Subgroups — #60835

Order 256.

1020 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	#3500	C₂	1	1	yes	maximal, characteristic, complemented
2	#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	#3225	C₂	1	2	yes	maximal, complemented
4	#3224	C₂	1	2	yes	maximal, complemented
5	#3223	C₂	1	2	yes	maximal, complemented
6	#3222	C₂	1	2	yes	maximal, complemented
7	#3219	C₂	1	2	yes	maximal, complemented
8	#3215	C₂	1	2	yes	maximal, complemented
9	#3211	C₂	1	2	yes	maximal, complemented
10	#3210	C₂	1	2	yes	maximal, complemented
11	#3156	C₂	1	1	yes	maximal, characteristic, complemented
12	#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	#3037	C₂	1	1	yes	maximal, characteristic, complemented
17	#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	#3011	C₂	1	1	yes	maximal, characteristic, complemented
22	#3009	C₂	1	1	yes	maximal, characteristic, complemented
23	#2925	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
27	C₂×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
30	C₂×#135	C₂²	1	1	yes	characteristic
31	C₂×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
34	#548	—	2	1	no	—
35	#548	—	2	1	no	—
36	#546	—	2	2	no	—
37	#546	—	2	1	no	—
38	#546	—	2	2	no	—
39	#546	—	2	1	no	—
40	#544	C₂²	1	1	yes	characteristic, complemented
41	#542	—	2	1	no	—
42	#542	C₂²	1	2	yes	complemented
43	#541	—	2	1	no	—
44	#541	C₂²	1	2	yes	complemented
45	#539	—	2	2	no	—
46	#537	C₂²	1	1	yes	characteristic
47	#536	C₂²	1	1	yes	characteristic
48	#536	C₂²	1	2	yes	—
49	#536	C₂²	1	1	yes	characteristic
50	#536	C₂²	1	1	yes	characteristic, complemented
51	#535	C₂²	1	1	yes	characteristic
52	#535	C₂²	1	2	yes	—
53	#533	—	2	1	no	—
54	#533	C₂²	1	2	yes	complemented
55	#532	C₂²	1	2	yes	—
56	#532	C₂²	1	1	yes	characteristic
57	#529	—	2	2	no	—
58	#529	—	2	1	no	—
59	#529	C₂²	1	2	yes	complemented
60	C₂×#124	C₂²	1	2	yes	—
61	C₂×#124	C₂²	1	1	yes	characteristic
62	C₄×#41	C₂²	1	1	yes	characteristic
63	C₄×#41	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
65	#497	C₂²	1	2	yes	complemented
66	#497	C₂²	1	2	yes	complemented
67	#497	C₂²	1	2	yes	complemented
68	#496	C₂²	1	2	yes	complemented
69	#495	C₂²	1	2	yes	complemented
70	#495	C₂²	1	2	yes	complemented
71	#494	C₂²	1	2	yes	complemented
72	#492	C₂²	1	2	yes	complemented
73	#491	C₂²	1	2	yes	complemented
74	#490	C₂²	1	2	yes	complemented
75	#489	C₂²	1	2	yes	complemented
76	#489	C₂²	1	2	yes	complemented
77	#488	C₂²	1	2	yes	complemented
78	#488	C₂²	1	2	yes	complemented
79	#487	C₂²	1	2	yes	complemented
80	#486	C₂²	1	2	yes	complemented
81	#464	C₂²	1	1	yes	characteristic, complemented
82	#464	C₂²	1	2	yes	complemented
83	#464	C₂²	1	2	yes	complemented
84	#464	C₂²	1	2	yes	complemented
85	#464	C₂²	1	2	yes	complemented
86	#464	C₂²	1	1	yes	characteristic, complemented
87	#464	C₂²	1	2	yes	complemented
88	#464	C₂²	1	2	yes	complemented
89	#464	C₂²	1	2	yes	complemented
90	#464	C₂²	1	2	yes	complemented
91	#463	C₂²	1	1	yes	characteristic, complemented
92	#463	C₂²	1	2	yes	complemented
