Subgroups — #61216

Order 256.

1030 conjugacy classes of subgroups.

The subgroup lattice has 614 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	#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	#3327	C₂	1	2	yes	maximal, complemented
4	#3326	C₂	1	2	yes	maximal, complemented
5	#3323	C₂	1	2	yes	maximal, complemented
6	#3322	C₂	1	2	yes	maximal, complemented
7	#3301	C₂	1	2	yes	maximal, complemented
8	#3300	C₂	1	2	yes	maximal, complemented
9	#3297	C₂	1	2	yes	maximal, complemented
10	#3296	C₂	1	2	yes	maximal, complemented
11	C₂×#488	C₂	1	1	yes	maximal, characteristic, complemented
12	#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	#3080	C₂	1	1	yes	maximal, characteristic, complemented
15	#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	#3040	C₂	1	1	yes	maximal, characteristic, complemented
18	#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
21	#2931	C₂	1	1	yes	maximal, characteristic, complemented
22	#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×#135	C₂²	1	1	yes	characteristic
29	C₂×#131	C₂²	1	1	yes	characteristic
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	#548	C₂²	1	2	yes	—
38	#548	C₂²	1	2	yes	—
39	#546	—	2	2	no	—
40	#546	—	2	2	no	—
41	#546	C₂²	1	2	yes	—
42	#546	C₂²	1	2	yes	—
43	#541	—	2	1	no	—
44	#540	—	2	1	no	—
45	#537	C₂²	1	1	yes	characteristic
46	#537	C₂²	1	1	yes	characteristic, complemented
47	#536	—	2	1	no	—
48	#536	C₂²	1	1	yes	characteristic
49	#535	—	2	1	no	—
50	#535	C₂²	1	1	yes	characteristic
51	#532	—	2	1	no	—
52	#532	C₂²	1	1	yes	characteristic
53	#529	—	2	1	no	—
54	#529	—	2	1	no	—
55	C₂×#125	C₂²	1	1	yes	characteristic, complemented
56	C₂×#124	—	2	1	no	—
57	C₂×#124	C₂²	1	1	yes	characteristic
58	#520	C₂²	1	1	yes	characteristic
59	#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41	C₂²	1	1	yes	characteristic
61	C₄×#41	C₂²	1	1	yes	characteristic, complemented
62	#488	C₂²	1	2	yes	complemented
63	#488	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	#479	C₂²	1	2	yes	complemented
75	#479	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	2	yes	complemented
87	#464	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#463	C₂²	1	2	yes	complemented
90	#452	C₂²	1	2	yes	—
91	#452	C₂²	1	2	yes	complemented
92	#451	C₂²	1	2	yes	complemented
93	#450	C₂²	1	2	yes	—
94	#449	C₂²	1	2	yes	—
95	#449	C₂²	1	2	yes	complemented
96	#448	C₂²	1	2	yes	complemented
97	#447	C₂²	1	2	yes	—
98	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
99	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
100	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
102	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
103	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
106	#436	C₂²	1	2	yes	complemented
107	#436	C₂²	1	2	yes	complemented
108	C₈×D₄	C₂²	1	2	yes	complemented
109	C₈×D₄	C₂²	1	2	yes	complemented
110	#428	C₂²	1	1	yes	characteristic, complemented
111	#428	C₂²	1	1	yes	characteristic, complemented
112	#427	C₂²	1	1	yes	characteristic, complemented
113	#423	C₂²	1	1	yes	characteristic, complemented
114	#419	C₂²	1	1	yes	characteristic, complemented
115	#419	C₂²	1	2	yes	complemented
116	#418	C₂²	1	1	yes	characteristic
117	#418	C₂²	1	2	yes	—
118	#417	C₂²	1	1	yes	characteristic
119	#417	C₂²	1	1	yes	characteristic
120	#417	C₂²	1	2	yes	—
121	#417	C₂²	1	2	yes	complemented
