Subgroups — #62051

Order 256.

1010 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	#3318	C₂	1	2	yes	maximal, complemented
9	#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	#3297	C₂	1	2	yes	maximal, complemented
11	D₄×D₈	C₂	1	2	yes	maximal, complemented
12	D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	#3264	C₂	1	2	yes	maximal, complemented
15	#3259	C₂	1	2	yes	maximal, complemented
16	#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	#3220	C₂	1	2	yes	maximal, complemented
18	#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	#3122	C₂	1	2	yes	maximal, complemented
20	#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	#3041	C₂	1	2	yes	maximal, complemented
22	C₂×#459	C₂	1	1	yes	maximal, characteristic, complemented
23	#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂²×D₈	C₂²	1	2	yes	complemented
26	C₂²×D₈	C₂²	1	2	yes	complemented
27	#560	—	2	2	no	—
28	#559	C₂²	1	1	yes	characteristic, complemented
29	#555	C₂²	1	1	yes	characteristic, complemented
30	#554	C₂²	1	1	yes	characteristic, complemented
31	#553	—	2	1	no	—
32	#553	C₂²	1	2	yes	complemented
33	#550	C₂²	1	1	yes	characteristic, complemented
34	#550	C₂²	1	1	yes	characteristic, complemented
35	#550	C₂²	1	1	yes	characteristic, complemented
36	#546	—	2	1	no	—
37	#546	—	2	2	no	—
38	#546	—	2	1	no	—
39	#546	C₂²	1	2	yes	complemented
40	D₄²	—	2	1	no	—
41	D₄²	C₂²	1	2	yes	complemented
42	D₄²	C₂²	1	1	yes	characteristic, complemented
43	D₄²	C₂²	1	2	yes	complemented
44	D₄²	C₂²	1	1	yes	characteristic, complemented
45	#540	—	2	1	no	—
46	#540	C₂²	1	2	yes	complemented
47	#540	C₂²	1	2	yes	complemented
48	#538	—	2	2	no	—
49	#535	—	2	1	no	—
50	#535	C₂²	1	2	yes	complemented
51	#534	—	2	2	no	—
52	#532	C₂²	1	1	yes	characteristic, complemented
53	C₂×#127	C₂²	1	1	yes	characteristic, complemented
54	#529	C₂²	1	1	yes	characteristic
55	#529	C₂²	1	1	yes	characteristic, complemented
56	#525	—	2	1	no	—
57	C₂×#121	—	2	1	no	—
58	#518	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
60	#496	C₂²	1	2	yes	complemented
61	#493	C₂²	1	1	yes	characteristic, complemented
62	#493	C₂²	1	2	yes	complemented
63	#493	C₂²	1	1	yes	characteristic, complemented
64	#490	C₂²	1	2	yes	complemented
65	#488	C₂²	1	2	yes	complemented
66	#486	C₂²	1	1	yes	characteristic, complemented
67	#486	C₂²	1	1	yes	characteristic, complemented
68	#484	C₂²	1	1	yes	characteristic, complemented
69	#482	C₂²	1	2	yes	complemented
70	#482	C₂²	1	2	yes	complemented
71	#481	C₂²	1	1	yes	characteristic, complemented
72	#478	C₂²	1	1	yes	characteristic, complemented
73	#478	C₂²	1	1	yes	characteristic, complemented
74	#478	C₂²	1	2	yes	complemented
75	#478	C₂²	1	2	yes	complemented
76	#478	C₂²	1	2	yes	complemented
77	#477	C₂²	1	1	yes	characteristic, complemented
78	#476	C₂²	1	1	yes	characteristic, complemented
79	#469	C₂²	1	2	yes	complemented
80	#469	C₂²	1	2	yes	complemented
81	#466	C₂²	1	2	yes	complemented
82	#466	C₂²	1	2	yes	complemented
83	#466	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	complemented
85	#463	C₂²	1	1	yes	characteristic, complemented
