Subgroups — #61201

Order 256.

1058 conjugacy classes of subgroups.

The subgroup lattice has 629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	#3323	C₂	1	2	yes	maximal, complemented
4	#3322	C₂	1	2	yes	maximal, complemented
5	#3318	C₂	1	2	yes	maximal, complemented
6	#3315	C₂	1	2	yes	maximal, complemented
7	#3310	C₂	1	2	yes	maximal, complemented
8	#3307	C₂	1	2	yes	maximal, complemented
9	#3297	C₂	1	2	yes	maximal, complemented
10	#3296	C₂	1	2	yes	maximal, complemented
11	#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#478	C₂	1	1	yes	maximal, characteristic, complemented
15	#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	#3060	C₂	1	1	yes	maximal, characteristic, complemented
17	#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×#135	C₂²	1	1	yes	characteristic, complemented
28	C₂×#135	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂×#131	C₂²	1	1	yes	characteristic, complemented
31	#553	—	2	2	no	—
32	#553	—	2	2	no	—
33	#553	C₂²	1	2	yes	complemented
34	#553	C₂²	1	2	yes	complemented
35	#552	C₂²	1	2	yes	complemented
36	#552	C₂²	1	2	yes	complemented
37	#547	—	2	1	no	—
38	#547	C₂²	1	2	yes	—
39	#546	—	2	1	no	—
40	#546	—	2	1	no	—
41	#546	C₂²	1	2	yes	—
42	#546	C₂²	1	2	yes	—
43	D₄²	—	2	1	no	—
44	D₄²	C₂²	1	2	yes	—
45	#541	—	2	1	no	—
46	#540	—	2	1	no	—
47	#537	C₂²	1	1	yes	characteristic
48	#537	C₂²	1	1	yes	characteristic
49	#537	C₂²	1	1	yes	characteristic, complemented
50	#537	C₂²	1	1	yes	characteristic, complemented
51	#534	—	2	2	no	—
52	#532	C₂²	1	1	yes	characteristic
53	#532	C₂²	1	1	yes	characteristic
54	#529	—	2	1	no	—
55	#529	—	2	1	no	—
56	C₂×#125	C₂²	1	1	yes	characteristic, complemented
57	C₂×#121	—	2	2	no	—
58	#520	C₂²	1	1	yes	characteristic, complemented
59	#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
62	#491	C₂²	1	2	yes	complemented
63	#490	C₂²	1	2	yes	complemented
64	#488	C₂²	1	2	yes	complemented
65	#488	C₂²	1	2	yes	complemented
66	#485	C₂²	1	2	yes	complemented
67	#485	C₂²	1	2	yes	complemented
68	#484	C₂²	1	2	yes	complemented
69	#483	C₂²	1	2	yes	complemented
70	#482	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#481	C₂²	1	2	yes	complemented
73	#480	C₂²	1	2	yes	complemented
74	#478	C₂²	1	2	yes	complemented
75	#478	C₂²	1	2	yes	complemented
76	#478	C₂²	1	2	yes	complemented
77	#478	C₂²	1	2	yes	complemented
78	#470	C₂²	1	2	yes	complemented
79	#469	C₂²	1	2	yes	complemented
80	#468	C₂²	1	2	yes	complemented
81	#468	C₂²	1	2	yes	complemented
82	#467	C₂²	1	2	yes	complemented
83	#466	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	complemented
85	#465	C₂²	1	2	yes	complemented
86	#464	C₂²	1	1	yes	characteristic, complemented
87	#464	C₂²	1	1	yes	characteristic, complemented
88	#463	C₂²	1	1	yes	characteristic, complemented
89	#463	C₂²	1	1	yes	characteristic, complemented
90	#462	C₂²	1	1	yes	characteristic, complemented
91	#461	C₂²	1	1	yes	characteristic, complemented
92	#460	C₂²	1	1	yes	characteristic, complemented
93	#459	C₂²	1	1	yes	characteristic, complemented
94	#452	C₂²	1	2	yes	complemented
95	#452	C₂²	1	2	yes	complemented
