Subgroups — #61968

Order 256.

960 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	#3401	C₂	1	2	yes	maximal, complemented
4	#3370	C₂	1	2	yes	maximal, complemented
5	#3323	C₂	1	2	yes	maximal, complemented
6	#3319	C₂	1	2	yes	maximal, complemented
7	#3317	C₂	1	2	yes	maximal, complemented
8	#3273	C₂	1	2	yes	maximal, complemented
9	#3268	C₂	1	2	yes	maximal, complemented
10	#3267	C₂	1	2	yes	maximal, complemented
11	#3254	C₂	1	1	yes	maximal, characteristic, complemented
12	#3252	C₂	1	1	yes	maximal, characteristic, complemented
13	#3247	C₂	1	1	yes	maximal, characteristic, complemented
14	#3217	C₂	1	1	yes	maximal, characteristic, complemented
15	#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	#3212	C₂	1	1	yes	maximal, characteristic, complemented
17	#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	#3038	C₂	1	1	yes	maximal, characteristic, complemented
21	#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×#135	C₂²	1	2	yes	complemented
27	#559	—	2	1	no	—
28	#559	C₂²	1	2	yes	complemented
29	#556	C₂²	1	1	yes	characteristic, complemented
30	#555	C₂²	1	1	yes	characteristic
31	#554	C₂²	1	1	yes	characteristic, complemented
32	#553	—	2	1	no	—
33	#552	—	2	1	no	—
34	#552	C₂²	1	1	yes	characteristic
35	#552	C₂²	1	1	yes	characteristic, complemented
36	#551	—	2	1	no	—
37	#551	—	2	1	no	—
38	#550	—	2	1	no	—
39	#550	C₂²	1	2	yes	—
40	#547	C₂²	1	1	yes	characteristic
41	#546	—	2	1	no	—
42	#546	—	2	1	no	—
43	#546	C₂²	1	1	yes	characteristic
44	#546	C₂²	1	2	yes	—
45	#546	C₂²	1	1	yes	characteristic, complemented
46	#546	C₂²	1	2	yes	complemented
47	#540	—	2	1	no	—
48	#540	—	2	1	no	—
49	#535	—	2	1	no	—
50	#533	C₂²	1	1	yes	characteristic, complemented
51	#533	C₂²	1	1	yes	characteristic, complemented
52	#532	C₂²	1	1	yes	characteristic
53	#532	C₂²	1	1	yes	characteristic
54	#532	C₂²	1	1	yes	characteristic, complemented
55	#532	C₂²	1	1	yes	characteristic, complemented
56	C₂×#127	C₂²	1	1	yes	characteristic, complemented
57	#529	—	2	1	no	—
58	#529	—	2	1	no	—
59	#529	C₂²	1	1	yes	characteristic
60	#529	C₂²	1	1	yes	characteristic, complemented
61	#525	—	2	1	no	—
62	#518	—	2	1	no	—
63	C₄×#41	C₂²	1	1	yes	characteristic
64	C₄×#41	C₂²	1	1	yes	characteristic
65	C₄×#41	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
67	C₂×#117	—	2	1	no	—
68	#497	C₂²	1	2	yes	complemented
69	#496	C₂²	1	2	yes	—
70	#495	C₂²	1	2	yes	complemented
71	#490	C₂²	1	2	yes	complemented
72	#489	C₂²	1	2	yes	complemented
73	#488	C₂²	1	2	yes	complemented
74	#485	C₂²	1	2	yes	complemented
75	#482	C₂²	1	2	yes	complemented
76	#481	C₂²	1	2	yes	complemented
77	#479	C₂²	1	2	yes	complemented
78	#478	C₂²	1	2	yes	complemented