93	#463	C₂²	1	1	yes	characteristic, complemented
94	#463	C₂²	1	2	yes	complemented
95	#462	C₂²	1	1	yes	characteristic, complemented
96	#462	C₂²	1	2	yes	complemented
97	#461	C₂²	1	1	yes	characteristic, complemented
98	#460	C₂²	1	1	yes	characteristic, complemented
99	#460	C₂²	1	2	yes	complemented
100	#459	C₂²	1	1	yes	characteristic, complemented
101	#452	C₂²	1	2	yes	—
102	#452	C₂²	1	2	yes	—
103	#452	C₂²	1	2	yes	—
104	#452	C₂²	1	2	yes	complemented
105	#452	C₂²	1	2	yes	complemented
106	#452	C₂²	1	2	yes	complemented
107	#451	C₂²	1	2	yes	complemented
108	#451	C₂²	1	2	yes	complemented
109	#451	C₂²	1	2	yes	complemented
110	#450	C₂²	1	2	yes	—
111	#450	C₂²	1	2	yes	—
112	#450	C₂²	1	2	yes	—
113	#449	C₂²	1	2	yes	—
114	#449	C₂²	1	2	yes	complemented
115	#448	C₂²	1	2	yes	complemented
116	#447	C₂²	1	2	yes	—
117	#433	C₂²	1	2	yes	complemented
118	#433	C₂²	1	2	yes	complemented
119	#432	C₂²	1	2	yes	complemented
120	#431	C₂²	1	2	yes	complemented
121	#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	#419	C₂²	1	1	yes	characteristic, complemented
124	#418	C₂²	1	1	yes	characteristic
125	#417	C₂²	1	1	yes	characteristic
126	#417	C₂²	1	1	yes	characteristic, complemented
127	#416	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102	C₂²	1	1	yes	characteristic
131	#408	C₂²	1	1	yes	characteristic
132	#408	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic, complemented
134	#405	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴	—	4	2	no	—
136	2₋¹⁺⁴	—	4	2	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	2	no	—
141	C₂×#41	—	2	1	no	—
142	C₂×#41	C₂³	1	1	yes	characteristic
143	C₂×#41	C₂³	1	1	yes	characteristic
144	C₂×#41	C₂³	1	1	yes	characteristic
145	C₂×#41	C₂³	1	2	yes	—
146	C₂×#41	C₂³	1	2	yes	—
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	1	yes	characteristic
151	C₂²×Q₈	C₂³	1	2	yes	—
152	C₂²×D₄	—	2	2	no	—
153	C₂²×D₄	—	2	1	no	—
154	C₂²×D₄	C₂³	1	1	yes	characteristic
155	C₂²×D₄	C₂³	1	2	yes	—
156	#137	—	4	2	no	—
157	#137	—	4	2	no	—
158	#137	—	4	2	no	—
159	AGL(1,ℤ/8)	—	4	2	no	—
160	#135	—	4	2	no	—
161	#135	—	4	2	no	—
162	C₂×Q₁₆	—	4	2	no	—
163	C₂×Q₁₆	C₂³	1	2	yes	—
164	C₂×Q₁₆	C₂³	1	2	yes	—
165	C₂×Q₁₆	C₂³	1	1	yes	characteristic
166	C₂×Q₁₆	C₂³	1	1	yes	characteristic
167	C₂×Q₁₆	C₂³	1	2	yes	—
168	C₂×Q₁₆	C₂³	1	2	yes	—
169	C₂×Q₁₆	C₂³	1	2	yes	—
170	C₂×SD₁₆	—	4	2	no	—
171	C₂×SD₁₆	C₂³	1	2	yes	—
172	C₂×SD₁₆	C₂³	1	2	yes	—
173	C₂×SD₁₆	C₂³	1	1	yes	characteristic
174	C₂×SD₁₆	C₂³	1	1	yes	characteristic
175	C₂×SD₁₆	C₂³	1	1	yes	characteristic
176	C₂×SD₁₆	C₂³	1	1	yes	characteristic
177	C₂×SD₁₆	C₂³	1	2	yes	—
178	C₂×SD₁₆	C₂³	1	2	yes	—
179	C₂×SD₁₆	C₂³	1	2	yes	—
180	C₂×SD₁₆	C₂³	1	2	yes	—
181	C₂×D₈	C₂³	1	1	yes	characteristic
182	C₂×D₈	C₂³	1	1	yes	characteristic
183	C₂×D₈	C₂³	1	2	yes	—
184	C₂×M₁₆	C₂³	1	1	yes	characteristic
185	C₂×M₁₆	C₂³	1	1	yes	characteristic
186	C₂²×C₈	C₂³	1	1	yes	characteristic
187	C₂²×C₈	C₂³	1	1	yes	characteristic
188	C₄⋊Q₈	—	2	1	no	—
189	C₄⋊Q₈	—	2	1	no	—
190	C₄⋊Q₈	C₂³	1	1	yes	characteristic