96	#450	C₂²	1	2	yes	complemented
97	#450	C₂²	1	2	yes	complemented
98	#449	C₂²	1	2	yes	complemented
99	#449	C₂²	1	2	yes	complemented
100	#447	C₂²	1	2	yes	complemented
101	#447	C₂²	1	2	yes	complemented
102	#442	C₂²	1	2	yes	complemented
103	#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×D₈	C₂²	1	2	yes	complemented
106	#436	C₂²	1	2	yes	complemented
107	#435	C₂²	1	2	yes	complemented
108	#435	C₂²	1	2	yes	complemented
109	C₈×D₄	C₂²	1	2	yes	complemented
110	#428	C₂²	1	1	yes	characteristic, complemented
111	C₂×#107	C₂²	1	1	yes	characteristic, complemented
112	C₂×#106	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
114	#418	C₂²	1	1	yes	characteristic
115	#418	C₂²	1	2	yes	complemented
116	#418	C₂²	1	2	yes	complemented
117	#417	C₂²	1	1	yes	characteristic, complemented
118	#417	C₂²	1	1	yes	characteristic, complemented
119	#417	C₂²	1	1	yes	characteristic, complemented
120	#417	C₂²	1	1	yes	characteristic, complemented
121	#417	C₂²	1	2	yes	complemented
122	#417	C₂²	1	2	yes	complemented
123	#417	C₂²	1	1	yes	characteristic, complemented
124	#416	C₂²	1	1	yes	characteristic, complemented
125	#416	C₂²	1	1	yes	characteristic, complemented
126	#416	C₂²	1	2	yes	complemented
127	#416	C₂²	1	2	yes	complemented
128	C₂×#102	C₂²	1	1	yes	characteristic
129	C₂×#102	C₂²	1	1	yes	characteristic
130	C₂×#102	C₂²	1	2	yes	complemented
131	C₂×#102	C₂²	1	2	yes	complemented
132	#408	C₂²	1	1	yes	characteristic, complemented
133	#408	C₂²	1	1	yes	characteristic, complemented
134	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)	—	2	4	no	—
136	H(5,𝔽₂)	—	2	4	no	—
137	H(5,𝔽₂)	—	4	2	no	—
138	H(5,𝔽₂)	—	4	2	no	—
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂×#41	C₂³	1	1	yes	characteristic
143	C₂×#41	C₂³	1	1	yes	characteristic
144	C₂×#41	C₂³	1	2	yes	—
145	C₂×#41	C₂³	1	2	yes	—
146	C₂×#41	C₂³	1	1	yes	characteristic
147	C₂×#41	C₂³	1	1	yes	characteristic
148	C₂²×D₄	—	2	2	no	—
149	C₂²×D₄	—	2	2	no	—
150	C₂²×D₄	—	2	1	no	—
151	C₂²×D₄	—	2	1	no	—
152	C₂²×D₄	—	2	2	no	—
153	C₂²×D₄	C₂³	1	2	yes	—
154	C₂²×D₄	C₂³	1	2	yes	—
155	C₂²×D₄	C₂³	1	1	yes	characteristic
156	C₂³×C₄	—	2	1	no	—
157	AGL(1,ℤ/8)	—	2	4	no	—
158	#135	—	4	2	no	—
159	#135	—	4	2	no	—
160	C₂×Q₁₆	C₂³	1	1	yes	characteristic
161	C₂×Q₁₆	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆	C₂³	1	2	yes	—
163	C₂×SD₁₆	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆	C₂³	1	1	yes	characteristic
166	C₂×SD₁₆	C₂³	1	1	yes	characteristic
167	C₂×D₈	C₂³	1	2	yes	—
168	C₂×D₈	C₂³	1	1	yes	characteristic
169	C₂×D₈	C₂³	1	1	yes	characteristic
170	#131	—	4	2	no	—
171	#131	—	4	2	no	—
172	C₂×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×M₁₆	C₂³	1	1	yes	characteristic
174	C₂×M₁₆	C₂³	1	2	yes	—
175	C₂×M₁₆	C₂³	1	2	yes	—
176	C₂²×C₈	C₂³	1	1	yes	characteristic
177	C₂²×C₈	C₂³	1	1	yes	characteristic
178	C₂²×C₈	C₂³	1	2	yes	—
179	C₂²×C₈	C₂³	1	2	yes	—
180	C₄⋊Q₈	D₄	1	1	yes	characteristic
181	C₄⋊Q₈	C₂³	1	1	yes	characteristic
182	#127	D₄	1	1	yes	characteristic
183	#127	C₂³	1	1	yes	characteristic
184	#126	—	2	2	no	—
185	#126	—	2	2	no	—
186	#126	—	2	2	no	—
