Subgroups — #61658

Order 256.

1055 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	#3331	C₂	1	1	yes	maximal, characteristic, complemented
4	#3325	C₂	1	1	yes	maximal, characteristic, complemented
5	#3323	C₂	1	2	yes	maximal, complemented
6	#3303	C₂	1	1	yes	maximal, characteristic, complemented
7	#3296	C₂	1	2	yes	maximal, complemented
8	#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	#3282	C₂	1	2	yes	maximal, complemented
11	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	#3275	C₂	1	2	yes	maximal, complemented
14	#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	#3204	C₂	1	2	yes	maximal, complemented
18	#3201	C₂	1	2	yes	maximal, complemented
19	#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	#3012	C₂	1	2	yes	maximal, complemented
22	#3009	C₂	1	2	yes	maximal, complemented
23	#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)	C₂²	1	2	yes	—
25	C₂×#137	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×#135	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆	C₂²	1	2	yes	complemented
29	#562	—	2	2	no	—
30	#555	—	2	1	no	—
31	#555	C₂²	1	1	yes	characteristic, complemented
32	#554	C₂²	1	1	yes	characteristic, complemented
33	#553	—	2	1	no	—
34	#552	C₂²	1	2	yes	complemented
35	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	#548	C₂²	1	2	yes	complemented
37	#547	—	2	1	no	—
38	#547	C₂²	1	1	yes	characteristic
39	#547	C₂²	1	1	yes	characteristic
40	#547	C₂²	1	1	yes	characteristic, complemented
41	#546	—	2	2	no	—
42	#546	C₂²	1	2	yes	—
43	#546	C₂²	1	2	yes	—
44	D₄²	—	2	1	no	—
45	D₄²	C₂²	1	1	yes	characteristic
46	D₄²	C₂²	1	1	yes	characteristic
47	#544	—	2	1	no	—
48	#542	—	2	2	no	—
49	#540	—	2	1	no	—
50	#537	C₂²	1	2	yes	—
51	#537	C₂²	1	2	yes	complemented
52	#536	C₂²	1	2	yes	complemented
53	#534	—	2	2	no	—
54	#533	C₂²	1	1	yes	characteristic, complemented
55	#532	C₂²	1	1	yes	characteristic
56	#532	C₂²	1	1	yes	characteristic
57	#529	C₂²	1	1	yes	characteristic, complemented
58	C₂×#121	—	2	1	no	—
59	C₂×#121	—	2	1	no	—
60	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
61	#495	C₂²	1	2	yes	complemented
62	#494	C₂²	1	1	yes	characteristic, complemented
63	#492	C₂²	1	1	yes	characteristic, complemented
64	#488	C₂²	1	2	yes	complemented
65	#487	C₂²	1	1	yes	characteristic, complemented
66	#486	C₂²	1	1	yes	characteristic, complemented
67	#485	C₂²	1	2	yes	complemented
68	#484	C₂²	1	1	yes	characteristic, complemented
69	#483	C₂²	1	2	yes	complemented
70	#483	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#481	C₂²	1	1	yes	characteristic, complemented
73	#481	C₂²	1	2	yes	complemented
74	#478	C₂²	1	1	yes	characteristic, complemented
75	#478	C₂²	1	1	yes	characteristic, complemented
76	#476	C₂²	1	1	yes	characteristic, complemented
77	#476	C₂²	1	1	yes	characteristic, complemented
78	#470	C₂²	1	2	yes	complemented
79	#470	C₂²	1	2	yes	complemented
80	#469	C₂²	1	2	yes	complemented
81	#468	C₂²	1	2	yes	complemented
82	#467	C₂²	1	2	yes	complemented
83	#465	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	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	#461	C₂²	1	1	yes	characteristic, complemented
93	#461	C₂²	1	1	yes	characteristic, complemented
94	#460	C₂²	1	1	yes	characteristic, complemented
95	#459	C₂²	1	1	yes	characteristic, complemented
96	#452	C₂²	1	2	yes	complemented
97	#452	C₂²	1	2	yes	complemented
98	#452	C₂²	1	2	yes	complemented
99	#452	C₂²	1	2	yes	complemented
100	#452	C₂²	1	2	yes	complemented
101	#452	C₂²	1	2	yes	complemented
102	#452	C₂²	1	2	yes	complemented
103	#451	C₂²	1	2	yes	complemented
104	#450	C₂²	1	2	yes	—
105	#450	C₂²	1	1	yes	characteristic