122	#416	C₂²	1	1	yes	characteristic
123	#416	C₂²	1	2	yes	—
124	#416	C₂²	1	2	yes	complemented
125	#416	C₂²	1	1	yes	characteristic, complemented
126	C₂×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×#103	C₂²	1	1	yes	characteristic, complemented
128	C₂×#103	C₂²	1	2	yes	complemented
129	C₂×#102	C₂²	1	1	yes	characteristic
130	C₂×#102	C₂²	1	1	yes	characteristic
131	C₂×#102	C₂²	1	2	yes	—
132	#408	C₂²	1	1	yes	characteristic
133	#408	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴	—	2	4	no	—
136	2₋¹⁺⁴	—	4	2	no	—
137	H(5,𝔽₂)	—	2	4	no	—
138	H(5,𝔽₂)	—	4	2	no	—
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	—	2	2	no	—
142	C₂×#41	C₂³	1	1	yes	characteristic
143	C₂×#41	C₂³	1	2	yes	—
144	C₂×#41	C₂³	1	2	yes	—
145	C₂×#41	C₂³	1	1	yes	characteristic
146	C₂×#41	C₂³	1	1	yes	characteristic
147	C₂×#41	C₂³	1	1	yes	characteristic
148	C₂²×Q₈	—	2	1	no	—
149	C₂²×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×Q₈	C₂³	1	2	yes	—
151	C₂²×D₄	—	2	1	no	—
152	C₂²×D₄	—	2	2	no	—
153	C₂²×D₄	C₂³	1	1	yes	characteristic
154	C₂²×D₄	C₂³	1	2	yes	—
155	#137	—	4	2	no	—
156	AGL(1,ℤ/8)	—	4	2	no	—
157	#135	—	2	4	no	—
158	C₂×Q₁₆	C₂³	1	1	yes	characteristic
159	C₂×Q₁₆	C₂³	1	2	yes	—
160	C₂×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆	C₂³	1	2	yes	—
163	C₂×SD₁₆	C₂³	1	2	yes	—
164	C₂×D₈	C₂³	1	1	yes	characteristic
165	C₂×D₈	C₂³	1	2	yes	—
166	#131	—	4	2	no	—
167	#131	—	4	2	no	—
168	C₂×M₁₆	C₂³	1	1	yes	characteristic
169	C₂×M₁₆	C₂³	1	1	yes	characteristic
170	C₂×M₁₆	C₂³	1	2	yes	—
171	C₂×M₁₆	C₂³	1	2	yes	—
172	C₂²×C₈	C₂³	1	1	yes	characteristic
173	C₂²×C₈	C₂³	1	1	yes	characteristic
174	C₂²×C₈	C₂³	1	2	yes	—
175	C₂²×C₈	C₂³	1	2	yes	—
176	C₄⋊Q₈	—	2	1	no	—
177	C₄⋊Q₈	D₄	1	1	yes	characteristic
178	#127	—	2	1	no	—
179	#127	D₄	1	1	yes	characteristic
180	#126	—	2	2	no	—
181	#126	—	2	2	no	—
182	#126	—	2	2	no	—
183	#126	—	2	2	no	—
184	#125	—	2	2	no	—
185	#125	—	2	2	no	—
186	#125	—	2	1	no	—
187	#125	—	2	1	no	—
188	#125	C₂³	1	2	yes	—
189	#125	C₂³	1	2	yes	—
190	#124	—	2	1	no	—
191	#124	—	2	1	no	—
192	#124	—	2	2	no	—
193	#124	—	2	2	no	—
194	#124	—	2	1	no	—
195	#124	—	2	1	no	—
196	#124	D₄	1	1	yes	characteristic
197	#124	D₄	1	1	yes	characteristic
198	#124	C₂³	1	2	yes	—
199	#124	C₂³	1	2	yes	—
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	#123	—	2	2	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	—	2	1	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	—	2	2	no	—
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂²⋊Q₈	C₂³	1	2	yes	—
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	—	2	2	no	—
225	#121	D₄	1	2	yes	—
226	#121	D₄	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	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
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	1	yes	characteristic
256	C₄×D₄	C₂³	1	2	yes	—
257	C₄×D₄	C₂³	1	2	yes	—
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#117	—	2	1	no	—
261	#117	—	2	1	no	—
262	#117	C₂³	1	1	yes	characteristic
263	#117	C₂³	1	1	yes	characteristic
264	#117	C₂³	1	2	yes	—
265	#117	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	C₂³	1	1	yes	characteristic
279	#107	C₂³	1	1	yes	characteristic
280	#107	C₂³	1	1	yes	characteristic
281	#107	C₂³	1	2	yes	—
282	#107	C₂³	1	2	yes	—
283	#106	C₂³	1	1	yes	characteristic
284	#106	C₂³	1	1	yes	characteristic
285	#106	C₂³	1	2	yes	—