187	#126	—	2	2	no	—
188	#125	—	2	2	no	—
189	#125	—	2	2	no	—
190	#125	—	2	1	no	—
191	#125	—	2	1	no	—
192	#125	C₂³	1	2	yes	—
193	#125	C₂³	1	2	yes	—
194	#124	D₄	1	1	yes	characteristic
195	#124	D₄	1	1	yes	characteristic
196	#124	C₂³	1	1	yes	characteristic
197	#124	C₂³	1	1	yes	characteristic
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	#123	—	2	2	no	—
202	#123	—	2	2	no	—
203	#123	—	2	2	no	—
204	#123	—	2	2	no	—
205	#123	—	2	2	no	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	—	2	1	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	#121	—	2	2	no	—
215	#121	—	2	2	no	—
216	#121	—	2	2	no	—
217	#121	—	2	1	no	—
218	#121	—	2	1	no	—
219	#121	—	2	1	no	—
220	#121	—	2	1	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	2	no	—
228	#121	—	2	2	no	—
229	#121	—	2	2	no	—
230	#121	D₄	1	2	yes	—
231	#121	D₄	1	2	yes	—
232	#121	C₂³	1	2	yes	—
233	#121	C₂³	1	2	yes	—
234	#121	C₂³	1	2	yes	—
235	#121	C₂³	1	2	yes	—
236	#120	—	2	2	no	—
237	#120	—	2	2	no	—
238	#120	—	2	2	no	—
239	#120	—	2	2	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×Q₈	—	2	1	no	—
242	C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	C₂³	1	2	yes	—
257	C₄×D₄	C₂³	1	2	yes	—
258	C₄×D₄	C₂³	1	1	yes	characteristic
259	C₄×D₄	C₂³	1	1	yes	characteristic
260	C₄×D₄	C₂³	1	2	yes	—
261	C₄×D₄	C₂³	1	2	yes	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	—	2	1	no	—
265	#117	C₂³	1	1	yes	characteristic
266	#117	C₂³	1	2	yes	—
267	#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³	1	1	yes	characteristic
281	#107	C₂³	1	2	yes	—
282	#107	C₂³	1	2	yes	—
283	#107	C₂³	1	2	yes	—
284	#106	C₂³	1	2	yes	—
285	#106	C₂³	1	2	yes	—
286	#106	C₂³	1	2	yes	—
287	C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₄⋊C₈	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
299	#103	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	1	yes	characteristic
305	#102	C₂³	1	1	yes	characteristic
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	2	yes	—
308	#102	C₂³	1	2	yes	—
309	#102	C₂³	1	2	yes	—
310	#102	C₂³	1	1	yes	characteristic
311	#102	C₂³	1	1	yes	characteristic
312	#102	C₂³	1	2	yes	—
313	#102	C₂³	1	2	yes	—
314	#102	C₂³	1	2	yes	—
315	C₂²⋊C₈	C₂³	1	2	yes	—
316	C₂²⋊C₈	C₂³	1	2	yes	—
317	C₂²⋊C₈	C₂³	1	2	yes	—
318	C₂²⋊C₈	C₂³	1	2	yes	—
319	#97	C₂³	1	2	yes	—
320	C₄×C₈	C₂³	1	2	yes	—
321	C₂⁴	—	2	1	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	4	no	—
329	#41	—	2	4	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	—	4	2	no	—
337	#41	—	4	2	no	—
338	#41	—	4	4	no	—
339	#41	—	4	4	no	—
340	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
341	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
342	C₂×Q₈	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈	C₂⁴	1	1	yes	characteristic
344	C₂×Q₈	C₂⁴	1	1	yes	characteristic
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	4	8	no	—
367	C₂×D₄	—	4	8	no	—
368	C₂×D₄	—	8	4	no	—
369	C₂×D₄	C₂×D₄	1	2	yes	—
370	C₂×D₄	C₂×D₄	1	2	yes	—
371	C₂×D₄	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄	C₂×D₄	1	2	yes	—
374	C₂×D₄	C₂×D₄	1	2	yes	—
375	C₂×D₄	#41	1	4	yes	—