86	#463	C₂²	1	1	yes	characteristic, complemented
87	#463	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#463	C₂²	1	2	yes	complemented
90	#460	C₂²	1	1	yes	characteristic, complemented
91	#459	C₂²	1	1	yes	characteristic
92	#459	C₂²	1	1	yes	characteristic, complemented
93	#459	C₂²	1	2	yes	complemented
94	#459	C₂²	1	2	yes	complemented
95	#459	C₂²	1	2	yes	complemented
96	#459	C₂²	1	1	yes	characteristic, complemented
97	#459	C₂²	1	2	yes	complemented
98	#459	C₂²	1	1	yes	characteristic, complemented
99	#459	C₂²	1	2	yes	complemented
100	#459	C₂²	1	2	yes	complemented
101	#459	C₂²	1	1	yes	characteristic, complemented
102	#459	C₂²	1	2	yes	complemented
103	#459	C₂²	1	2	yes	complemented
104	#450	C₂²	1	1	yes	characteristic, complemented
105	#449	C₂²	1	2	yes	complemented
106	#449	C₂²	1	2	yes	complemented
107	#447	C₂²	1	1	yes	characteristic
108	#447	C₂²	1	2	yes	complemented
109	#447	C₂²	1	2	yes	complemented
110	#447	C₂²	1	2	yes	complemented
111	#447	C₂²	1	2	yes	complemented
112	#447	C₂²	1	2	yes	complemented
113	#447	C₂²	1	2	yes	complemented
114	#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	#442	C₂²	1	2	yes	complemented
117	#442	C₂²	1	2	yes	complemented
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈	C₂²	1	2	yes	complemented
123	C₄×D₈	C₂²	1	2	yes	complemented
124	#436	C₂²	1	1	yes	characteristic, complemented
125	#435	C₂²	1	2	yes	complemented
126	C₈×D₄	C₂²	1	2	yes	complemented
127	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
128	#433	C₂²	1	2	yes	complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	#418	C₂²	1	2	yes	complemented
133	#416	C₂²	1	2	yes	complemented
134	C₂×#102	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂²×D₄	—	2	1	no	—
140	C₂²×D₄	—	2	2	no	—
141	C₂²×D₄	—	2	2	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	—	2	1	no	—
145	C₂²×D₄	C₂³	1	1	yes	characteristic
146	C₂²×D₄	C₂³	1	2	yes	—
147	C₂²×D₄	C₂³	1	2	yes	—
148	C₂²×D₄	C₂³	1	2	yes	—
149	C₂³×C₄	—	2	1	no	—
150	AGL(1,ℤ/8)	—	4	4	no	—
151	C₂×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×D₈	—	4	4	no	—
155	C₂×D₈	—	4	4	no	—
156	C₂×D₈	C₂³	1	1	yes	characteristic
157	C₂×D₈	C₂³	1	2	yes	—
158	C₂×D₈	C₂³	1	2	yes	—
159	C₂×D₈	C₂³	1	2	yes	—
160	C₂×D₈	C₂³	1	2	yes	—
161	C₂×D₈	C₂³	1	2	yes	—
162	C₂×D₈	C₂³	1	2	yes	—
163	C₂×D₈	C₂³	1	2	yes	—
164	C₂×D₈	C₂³	1	1	yes	characteristic
165	C₂×D₈	C₂³	1	2	yes	—
166	C₂×D₈	C₂³	1	2	yes	—
167	C₂×M₁₆	C₂³	1	2	yes	—
168	C₂²×C₈	C₂³	1	2	yes	—
169	C₂²×C₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	#127	—	2	1	no	—
172	#127	—	2	1	no	—
173	#127	—	2	1	no	—
174	#127	C₂³	1	2	yes	—
175	#127	C₂³	1	1	yes	characteristic
176	#127	C₂³	1	1	yes	characteristic
177	#127	C₂³	1	1	yes	characteristic
178	#127	C₂³	1	2	yes	—
179	#127	C₂³	1	2	yes	—
180	#126	—	2	2	no	—
181	#126	—	2	1	no	—
182	#126	D₄	1	2	yes	—
183	#125	D₄	1	1	yes	characteristic
184	#125	C₂³	1	1	yes	characteristic
185	#125	C₂³	1	2	yes	—
186	#124	—	2	1	no	—
187	#124	—	2	2	no	—
188	#124	—	2	1	no	—
189	#124	D₄	1	1	yes	characteristic
190	#124	C₂³	1	1	yes	characteristic
191	#124	C₂³	1	2	yes	—
