Subgroups — C₂×#3540 #62728

Order 256.

3709 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3540	C₂	1	32	yes	maximal, direct product factor
2	C₂×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
3	C₂×#560	C₂	1	2	yes	maximal, complemented
4	C₂×#559	C₂	1	2	yes	maximal, complemented
5	C₂×#556	C₂	1	2	yes	maximal, complemented
6	C₂×#555	C₂	1	2	yes	maximal, complemented
7	C₂×#551	C₂	1	2	yes	maximal, complemented
8	C₂×#548	C₂	1	2	yes	maximal, complemented
9	C₂×#546	C₂	1	2	yes	maximal, complemented
10	C₂×#542	C₂	1	2	yes	maximal, complemented
11	C₂×#542	C₂	1	4	yes	maximal, complemented
12	C₂×#538	C₂	1	4	yes	maximal, complemented
13	C₂×#536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#525	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#525	C₂	1	2	yes	maximal, complemented
17	C₂²×#41	C₂²	1	1	yes	characteristic
18	C₂²×#41	C₂²	1	2	yes	—
19	C₂³×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂⁴×C₄	C₂²	1	1	yes	characteristic, complemented
22	H(3,𝔽₄)	C₂²	1	32	yes	complemented
23	#560	C₂²	1	32	yes	complemented
24	#559	C₂²	1	32	yes	complemented
25	#556	C₂²	1	32	yes	complemented
26	#555	C₂²	1	32	yes	complemented
27	#551	C₂²	1	32	yes	complemented
28	#548	C₂²	1	32	yes	complemented
29	#546	C₂²	1	32	yes	complemented
30	#542	C₂²	1	32	yes	complemented
31	#542	C₂²	1	64	yes	complemented
32	#538	C₂²	1	64	yes	complemented
33	#536	C₂²	1	16	yes	complemented
34	#535	C₂²	1	16	yes	complemented
35	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×#127	C₂²	1	2	yes	—
38	C₂×#126	C₂²	1	4	yes	complemented
39	C₂×#126	C₂²	1	4	yes	complemented
40	C₂×#126	C₂²	1	4	yes	complemented
41	C₂×#124	C₂²	1	2	yes	—
42	C₂×#124	C₂²	1	4	yes	—
43	C₂×#124	C₂²	1	2	yes	complemented
44	C₂×#124	C₂²	1	4	yes	complemented
45	C₂×#124	C₂²	1	2	yes	complemented
46	C₂×#124	C₂²	1	4	yes	complemented
47	C₂×#124	C₂²	1	4	yes	complemented
48	C₂×#124	C₂²	1	4	yes	complemented
49	#525	C₂²	1	16	yes	complemented
50	#525	C₂²	1	32	yes	complemented
51	C₂×#123	C₂²	1	1	yes	characteristic
52	C₂×#123	C₂²	1	4	yes	complemented
53	C₂×#123	C₂²	1	1	yes	characteristic, complemented
54	C₂×#123	C₂²	1	2	yes	complemented
55	C₂×#123	C₂²	1	2	yes	complemented
56	C₂×#123	C₂²	1	4	yes	complemented
57	C₂×#123	C₂²	1	4	yes	complemented
58	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
64	C₂×#121	C₂²	1	2	yes	—
65	C₂×#121	C₂²	1	2	yes	—
66	C₂×#121	C₂²	1	2	yes	—
67	C₂×#121	C₂²	1	4	yes	—
68	C₂×#121	C₂²	1	2	yes	complemented
69	C₂×#121	C₂²	1	4	yes	complemented