376	C₂×D₄	C₂⁴	1	1	yes	characteristic
377	C₂×D₄	C₂⁴	1	1	yes	characteristic
378	C₂×D₄	C₂⁴	1	1	yes	characteristic
379	C₂×D₄	C₂⁴	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	8	2	no	—
395	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴	1	2	yes	—
398	C₂²×C₄	C₂⁴	1	2	yes	—
399	C₂²×C₄	C₂⁴	1	1	yes	characteristic
400	Q₁₆	—	4	1	no	—
401	Q₁₆	—	4	1	no	—
402	SD₁₆	—	2	4	no	—
403	SD₁₆	—	4	1	no	—
404	SD₁₆	—	4	1	no	—
405	SD₁₆	—	4	1	no	—
406	SD₁₆	—	4	1	no	—
407	D₈	—	2	4	no	—
408	D₈	—	4	1	no	—
409	D₈	—	4	1	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	4	2	no	—
413	M₁₆	—	4	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	4	2	no	—
417	C₂×C₈	—	4	2	no	—
418	C₂×C₈	C₂⁴	1	2	yes	—
419	C₂×C₈	C₂⁴	1	2	yes	—
420	C₂×C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₈	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	C₂×D₄	1	2	yes	—
442	C₄⋊C₄	C₂×D₄	1	2	yes	—
443	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄	C₂⁴	1	2	yes	—
445	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄	C₂⁴	1	2	yes	—
447	C₄⋊C₄	C₂⁴	1	2	yes	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄	C₂×D₄	1	2	yes	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	C₂×D₄	1	1	yes	characteristic
477	C₄²	C₂×D₄	1	1	yes	characteristic
478	C₄²	C₂⁴	1	1	yes	characteristic
479	C₄²	C₂⁴	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	8	1	no	—
488	C₂³	—	8	1	no	—
489	C₂³	—	8	2	no	—
490	C₂³	—	8	2	no	—
491	C₂³	—	8	2	no	—
492	C₂³	—	8	2	no	—
493	C₂³	C₂²×D₄	1	2	yes	—
494	C₂³	C₂²×D₄	1	2	yes	—
495	C₂³	C₂²×D₄	1	1	yes	characteristic
496	Q₈	—	2	2	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	4	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	2	no	—
508	D₄	—	2	2	no	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	1	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	4	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	4	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	8	1	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	2	no	—
529	D₄	—	8	2	no	—
530	D₄	—	8	2	no	—
531	D₄	C₂×#41	1	4	yes	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	8	1	no	—
553	C₂×C₄	—	8	1	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	—	8	2	no	—
556	C₂×C₄	—	8	1	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	1	no	—
559	C₂×C₄	—	8	1	no	—
560	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄	1	2	yes	—
563	C₂×C₄	C₂²×D₄	1	2	yes	—
564	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄	C₂×#41	1	2	yes	—
568	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
569	C₂×C₄	C₂⁵	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	2	1	no	—
574	C₈	—	2	1	no	—
575	C₈	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	8	4	no	—
597	C₂²	—	16	4	no	—
598	C₂²	—	16	4	no	—
599	C₂²	#546	1	2	yes	—
600	C₂²	C₂³×D₄	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	#546	1	2	yes	—
616	C₄	C₂²×#41	1	1	yes	characteristic
617	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂	—	2	2	no	—
619	C₂	—	4	2	no	—
620	C₂	—	4	2	no	—
621	C₂	—	4	4	no	—
622	C₂	—	8	1	no	—
623	C₂	—	8	1	no	—
624	C₂	—	8	1	no	—