79	#477	C₂²	1	1	yes	characteristic, complemented
80	#477	C₂²	1	1	yes	characteristic, complemented
81	#476	C₂²	1	1	yes	characteristic, complemented
82	#476	C₂²	1	1	yes	characteristic, complemented
83	#474	C₂²	1	2	yes	complemented
84	#470	C₂²	1	2	yes	complemented
85	#468	C₂²	1	2	yes	—
86	#468	C₂²	1	2	yes	complemented
87	#468	C₂²	1	2	yes	complemented
88	#466	C₂²	1	2	yes	complemented
89	#465	C₂²	1	2	yes	complemented
90	#464	C₂²	1	2	yes	complemented
91	#464	C₂²	1	2	yes	complemented
92	#463	C₂²	1	2	yes	complemented
93	#463	C₂²	1	2	yes	complemented
94	#463	C₂²	1	2	yes	complemented
95	#463	C₂²	1	2	yes	complemented
96	#462	C₂²	1	1	yes	characteristic, complemented
97	#462	C₂²	1	1	yes	characteristic, complemented
98	#461	C₂²	1	1	yes	characteristic, complemented
99	#461	C₂²	1	2	yes	complemented
100	#461	C₂²	1	1	yes	characteristic, complemented
101	#460	C₂²	1	1	yes	characteristic, complemented
102	#460	C₂²	1	2	yes	complemented
103	#460	C₂²	1	1	yes	characteristic, complemented
104	#460	C₂²	1	1	yes	characteristic, complemented
105	#460	C₂²	1	1	yes	characteristic, complemented
106	#459	C₂²	1	1	yes	characteristic
107	#459	C₂²	1	1	yes	characteristic
108	#459	C₂²	1	1	yes	characteristic
109	#459	C₂²	1	2	yes	—
110	#459	C₂²	1	1	yes	characteristic
111	#452	C₂²	1	2	yes	—
112	#452	C₂²	1	2	yes	complemented
113	#452	C₂²	1	2	yes	complemented
114	#452	C₂²	1	2	yes	complemented
115	#450	C₂²	1	2	yes	complemented
116	#449	C₂²	1	2	yes	complemented
117	#449	C₂²	1	2	yes	complemented
118	#447	C₂²	1	2	yes	—
119	#447	C₂²	1	2	yes	complemented
120	#446	C₂²	1	2	yes	complemented
121	#442	C₂²	1	2	yes	complemented
122	#442	C₂²	1	2	yes	complemented
123	#441	C₂²	1	2	yes	complemented
124	#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆	C₂²	1	2	yes	complemented
126	C₄×D₈	C₂²	1	2	yes	complemented
127	#436	C₂²	1	2	yes	—
128	#435	C₂²	1	2	yes	complemented
129	#435	C₂²	1	2	yes	complemented
130	#432	C₂²	1	1	yes	characteristic, complemented
131	#432	C₂²	1	1	yes	characteristic, complemented
132	#431	C₂²	1	1	yes	characteristic, complemented
133	#423	C₂²	1	1	yes	characteristic, complemented
134	#423	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	#418	C₂²	1	2	yes	complemented
137	#417	C₂²	1	2	yes	complemented
138	#416	C₂²	1	2	yes	complemented
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	D₄	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	C₂²×D₄	—	2	1	no	—
147	C₂²×D₄	—	2	1	no	—
148	C₂²×D₄	C₂³	1	1	yes	characteristic
149	C₂²×D₄	C₂³	1	2	yes	—
150	C₂³×C₄	—	2	1	no	—
151	AGL(1,ℤ/8)	—	4	4	no	—
152	AGL(1,ℤ/8)	—	4	4	no	—
153	#135	—	4	4	no	—
154	C₂×Q₁₆	C₂³	1	2	yes	—
155	C₂×Q₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×SD₁₆	C₂³	1	2	yes	—
