Subgroups — #60272

Order 256.

916 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3475	C₂	1	1	yes	maximal, characteristic
2	#2995	C₂	1	2	yes	maximal, complemented
3	#2995	C₂	1	2	yes	maximal, complemented
4	#2994	C₂	1	2	yes	maximal, complemented
5	#2993	C₂	1	2	yes	maximal, complemented
6	#2992	C₂	1	2	yes	maximal, complemented
7	#2992	C₂	1	2	yes	maximal, complemented
8	#2990	C₂	1	2	yes	maximal, complemented
9	#2989	C₂	1	2	yes	maximal, complemented
10	#2962	C₂	1	1	yes	maximal, characteristic, complemented
11	#2961	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	#2933	C₂	1	1	yes	maximal, characteristic, complemented
14	#2933	C₂	1	1	yes	maximal, characteristic, complemented
15	#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	#2929	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#435	C₂	1	1	yes	maximal, characteristic, complemented
18	#2924	C₂	1	1	yes	maximal, characteristic, complemented
19	#2924	C₂	1	1	yes	maximal, characteristic, complemented
20	#2923	C₂	1	1	yes	maximal, characteristic, complemented
21	#2906	C₂	1	1	yes	maximal, characteristic, complemented
22	#2905	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#424	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#131	C₂²	1	1	yes	characteristic
25	C₂×#131	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆	C₂²	1	1	yes	characteristic
29	C₂³×C₈	C₂²	1	1	yes	characteristic
30	#556	C₄	1	1	yes	characteristic
31	#555	C₄	1	1	yes	characteristic
32	#554	C₄	1	1	yes	characteristic
33	#553	C₄	1	1	yes	characteristic
34	#553	C₄	1	1	yes	characteristic
35	#552	C₄	1	1	yes	characteristic
36	#552	C₄	1	1	yes	characteristic
37	#552	C₄	1	2	yes	—
38	#551	C₄	1	2	yes	—
39	#551	C₄	1	2	yes	—
40	#547	C₄	1	1	yes	characteristic
41	#546	C₄	1	2	yes	—
42	#533	C₂²	1	1	yes	characteristic
43	#529	C₂²	1	2	yes	—
44	#529	C₂²	1	2	yes	—
45	#529	C₂²	1	2	yes	—
46	#525	C₂²	1	1	yes	characteristic
47	#525	C₂²	1	1	yes	characteristic
48	C₄×#41	C₂²	1	2	yes	—
49	C₄×#41	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×#117	C₂²	1	1	yes	characteristic
52	C₂×#117	C₂²	1	1	yes	characteristic
53	#446	C₂²	1	2	yes	complemented
54	#446	C₂²	1	2	yes	complemented
55	#446	C₂²	1	2	yes	complemented
56	#446	C₂²	1	2	yes	complemented
57	#446	C₂²	1	2	yes	complemented
58	#446	C₂²	1	2	yes	complemented
59	#446	C₂²	1	2	yes	complemented
60	C₈×Q₈	C₂²	1	2	yes	complemented
61	#436	C₂²	1	2	yes	—
62	#436	C₂²	1	2	yes	complemented
63	#436	C₂²	1	2	yes	complemented
64	#436	C₂²	1	2	yes	complemented
65	#436	C₂²	1	2	yes	complemented
66	#435	C₂²	1	1	yes	characteristic
67	#435	C₂²	1	1	yes	characteristic
68	#435	C₂²	1	1	yes	characteristic
69	#435	C₂²	1	1	yes	characteristic
70	#435	C₂²	1	1	yes	characteristic
71	#435	C₂²	1	1	yes	characteristic
72	#435	C₂²	1	1	yes	characteristic
73	#435	C₂²	1	1	yes	characteristic
74	#435	C₂²	1	2	yes	—
75	#435	C₂²	1	2	yes	—
76	#435	C₂²	1	2	yes	complemented
77	#435	C₂²	1	2	yes	complemented
78	#435	C₂²	1	2	yes	complemented
79	#435	C₂²	1	2	yes	complemented
80	#435	C₂²	1	2	yes	complemented
81	#435	C₂²	1	2	yes	complemented
82	#435	C₂²	1	2	yes	complemented
83	#435	C₂²	1	2	yes	complemented
84	C₈×D₄	C₂²	1	2	yes	—
85	C₈×D₄	C₂²	1	2	yes	complemented
86	C₈×D₄	C₂²	1	2	yes	complemented
87	C₈×D₄	C₂²	1	2	yes	complemented
88	C₈×D₄	C₂²	1	2	yes	complemented