192	#123	—	2	1	no	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	D₄	1	2	yes	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	D₄	1	1	yes	characteristic
204	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	#121	—	2	2	no	—
206	#121	—	2	1	no	—
207	#121	—	2	1	no	—
208	#121	—	2	1	no	—
209	#121	—	2	1	no	—
210	#121	—	2	2	no	—
211	#121	—	2	2	no	—
212	#121	—	2	2	no	—
213	#121	—	2	2	no	—
214	#121	—	2	2	no	—
215	#121	—	2	1	no	—
216	#121	—	2	1	no	—
217	#121	—	2	2	no	—
218	#121	—	2	2	no	—
219	#121	—	2	2	no	—
220	#121	—	2	2	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	D₄	1	1	yes	characteristic
225	#121	C₂³	1	1	yes	characteristic
226	#121	C₂³	1	2	yes	—
227	#121	C₂³	1	2	yes	—
228	#121	C₂³	1	2	yes	—
229	#121	C₂³	1	2	yes	—
230	#121	C₂³	1	2	yes	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	#120	—	2	2	no	—
234	#120	—	2	2	no	—
235	#120	—	2	2	no	—
236	#120	—	2	2	no	—
237	#120	—	2	2	no	—
238	#120	—	2	2	no	—
239	#120	—	2	2	no	—
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	C₂³	1	1	yes	characteristic
252	C₄×D₄	C₂³	1	1	yes	characteristic
253	C₄×D₄	C₂³	1	1	yes	characteristic
254	C₄×D₄	C₂³	1	1	yes	characteristic
255	C₄×D₄	C₂³	1	2	yes	—
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	2	yes	—
260	C₄×D₄	C₂³	1	2	yes	—
261	C₄×D₄	C₂³	1	2	yes	—
262	C₄×D₄	C₂³	1	1	yes	characteristic
263	#117	—	2	1	no	—
264	#117	—	2	1	no	—
265	#117	C₂³	1	2	yes	—
266	#117	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	2	yes	—
276	#107	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	1	yes	characteristic
279	#106	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	2	yes	—
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	1	yes	characteristic
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	1	yes	characteristic
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	1	yes	characteristic
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	#97	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	—	2	1	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	2	2	no	—
318	C₂⁴	—	2	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	2	no	—
321	#41	—	8	2	no	—
322	#41	—	8	2	no	—
323	#41	—	8	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	8	2	no	—
359	C₂×D₄	—	8	2	no	—
360	C₂×D₄	—	8	2	no	—
361	C₂×D₄	—	8	2	no	—
362	C₂×D₄	—	8	4	no	—
363	C₂×D₄	—	8	4	no	—
364	C₂×D₄	C₂×D₄	1	2	yes	—
365	C₂×D₄	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄	C₂⁴	1	2	yes	—
367	C₂×D₄	C₂⁴	1	1	yes	characteristic
368	C₂×D₄	C₂⁴	1	2	yes	—
369	C₂×D₄	C₂⁴	1	1	yes	characteristic
370	C₂×D₄	C₂⁴	1	2	yes	—
371	C₂×D₄	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	8	2	no	—
385	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴	1	2	yes	—
389	SD₁₆	—	2	2	no	—
390	SD₁₆	—	4	1	no	—
391	SD₁₆	—	4	2	no	—
392	D₈	—	2	2	no	—
393	D₈	—	2	4	no	—
394	D₈	—	2	4	no	—
395	D₈	—	4	2	no	—
396	D₈	—	4	2	no	—
397	D₈	—	4	2	no	—
398	D₈	—	4	2	no	—
399	D₈	—	4	2	no	—
400	D₈	—	4	1	no	—
401	D₈	—	4	2	no	—
402	D₈	—	4	2	no	—
403	M₁₆	—	4	2	no	—
