Subgroups — C₂×#13115437 #15865165

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718660	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718658	C₂	1	1	yes	maximal, characteristic
3	#13115437	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718144	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718124	C₂	1	1	yes	maximal, characteristic
6	C₂×#11718124	C₂	1	1	yes	maximal, characteristic
7	C₂×#11718142	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂³×#1055	C₂²	1	1	yes	characteristic
16	C₁₃×#427	C₄	1	4	yes	complemented
17	C₁₃×#427	C₂²	1	4	yes	—
18	C₂×C₁₃×#107	C₄	1	1	yes	characteristic, complemented
19	C₂×C₁₃×#107	C₄	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#106	C₄	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#106	C₄	1	1	yes	characteristic, complemented
22	#11718660	—	2	2	no	—
23	#11718660	C₂²	1	4	yes	—
24	#11718658	—	2	2	no	—
25	#11718658	C₂²	1	4	yes	—
26	C₂×C₄⋊#1055	—	2	1	no	—
27	C₂×C₄⋊#1055	—	2	1	no	—
28	C₂×#88043	—	2	1	no	—
29	C₂×C₄×#1055	—	2	1	no	—
30	#11718144	C₂²	1	4	yes	—
31	#11718142	C₂²	1	4	yes	—
32	#11718124	C₂²	1	4	yes	—
33	#11718124	C₂²	1	4	yes	—
34	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂³×Dic₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	—	2	2	no	—
37	C₂²×C₈×C₁₃	—	2	2	no	—
38	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₁₃×#117	—	2	1	no	—
43	C₁₃×#117	—	2	1	no	—
44	C₁₃×#117	—	2	1	no	—
45	C₁₃×#117	—	2	1	no	—
46	C₁₃×#117	C₂×C₄	1	2	yes	—
47	C₁₃×#117	C₂×C₄	1	2	yes	—
48	C₁₃×#117	C₂³	1	2	yes	—
49	C₁₃×#117	C₂³	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
56	C₂×C₄²×C₁₃	—	2	1	no	—
57	C₂×C₄²×C₁₃	—	2	1	no	—
58	C₂×C₄×Dic₁₃	—	2	2	no	—
59	C₂×C₄×Dic₁₃	—	2	2	no	—
60	C₂×C₄×Dic₁₃	—	2	1	no	—
61	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
62	C₂×#6099	—	2	1	no	—
63	C₂×#6099	—	2	2	no	—
64	C₂×#6099	—	2	1	no	—
65	C₂×#6099	—	2	2	no	—
66	C₂×#6099	—	2	2	no	—
67	C₂×#6099	Q₈	1	4	yes	—
68	C₂×#6099	C₂³	1	2	yes	—
69	C₂×#6099	C₂³	1	2	yes	—
70	C₂²×#1055	—	2	1	no	—
71	C₂²×#1055	—	2	2	no	—
72	C₂²×#1055	—	2	2	no	—
73	C₂²×#1055	—	2	1	no	—
74	C₂²×#1055	D₄	1	2	yes	—
75	C₂²×#1055	D₄	1	1	yes	characteristic
76	C₂²×#1055	D₄	1	1	yes	characteristic
77	C₂²×#1055	C₂³	1	2	yes	—
78	C₁₃×#107	C₂×C₄	1	4	yes	complemented
79	C₁₃×#107	C₂×C₄	1	4	yes	complemented
80	C₁₃×#106	C₂×C₄	1	4	yes	complemented
81	C₁₃×#106	C₂×C₄	1	4	yes	complemented
82	C₄⋊#1055	—	2	4	no	—
83	C₄⋊#1055	—	2	4	no	—
84	#88043	—	2	4	no	—
85	C₄×#1055	—	2	4	no	—
86	C₂×#1922	—	13	1	no	maximal, Sylow
87	C₂⁴×C₁₃	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₁₃	#41	1	2	yes	—
98	C₂²×C₄×C₁₃	#41	1	2	yes	—
99	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	#41	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₁₃	—	2	4	no	—
103	C₂²×Dic₁₃	—	2	2	no	—
104	C₂²×Dic₁₃	—	4	2	no	—
105	C₂²×Dic₁₃	—	4	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	4	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
118	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
119	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