70	C₂×#121	C₂²	1	4	yes	complemented
71	C₂×#120	C₂²	1	1	yes	characteristic
72	C₂×#120	C₂²	1	2	yes	—
73	C₂×#120	C₂²	1	4	yes	—
74	C₂×#120	C₂²	1	1	yes	characteristic, complemented
75	C₂×#120	C₂²	1	4	yes	complemented
76	C₂×#120	C₂²	1	2	yes	complemented
77	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
78	C₂×C₄×Q₈	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄	C₂²	1	2	yes	—
80	C₂×C₄×D₄	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄	C₂²	1	4	yes	complemented
83	C₂×C₄×D₄	C₂²	1	4	yes	complemented
84	C₂×C₄×D₄	C₂²	1	2	yes	complemented
85	C₂×#117	C₂²	1	1	yes	characteristic, complemented
86	C₂×#117	C₂²	1	2	yes	complemented
87	C₂×#117	C₂²	1	1	yes	characteristic, complemented
88	C₂×#117	C₂²	1	1	yes	characteristic, complemented
89	C₂×#117	C₂²	1	4	yes	complemented
90	C₂²×C₂²⋊C₄	C₂²	1	4	yes	complemented
91	C₂⁵	C₂³	1	2	yes	—
92	C₂⁵	C₂³	1	1	yes	characteristic
93	C₂×#41	—	4	4	no	—
94	C₂×#41	—	4	8	no	—
95	C₂×#41	C₂³	1	8	yes	—
96	C₂×#41	C₂³	1	16	yes	—
97	C₂²×Q₈	—	4	4	no	—
98	C₂²×Q₈	C₂³	1	2	yes	—
99	C₂²×Q₈	C₂³	1	4	yes	—
100	C₂²×Q₈	C₂³	1	2	yes	—
101	C₂²×Q₈	C₂³	1	1	yes	characteristic
102	C₂²×Q₈	C₂³	1	8	yes	complemented
103	C₂²×D₄	—	4	4	no	—
104	C₂²×D₄	C₂³	1	2	yes	—
105	C₂²×D₄	C₂³	1	2	yes	—
106	C₂²×D₄	C₂³	1	4	yes	—
107	C₂²×D₄	C₂³	1	4	yes	—
108	C₂²×D₄	C₂³	1	2	yes	—
109	C₂²×D₄	C₂³	1	4	yes	—
110	C₂²×D₄	C₂³	1	1	yes	characteristic
111	C₂²×D₄	C₂³	1	4	yes	—
112	C₂²×D₄	C₂³	1	1	yes	characteristic
113	C₂²×D₄	C₂³	1	1	yes	characteristic
114	C₂²×D₄	C₂³	1	2	yes	—
115	C₂²×D₄	C₂³	1	8	yes	complemented
116	C₂³×C₄	—	4	4	no	—
117	C₂³×C₄	C₂³	1	1	yes	characteristic
118	C₂³×C₄	C₂³	1	2	yes	—
119	C₂³×C₄	C₂³	1	1	yes	characteristic
120	C₂³×C₄	C₂³	1	1	yes	characteristic
121	C₂³×C₄	C₂³	1	4	yes	—
122	C₂³×C₄	C₂³	1	4	yes	—
123	C₂³×C₄	C₂³	1	1	yes	characteristic
124	C₂³×C₄	C₂³	1	2	yes	—
125	C₂³×C₄	C₂³	1	2	yes	—
126	C₂³×C₄	C₂³	1	8	yes	complemented
127	C₄⋊Q₈	C₂³	1	16	yes	complemented
128	C₄⋊Q₈	C₂³	1	16	yes	complemented
129	#127	C₂³	1	16	yes	—
130	#126	C₂³	1	32	yes	complemented
131	#126	C₂³	1	32	yes	complemented
132	#126	C₂³	1	32	yes	complemented
133	#124	C₂³	1	16	yes	—
134	#124	C₂³	1	32	yes	—
135	#124	C₂³	1	16	yes	complemented
136	#124	C₂³	1	32	yes	complemented
137	#124	C₂³	1	16	yes	complemented
138	#124	C₂³	1	32	yes	complemented
139	#124	C₂³	1	32	yes	complemented
140	#124	C₂³	1	32	yes	complemented
141	#123	C₂³	1	8	yes	—
142	#123	C₂³	1	32	yes	complemented
143	#123	C₂³	1	8	yes	complemented
144	#123	C₂³	1	16	yes	complemented