158	C₂×SD₁₆	C₂³	1	2	yes	—
159	C₂×SD₁₆	C₂³	1	2	yes	—
160	C₂×SD₁₆	C₂³	1	2	yes	—
161	C₂×SD₁₆	C₂³	1	2	yes	—
162	C₂×D₈	C₂³	1	2	yes	—
163	C₂×D₈	C₂³	1	2	yes	—
164	C₂×D₈	C₂³	1	2	yes	—
165	C₂×D₈	C₂³	1	2	yes	—
166	C₂×M₁₆	C₂³	1	2	yes	—
167	C₂×M₁₆	C₂³	1	2	yes	—
168	C₂²×C₈	C₂³	1	2	yes	—
169	C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	#127	—	2	2	no	—
174	#127	—	2	1	no	—
175	#127	—	2	1	no	—
176	#127	C₂³	1	1	yes	characteristic
177	#127	C₂³	1	1	yes	characteristic
178	#127	C₂³	1	2	yes	—
179	#126	—	2	1	no	—
180	#126	—	2	1	no	—
181	#126	—	2	1	no	—
182	#126	—	2	1	no	—
183	#126	—	2	1	no	—
184	#126	—	2	1	no	—
185	#125	—	2	1	no	—
186	#125	—	2	1	no	—
187	#125	—	2	1	no	—
188	#125	—	2	1	no	—
189	#125	C₂³	1	1	yes	characteristic
190	#125	C₂³	1	1	yes	characteristic
191	#124	—	2	2	no	—
192	#124	—	2	1	no	—
193	#124	—	2	1	no	—
194	#124	—	2	1	no	—
195	#124	—	2	1	no	—
196	#124	C₂³	1	1	yes	characteristic
197	#124	C₂³	1	1	yes	characteristic
198	#124	C₂³	1	2	yes	—
199	#124	C₂³	1	2	yes	—
200	#123	—	2	1	no	—
201	#123	—	2	1	no	—
202	#123	—	2	1	no	—
203	#123	—	2	1	no	—
204	#123	—	2	1	no	—
205	#123	—	2	1	no	—
206	#123	—	2	2	no	—
207	#123	—	2	2	no	—
208	#123	—	2	2	no	—
209	#123	—	2	2	no	—
210	#123	—	2	1	no	—
211	#123	—	2	1	no	—
212	C₂²⋊Q₈	—	2	1	no	—
213	C₂²⋊Q₈	—	2	1	no	—
214	C₂²⋊Q₈	—	2	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	C₂²⋊Q₈	—	2	1	no	—
218	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	#121	—	2	1	no	—
224	#121	—	2	1	no	—
225	#121	—	2	1	no	—
226	#121	—	2	1	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	1	no	—
233	#121	—	2	2	no	—
234	#121	—	2	2	no	—
235	#121	—	2	2	no	—
236	#121	—	2	2	no	—
237	#121	C₂³	1	1	yes	characteristic
238	#121	C₂³	1	1	yes	characteristic
239	#121	C₂³	1	2	yes	—
240	#121	C₂³	1	2	yes	—
241	#120	—	2	1	no	—
242	#120	—	2	1	no	—
243	#120	—	2	2	no	—
244	#120	—	2	2	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×Q₈	D₄	1	1	yes	characteristic
248	C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₄×Q₈	C₂³	1	2	yes	—
253	C₄×Q₈	C₂³	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	D₄	1	1	yes	characteristic
271	C₄×D₄	D₄	1	1	yes	characteristic
272	C₄×D₄	D₄	1	1	yes	characteristic
273	C₄×D₄	C₂³	1	1	yes	characteristic
274	C₄×D₄	C₂³	1	1	yes	characteristic
275	C₄×D₄	C₂³	1	1	yes	characteristic
276	C₄×D₄	C₂³	1	1	yes	characteristic
277	C₄×D₄	C₂³	1	1	yes	characteristic
278	C₄×D₄	C₂³	1	1	yes	characteristic
279	C₄×D₄	C₂³	1	2	yes	—
280	C₄×D₄	C₂³	1	2	yes	—
281	C₄×D₄	C₂³	1	1	yes	characteristic
282	C₄×D₄	C₂³	1	1	yes	characteristic
283	C₄×D₄	C₂³	1	1	yes	characteristic
284	#117	—	2	1	no	—
285	#117	—	2	1	no	—
286	#117	—	2	1	no	—
287	#117	—	2	1	no	—
