Subgroups — #60983

Order 256.

834 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	#3261	C₂	1	2	yes	maximal, complemented
4	#3258	C₂	1	2	yes	maximal, complemented
5	#3242	C₂	1	2	yes	maximal, complemented
6	#3236	C₂	1	1	yes	maximal, characteristic, complemented
7	#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	#3223	C₂	1	2	yes	maximal, complemented
9	#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	#3196	C₂	1	1	yes	maximal, characteristic
12	#3195	C₂	1	1	yes	maximal, characteristic, complemented
13	#3190	C₂	1	1	yes	maximal, characteristic
14	#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	#3178	C₂	1	2	yes	maximal, complemented
16	#3177	C₂	1	2	yes	maximal, complemented
17	#3127	C₂	1	2	yes	maximal, complemented
18	#3120	C₂	1	2	yes	maximal, complemented
19	#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	#3113	C₂	1	1	yes	maximal, characteristic, complemented
21	#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#556	—	2	1	no	—
25	#554	—	2	1	no	—
26	#552	—	2	1	no	—
27	#552	—	2	1	no	—
28	#552	—	2	1	no	—
29	#552	—	2	1	no	—
30	#551	—	2	1	no	—
31	#551	—	2	1	no	—
32	#544	C₂²	1	1	yes	characteristic
33	#542	C₂²	1	1	yes	characteristic
34	#542	C₂²	1	1	yes	characteristic
35	#541	—	2	1	no	—
36	#541	—	2	1	no	—
37	#541	—	2	1	no	—
38	#541	—	2	1	no	—
39	#541	C₂²	1	2	yes	—
40	#541	C₂²	1	1	yes	characteristic
41	#541	C₂²	1	2	yes	—
42	#541	C₂²	1	2	yes	—
43	#541	C₂²	1	2	yes	—
44	#541	C₂²	1	1	yes	characteristic
45	#536	C₂²	1	1	yes	characteristic
46	#533	C₂²	1	1	yes	characteristic
47	#533	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
49	#529	C₂²	1	1	yes	characteristic
50	#529	C₂²	1	1	yes	characteristic
51	C₂×#126	—	2	1	no	—
52	C₂×#126	—	2	1	no	—
53	C₂×#125	—	2	1	no	—
54	C₂×#125	—	2	1	no	—
55	C₂×#125	C₂²	1	1	yes	characteristic
56	#525	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	#520	C₂²	1	1	yes	characteristic
61	#519	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
63	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
64	C₂×#117	C₂²	1	1	yes	characteristic
65	#501	C₂²	1	2	yes	complemented
66	#499	C₂²	1	2	yes	complemented
67	#497	C₂²	1	2	yes	complemented
68	#494	C₂²	1	2	yes	complemented
69	#491	C₂²	1	2	yes	complemented
70	#491	C₂²	1	2	yes	complemented
71	#488	C₂²	1	2	yes	complemented
72	#487	C₂²	1	2	yes	complemented
73	#485	C₂²	1	2	yes	—
74	#485	C₂²	1	2	yes	—
75	#484	C₂²	1	1	yes	characteristic
76	#484	C₂²	1	1	yes	characteristic
77	#484	C₂²	1	1	yes	characteristic
78	#484	C₂²	1	2	yes	—
79	#483	C₂²	1	1	yes	characteristic
80	#483	C₂²	1	1	yes	characteristic
81	#483	C₂²	1	1	yes	characteristic
82	#483	C₂²	1	2	yes	—
83	#481	C₂²	1	1	yes	characteristic
84	#480	C₂²	1	1	yes	characteristic
85	#479	C₂²	1	2	yes	complemented
86	#479	C₂²	1	2	yes	complemented
87	#479	C₂²	1	2	yes	complemented
88	#479	C₂²	1	2	yes	complemented
89	#479	C₂²	1	2	yes	complemented
90	#478	C₂²	1	2	yes	complemented
91	#477	C₂²	1	2	yes	complemented
92	#475	C₂²	1	2	yes	complemented
93	#470	C₂²	1	2	yes	—
94	#470	C₂²	1	2	yes	—
95	#470	C₂²	1	2	yes	—
96	#468	C₂²	1	2	yes	—
97	#467	C₂²	1	2	yes	—
98	#467	C₂²	1	2	yes	—
99	#467	C₂²	1	2	yes	—
100	#465	C₂²	1	2	yes	—