145	#123	C₂³	1	16	yes	complemented
146	#123	C₂³	1	32	yes	complemented
147	#123	C₂³	1	32	yes	complemented
148	C₂²⋊Q₈	C₂³	1	16	yes	complemented
149	C₂²⋊Q₈	C₂³	1	16	yes	complemented
150	C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₂²⋊Q₈	C₂³	1	16	yes	complemented
152	C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	#121	C₂³	1	16	yes	—
155	#121	C₂³	1	16	yes	—
156	#121	C₂³	1	16	yes	—
157	#121	C₂³	1	32	yes	—
158	#121	C₂³	1	16	yes	complemented
159	#121	C₂³	1	32	yes	complemented
160	#121	C₂³	1	32	yes	complemented
161	#120	C₂³	1	8	yes	—
162	#120	C₂³	1	16	yes	—
163	#120	C₂³	1	32	yes	—
164	#120	C₂³	1	8	yes	complemented
165	#120	C₂³	1	32	yes	complemented
166	#120	C₂³	1	16	yes	complemented
167	C₄×Q₈	C₂³	1	16	yes	complemented
168	C₄×Q₈	C₂³	1	32	yes	complemented
169	C₄×D₄	C₂³	1	16	yes	—
170	C₄×D₄	C₂³	1	32	yes	complemented
171	C₄×D₄	C₂³	1	16	yes	complemented
172	C₄×D₄	C₂³	1	32	yes	complemented
173	C₄×D₄	C₂³	1	32	yes	complemented
174	C₄×D₄	C₂³	1	16	yes	complemented
175	#117	C₂³	1	8	yes	complemented
176	#117	C₂³	1	16	yes	complemented
177	#117	C₂³	1	8	yes	complemented
178	#117	C₂³	1	8	yes	complemented
179	#117	C₂³	1	32	yes	complemented
180	C₂×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄	C₂³	1	4	yes	—
190	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
192	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
193	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
196	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
206	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
207	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄	C₂³	1	32	yes	complemented
209	C₂×C₄²	C₂³	1	2	yes	—
210	C₂×C₄²	C₂³	1	4	yes	—
211	C₂×C₄²	C₂³	1	2	yes	—
212	C₂×C₄²	C₂³	1	2	yes	—
213	C₂×C₄²	C₂³	1	4	yes	—
214	C₂⁴	—	4	2	no	—
215	C₂⁴	—	4	4	no	—
216	C₂⁴	—	4	4	no	—
217	C₂⁴	—	4	8	no	—
218	C₂⁴	C₂⁴	1	1	yes	characteristic
219	C₂⁴	C₂⁴	1	1	yes	characteristic
220	C₂⁴	C₂⁴	1	2	yes	—
221	C₂⁴	C₂⁴	1	4	yes	—
222	C₂⁴	C₂⁴	1	1	yes	characteristic
223	C₂⁴	C₂⁴	1	8	yes	—
224	C₂⁴	C₂⁴	1	4	yes	—
225	#41	—	4	16	no	—
226	#41	—	4	32	no	—
227	C₂×Q₈	—	2	8	no	—
228	C₂×Q₈	—	4	4	no	—
229	C₂×Q₈	—	4	8	no	—
230	C₂×Q₈	—	4	2	no	—
231	C₂×Q₈	—	4	16	no	—
232	C₂×Q₈	C₂⁴	1	8	yes	—
233	C₂×Q₈	C₂⁴	1	16	yes	—
234	C₂×Q₈	C₂⁴	1	8	yes	—
235	C₂×Q₈	C₂⁴	1	4	yes	—
236	C₂×D₄	—	2	8	no	—
237	C₂×D₄	—	4	16	no	—
238	C₂×D₄	—	4	4	no	—
239	C₂×D₄	—	4	4	no	—
240	C₂×D₄	—	4	8	no	—
241	C₂×D₄	—	4	8	no	—
242	C₂×D₄	—	4	8	no	—
243	C₂×D₄	—	4	4	no	—
244	C₂×D₄	—	4	2	no	—
245	C₂×D₄	—	4	2	no	—