288	#117	—	2	1	no	—
289	#117	—	2	1	no	—
290	#117	—	2	1	no	—
291	#117	—	2	1	no	—
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	D₄	1	1	yes	characteristic
295	#117	D₄	1	1	yes	characteristic
296	#117	D₄	1	1	yes	characteristic
297	#117	C₂³	1	1	yes	characteristic
298	#117	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	C₂³	1	1	yes	characteristic
310	C₂×C₄²	C₂³	1	1	yes	characteristic
311	C₂×C₄²	C₂³	1	1	yes	characteristic
312	#107	C₂³	1	2	yes	—
313	#107	C₂³	1	2	yes	—
314	#106	C₂³	1	2	yes	—
315	#106	C₂³	1	2	yes	—
316	C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₄⋊C₈	C₂³	1	1	yes	characteristic
318	C₄⋊C₈	C₂³	1	2	yes	—
319	C₄⋊C₈	C₂³	1	1	yes	characteristic
320	C₄⋊C₈	C₂³	1	2	yes	—
321	C₄⋊C₈	C₂³	1	2	yes	—
322	C₄⋊C₈	C₂³	1	1	yes	characteristic
323	#103	C₂³	1	2	yes	—
324	#103	C₂³	1	2	yes	—
325	#103	C₂³	1	2	yes	—
326	#103	C₂³	1	2	yes	—
327	#103	C₂³	1	2	yes	—
328	#103	C₂³	1	2	yes	—
329	#102	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	#102	C₂³	1	2	yes	—
333	#102	C₂³	1	2	yes	—
334	#102	C₂³	1	2	yes	—
335	#102	C₂³	1	2	yes	—
336	#102	C₂³	1	2	yes	—
337	#102	C₂³	1	2	yes	—
338	#102	C₂³	1	2	yes	—
339	C₂²⋊C₈	C₂³	1	2	yes	—
340	C₂²⋊C₈	C₂³	1	2	yes	—
341	C₂²⋊C₈	C₂³	1	2	yes	—
342	#97	C₂³	1	2	yes	—
343	#97	C₂³	1	2	yes	—
344	C₄×C₈	C₂³	1	2	yes	—
345	C₂⁴	—	2	1	no	—
346	C₂⁴	—	2	2	no	—
347	#41	—	2	2	no	—
348	#41	—	2	2	no	—
349	#41	—	4	2	no	—
350	#41	—	4	1	no	—
351	#41	—	4	1	no	—
352	#41	—	4	2	no	—
353	#41	—	4	2	no	—
354	#41	—	4	2	no	—
355	#41	—	4	2	no	—
356	#41	—	8	2	no	—
357	#41	—	8	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
361	C₂×Q₈	C₂⁴	1	2	yes	—
362	C₂×Q₈	C₂⁴	1	1	yes	characteristic
363	C₂×Q₈	C₂⁴	1	1	yes	characteristic
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	8	2	no	—
386	C₂×D₄	C₂×D₄	1	1	yes	characteristic
387	C₂×D₄	C₂×D₄	1	1	yes	characteristic
388	C₂×D₄	C₂×D₄	1	1	yes	characteristic
389	C₂×D₄	C₂⁴	1	2	yes	—
390	C₂×D₄	C₂⁴	1	2	yes	—
391	C₂×D₄	C₂⁴	1	1	yes	characteristic
392	C₂×D₄	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	4	4	no	—
407	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴	1	1	yes	characteristic
416	Q₁₆	—	4	2	no	—
417	Q₁₆	—	4	2	no	—
418	SD₁₆	—	2	4	no	—
419	SD₁₆	—	4	2	no	—
420	SD₁₆	—	4	2	no	—
421	SD₁₆	—	4	2	no	—
422	SD₁₆	—	4	2	no	—
423	SD₁₆	—	4	2	no	—
424	D₈	—	2	4	no	—
425	D₈	—	2	4	no	—
426	D₈	—	4	2	no	—
427	D₈	—	4	2	no	—
428	M₁₆	—	4	2	no	—
429	M₁₆	—	4	2	no	—
430	C₂×C₈	—	4	2	no	—
431	C₂×C₈	C₂⁴	1	2	yes	—
432	C₂×C₈	C₂⁴	1	2	yes	—
433	C₂×C₈	C₂⁴	1	2	yes	—
434	C₂×C₈	C₂⁴	1	2	yes	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
457	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
458	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