120	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
121	C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₁₃×C₂²⋊C₄	—	2	2	no	—
124	C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄×Dic₁₃	—	2	2	no	—
130	C₄×Dic₁₃	—	2	2	no	—
131	C₄×Dic₁₃	—	4	2	no	—
132	#6099	—	2	4	no	—
133	#6099	—	2	2	no	—
134	#6099	—	2	2	no	—
135	#6099	—	2	2	no	—
136	#6099	—	4	2	no	—
137	#6099	C₂×Q₈	1	4	yes	—
138	C₂×#1055	—	2	4	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	—	2	2	no	—
141	C₂×#1055	—	2	4	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	—	2	2	no	—
146	C₂×#1055	—	4	2	no	—
147	C₂×#1055	C₂×D₄	1	2	yes	—
148	C₂×#1055	C₂×D₄	1	2	yes	—
149	C₂×#427	D₁₃	1	1	yes	characteristic
150	C₂×#424	—	13	1	no	—
151	C₂×#405	—	13	1	no	—
152	#1922	—	13	8	no	—
153	C₂×#341	—	13	1	no	—
154	C₂×#339	—	13	1	no	—
155	C₂×#339	—	13	1	no	—
156	C₂×#336	—	13	1	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
160	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₁₃	#125	1	2	yes	—
162	C₂³×C₁₃	#126	1	2	yes	—
163	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	#117	1	2	yes	—
173	C₂×C₄×C₁₃	#117	1	2	yes	—
174	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
177	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₃	#123	1	2	yes	—
181	C₂×C₄×C₁₃	#123	1	2	yes	—
182	C₂×C₄×C₁₃	#125	1	2	yes	—
183	C₂×C₄×C₁₃	#126	1	2	yes	—
184	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×Dic₁₃	—	2	4	no	—
191	C₂×Dic₁₃	—	4	8	no	—
192	C₂×Dic₁₃	—	4	2	no	—
193	C₂×Dic₁₃	—	4	2	no	—
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	2	2	no	—
196	#1055	—	2	4	no	—
197	#1055	—	2	2	no	—
198	#1055	—	2	2	no	—
199	#1055	—	4	2	no	—
200	C₂²×M₁₆	—	13	1	no	—
201	C₂²×M₁₆	—	13	1	no	—
202	C₂³×C₈	—	13	1	no	—
203	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
204	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
205	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
206	C₂²×C₄²	—	13	1	no	—
207	#427	Dic₁₃	1	4	yes	complemented
208	#427	C₂×D₁₃	1	4	yes	—
209	C₂×#107	Dic₁₃	1	1	yes	characteristic, complemented
210	C₂×#107	Dic₁₃	1	1	yes	characteristic, complemented
211	C₂×#106	Dic₁₃	1	1	yes	characteristic, complemented
212	C₂×#106	Dic₁₃	1	1	yes	characteristic, complemented
213	#424	—	13	4	no	—
214	#424	—	26	2	no	—
215	C₂×C₄⋊C₈	—	26	1	no	—
216	C₂×C₄⋊C₈	—	26	1	no	—
217	#405	—	13	4	no	—
218	#405	—	26	2	no	—
219	C₂×#97	—	26	1	no	—
220	C₂×C₄×C₈	—	26	1	no	—
221	#341	—	13	4	no	—
222	#339	—	13	4	no	—
223	#339	—	13	4	no	—
224	#336	—	13	4	no	—
225	C₂²×C₁₃	—	2	4	no	—
226	C₂²×C₁₃	—	2	4	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	#387	1	2	yes	—
232	C₂²×C₁₃	#387	1	2	yes	—
233	C₂²×C₁₃	#443	1	2	yes	—
234	C₂²×C₁₃	#444	1	2	yes	—
235	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
236	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
237	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	2	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	#387	1	2	yes	—
243	C₄×C₁₃	#387	1	2	yes	—
244	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
245	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