246	C₂×D₄	—	4	2	no	—
247	C₂×D₄	—	4	8	no	—
248	C₂×D₄	C₂⁴	1	8	yes	—
249	C₂×D₄	C₂⁴	1	8	yes	—
250	C₂×D₄	C₂⁴	1	16	yes	—
251	C₂×D₄	C₂⁴	1	16	yes	—
252	C₂×D₄	C₂⁴	1	8	yes	—
253	C₂×D₄	C₂⁴	1	16	yes	—
254	C₂×D₄	C₂⁴	1	4	yes	—
255	C₂×D₄	C₂⁴	1	16	yes	—
256	C₂×D₄	C₂⁴	1	4	yes	—
257	C₂×D₄	C₂⁴	1	4	yes	—
258	C₂×D₄	C₂⁴	1	8	yes	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	4	16	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	4	8	no	—
267	C₂²×C₄	—	4	4	no	—
268	C₂²×C₄	—	4	8	no	—
269	C₂²×C₄	C₂⁴	1	4	yes	—
270	C₂²×C₄	C₂⁴	1	8	yes	—
271	C₂²×C₄	C₂⁴	1	4	yes	—
272	C₂²×C₄	C₂⁴	1	4	yes	—
273	C₂²×C₄	C₂⁴	1	2	yes	—
274	C₂²×C₄	C₂⁴	1	4	yes	—
275	C₂²×C₄	C₂⁴	1	4	yes	—
276	C₂²×C₄	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄	C₂⁴	1	2	yes	—
278	C₂²×C₄	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴	1	2	yes	—
280	C₂²×C₄	C₂⁴	1	4	yes	—
281	C₂²×C₄	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴	1	16	yes	—
283	C₂²×C₄	C₂⁴	1	16	yes	—
284	C₂²×C₄	C₂⁴	1	4	yes	—
285	C₂²×C₄	C₂⁴	1	8	yes	—
286	C₂²×C₄	C₂⁴	1	8	yes	—
287	C₂²×C₄	C₂⁴	1	1	yes	characteristic
288	C₄⋊C₄	C₂⁴	1	8	yes	—
289	C₄⋊C₄	C₂⁴	1	8	yes	—
290	C₄⋊C₄	C₂⁴	1	8	yes	—
291	C₄⋊C₄	C₂⁴	1	8	yes	—
292	C₄⋊C₄	C₂⁴	1	16	yes	—
293	C₄⋊C₄	C₂⁴	1	8	yes	—
294	C₄⋊C₄	C₂⁴	1	16	yes	—
295	C₄⋊C₄	C₂⁴	1	16	yes	—
296	C₄⋊C₄	C₂⁴	1	16	yes	—
297	C₄⋊C₄	C₂⁴	1	16	yes	—
298	C₂²⋊C₄	C₂⁴	1	8	yes	—
299	C₂²⋊C₄	C₂⁴	1	16	yes	—
300	C₂²⋊C₄	C₂⁴	1	16	yes	—
301	C₂²⋊C₄	C₂⁴	1	16	yes	—
302	C₂²⋊C₄	C₂⁴	1	8	yes	—
303	C₂²⋊C₄	C₂⁴	1	16	yes	—
304	C₂²⋊C₄	C₂⁴	1	4	yes	—
305	C₂²⋊C₄	C₂⁴	1	16	yes	—
306	C₂²⋊C₄	C₂⁴	1	4	yes	—
307	C₂²⋊C₄	C₂⁴	1	8	yes	—
308	C₂²⋊C₄	C₂⁴	1	8	yes	—
309	C₂²⋊C₄	C₂⁴	1	8	yes	—
310	C₂²⋊C₄	C₂⁴	1	16	yes	—
311	C₂²⋊C₄	C₂⁴	1	8	yes	—
312	C₂²⋊C₄	C₂⁴	1	16	yes	—
313	C₂²⋊C₄	C₂⁴	1	16	yes	—
314	C₂²⋊C₄	C₂⁴	1	16	yes	—
315	C₂²⋊C₄	C₂⁴	1	16	yes	—
316	C₄²	C₂⁴	1	8	yes	—
317	C₄²	C₂⁴	1	16	yes	—
318	C₄²	C₂⁴	1	8	yes	—
319	C₄²	C₂⁴	1	8	yes	—
320	C₄²	C₂⁴	1	16	yes	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	8	no	—
326	C₂³	—	2	8	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	4	8	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	4	16	no	—
337	C₂³	—	4	16	no	—
338	C₂³	—	8	16	no	—
339	C₂³	C₂⁵	1	2	yes	—
340	C₂³	C₂⁵	1	2	yes	—
341	C₂³	C₂⁵	1	4	yes	—
342	C₂³	C₂⁵	1	8	yes	—
343	C₂³	C₂⁵	1	2	yes	—
344	C₂³	C₂⁵	1	1	yes	characteristic
345	Q₈	—	2	16	no	—
346	Q₈	—	4	8	no	—
347	Q₈	—	4	16	no	—
348	Q₈	—	4	4	no	—
349	D₄	—	2	16	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	16	no	—
353	D₄	—	4	16	no	—