462	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
465	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄	C₂⁴	1	2	yes	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
495	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
496	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
497	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
498	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
499	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	2	no	—
507	C₄²	C₂×D₄	1	1	yes	characteristic
508	C₄²	C₂×D₄	1	1	yes	characteristic
509	C₄²	C₂×D₄	1	1	yes	characteristic
510	C₄²	C₂×D₄	1	1	yes	characteristic
511	C₄²	C₂×D₄	1	1	yes	characteristic
512	C₄²	C₂×D₄	1	1	yes	characteristic
513	C₄²	C₂⁴	1	1	yes	characteristic
514	C₄²	C₂⁴	1	1	yes	characteristic
515	C₄²	C₂⁴	1	1	yes	characteristic
516	C₄²	C₂⁴	1	1	yes	characteristic
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	2	no	—
523	C₂³	—	4	4	no	—
524	C₂³	—	8	1	no	—
525	C₂³	—	8	2	no	—
526	C₂³	—	8	2	no	—
527	C₂³	C₂²×D₄	1	1	yes	characteristic
528	C₂³	C₂²×D₄	1	1	yes	characteristic
529	C₂³	C₂²×D₄	1	1	yes	characteristic
530	Q₈	—	2	2	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	2	no	—
538	Q₈	—	8	1	no	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	2	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	4	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	8	2	no	—
558	D₄	—	8	2	no	—
559	D₄	—	8	1	no	—
560	D₄	—	8	1	no	—
561	D₄	—	8	2	no	—
562	D₄	—	8	2	no	—
563	D₄	—	8	2	no	—
564	D₄	—	8	2	no	—
565	D₄	H(5,𝔽₂)	1	2	yes	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	8	1	no	—
594	C₂×C₄	—	8	1	no	—
595	C₂×C₄	—	8	2	no	—
596	C₂×C₄	—	8	2	no	—
597	C₂×C₄	—	8	2	no	—
598	C₂×C₄	—	8	2	no	—
599	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
600	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₄	C₂⁵	1	1	yes	characteristic
611	C₈	—	2	2	no	—
612	C₈	—	2	2	no	—
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	8	4	no	—
637	C₂²	—	16	4	no	—
638	C₂²	C₂³×D₄	1	1	yes	characteristic
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	1	no	—
643	C₄	—	2	1	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	#575	1	2	yes	—
658	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
659	C₄	#585	1	1	yes	characteristic
660	C₂	—	4	1	no	—
661	C₂	—	4	1	no	—
662	C₂	—	4	1	no	—
663	C₂	—	4	2	no	—
664	C₂	—	8	1	no	—
665	C₂	—	8	2	no	—
666	C₂	—	8	2	no	—
667	C₂	#3488	1	1	yes	characteristic
668	C₂	C₂×#575	1	1	yes	characteristic
669	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 ◁ C₄×#41 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3508	C₂	semidirect
2. #3475	C₂	semidirect
3. #3401	C₂	semidirect