106	#450	C₂²	1	2	yes	complemented
107	#450	C₂²	1	2	yes	complemented
108	#450	C₂²	1	2	yes	complemented
109	#449	C₂²	1	2	yes	complemented
110	#449	C₂²	1	2	yes	complemented
111	#449	C₂²	1	2	yes	complemented
112	#448	C₂²	1	2	yes	complemented
113	#447	C₂²	1	1	yes	characteristic
114	#447	C₂²	1	2	yes	complemented
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆	C₂²	1	2	yes	complemented
117	C₄×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
121	#436	C₂²	1	1	yes	characteristic, complemented
122	#436	C₂²	1	2	yes	complemented
123	#436	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄	C₂²	1	2	yes	complemented
126	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
127	#431	C₂²	1	1	yes	characteristic, complemented
128	#431	C₂²	1	1	yes	characteristic, complemented
129	#418	C₂²	1	2	yes	complemented
130	#417	C₂²	1	2	yes	complemented
131	#416	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
133	#408	C₂²	1	2	yes	complemented
134	#408	C₂²	1	2	yes	complemented
135	H(5,𝔽₂)	—	4	4	no	—
136	H(5,𝔽₂)	—	4	4	no	—
137	C₂×#41	—	2	2	no	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂×#41	C₂³	1	2	yes	—
140	C₂×#41	C₂³	1	2	yes	—
141	C₂×#41	C₂³	1	2	yes	—
142	C₂×#41	C₂³	1	2	yes	—
143	C₂²×Q₈	C₂³	1	2	yes	—
144	C₂²×D₄	—	2	2	no	—
145	C₂²×D₄	—	2	2	no	—
146	C₂²×D₄	—	2	2	no	—
147	C₂²×D₄	—	2	1	no	—
148	C₂²×D₄	—	2	1	no	—
149	C₂²×D₄	C₂³	1	1	yes	characteristic
150	C₂²×D₄	C₂³	1	2	yes	—
151	C₂²×D₄	C₂³	1	2	yes	—
152	C₂³×C₄	—	2	1	no	—
153	#137	—	4	4	no	—
154	AGL(1,ℤ/8)	—	4	4	no	—
155	#135	—	4	4	no	—
156	C₂×Q₁₆	C₂³	1	2	yes	—
157	C₂×Q₁₆	C₂³	1	2	yes	—
158	C₂×Q₁₆	C₂³	1	2	yes	—
159	C₂×SD₁₆	—	4	4	no	—
160	C₂×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆	C₂³	1	2	yes	—
162	C₂×SD₁₆	C₂³	1	2	yes	—
163	C₂×SD₁₆	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆	C₂³	1	2	yes	—
165	C₂×SD₁₆	C₂³	1	2	yes	—
166	C₂×SD₁₆	C₂³	1	2	yes	—
167	C₂×SD₁₆	C₂³	1	2	yes	—
168	C₂×D₈	C₂³	1	1	yes	characteristic
169	C₂×D₈	C₂³	1	1	yes	characteristic
170	C₂×D₈	C₂³	1	2	yes	—
171	C₂×M₁₆	C₂³	1	2	yes	—
172	C₂×M₁₆	C₂³	1	2	yes	—
173	C₂²×C₈	C₂³	1	2	yes	—
174	C₂²×C₈	C₂³	1	2	yes	—
175	C₄⋊Q₈	—	2	2	no	—
176	C₄⋊Q₈	—	2	1	no	—
177	C₄⋊Q₈	D₄	1	1	yes	characteristic
178	C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	#127	D₄	1	1	yes	characteristic
182	#127	C₂³	1	1	yes	characteristic
183	#126	—	2	2	no	—
184	#126	—	2	1	no	—
185	#125	—	2	2	no	—
186	#125	—	2	1	no	—
187	#125	—	2	1	no	—
188	#125	C₂³	1	1	yes	characteristic
189	#124	—	2	2	no	—
190	#124	—	2	2	no	—
191	#124	—	2	2	no	—
192	#124	D₄	1	2	yes	—
193	#124	C₂³	1	1	yes	characteristic
194	#124	C₂³	1	2	yes	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	#123	—	2	1	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	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂²⋊Q₈	C₂³	1	2	yes	—
217	#121	—	2	2	no	—
218	#121	—	2	2	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	2	no	—
227	#121	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	—	2	1	no	—
230	#121	—	2	1	no	—
231	#121	—	2	1	no	—
232	#121	—	2	2	no	—
233	#121	—	2	2	no	—
234	#121	D₄	1	1	yes	characteristic
235	#121	D₄	1	1	yes	characteristic
236	#121	D₄	1	2	yes	—
237	#121	C₂³	1	1	yes	characteristic
238	#121	C₂³	1	2	yes	—
239	#121	C₂³	1	2	yes	—
240	#121	C₂³	1	2	yes	—
241	#120	—	2	2	no	—
242	#120	—	2	2	no	—
243	#120	—	2	2	no	—
244	#120	—	2	2	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₄×Q₈	C₂³	1	2	yes	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	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	1	yes	characteristic
257	C₄×D₄	C₂³	1	1	yes	characteristic
258	C₄×D₄	C₂³	1	1	yes	characteristic
259	C₄×D₄	C₂³	1	1	yes	characteristic