354	D₄	—	4	16	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	16	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	16	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	8	no	—
375	C₂×C₄	—	4	16	no	—
376	C₂×C₄	—	4	8	no	—
377	C₂×C₄	—	4	16	no	—
378	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
379	C₂×C₄	C₂⁵	1	4	yes	—
380	C₂×C₄	C₂⁵	1	8	yes	—
381	C₂×C₄	C₂⁵	1	8	yes	—
382	C₂×C₄	C₂⁵	1	2	yes	—
383	C₂×C₄	C₂⁵	1	4	yes	—
384	C₂×C₄	C₂⁵	1	2	yes	—
385	C₂×C₄	C₂⁵	1	4	yes	—
386	C₂×C₄	C₂⁵	1	8	yes	—
387	C₂×C₄	C₂⁵	1	2	yes	—
388	C₂×C₄	C₂⁵	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	8	no	—
394	C₂²	—	2	8	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	4	16	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	16	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	16	no	—
408	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₂²	#585	1	4	yes	—
410	C₂²	C₂⁶	1	1	yes	characteristic
411	C₄	—	2	4	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	8	no	—
416	C₄	—	2	4	no	—
417	C₄	—	2	8	no	—
418	C₄	—	2	8	no	—
419	C₄	—	2	4	no	—
420	C₄	C₂×H(5,𝔽₂)	1	4	yes	—
421	C₂	—	4	2	no	—
422	C₂	—	4	4	no	—
423	C₂	—	4	2	no	—
424	C₂	—	4	8	no	—
425	C₂	—	4	2	no	—
426	C₂	#3540	1	4	yes	direct product factor
427	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂	C₂×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3540	C₂	direct (N × H)
2. C₂×H(3,𝔽₄)	C₂	semidirect
3. C₂×#560	C₂	semidirect
4. C₂×#559	C₂	semidirect
5. C₂×#556	C₂	semidirect
6. C₂×#555	C₂	semidirect
7. C₂×#551	C₂	semidirect
8. C₂×#548	C₂	semidirect
9. C₂×#546	C₂	semidirect
10. C₂×#542	C₂	semidirect
11. C₂×#542	C₂	semidirect
12. C₂×#538	C₂	semidirect
13. C₂×#536	C₂	semidirect
14. C₂×#535	C₂	semidirect
15. C₂×#525	C₂	semidirect
16. C₂×#525	C₂	semidirect
19. C₂³×Q₈	C₂²	semidirect
20. C₂³×D₄	C₂²	semidirect
21. C₂⁴×C₄	C₂²	semidirect
22. H(3,𝔽₄)	C₂²	semidirect
23. #560	C₂²	semidirect
24. #559	C₂²	semidirect
25. #556	C₂²	semidirect
26. #555	C₂²	semidirect
27. #551	C₂²	semidirect
28. #548	C₂²	semidirect
29. #546	C₂²	semidirect
30. #542	C₂²	semidirect
31. #542	C₂²	semidirect
32. #538	C₂²	semidirect
33. #536	C₂²	semidirect
34. #535	C₂²	semidirect
35. C₂×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₄⋊Q₈	C₂²	semidirect
38. C₂×#126	C₂²	semidirect
39. C₂×#126	C₂²	semidirect
40. C₂×#126	C₂²	semidirect
43. C₂×#124	C₂²	semidirect
44. C₂×#124	C₂²	semidirect
45. C₂×#124	C₂²	semidirect
46. C₂×#124	C₂²	semidirect
47. C₂×#124	C₂²	semidirect
48. C₂×#124	C₂²	semidirect