4. #3370	C₂	semidirect
5. #3323	C₂	semidirect
6. #3319	C₂	semidirect
7. #3317	C₂	semidirect
8. #3273	C₂	semidirect
9. #3268	C₂	semidirect
10. #3267	C₂	semidirect
11. #3254	C₂	semidirect
12. #3252	C₂	semidirect
13. #3247	C₂	semidirect
14. #3217	C₂	semidirect
15. #3216	C₂	semidirect
16. #3212	C₂	semidirect
17. #3116	C₂	semidirect
18. #3109	C₂	semidirect
19. #3106	C₂	semidirect
20. #3038	C₂	semidirect
21. #3036	C₂	semidirect
22. #3035	C₂	semidirect
23. #2989	C₂	semidirect
25. C₂×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×#135	C₂²	semidirect
28. #559	C₂²	semidirect
29. #556	C₂²	semidirect
31. #554	C₂²	semidirect
35. #552	C₂²	semidirect
45. #546	C₂²	semidirect
46. #546	C₂²	semidirect
50. #533	C₂²	semidirect
51. #533	C₂²	semidirect
54. #532	C₂²	semidirect
55. #532	C₂²	semidirect
56. C₂×#127	C₂²	semidirect
60. #529	C₂²	semidirect
65. C₄×#41	C₂²	semidirect
66. C₂×C₄×D₄	C₂²	semidirect
68. #497	C₂²	semidirect
70. #495	C₂²	semidirect
71. #490	C₂²	semidirect
72. #489	C₂²	semidirect
73. #488	C₂²	semidirect
74. #485	C₂²	semidirect
75. #482	C₂²	semidirect
76. #481	C₂²	semidirect
77. #479	C₂²	semidirect
78. #478	C₂²	semidirect
79. #477	C₂²	semidirect
80. #477	C₂²	semidirect
81. #476	C₂²	semidirect
82. #476	C₂²	semidirect
83. #474	C₂²	semidirect
84. #470	C₂²	semidirect
86. #468	C₂²	semidirect
87. #468	C₂²	semidirect
88. #466	C₂²	semidirect
89. #465	C₂²	semidirect
90. #464	C₂²	semidirect
91. #464	C₂²	semidirect
92. #463	C₂²	semidirect
93. #463	C₂²	semidirect
94. #463	C₂²	semidirect
95. #463	C₂²	semidirect
96. #462	C₂²	semidirect
97. #462	C₂²	semidirect
98. #461	C₂²	semidirect
99. #461	C₂²	semidirect
100. #461	C₂²	semidirect
101. #460	C₂²	semidirect
102. #460	C₂²	semidirect
103. #460	C₂²	semidirect
104. #460	C₂²	semidirect
105. #460	C₂²	semidirect
112. #452	C₂²	semidirect
113. #452	C₂²	semidirect
114. #452	C₂²	semidirect
115. #450	C₂²	semidirect
116. #449	C₂²	semidirect
117. #449	C₂²	semidirect
119. #447	C₂²	semidirect
120. #446	C₂²	semidirect
121. #442	C₂²	semidirect
122. #442	C₂²	semidirect
123. #441	C₂²	semidirect
124. #440	C₂²	semidirect
125. C₄×SD₁₆	C₂²	semidirect
126. C₄×D₈	C₂²	semidirect
128. #435	C₂²	semidirect
129. #435	C₂²	semidirect
130. #432	C₂²	semidirect
131. #432	C₂²	semidirect
132. #431	C₂²	semidirect
133. #423	C₂²	semidirect
134. #423	C₂²	semidirect
135. C₂×C₄⋊C₈	C₂²	semidirect
136. #418	C₂²	semidirect
137. #417	C₂²	semidirect
138. #416	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3508	2
#3475	2
#3401	2
#3370	2
#3323	2
#3319	2
#3317	2
#3273	2
#3268	2
#3267	2
#3254	2
#3252	2
#3247	2
#3217	2
#3216	2
#3212	2
#3116	2
#3109	2
#3106	2
#3038	2
#3036	2
#3035	2
#2989	2