246	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
247	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
248	Dic₁₃	—	4	4	no	—
249	C₂³×C₄	—	26	1	no	—
250	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
251	C₂×M₁₆	—	13	4	no	—
252	C₂×M₁₆	—	13	2	no	—
253	C₂×M₁₆	—	13	2	no	—
254	C₂×M₁₆	—	26	2	no	—
255	C₂×M₁₆	—	26	1	no	—
256	C₂×M₁₆	—	26	1	no	—
257	C₂×M₁₆	—	26	2	no	—
258	C₂×M₁₆	—	26	2	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	13	2	no	—
262	C₂²×C₈	—	13	1	no	—
263	C₂²×C₈	—	13	1	no	—
264	C₂²×C₈	—	13	2	no	—
265	C₂²×C₈	—	26	2	no	—
266	C₂²×C₈	—	26	1	no	—
267	C₂²×C₈	—	26	2	no	—
268	C₂²×C₈	—	26	1	no	—
269	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
270	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
271	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
272	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
273	#117	—	2	1	no	—
274	#117	—	2	1	no	—
275	#117	—	2	1	no	—
276	#117	—	2	1	no	—
277	#117	C₂×Dic₁₃	1	2	yes	—
278	#117	C₂×Dic₁₃	1	2	yes	—
279	#117	C₂²×D₁₃	1	2	yes	—
280	#117	C₂²×D₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	13	2	no	—
290	C₂×C₄²	—	26	2	no	—
291	C₂×C₄²	—	26	2	no	—
292	C₂×C₄²	—	26	1	no	—
293	#107	C₂×Dic₁₃	1	4	yes	complemented
294	#107	C₂×Dic₁₃	1	4	yes	complemented
295	#106	C₂×Dic₁₃	1	4	yes	complemented
296	#106	C₂×Dic₁₃	1	4	yes	complemented
297	C₄⋊C₈	—	26	4	no	—
298	C₄⋊C₈	—	26	4	no	—
299	#97	—	26	4	no	—
300	C₄×C₈	—	26	4	no	—
301	C₂×C₁₃	—	2	1	no	—
302	C₂×C₁₃	—	2	1	no	—
303	C₂×C₁₃	—	2	2	no	—
304	C₂×C₁₃	#1922	1	4	yes	complemented
305	C₂×C₁₃	C₂×#387	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
307	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
308	C₂⁴	#6129	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	26	4	no	—
314	C₂²×C₄	—	26	2	no	—
315	C₂²×C₄	—	52	2	no	—
316	C₂²×C₄	—	52	2	no	—
317	C₂²×C₄	#6127	1	2	yes	—
318	C₂²×C₄	#6127	1	2	yes	—
319	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
321	C₂²×C₄	#6129	1	1	yes	characteristic
322	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
323	C₂²×C₄	#6131	1	2	yes	—
324	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
327	M₁₆	—	13	4	no	—
328	M₁₆	—	26	4	no	—
329	M₁₆	—	26	2	no	—
330	M₁₆	—	26	2	no	—
331	M₁₆	—	26	2	no	—
332	M₁₆	—	52	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	13	2	no	—
339	C₂×C₈	—	13	2	no	—
340	C₂×C₈	—	26	2	no	—
341	C₂×C₈	—	26	2	no	—
342	C₂×C₈	—	26	4	no	—
343	C₂×C₈	—	26	4	no	—
344	C₂×C₈	—	26	2	no	—
345	C₂×C₈	—	26	2	no	—
346	C₂×C₈	—	26	2	no	—
347	C₂×C₈	—	26	2	no	—
348	C₂×C₈	—	52	2	no	—
349	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
350	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
356	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
357	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
358	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	26	2	no	—
368	C₄²	—	26	2	no	—
369	C₄²	—	52	2	no	—
370	C₁₃	C₂×#1922	1	1	yes	characteristic, complemented, Sylow
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	#88143	1	2	yes	—
374	C₂³	#88152	1	2	yes	—