404	C₂×C₈	—	4	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	C₂⁴	1	1	yes	characteristic
407	C₂×C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₈	C₂⁴	1	1	yes	characteristic
410	C₂×C₈	C₂⁴	1	2	yes	—
411	C₂×C₈	C₂⁴	1	2	yes	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₄⋊C₄	C₂×D₄	1	2	yes	—
424	C₄⋊C₄	C₂×D₄	1	2	yes	—
425	C₄⋊C₄	C₂×D₄	1	2	yes	—
426	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄	C₂⁴	1	2	yes	—
429	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄	C₂×D₄	1	2	yes	—
455	C₂²⋊C₄	C₂×D₄	1	2	yes	—
456	C₂²⋊C₄	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄	C₂×D₄	1	2	yes	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	1	no	—
460	C₄²	C₂×D₄	1	1	yes	characteristic
461	C₄²	C₂×D₄	1	1	yes	characteristic
462	C₄²	C₂⁴	1	1	yes	characteristic
463	C₄²	C₂⁴	1	2	yes	—
464	C₄²	C₂⁴	1	1	yes	characteristic
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	8	1	no	—
476	C₂³	—	8	2	no	—
477	C₂³	—	8	2	no	—
478	C₂³	—	8	2	no	—
479	C₂³	—	8	2	no	—
480	C₂³	—	8	2	no	—
481	C₂³	—	8	2	no	—
482	C₂³	—	8	2	no	—
483	C₂³	C₂²×D₄	1	2	yes	—
484	C₂³	C₂²×D₄	1	1	yes	characteristic
485	Q₈	—	2	2	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	8	1	no	—
489	D₄	—	2	4	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	1	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	1	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	1	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	1	no	—
499	D₄	—	2	1	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	4	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	8	2	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	2	no	—
513	D₄	—	8	1	no	—
514	D₄	—	8	1	no	—
515	D₄	—	8	2	no	—
516	D₄	—	8	2	no	—
517	D₄	—	8	1	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	2	no	—
520	D₄	—	8	2	no	—
521	D₄	—	8	2	no	—
522	D₄	—	8	2	no	—
523	D₄	—	8	2	no	—
524	D₄	—	8	2	no	—
525	D₄	H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	1	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	C₂²×D₄	1	2	yes	—
551	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄	1	2	yes	—
556	C₂×C₄	C₂²×D₄	1	2	yes	—
557	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄	C₂⁵	1	1	yes	characteristic
559	C₈	—	2	1	no	—
560	C₈	—	2	2	no	—
561	C₈	—	2	2	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	8	4	no	—
589	C₂²	—	16	4	no	—
590	C₂²	—	16	4	no	—
591	C₂²	—	16	4	no	—
592	C₂²	#576	1	2	yes	—
593	C₂²	C₂³×D₄	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	2	no	—
607	C₄	#576	1	2	yes	—
608	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
609	C₄	#585	1	1	yes	characteristic
610	C₂	—	2	2	no	—
611	C₂	—	4	2	no	—
612	C₂	—	4	2	no	—
613	C₂	—	8	1	no	—
614	C₂	—	8	2	no	—
615	C₂	—	8	2	no	—
616	C₂	—	8	1	no	—
617	C₂	—	8	2	no	—
618	C₂	#3488	1	1	yes	characteristic
619	C₂	C₂×#576	1	1	yes	characteristic
620	C₂	C₂×#576	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 ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3543	C₂	semidirect
2. #3519	C₂	semidirect
3. #3399	C₂	semidirect
4. #3391	C₂	semidirect
5. #3366	C₂	semidirect
6. #3361	C₂	semidirect
7. #3325	C₂	semidirect