286	#106	C₂³	1	2	yes	—
287	C₄⋊C₈	C₂³	1	2	yes	—
288	C₄⋊C₈	C₂³	1	2	yes	—
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	1	yes	characteristic
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
299	#103	C₂³	1	1	yes	characteristic
300	#103	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	2	yes	—
308	#102	C₂³	1	1	yes	characteristic
309	#102	C₂³	1	2	yes	—
310	#102	C₂³	1	2	yes	—
311	#102	C₂³	1	1	yes	characteristic
312	#102	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂²⋊C₈	C₂³	1	2	yes	—
315	C₂²⋊C₈	C₂³	1	2	yes	—
316	C₂²⋊C₈	C₂³	1	2	yes	—
317	C₄×C₈	C₂³	1	1	yes	characteristic
318	C₄×C₈	C₂³	1	1	yes	characteristic
319	C₄×C₈	C₂³	1	1	yes	characteristic
320	C₄×C₈	C₂³	1	1	yes	characteristic
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	2	1	no	—
323	#41	—	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	—	4	2	no	—
333	#41	—	4	2	no	—
334	#41	—	4	4	no	—
335	#41	—	4	4	no	—
336	#41	—	4	8	no	—
337	#41	#41	1	4	yes	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
346	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
347	C₂×Q₈	C₂⁴	1	2	yes	—
348	C₂×Q₈	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈	C₂⁴	1	1	yes	characteristic
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	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	—	2	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	8	no	—
366	C₂×D₄	C₂×D₄	1	2	yes	—
367	C₂×D₄	C₂×D₄	1	2	yes	—
368	C₂×D₄	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄	C₂×D₄	1	2	yes	—
371	C₂×D₄	C₂×D₄	1	2	yes	—
372	C₂×D₄	C₂⁴	1	2	yes	—
373	C₂×D₄	C₂⁴	1	1	yes	characteristic
374	C₂×D₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	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	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴	1	2	yes	—
392	C₂²×C₄	C₂⁴	1	2	yes	—
393	C₂²×C₄	C₂⁴	1	1	yes	characteristic
394	Q₁₆	—	2	2	no	—
395	Q₁₆	—	4	2	no	—
396	SD₁₆	—	2	2	no	—
397	SD₁₆	—	2	2	no	—
398	SD₁₆	—	4	2	no	—
399	SD₁₆	—	4	2	no	—
400	D₈	—	2	2	no	—
401	D₈	—	4	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	4	2	no	—
405	M₁₆	—	4	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	—	4	2	no	—
410	C₂×C₈	C₂⁴	1	1	yes	characteristic
411	C₂×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₈	C₂⁴	1	2	yes	—
415	C₂×C₈	C₂⁴	1	2	yes	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂×D₄	1	2	yes	—
433	C₄⋊C₄	C₂×D₄	1	2	yes	—
434	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄	C₂⁴	1	2	yes	—
437	C₄⋊C₄	C₂⁴	1	2	yes	—
438	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	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	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	C₂×D₄	1	1	yes	characteristic
473	C₄²	C₂×D₄	1	1	yes	characteristic
474	C₄²	C₂⁴	1	1	yes	characteristic
475	C₄²	C₂⁴	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	8	1	no	—
482	C₂³	—	8	1	no	—
483	C₂³	—	8	2	no	—
484	C₂³	—	8	2	no	—
485	C₂³	C₂²×D₄	1	2	yes	—
486	C₂³	C₂²×D₄	1	2	yes	—
487	C₂³	C₂²×D₄	1	1	yes	characteristic
488	Q₈	—	2	2	no	—
489	Q₈	—	2	2	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	2	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	4	4	no	—
496	Q₈	—	4	2	no	—
497	Q₈	C₂×#41	1	2	yes	—
498	D₄	—	2	4	no	—
499	D₄	—	2	4	no	—
500	D₄	—	2	4	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	2	no	—
503	D₄	—	2	1	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	4	no	—