191	C₄⋊Q₈	C₂³	1	2	yes	—
192	C₄⋊Q₈	C₂³	1	2	yes	—
193	C₄⋊Q₈	C₂³	1	2	yes	—
194	#127	C₂³	1	1	yes	characteristic
195	#127	C₂³	1	2	yes	—
196	#126	—	2	2	no	—
197	#126	—	2	2	no	—
198	#126	—	2	2	no	—
199	#126	—	2	2	no	—
200	#125	—	2	2	no	—
201	#125	—	2	1	no	—
202	#125	—	2	2	no	—
203	#125	—	2	2	no	—
204	#125	C₂³	1	2	yes	—
205	#124	—	2	1	no	—
206	#124	—	2	2	no	—
207	#124	—	2	1	no	—
208	#124	—	2	2	no	—
209	#124	—	2	1	no	—
210	#124	—	2	2	no	—
211	#124	C₂³	1	1	yes	characteristic
212	#124	C₂³	1	2	yes	—
213	#124	C₂³	1	2	yes	—
214	#124	C₂³	1	2	yes	—
215	#124	C₂³	1	2	yes	—
216	#124	C₂³	1	2	yes	—
217	#124	C₂³	1	1	yes	characteristic
218	#123	—	2	2	no	—
219	#123	—	2	2	no	—
220	#123	—	2	2	no	—
221	#123	—	2	2	no	—
222	#123	—	2	2	no	—
223	#123	—	2	2	no	—
224	#123	—	2	2	no	—
225	C₂²⋊Q₈	—	2	1	no	—
226	C₂²⋊Q₈	—	2	2	no	—
227	C₂²⋊Q₈	—	2	1	no	—
228	C₂²⋊Q₈	—	2	1	no	—
229	C₂²⋊Q₈	—	2	2	no	—
230	C₂²⋊Q₈	—	2	1	no	—
231	C₂²⋊Q₈	—	2	2	no	—
232	C₂²⋊Q₈	—	2	1	no	—
233	C₂²⋊Q₈	—	2	2	no	—
234	C₂²⋊Q₈	—	2	2	no	—
235	C₂²⋊Q₈	C₂³	1	2	yes	—
236	C₂²⋊Q₈	C₂³	1	2	yes	—
237	C₂²⋊Q₈	C₂³	1	2	yes	—
238	#121	—	2	2	no	—
239	#121	—	2	1	no	—
240	#121	—	2	1	no	—
241	#121	—	2	1	no	—
242	#121	—	2	2	no	—
243	#121	—	2	2	no	—
244	#121	—	2	1	no	—
245	#121	—	2	2	no	—
246	#121	—	2	1	no	—
247	#121	—	2	2	no	—
248	#121	C₂³	1	2	yes	—
249	#120	—	2	2	no	—
250	#120	—	2	2	no	—
251	#120	—	2	2	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	D₄	1	1	yes	characteristic
256	C₄×Q₈	D₄	1	1	yes	characteristic
257	C₄×Q₈	C₂³	1	2	yes	—
258	C₄×Q₈	C₂³	1	2	yes	—
259	C₄×Q₈	C₂³	1	1	yes	characteristic
260	C₄×Q₈	C₂³	1	1	yes	characteristic
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	D₄	1	1	yes	characteristic
269	C₄×D₄	D₄	1	2	yes	—
270	C₄×D₄	D₄	1	2	yes	—
271	C₄×D₄	D₄	1	1	yes	characteristic
272	C₄×D₄	C₂³	1	1	yes	characteristic
273	C₄×D₄	C₂³	1	1	yes	characteristic
274	#117	—	2	2	no	—
275	#117	—	2	1	no	—
276	#117	—	2	2	no	—
277	#117	C₂³	1	1	yes	characteristic
278	#117	C₂³	1	1	yes	characteristic
279	#117	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³	1	1	yes	characteristic
289	C₂×C₄²	C₂³	1	2	yes	—
290	C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₄⋊C₈	C₂³	1	1	yes	characteristic
293	C₄⋊C₈	C₂³	1	1	yes	characteristic
294	C₄⋊C₈	C₂³	1	2	yes	—
295	C₄⋊C₈	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	1	yes	characteristic
299	#103	C₂³	1	1	yes	characteristic
300	#103	C₂³	1	1	yes	characteristic
301	#103	C₂³	1	1	yes	characteristic
302	#103	C₂³	1	2	yes	—
303	#103	C₂³	1	2	yes	—
304	#103	C₂³	1	2	yes	—
305	#103	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	1	yes	characteristic
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	#102	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	C₂²⋊C₈	C₂³	1	2	yes	—
320	#97	C₂³	1	2	yes	—
321	#97	C₂³	1	2	yes	—
322	C₄×C₈	C₂³	1	2	yes	—
323	C₄×C₈	C₂³	1	2	yes	—
324	C₂⁴	—	2	2	no	—
325	C₂⁴	—	2	1	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	4	2	no	—
335	#41	—	4	2	no	—
336	#41	—	4	2	no	—