101	#464	C₂²	1	2	yes	complemented
102	#464	C₂²	1	2	yes	complemented
103	#462	C₂²	1	2	yes	complemented
104	#462	C₂²	1	2	yes	complemented
105	#462	C₂²	1	2	yes	complemented
106	#462	C₂²	1	2	yes	complemented
107	#462	C₂²	1	2	yes	complemented
108	#461	C₂²	1	2	yes	complemented
109	#452	C₂²	1	2	yes	—
110	#452	C₂²	1	2	yes	—
111	#451	C₂²	1	1	yes	characteristic
112	#451	C₂²	1	1	yes	characteristic
113	#451	C₂²	1	1	yes	characteristic
114	#451	C₂²	1	1	yes	characteristic
115	#451	C₂²	1	1	yes	characteristic
116	#451	C₂²	1	1	yes	characteristic
117	#451	C₂²	1	2	yes	—
118	#451	C₂²	1	2	yes	—
119	#448	C₂²	1	1	yes	characteristic
120	#448	C₂²	1	1	yes	characteristic
121	#441	C₂²	1	2	yes	complemented
122	#441	C₂²	1	2	yes	complemented
123	#441	C₂²	1	2	yes	complemented
124	#440	C₂²	1	2	yes	complemented
125	C₄×Q₁₆	C₂²	1	2	yes	complemented
126	C₄×Q₁₆	C₂²	1	2	yes	complemented
127	C₄×Q₁₆	C₂²	1	2	yes	complemented
128	C₄×SD₁₆	C₂²	1	2	yes	complemented
129	#433	C₂²	1	2	yes	—
130	#433	C₂²	1	2	yes	—
131	#432	C₂²	1	1	yes	characteristic
132	#432	C₂²	1	1	yes	characteristic
133	#431	C₂²	1	1	yes	characteristic
134	#431	C₂²	1	1	yes	characteristic
135	#424	C₂²	1	2	yes	—
136	#407	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	#405	C₂²	1	2	yes	—
139	C₂×#41	C₂³	1	1	yes	characteristic
140	C₂²×Q₈	C₂³	1	1	yes	characteristic
141	C₂²×Q₈	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	C₂³	1	1	yes	characteristic
143	C₂³×C₄	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆	C₂³	1	2	yes	—
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×Q₁₆	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×Q₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×M₁₆	C₂³	1	2	yes	—
153	C₂²×C₈	C₂³	1	2	yes	—
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	—	2	1	no	—
157	C₄⋊Q₈	C₂³	1	2	yes	—
158	C₄⋊Q₈	C₂³	1	2	yes	—
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	#126	—	2	1	no	—
164	#126	—	2	1	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	1	no	—
174	#126	—	2	1	no	—
175	#126	—	2	1	no	—
176	#126	—	2	1	no	—
177	#126	—	2	1	no	—
178	#126	—	2	1	no	—
179	#125	—	2	2	no	—
180	#125	—	2	2	no	—
181	#125	—	2	2	no	—
182	#125	—	2	2	no	—
183	#125	—	2	2	no	—
184	#125	—	2	2	no	—
185	#125	—	2	2	no	—
186	#125	—	2	2	no	—
187	#125	—	2	1	no	—
188	#125	—	2	1	no	—
189	#125	—	2	1	no	—
190	#125	—	2	1	no	—
191	#125	—	2	1	no	—
192	#125	—	2	1	no	—
193	#125	—	2	1	no	—
194	#125	—	2	1	no	—
195	#125	—	2	1	no	—
196	#125	C₂³	1	2	yes	—
197	#125	C₂³	1	2	yes	—
198	#125	C₂³	1	1	yes	characteristic
199	#125	C₂³	1	1	yes	characteristic
200	#124	—	2	1	no	—
201	#124	—	2	1	no	—
202	#124	C₂³	1	1	yes	characteristic
203	#124	C₂³	1	1	yes	characteristic
204	#123	—	2	1	no	—
205	#123	—	2	1	no	—
206	#123	—	2	1	no	—
207	#123	—	2	1	no	—
208	#123	—	2	1	no	—
209	#123	—	2	1	no	—
210	#123	—	2	1	no	—
211	C₂²⋊Q₈	—	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	—	2	1	no	—
219	C₂²⋊Q₈	—	2	1	no	—
220	C₂²⋊Q₈	—	2	1	no	—
221	C₂²⋊Q₈	—	2	1	no	—
222	C₂²⋊Q₈	—	2	1	no	—
223	C₂²⋊Q₈	—	2	1	no	—
224	C₂²⋊Q₈	—	2	1	no	—
225	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂²⋊Q₈	C₂³	1	2	yes	—
228	C₂²⋊Q₈	C₂³	1	2	yes	—
229	C₂²⋊Q₈	C₂³	1	2	yes	—