260	C₄×D₄	C₂³	1	1	yes	characteristic
261	C₄×D₄	C₂³	1	1	yes	characteristic
262	C₄×D₄	C₂³	1	1	yes	characteristic
263	C₄×D₄	C₂³	1	2	yes	—
264	#117	—	2	1	no	—
265	#117	—	2	1	no	—
266	#117	—	2	2	no	—
267	#117	—	2	1	no	—
268	#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	C₂³	1	1	yes	characteristic
278	#107	C₂³	1	1	yes	characteristic
279	#107	C₂³	1	1	yes	characteristic
280	#106	C₂³	1	2	yes	—
281	#106	C₂³	1	1	yes	characteristic
282	#106	C₂³	1	2	yes	—
283	#106	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₄⋊C₈	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	1	yes	characteristic
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	1	yes	characteristic
307	#102	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	1	yes	characteristic
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂²⋊C₈	C₂³	1	2	yes	—
315	C₄×C₈	C₂³	1	1	yes	characteristic
316	C₄×C₈	C₂³	1	1	yes	characteristic
317	C₄×C₈	C₂³	1	2	yes	—
318	C₂⁴	—	2	1	no	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	—	2	2	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	4	2	no	—
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	8	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	C₂×D₄	1	2	yes	—
337	C₂×Q₈	C₂⁴	1	2	yes	—
338	C₂×Q₈	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈	C₂⁴	1	2	yes	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	8	no	—
360	C₂×D₄	—	4	8	no	—
361	C₂×D₄	—	4	8	no	—
362	C₂×D₄	—	8	2	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄	C₂×D₄	1	2	yes	—
367	C₂×D₄	C₂×D₄	1	2	yes	—
368	C₂×D₄	C₂×D₄	1	2	yes	—
369	C₂×D₄	C₂×D₄	1	2	yes	—
370	C₂×D₄	C₂⁴	1	2	yes	—
371	C₂×D₄	C₂⁴	1	1	yes	characteristic
372	C₂×D₄	C₂⁴	1	1	yes	characteristic
373	C₂×D₄	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	8	2	no	—
387	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴	1	2	yes	—
391	C₂²×C₄	C₂⁴	1	2	yes	—
392	Q₁₆	—	4	2	no	—
393	Q₁₆	—	4	2	no	—
394	Q₁₆	—	4	2	no	—
395	SD₁₆	—	2	2	no	—
396	SD₁₆	—	2	4	no	—
397	SD₁₆	—	2	4	no	—
398	SD₁₆	—	2	2	no	—
399	SD₁₆	—	4	2	no	—
400	SD₁₆	—	4	2	no	—
401	SD₁₆	—	4	2	no	—
402	SD₁₆	—	4	2	no	—
403	D₈	—	2	2	no	—
404	D₈	—	2	2	no	—
405	D₈	—	4	2	no	—
406	M₁₆	—	4	2	no	—
407	M₁₆	—	4	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	2	yes	—
414	C₂×C₈	C₂⁴	1	2	yes	—
415	C₂×C₈	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄	C₂×D₄	1	2	yes	—
437	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄	C₂⁴	1	2	yes	—
439	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	1	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	C₂×D₄	1	1	yes	characteristic
471	C₄²	C₂×D₄	1	1	yes	characteristic
472	C₄²	C₂⁴	1	1	yes	characteristic
473	C₄²	C₂⁴	1	1	yes	characteristic
474	C₂³	—	2	4	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	8	1	no	—
482	C₂³	—	8	1	no	—
483	C₂³	—	8	2	no	—
484	C₂³	—	8	2	no	—
485	C₂³	—	8	2	no	—
486	C₂³	—	8	2	no	—
487	C₂³	C₂²×D₄	1	2	yes	—
488	C₂³	C₂²×D₄	1	2	yes	—
489	C₂³	C₂²×D₄	1	1	yes	characteristic
490	Q₈	—	2	1	no	—
491	Q₈	—	2	2	no	—
492	Q₈	—	2	2	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	2	2	no	—
496	Q₈	—	4	2	no	—
497	Q₈	—	8	1	no	—
498	Q₈	—	8	2	no	—
499	D₄	—	2	4	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	1	no	—
503	D₄	—	2	1	no	—
504	D₄	—	2	1	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	4	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	2	no	—
518	D₄	—	8	1	no	—
519	D₄	—	8	1	no	—
520	D₄	—	8	2	no	—
521	D₄	—	8	2	no	—
522	D₄	—	8	2	no	—
523	D₄	—	8	2	no	—
524	D₄	H(5,𝔽₂)	1	2	yes	—
525	D₄	H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	—	8	1	no	—
553	C₂×C₄	—	8	2	no	—
554	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄	1	2	yes	—