337	#41	—	4	2	no	—
338	#41	—	4	8	no	—
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
353	C₂×Q₈	C₂⁴	1	2	yes	—
354	C₂×Q₈	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈	C₂⁴	1	2	yes	—
357	C₂×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
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	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	C₂×D₄	1	2	yes	—
377	C₂×D₄	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄	C₂⁴	1	2	yes	—
379	C₂×D₄	C₂⁴	1	1	yes	characteristic
380	C₂×D₄	C₂⁴	1	1	yes	characteristic
381	C₂×D₄	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄	1	2	yes	—
396	C₂²×C₄	C₂×D₄	1	2	yes	—
397	C₂²×C₄	C₂⁴	1	2	yes	—
398	C₂²×C₄	C₂⁴	1	1	yes	characteristic
399	Q₁₆	—	4	2	no	—
400	Q₁₆	—	4	2	no	—
401	Q₁₆	—	4	1	no	—
402	Q₁₆	—	4	1	no	—
403	Q₁₆	—	4	2	no	—
404	Q₁₆	—	4	2	no	—
405	Q₁₆	—	4	2	no	—
406	SD₁₆	—	4	2	no	—
407	SD₁₆	—	4	2	no	—
408	SD₁₆	—	4	1	no	—
409	SD₁₆	—	4	1	no	—
410	SD₁₆	—	4	1	no	—
411	SD₁₆	—	4	1	no	—
412	SD₁₆	—	4	2	no	—
413	SD₁₆	—	4	2	no	—
414	SD₁₆	—	4	2	no	—
415	SD₁₆	—	4	2	no	—
416	D₈	—	4	1	no	—
417	D₈	—	4	1	no	—
418	D₈	—	4	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₈	C₂⁴	1	2	yes	—
426	C₂×C₈	C₂⁴	1	2	yes	—
427	C₂×C₈	C₂⁴	1	1	yes	characteristic
428	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	C₂×D₄	1	2	yes	—
447	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄	1	2	yes	—
450	C₄⋊C₄	C₂⁴	1	2	yes	—
451	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	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	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄	C₂×D₄	1	2	yes	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	2	no	—
482	C₄²	C₂×D₄	1	1	yes	characteristic
483	C₄²	C₂×D₄	1	2	yes	—
484	C₄²	C₂×D₄	1	1	yes	characteristic
485	C₄²	C₂×D₄	1	2	yes	—
486	C₄²	C₂⁴	1	2	yes	—
487	C₄²	C₂⁴	1	1	yes	characteristic
488	C₄²	C₂⁴	1	1	yes	characteristic
489	C₂³	—	2	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	8	1	no	—
496	C₂³	—	8	1	no	—
497	C₂³	—	8	2	no	—
498	C₂³	—	8	2	no	—
499	C₂³	C₂²×D₄	1	2	yes	—
500	C₂³	C₂²×D₄	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	2	2	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	2	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	2	2	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	4	4	no	—
513	Q₈	—	4	2	no	—
514	Q₈	—	4	2	no	—
515	Q₈	—	8	2	no	—
516	D₄	—	2	4	no	—
517	D₄	—	2	2	no	—
518	D₄	—	2	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	8	1	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	2	no	—
537	D₄	—	8	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	8	1	no	—
562	C₂×C₄	—	8	1	no	—
563	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	2	yes	—
568	C₂×C₄	C₂²×D₄	1	2	yes	—
569	C₂×C₄	C₂²×D₄	1	2	yes	—
570	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
572	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
573	C₂×C₄	C₂⁵	1	1	yes	characteristic
574	C₈	—	2	1	no	—
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	2	no	—