230	C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
232	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
233	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
234	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
235	#121	C₂³	1	1	yes	characteristic
236	#121	C₂³	1	1	yes	characteristic
237	#120	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×Q₈	—	2	1	no	—
242	C₄×Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	C₂³	1	2	yes	—
247	C₄×Q₈	C₂³	1	2	yes	—
248	C₄×Q₈	C₂³	1	2	yes	—
249	C₄×Q₈	C₂³	1	2	yes	—
250	C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₄×Q₈	C₂³	1	1	yes	characteristic
253	C₄×Q₈	C₂³	1	1	yes	characteristic
254	C₄×Q₈	C₂³	1	1	yes	characteristic
255	C₄×Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	C₂³	1	1	yes	characteristic
263	C₄×D₄	C₂³	1	1	yes	characteristic
264	#117	—	2	1	no	—
265	#117	—	2	1	no	—
266	#117	—	2	1	no	—
267	#117	—	2	1	no	—
268	#117	—	2	1	no	—
269	#117	—	2	1	no	—
270	#117	—	2	1	no	—
271	#117	D₄	1	1	yes	characteristic
272	#117	D₄	1	1	yes	characteristic
273	#117	D₄	1	1	yes	characteristic
274	#117	D₄	1	1	yes	characteristic
275	#117	C₂³	1	1	yes	characteristic
276	#117	C₂³	1	1	yes	characteristic
277	#117	C₂³	1	1	yes	characteristic
278	#117	C₂³	1	1	yes	characteristic
279	#117	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
291	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	C₂×C₄²	C₂³	1	1	yes	characteristic
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#107	C₂³	1	2	yes	—
307	#107	C₂³	1	2	yes	—
308	#106	C₂³	1	2	yes	—
309	#106	C₂³	1	2	yes	—
310	#106	C₂³	1	2	yes	—
311	#106	C₂³	1	2	yes	—
312	C₄⋊C₈	C₂³	1	2	yes	—
313	C₄⋊C₈	C₂³	1	2	yes	—
314	C₄⋊C₈	C₂³	1	2	yes	—
315	C₄⋊C₈	C₂³	1	2	yes	—
316	#103	C₂³	1	2	yes	—
317	#103	C₂³	1	2	yes	—
318	#103	C₂³	1	2	yes	—
319	#103	C₂³	1	2	yes	—
320	#103	C₂³	1	2	yes	—
321	#103	C₂³	1	2	yes	—
322	#103	C₂³	1	2	yes	—
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	#103	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈	C₂³	1	2	yes	—
335	C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈	C₂³	1	2	yes	—
338	#97	C₂³	1	2	yes	—
339	#97	C₂³	1	2	yes	—
340	C₄×C₈	C₂³	1	2	yes	—
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	C₂×D₄	1	1	yes	characteristic
343	#41	—	4	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈	C₂⁴	1	2	yes	—
355	C₂×Q₈	C₂⁴	1	2	yes	—
356	C₂×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴	1	1	yes	characteristic
381	Q₁₆	—	4	2	no	—
382	Q₁₆	—	4	2	no	—
383	Q₁₆	—	4	2	no	—
384	Q₁₆	—	4	2	no	—
385	Q₁₆	—	4	2	no	—
386	Q₁₆	—	4	2	no	—
387	SD₁₆	—	4	2	no	—
388	SD₁₆	—	4	2	no	—
389	M₁₆	—	4	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	C₂⁴	1	2	yes	—
392	C₂×C₈	C₂⁴	1	2	yes	—
393	C₂×C₈	C₂⁴	1	2	yes	—
394	C₂×C₈	C₂⁴	1	2	yes	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	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	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄	C₂⁴	1	2	yes	—
445	C₄⋊C₄	C₂⁴	1	2	yes	—
446	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
470	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
471	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
472	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