49. #525	C₂²	semidirect
50. #525	C₂²	semidirect
52. C₂×#123	C₂²	semidirect
53. C₂×#123	C₂²	semidirect
54. C₂×#123	C₂²	semidirect
55. C₂×#123	C₂²	semidirect
56. C₂×#123	C₂²	semidirect
57. C₂×#123	C₂²	semidirect
58. C₂×C₂²⋊Q₈	C₂²	semidirect
59. C₂×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₂²⋊Q₈	C₂²	semidirect
61. C₂×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₂²⋊Q₈	C₂²	semidirect
68. C₂×#121	C₂²	semidirect
69. C₂×#121	C₂²	semidirect
70. C₂×#121	C₂²	semidirect
74. C₂×#120	C₂²	semidirect
75. C₂×#120	C₂²	semidirect
76. C₂×#120	C₂²	semidirect
77. C₂×C₄×Q₈	C₂²	semidirect
78. C₂×C₄×Q₈	C₂²	semidirect
80. C₂×C₄×D₄	C₂²	semidirect
81. C₂×C₄×D₄	C₂²	semidirect
82. C₂×C₄×D₄	C₂²	semidirect
83. C₂×C₄×D₄	C₂²	semidirect
84. C₂×C₄×D₄	C₂²	semidirect
85. C₂×#117	C₂²	semidirect
86. C₂×#117	C₂²	semidirect
87. C₂×#117	C₂²	semidirect
88. C₂×#117	C₂²	semidirect
89. C₂×#117	C₂²	semidirect
90. C₂²×C₂²⋊C₄	C₂²	semidirect
102. C₂²×Q₈	C₂³	semidirect
115. C₂²×D₄	C₂³	semidirect
126. C₂³×C₄	C₂³	semidirect
127. C₄⋊Q₈	C₂³	semidirect
128. C₄⋊Q₈	C₂³	semidirect
130. #126	C₂³	semidirect
131. #126	C₂³	semidirect
132. #126	C₂³	semidirect
135. #124	C₂³	semidirect
136. #124	C₂³	semidirect
137. #124	C₂³	semidirect
138. #124	C₂³	semidirect
139. #124	C₂³	semidirect
140. #124	C₂³	semidirect
142. #123	C₂³	semidirect
143. #123	C₂³	semidirect
144. #123	C₂³	semidirect
145. #123	C₂³	semidirect
146. #123	C₂³	semidirect
147. #123	C₂³	semidirect
148. C₂²⋊Q₈	C₂³	semidirect
149. C₂²⋊Q₈	C₂³	semidirect
150. C₂²⋊Q₈	C₂³	semidirect
151. C₂²⋊Q₈	C₂³	semidirect
152. C₂²⋊Q₈	C₂³	semidirect
153. C₂²⋊Q₈	C₂³	semidirect
158. #121	C₂³	semidirect
159. #121	C₂³	semidirect
160. #121	C₂³	semidirect
164. #120	C₂³	semidirect
165. #120	C₂³	semidirect
166. #120	C₂³	semidirect
167. C₄×Q₈	C₂³	semidirect
168. C₄×Q₈	C₂³	semidirect
170. C₄×D₄	C₂³	semidirect
171. C₄×D₄	C₂³	semidirect
172. C₄×D₄	C₂³	semidirect
173. C₄×D₄	C₂³	semidirect
174. C₄×D₄	C₂³	semidirect
175. #117	C₂³	semidirect
176. #117	C₂³	semidirect
177. #117	C₂³	semidirect
178. #117	C₂³	semidirect
179. #117	C₂³	semidirect
208. C₂×C₂²⋊C₄	C₂³	semidirect
426. C₂	#3540	direct (N × H)

Maximal subgroups

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

subgroup	index
#3540	2
C₂×H(3,𝔽₄)	2
C₂×#560	2
C₂×#559	2
C₂×#556	2
C₂×#555	2
C₂×#551	2
C₂×#548	2
C₂×#546	2
C₂×#542	2
C₂×#538	2
C₂×#536	2
C₂×#535	2
C₂×#525	2

Subgroups — C2×#3540 #62728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3540 #62728