556	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄	1	2	yes	—
560	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄	C₂⁵	1	1	yes	characteristic
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	2	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	2	no	—
567	C₈	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	8	4	no	—
590	C₂²	—	16	4	no	—
591	C₂²	—	16	4	no	—
592	C₂²	C₂³×D₄	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	#577	1	2	yes	—
608	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
609	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂	—	4	1	no	—
611	C₂	—	4	2	no	—
612	C₂	—	4	2	no	—
613	C₂	—	4	2	no	—
614	C₂	—	4	2	no	—
615	C₂	—	8	1	no	—
616	C₂	—	8	2	no	—
617	C₂	#3484	1	1	yes	characteristic
618	C₂	C₂×#577	1	1	yes	characteristic
619	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. #3547	C₂	semidirect
2. #3496	C₂	semidirect
3. #3331	C₂	semidirect
4. #3325	C₂	semidirect
5. #3323	C₂	semidirect
6. #3303	C₂	semidirect
7. #3296	C₂	semidirect
8. #3295	C₂	semidirect
9. #3283	C₂	semidirect
10. #3282	C₂	semidirect
11. D₄×SD₁₆	C₂	semidirect
12. #3276	C₂	semidirect
13. #3275	C₂	semidirect
14. #3272	C₂	semidirect
15. #3212	C₂	semidirect
16. #3210	C₂	semidirect
17. #3204	C₂	semidirect
18. #3201	C₂	semidirect
19. #3105	C₂	semidirect
20. #3101	C₂	semidirect
21. #3012	C₂	semidirect
22. #3009	C₂	semidirect
23. #2979	C₂	semidirect
25. C₂×#137	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×#135	C₂²	semidirect
28. C₂²×SD₁₆	C₂²	semidirect
31. #555	C₂²	semidirect
32. #554	C₂²	semidirect
34. #552	C₂²	semidirect
35. D₄×Q₈	C₂²	semidirect
36. #548	C₂²	semidirect
40. #547	C₂²	semidirect
51. #537	C₂²	semidirect
52. #536	C₂²	semidirect
54. #533	C₂²	semidirect
57. #529	C₂²	semidirect
61. #495	C₂²	semidirect
62. #494	C₂²	semidirect
63. #492	C₂²	semidirect
64. #488	C₂²	semidirect
65. #487	C₂²	semidirect
66. #486	C₂²	semidirect
67. #485	C₂²	semidirect
68. #484	C₂²	semidirect
69. #483	C₂²	semidirect
70. #483	C₂²	semidirect
71. #482	C₂²	semidirect
72. #481	C₂²	semidirect
73. #481	C₂²	semidirect
74. #478	C₂²	semidirect
75. #478	C₂²	semidirect
76. #476	C₂²	semidirect
77. #476	C₂²	semidirect
78. #470	C₂²	semidirect
79. #470	C₂²	semidirect
80. #469	C₂²	semidirect
81. #468	C₂²	semidirect
82. #467	C₂²	semidirect
83. #465	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. #461	C₂²	semidirect
93. #461	C₂²	semidirect
94. #460	C₂²	semidirect
95. #459	C₂²	semidirect
96. #452	C₂²	semidirect
97. #452	C₂²	semidirect
98. #452	C₂²	semidirect
99. #452	C₂²	semidirect
100. #452	C₂²	semidirect
101. #452	C₂²	semidirect
102. #452	C₂²	semidirect
103. #451	C₂²	semidirect
106. #450	C₂²	semidirect
107. #450	C₂²	semidirect
108. #450	C₂²	semidirect
109. #449	C₂²	semidirect
110. #449	C₂²	semidirect
111. #449	C₂²	semidirect
112. #448	C₂²	semidirect
114. #447	C₂²	semidirect
115. C₄×SD₁₆	C₂²	semidirect
116. C₄×SD₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
119. C₄×D₈	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
121. #436	C₂²	semidirect
122. #436	C₂²	semidirect
123. #436	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. C₈×D₄	C₂²	semidirect
126. C₈×D₄	C₂²	semidirect
127. #431	C₂²	semidirect
128. #431	C₂²	semidirect
129. #418	C₂²	semidirect
130. #417	C₂²	semidirect
131. #416	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. #408	C₂²	semidirect
134. #408	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3547	2
#3496	2
#3331	2
#3325	2
#3323	2
#3303	2
#3296	2
#3295	2
#3283	2
#3282	2
D₄×SD₁₆	2
#3276	2
#3275	2
#3272	2
#3212	2
#3210	2
#3204	2
#3201	2
#3105	2
#3101	2
#3012	2
#3009	2
#2979	2