473	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
474	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	C₂×D₄	1	1	yes	characteristic
489	C₄²	C₂×D₄	1	1	yes	characteristic
490	C₄²	C₂×D₄	1	1	yes	characteristic
491	C₄²	C₂×D₄	1	1	yes	characteristic
492	C₄²	C₂⁴	1	1	yes	characteristic
493	C₄²	C₂⁴	1	1	yes	characteristic
494	C₄²	C₂⁴	1	1	yes	characteristic
495	C₄²	C₂⁴	1	1	yes	characteristic
496	C₂³	—	2	2	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	C₂²×D₄	1	1	yes	characteristic
501	C₂³	C₂²×D₄	1	1	yes	characteristic
502	C₂³	C₂²×D₄	1	1	yes	characteristic
503	Q₈	—	2	2	no	—
504	Q₈	—	2	2	no	—
505	Q₈	—	2	2	no	—
506	Q₈	—	2	2	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	2	2	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	2	no	—
513	Q₈	—	8	1	no	—
514	Q₈	—	8	1	no	—
515	D₄	—	2	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	8	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	8	1	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	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	1	yes	characteristic
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	1	yes	characteristic
560	C₂×C₄	C₂⁵	1	1	yes	characteristic
561	C₈	—	2	2	no	—
562	C₈	—	2	2	no	—
563	C₈	—	2	2	no	—
564	C₈	—	2	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	8	2	no	—
577	C₂²	#578	1	2	yes	—
578	C₂²	C₂³×D₄	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	1	no	—
601	C₄	#585	1	2	yes	—
602	C₂	—	2	2	no	—
603	C₂	—	4	1	no	—
604	C₂	—	4	1	no	—
605	C₂	—	8	1	no	—
606	C₂	#3449	1	1	yes	characteristic
607	C₂	C₂×#578	1	1	yes	characteristic
608	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#541	C₂	semidirect
3. #3261	C₂	semidirect
4. #3258	C₂	semidirect
5. #3242	C₂	semidirect
6. #3236	C₂	semidirect
7. #3232	C₂	semidirect
8. #3223	C₂	semidirect
9. #3218	C₂	semidirect
10. #3209	C₂	semidirect
12. #3195	C₂	semidirect
14. #3189	C₂	semidirect
15. #3178	C₂	semidirect
16. #3177	C₂	semidirect
17. #3127	C₂	semidirect
18. #3120	C₂	semidirect
19. #3117	C₂	semidirect
20. #3113	C₂	semidirect
21. #3108	C₂	semidirect
22. #3104	C₂	semidirect
23. #2924	C₂	semidirect
65. #501	C₂²	semidirect
66. #499	C₂²	semidirect
67. #497	C₂²	semidirect
68. #494	C₂²	semidirect
69. #491	C₂²	semidirect
70. #491	C₂²	semidirect
71. #488	C₂²	semidirect
72. #487	C₂²	semidirect
85. #479	C₂²	semidirect
86. #479	C₂²	semidirect
87. #479	C₂²	semidirect
88. #479	C₂²	semidirect
89. #479	C₂²	semidirect
90. #478	C₂²	semidirect
91. #477	C₂²	semidirect
92. #475	C₂²	semidirect
101. #464	C₂²	semidirect
102. #464	C₂²	semidirect
103. #462	C₂²	semidirect
104. #462	C₂²	semidirect
105. #462	C₂²	semidirect
106. #462	C₂²	semidirect
107. #462	C₂²	semidirect
108. #461	C₂²	semidirect
121. #441	C₂²	semidirect
122. #441	C₂²	semidirect
123. #441	C₂²	semidirect
124. #440	C₂²	semidirect
125. C₄×Q₁₆	C₂²	semidirect
126. C₄×Q₁₆	C₂²	semidirect
127. C₄×Q₁₆	C₂²	semidirect
128. C₄×SD₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3495	2
C₂×#541	2
#3261	2
#3258	2
#3242	2
#3236	2
#3232	2
#3223	2
#3218	2
#3209	2
#3196	2
#3195	2
#3190	2
#3189	2
#3178	2
#3177	2
#3127	2
#3120	2
#3117	2
#3113	2
#3108	2
#3104	2
#2924	2