375	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
376	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
377	C₂³	C₂×#6129	1	1	yes	characteristic
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	26	4	no	—
387	C₂×C₄	—	52	8	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	—	52	2	no	—
390	C₂×C₄	#88143	1	2	yes	—
391	C₂×C₄	#88148	1	2	yes	—
392	C₂×C₄	#88148	1	2	yes	—
393	C₂×C₄	#88150	1	2	yes	—
394	C₂×C₄	#88150	1	2	yes	—
395	C₂×C₄	#88152	1	2	yes	—
396	C₂×C₄	#88180	1	2	yes	—
397	C₂×C₄	#88180	1	2	yes	—
398	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
399	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
400	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
401	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
402	C₂×C₄	C₂×#6127	1	1	yes	characteristic
403	C₂×C₄	C₂×#6127	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
405	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
406	C₂×C₄	C₂×#6131	1	1	yes	characteristic
407	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	26	2	no	—
411	C₈	—	26	2	no	—
412	C₈	—	26	4	no	—
413	C₈	—	52	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	#11718642	1	2	yes	—
421	C₂²	#11718642	1	2	yes	—
422	C₂²	#11718857	1	2	yes	—
423	C₂²	#11718858	1	2	yes	—
424	C₂²	C₂×#88143	1	1	yes	characteristic
425	C₂²	C₂×#88152	1	1	yes	characteristic
426	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	52	4	no	—
432	C₄	#11718642	1	2	yes	—
433	C₄	#11718642	1	2	yes	—
434	C₄	C₂×#88148	1	1	yes	characteristic
435	C₄	C₂×#88150	1	1	yes	characteristic
436	C₄	C₂×#88180	1	1	yes	characteristic
437	C₄	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
438	C₂	—	2	1	no	—
439	C₂	—	2	1	no	—
440	C₂	—	2	2	no	—
441	C₂	#13115437	1	4	yes	direct product factor
442	C₂	C₂×#11718642	1	1	yes	characteristic
443	C₂	C₂×#11718857	1	1	yes	characteristic
444	C₂	C₂×#11718858	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#427	C₂
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂⁴×C₁₃	#41
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#427	D₁₃
hypocenter	C₁₃	C₂×#1922
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
3. #13115437	C₂	direct (N × H)
16. C₁₃×#427	C₄	semidirect
18. C₂×C₁₃×#107	C₄	semidirect
19. C₂×C₁₃×#107	C₄	semidirect
20. C₂×C₁₃×#106	C₄	semidirect
21. C₂×C₁₃×#106	C₄	semidirect
78. C₁₃×#107	C₂×C₄	semidirect
79. C₁₃×#107	C₂×C₄	semidirect
80. C₁₃×#106	C₂×C₄	semidirect
81. C₁₃×#106	C₂×C₄	semidirect
207. #427	Dic₁₃	semidirect
209. C₂×#107	Dic₁₃	semidirect
210. C₂×#107	Dic₁₃	semidirect
211. C₂×#106	Dic₁₃	semidirect
212. C₂×#106	Dic₁₃	semidirect
293. #107	C₂×Dic₁₃	semidirect
294. #107	C₂×Dic₁₃	semidirect
295. #106	C₂×Dic₁₃	semidirect
296. #106	C₂×Dic₁₃	semidirect
304. C₂×C₁₃	#1922	semidirect
370. C₁₃	C₂×#1922	semidirect
441. C₂	#13115437	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×#11718660	2
C₂×#11718658	2
#13115437	2
C₂×#11718144	2
C₂×#11718124	2
C₂×#11718142	2
C₂×C₁₃×#427	2
C₂×#1922	13

Subgroups — C2×#13115437 #15865165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115437 #15865165