625	C₂	C₂×#546	1	1	yes	characteristic
626	C₂	#3584	1	1	yes	characteristic
627	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #532 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3512	C₂	semidirect
2. #3496	C₂	semidirect
3. #3323	C₂	semidirect
4. #3322	C₂	semidirect
5. #3318	C₂	semidirect
6. #3315	C₂	semidirect
7. #3310	C₂	semidirect
8. #3307	C₂	semidirect
9. #3297	C₂	semidirect
10. #3296	C₂	semidirect
11. #3142	C₂	semidirect
12. #3099	C₂	semidirect
13. #3098	C₂	semidirect
14. C₂×#478	C₂	semidirect
15. #3061	C₂	semidirect
16. #3060	C₂	semidirect
17. #3035	C₂	semidirect
18. #3012	C₂	semidirect
19. #3012	C₂	semidirect
20. C₄×AGL(1,ℤ/8)	C₂	semidirect
21. #2935	C₂	semidirect
22. #2897	C₂	semidirect
23. #2897	C₂	semidirect
27. C₂×#135	C₂²	semidirect
28. C₂×#135	C₂²	semidirect
29. C₂×#131	C₂²	semidirect
30. C₂×#131	C₂²	semidirect
33. #553	C₂²	semidirect
34. #553	C₂²	semidirect
35. #552	C₂²	semidirect
36. #552	C₂²	semidirect
49. #537	C₂²	semidirect
50. #537	C₂²	semidirect
56. C₂×#125	C₂²	semidirect
58. #520	C₂²	semidirect
59. #520	C₂²	semidirect
60. C₄×#41	C₂²	semidirect
62. #491	C₂²	semidirect
63. #490	C₂²	semidirect
64. #488	C₂²	semidirect
65. #488	C₂²	semidirect
66. #485	C₂²	semidirect
67. #485	C₂²	semidirect
68. #484	C₂²	semidirect
69. #483	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
72. #481	C₂²	semidirect
73. #480	C₂²	semidirect
74. #478	C₂²	semidirect
75. #478	C₂²	semidirect
76. #478	C₂²	semidirect
77. #478	C₂²	semidirect
78. #470	C₂²	semidirect
79. #469	C₂²	semidirect
80. #468	C₂²	semidirect
81. #468	C₂²	semidirect
82. #467	C₂²	semidirect
83. #466	C₂²	semidirect
84. #465	C₂²	semidirect
85. #465	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
88. #463	C₂²	semidirect
89. #463	C₂²	semidirect
90. #462	C₂²	semidirect
91. #461	C₂²	semidirect
92. #460	C₂²	semidirect
93. #459	C₂²	semidirect
94. #452	C₂²	semidirect
95. #452	C₂²	semidirect
96. #450	C₂²	semidirect
97. #450	C₂²	semidirect
98. #449	C₂²	semidirect
99. #449	C₂²	semidirect
100. #447	C₂²	semidirect
101. #447	C₂²	semidirect
102. #442	C₂²	semidirect
103. #440	C₂²	semidirect
104. C₄×SD₁₆	C₂²	semidirect
105. C₄×D₈	C₂²	semidirect
106. #436	C₂²	semidirect
107. #435	C₂²	semidirect
108. #435	C₂²	semidirect
109. C₈×D₄	C₂²	semidirect
110. #428	C₂²	semidirect
111. C₂×#107	C₂²	semidirect
112. C₂×#106	C₂²	semidirect
113. C₂×C₄⋊C₈	C₂²	semidirect
115. #418	C₂²	semidirect
116. #418	C₂²	semidirect
117. #417	C₂²	semidirect
118. #417	C₂²	semidirect
119. #417	C₂²	semidirect
120. #417	C₂²	semidirect
121. #417	C₂²	semidirect
122. #417	C₂²	semidirect
123. #417	C₂²	semidirect
124. #416	C₂²	semidirect
125. #416	C₂²	semidirect
126. #416	C₂²	semidirect
127. #416	C₂²	semidirect
130. C₂×#102	C₂²	semidirect
131. C₂×#102	C₂²	semidirect
132. #408	C₂²	semidirect
133. #408	C₂²	semidirect
134. C₄×M₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3512	2
#3496	2
#3323	2
#3322	2
#3318	2
#3315	2
#3310	2
#3307	2
#3297	2
#3296	2
#3142	2
#3099	2
#3098	2
C₂×#478	2
#3061	2
#3060	2
#3035	2
#3012	2
C₄×AGL(1,ℤ/8)	2
#2935	2
#2897	2