8. #3318	C₂	semidirect
9. #3305	C₂	semidirect
10. #3297	C₂	semidirect
11. D₄×D₈	C₂	semidirect
12. D₄×D₈	C₂	semidirect
13. #3274	C₂	semidirect
14. #3264	C₂	semidirect
15. #3259	C₂	semidirect
16. #3247	C₂	semidirect
17. #3220	C₂	semidirect
18. #3205	C₂	semidirect
19. #3122	C₂	semidirect
20. #3105	C₂	semidirect
21. #3041	C₂	semidirect
22. C₂×#459	C₂	semidirect
23. #2994	C₂	semidirect
24. C₂×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂²×D₈	C₂²	semidirect
26. C₂²×D₈	C₂²	semidirect
28. #559	C₂²	semidirect
29. #555	C₂²	semidirect
30. #554	C₂²	semidirect
32. #553	C₂²	semidirect
33. #550	C₂²	semidirect
34. #550	C₂²	semidirect
35. #550	C₂²	semidirect
39. #546	C₂²	semidirect
41. D₄²	C₂²	semidirect
42. D₄²	C₂²	semidirect
43. D₄²	C₂²	semidirect
44. D₄²	C₂²	semidirect
46. #540	C₂²	semidirect
47. #540	C₂²	semidirect
50. #535	C₂²	semidirect
52. #532	C₂²	semidirect
53. C₂×#127	C₂²	semidirect
55. #529	C₂²	semidirect
58. #518	C₂²	semidirect
59. C₂×C₄×D₄	C₂²	semidirect
60. #496	C₂²	semidirect
61. #493	C₂²	semidirect
62. #493	C₂²	semidirect
63. #493	C₂²	semidirect
64. #490	C₂²	semidirect
65. #488	C₂²	semidirect
66. #486	C₂²	semidirect
67. #486	C₂²	semidirect
68. #484	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
71. #481	C₂²	semidirect
72. #478	C₂²	semidirect
73. #478	C₂²	semidirect
74. #478	C₂²	semidirect
75. #478	C₂²	semidirect
76. #478	C₂²	semidirect
77. #477	C₂²	semidirect
78. #476	C₂²	semidirect
79. #469	C₂²	semidirect
80. #469	C₂²	semidirect
81. #466	C₂²	semidirect
82. #466	C₂²	semidirect
83. #466	C₂²	semidirect
84. #465	C₂²	semidirect
85. #463	C₂²	semidirect
86. #463	C₂²	semidirect
87. #463	C₂²	semidirect
88. #463	C₂²	semidirect
89. #463	C₂²	semidirect
90. #460	C₂²	semidirect
92. #459	C₂²	semidirect
93. #459	C₂²	semidirect
94. #459	C₂²	semidirect
95. #459	C₂²	semidirect
96. #459	C₂²	semidirect
97. #459	C₂²	semidirect
98. #459	C₂²	semidirect
99. #459	C₂²	semidirect
100. #459	C₂²	semidirect
101. #459	C₂²	semidirect
102. #459	C₂²	semidirect
103. #459	C₂²	semidirect
104. #450	C₂²	semidirect
105. #449	C₂²	semidirect
106. #449	C₂²	semidirect
108. #447	C₂²	semidirect
109. #447	C₂²	semidirect
110. #447	C₂²	semidirect
111. #447	C₂²	semidirect
112. #447	C₂²	semidirect
113. #447	C₂²	semidirect
114. #446	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
116. #442	C₂²	semidirect
117. #442	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
119. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
121. C₄×D₈	C₂²	semidirect
122. C₄×D₈	C₂²	semidirect
123. C₄×D₈	C₂²	semidirect
124. #436	C₂²	semidirect
125. #435	C₂²	semidirect
126. C₈×D₄	C₂²	semidirect
127. C₈×D₄	C₂²	semidirect
128. #433	C₂²	semidirect
129. #431	C₂²	semidirect
130. #424	C₂²	semidirect
131. C₂×C₄⋊C₈	C₂²	semidirect
132. #418	C₂²	semidirect
133. #416	C₂²	semidirect
134. C₂×#102	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3543	2
#3519	2
#3399	2
#3391	2
#3366	2
#3361	2
#3325	2
#3318	2
#3305	2
#3297	2
D₄×D₈	2
#3274	2
#3264	2
#3259	2
#3247	2
#3220	2
#3205	2
#3122	2
#3105	2
#3041	2
C₂×#459	2
#2994	2