579	C₈	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	16	2	no	—
598	C₂²	—	16	4	no	—
599	C₂²	#535	1	2	yes	—
600	C₂²	C₂³×D₄	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	#535	1	2	yes	—
617	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂	—	2	2	no	—
620	C₂	—	4	2	no	—
621	C₂	—	8	1	no	—
622	C₂	—	8	1	no	—
623	C₂	—	8	2	no	—
624	C₂	—	8	1	no	—
625	C₂	C₂×#535	1	1	yes	characteristic
626	C₂	#3584	1	1	yes	characteristic
627	C₂	#3586	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. #3500	C₂	semidirect
2. #3461	C₂	semidirect
3. #3225	C₂	semidirect
4. #3224	C₂	semidirect
5. #3223	C₂	semidirect
6. #3222	C₂	semidirect
7. #3219	C₂	semidirect
8. #3215	C₂	semidirect
9. #3211	C₂	semidirect
10. #3210	C₂	semidirect
11. #3156	C₂	semidirect
12. #3154	C₂	semidirect
13. #3137	C₂	semidirect
14. #3136	C₂	semidirect
15. #3040	C₂	semidirect
16. #3037	C₂	semidirect
17. #3035	C₂	semidirect
18. C₂×#464	C₂	semidirect
19. #3013	C₂	semidirect
20. #3012	C₂	semidirect
21. #3011	C₂	semidirect
22. #3009	C₂	semidirect
23. #2925	C₂	semidirect
27. C₂×#137	C₂²	semidirect
28. C₂×#137	C₂²	semidirect
31. C₂×#135	C₂²	semidirect
32. C₂²×Q₁₆	C₂²	semidirect
40. #544	C₂²	semidirect
42. #542	C₂²	semidirect
44. #541	C₂²	semidirect
50. #536	C₂²	semidirect
54. #533	C₂²	semidirect
59. #529	C₂²	semidirect
63. C₄×#41	C₂²	semidirect
64. C₂×C₄×Q₈	C₂²	semidirect
65. #497	C₂²	semidirect
66. #497	C₂²	semidirect
67. #497	C₂²	semidirect
68. #496	C₂²	semidirect
69. #495	C₂²	semidirect
70. #495	C₂²	semidirect
71. #494	C₂²	semidirect
72. #492	C₂²	semidirect
73. #491	C₂²	semidirect
74. #490	C₂²	semidirect
75. #489	C₂²	semidirect
76. #489	C₂²	semidirect
77. #488	C₂²	semidirect
78. #488	C₂²	semidirect
79. #487	C₂²	semidirect
80. #486	C₂²	semidirect
81. #464	C₂²	semidirect
82. #464	C₂²	semidirect
83. #464	C₂²	semidirect
84. #464	C₂²	semidirect
85. #464	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
88. #464	C₂²	semidirect
89. #464	C₂²	semidirect
90. #464	C₂²	semidirect
91. #463	C₂²	semidirect
92. #463	C₂²	semidirect
93. #463	C₂²	semidirect
94. #463	C₂²	semidirect
95. #462	C₂²	semidirect
96. #462	C₂²	semidirect
97. #461	C₂²	semidirect
98. #460	C₂²	semidirect
99. #460	C₂²	semidirect
100. #459	C₂²	semidirect
104. #452	C₂²	semidirect
105. #452	C₂²	semidirect
106. #452	C₂²	semidirect
107. #451	C₂²	semidirect
108. #451	C₂²	semidirect
109. #451	C₂²	semidirect
114. #449	C₂²	semidirect
115. #448	C₂²	semidirect
117. #433	C₂²	semidirect
118. #433	C₂²	semidirect
119. #432	C₂²	semidirect
120. #431	C₂²	semidirect
121. #423	C₂²	semidirect
122. C₂×C₄⋊C₈	C₂²	semidirect
123. #419	C₂²	semidirect
126. #417	C₂²	semidirect
128. #416	C₂²	semidirect
129. C₂×#103	C₂²	semidirect
133. #405	C₂²	semidirect
134. #405	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3500	2
#3461	2
#3225	2
#3224	2
#3223	2
#3222	2
#3219	2
#3215	2
#3211	2
#3210	2
#3156	2
#3154	2
#3137	2
#3136	2
#3040	2
#3037	2
#3035	2
C₂×#464	2
#3013	2
#3012	2
#3011	2
#3009	2
#2925	2