₂×D₄	—	52	1	no	—
431	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
433	C₂²×C₄	#6127	1	1	yes	characteristic
434	C₂²×C₄	#6127	1	1	yes	characteristic
435	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
436	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
437	C₂²×C₄	#6129	1	1	yes	characteristic
438	C₂²×C₄	#6129	1	1	yes	characteristic
439	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
440	C₂²×C₄	#6131	1	1	yes	characteristic
441	C₂²×C₄	#6131	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
445	M₁₆	—	2	2	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	4	1	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	—	13	4	no	—
456	M₁₆	—	26	2	no	—
457	M₁₆	—	26	2	no	—
458	M₁₆	—	26	2	no	—
459	M₁₆	—	26	2	no	—
460	M₁₆	—	26	2	no	—
461	M₁₆	—	26	2	no	—
462	M₁₆	—	26	2	no	—
463	M₁₆	—	52	1	no	—
464	M₁₆	—	52	1	no	—
465	M₁₆	—	52	1	no	—
466	M₁₆	—	52	1	no	—
467	M₁₆	C₂×D₅₂	1	4	yes	—
468	M₁₆	C₂×C₂²⋊D₁₃	1	4	yes	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	26	2	no	—
479	C₂×C₈	—	26	2	no	—
480	C₂×C₈	—	26	2	no	—
481	C₂×C₈	—	26	2	no	—
482	C₂×C₈	—	26	2	no	—
483	C₂×C₈	—	52	1	no	—
484	C₂×C₈	—	52	1	no	—
485	C₂×C₈	—	52	1	no	—
486	C₂×C₈	—	52	1	no	—
487	C₁₃	C₂×#2069	1	1	yes	characteristic, complemented, Sylow
488	C₂³	—	4	2	no	—
489	C₂³	—	26	4	no	—
490	C₂³	—	26	4	no	—
491	C₂³	—	26	4	no	—
492	C₂³	—	52	2	no	—
493	C₂³	—	52	2	no	—
494	C₂³	—	52	2	no	—
495	C₂³	—	52	2	no	—
496	C₂³	—	104	4	no	—
497	C₂³	—	104	4	no	—
498	C₂³	—	104	4	no	—
499	C₂³	—	104	4	no	—
500	C₂³	—	104	4	no	—
501	C₂³	—	104	4	no	—
502	C₂³	—	104	4	no	—
503	C₂³	#88150	1	1	yes	characteristic
504	C₂³	#88150	1	1	yes	characteristic
505	C₂³	#88151	1	1	yes	characteristic
506	C₂³	#88151	1	1	yes	characteristic
507	C₂³	#88200	1	1	yes	characteristic
508	C₂³	#88200	1	1	yes	characteristic
509	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
510	D₄	—	52	2	no	—
511	D₄	—	52	2	no	—
512	D₄	—	52	2	no	—
513	D₄	—	52	2	no	—
514	D₄	—	52	2	no	—
515	D₄	—	52	2	no	—
516	D₄	—	52	2	no	—
517	D₄	—	52	2	no	—
518	C₂×C₄	#88149	1	1	yes	characteristic
519	C₂×C₄	#88149	1	1	yes	characteristic
520	C₂×C₄	#88149	1	1	yes	characteristic
521	C₂×C₄	#88149	1	1	yes	characteristic
522	C₂×C₄	#88150	1	1	yes	characteristic
523	C₂×C₄	#88150	1	1	yes	characteristic
524	C₂×C₄	#88151	1	1	yes	characteristic
525	C₂×C₄	#88151	1	1	yes	characteristic
526	C₂×C₄	#88152	1	1	yes	characteristic
527	C₂×C₄	#88152	1	1	yes	characteristic
528	C₂×C₄	#88152	1	1	yes	characteristic
529	C₂×C₄	#88152	1	1	yes	characteristic
530	C₂×C₄	#88184	1	1	yes	characteristic
531	C₂×C₄	#88184	1	1	yes	characteristic
532	C₂×C₄	#88184	1	1	yes	characteristic
533	C₂×C₄	#88184	1	1	yes	characteristic
534	C₂×C₄	#88193	1	1	yes	characteristic
535	C₂×C₄	#88193	1	1	yes	characteristic
536	C₂×C₄	#88193	1	1	yes	characteristic
537	C₂×C₄	#88193	1	1	yes	characteristic
538	C₂×C₄	#88200	1	1	yes	characteristic
539	C₂×C₄	#88200	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
541	C₂×C₄	C₂×#6127	1	1	yes	characteristic
542	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂×#6129	1	1	yes	characteristic
544	C₂×C₄	C₂×#6131	1	1	yes	characteristic
545	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
546	C₈	—	2	4	no	—
547	C₈	—	2	4	no	—
548	C₈	—	4	2	no	—
549	C₈	—	26	4	no	—
550	C₈	—	52	2	no	—
551	C₈	—	52	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	52	4	no	—
560	C₂²	—	104	4	no	—
561	C₂²	—	104	4	no	—
562	C₂²	—	104	4	no	—
563	C₂²	—	104	4	no	—
564	C₂²	—	104	4	no	—
565	C₂²	—	104	4	no	—
566	C₂²	—	104	4	no	—
567	C₂²	#11718655	1	1	yes	characteristic
568	C₂²	#11718655	1	1	yes	characteristic
569	C₂²	#11718655	1	1	yes	characteristic
570	C₂²	#11718655	1	1	yes	characteristic
571	C₂²	C₂×#88150	1	1	yes	characteristic
572	C₂²	C₂×#88151	1	1	yes	characteristic
573	C₂²	C₂×#88200	1	1	yes	characteristic
574	C₄	#11718655	1	1	yes	characteristic
575	C₄	#11718655	1	1	yes	characteristic
576	C₄	#11718655	1	1	yes	characteristic
577	C₄	#11718655	1	1	yes	characteristic
578	C₄	C₂×#88149	1	1	yes	characteristic
579	C₄	C₂×#88152	1	1	yes	characteristic
580	C₄	C₂×#88184	1	1	yes	characteristic
581	C₄	C₂×#88193	1	1	yes	characteristic
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	104	4	no	—
589	C₂	#13116233	1	2	yes	direct product factor
590	C₂	C₂×#11718655	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718655
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#430	C₂
socle	C₂²×C₁₃	#396
prime radical	C₂³×D₅₂	C₂²
hypercenter	C₂×#430	D₁₃
hypocenter	C₁₃	C₂×#2069
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
1. C₂×#11718786	C₂	semidirect
2. C₂×#11718785	C₂	semidirect
6. #13116233	C₂	direct (N × H)
7. C₂×#11718152	C₂	semidirect
8. C₂×C₁₃×#430	C₂	semidirect
17. C₁₃×#430	C₂²	semidirect
29. #11718786	C₂²	semidirect
31. #11718785	C₂²	semidirect
34. #11718152	C₂²	semidirect
195. C₂×#430	D₁₃	semidirect
277. #430	C₂×D₁₃	semidirect
391. C₂×C₁₃	#2069	semidirect
487. C₁₃	C₂×#2069	semidirect
589. C₂	#13116233	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×#11718786	2
C₂×#11718785	2
C₂²×#88063	2
#13116233	2
C₂×#11718152	2
C₂×C₁₃×#430	2
C₂×#2069	13

Subgroups — C2×#13116233 #15891635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116233 #15891635