511	D₄	—	4	4	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	8	2	no	—
516	D₄	—	8	2	no	—
517	D₄	—	8	2	no	—
518	D₄	—	8	2	no	—
519	D₄	C₂×#41	1	2	yes	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	4	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	1	no	—
544	C₂×C₄	—	8	1	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	—	8	2	no	—
547	C₂×C₄	—	8	1	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄	1	2	yes	—
552	C₂×C₄	C₂²×D₄	1	2	yes	—
553	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄	C₂×#41	1	2	yes	—
557	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
558	C₂×C₄	C₂⁵	1	1	yes	characteristic
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	2	no	—
564	C₈	—	2	2	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	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	16	2	no	—
583	C₂²	—	16	4	no	—
584	C₂²	#546	1	2	yes	—
585	C₂²	C₂³×D₄	1	1	yes	characteristic
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	1	no	—
601	C₄	#546	1	2	yes	—
602	C₄	C₂²×#41	1	1	yes	characteristic
603	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂	—	2	2	no	—
605	C₂	—	4	2	no	—
606	C₂	—	4	2	no	—
607	C₂	—	4	2	no	—
608	C₂	—	8	1	no	—
609	C₂	—	8	2	no	—
610	C₂	C₂×#546	1	1	yes	characteristic
611	C₂	#3584	1	1	yes	characteristic
612	C₂	#3584	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. #3500	C₂	semidirect
3. #3327	C₂	semidirect
4. #3326	C₂	semidirect
5. #3323	C₂	semidirect
6. #3322	C₂	semidirect
7. #3301	C₂	semidirect
8. #3300	C₂	semidirect
9. #3297	C₂	semidirect
10. #3296	C₂	semidirect
11. C₂×#488	C₂	semidirect
12. #3097	C₂	semidirect
13. #3096	C₂	semidirect
14. #3080	C₂	semidirect
15. #3063	C₂	semidirect
16. #3062	C₂	semidirect
17. #3040	C₂	semidirect
18. #3013	C₂	semidirect
19. #3012	C₂	semidirect
20. C₄×#135	C₂	semidirect
21. #2931	C₂	semidirect
22. #2898	C₂	semidirect
23. #2897	C₂	semidirect
26. C₂×#137	C₂²	semidirect
30. C₂×#131	C₂²	semidirect
33. #553	C₂²	semidirect
34. #553	C₂²	semidirect
35. #552	C₂²	semidirect
36. #552	C₂²	semidirect
46. #537	C₂²	semidirect
55. C₂×#125	C₂²	semidirect
59. #520	C₂²	semidirect
61. C₄×#41	C₂²	semidirect
62. #488	C₂²	semidirect
63. #488	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. #479	C₂²	semidirect
75. #479	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
91. #452	C₂²	semidirect
92. #451	C₂²	semidirect
95. #449	C₂²	semidirect
96. #448	C₂²	semidirect
98. C₄×Q₁₆	C₂²	semidirect
99. C₄×Q₁₆	C₂²	semidirect
100. C₄×SD₁₆	C₂²	semidirect
101. C₄×SD₁₆	C₂²	semidirect
102. C₄×SD₁₆	C₂²	semidirect
103. C₄×SD₁₆	C₂²	semidirect
104. C₄×D₈	C₂²	semidirect
105. C₄×D₈	C₂²	semidirect
106. #436	C₂²	semidirect
107. #436	C₂²	semidirect
108. C₈×D₄	C₂²	semidirect
109. C₈×D₄	C₂²	semidirect
110. #428	C₂²	semidirect
111. #428	C₂²	semidirect
112. #427	C₂²	semidirect
113. #423	C₂²	semidirect
114. #419	C₂²	semidirect
115. #419	C₂²	semidirect
121. #417	C₂²	semidirect
124. #416	C₂²	semidirect
125. #416	C₂²	semidirect
126. C₂×#103	C₂²	semidirect
127. C₂×#103	C₂²	semidirect
128. C₂×#103	C₂²	semidirect
133. #408	C₂²	semidirect
134. C₂×C₄×C₈	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
#3500	2
#3327	2
#3326	2
#3323	2
#3322	2
#3301	2
#3300	2
#3297	2
#3296	2
C₂×#488	2
#3097	2
#3096	2
#3080	2
#3063	2
#3062	2
#3040	2
#3013	2
#3012	2
C₄×#135	2
#2931	2
#2898	2
#2897	2