89	#433	C₂²	1	2	yes	complemented
90	#433	C₂²	1	2	yes	complemented
91	#433	C₂²	1	2	yes	complemented
92	#433	C₂²	1	2	yes	complemented
93	#433	C₂²	1	2	yes	complemented
94	#433	C₂²	1	2	yes	complemented
95	#432	C₂²	1	2	yes	complemented
96	#432	C₂²	1	2	yes	complemented
97	#432	C₂²	1	2	yes	complemented
98	#432	C₂²	1	2	yes	complemented
99	#431	C₂²	1	2	yes	complemented
100	#431	C₂²	1	2	yes	complemented
101	#424	C₂²	1	1	yes	characteristic
102	#424	C₂²	1	1	yes	characteristic
103	#424	C₂²	1	1	yes	characteristic
104	#424	C₂²	1	1	yes	characteristic
105	#424	C₂²	1	1	yes	characteristic
106	#424	C₂²	1	1	yes	characteristic
107	#424	C₂²	1	1	yes	characteristic
108	#424	C₂²	1	1	yes	characteristic
109	#424	C₂²	1	2	yes	complemented
110	#424	C₂²	1	2	yes	complemented
111	#424	C₂²	1	2	yes	complemented
112	#424	C₂²	1	2	yes	complemented
113	#424	C₂²	1	2	yes	complemented
114	#424	C₂²	1	2	yes	complemented
115	#423	C₂²	1	1	yes	characteristic
116	#423	C₂²	1	2	yes	complemented
117	#423	C₂²	1	2	yes	complemented
118	#423	C₂²	1	2	yes	complemented
119	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
120	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
121	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
123	#408	C₂²	1	1	yes	characteristic
124	#408	C₂²	1	1	yes	characteristic
125	#407	C₂²	1	1	yes	characteristic
126	#407	C₂²	1	1	yes	characteristic
127	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
128	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
129	#405	C₂²	1	1	yes	characteristic
130	#405	C₂²	1	1	yes	characteristic
131	#405	C₂²	1	1	yes	characteristic
132	#405	C₂²	1	1	yes	characteristic
133	C₄×M₁₆	C₂²	1	1	yes	characteristic
134	C₂×#97	C₂²	1	1	yes	characteristic
135	C₂×#41	C₂×C₄	1	2	yes	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
138	C₂³×C₄	C₂³	1	1	yes	characteristic
139	C₂³×C₄	C₂³	1	1	yes	characteristic
140	#131	—	4	2	no	—
141	#131	—	4	2	no	—
142	C₂×M₁₆	—	4	2	no	—
143	C₂×M₁₆	—	4	2	no	—
144	C₂×M₁₆	—	4	2	no	—
145	C₂×M₁₆	C₂³	1	1	yes	characteristic
146	C₂×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×M₁₆	C₂³	1	1	yes	characteristic
149	C₂×M₁₆	C₂³	1	1	yes	characteristic
150	C₂×M₁₆	C₂³	1	1	yes	characteristic
151	C₂×M₁₆	C₂³	1	2	yes	—
152	C₂×M₁₆	C₂³	1	1	yes	characteristic
153	C₂×M₁₆	C₂³	1	1	yes	characteristic
154	C₂×M₁₆	C₂³	1	2	yes	—
155	C₂×M₁₆	C₂³	1	2	yes	—
156	C₂×M₁₆	C₂³	1	2	yes	—
157	C₂²×C₈	—	4	2	no	—
158	C₂²×C₈	C₂³	1	1	yes	characteristic
159	C₂²×C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₈	C₂³	1	1	yes	characteristic
162	C₂²×C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₈	C₂³	1	1	yes	characteristic
164	C₂²×C₈	C₂³	1	1	yes	characteristic
165	C₂²×C₈	C₂³	1	1	yes	characteristic
166	C₂²×C₈	C₂³	1	2	yes	—
167	C₂²×C₈	C₂³	1	2	yes	—
168	C₂²×C₈	C₂³	1	2	yes	—
169	C₂²×C₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
171	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
172	#126	C₂×C₄	1	2	yes	—
173	#126	C₂×C₄	1	2	yes	—
174	#126	C₂×C₄	1	2	yes	—
175	#126	C₂×C₄	1	2	yes	—
176	#126	C₂×C₄	1	2	yes	—
177	#126	C₂×C₄	1	2	yes	—
178	#125	C₂×C₄	1	2	yes	—
179	#125	C₂×C₄	1	2	yes	—
180	#125	C₂×C₄	1	2	yes	—
181	#125	C₂×C₄	1	1	yes	characteristic
182	#125	C₂×C₄	1	1	yes	characteristic
183	#124	C₂×C₄	1	2	yes	—
184	#124	C₂×C₄	1	2	yes	—
185	#124	C₂×C₄	1	2	yes	—
186	#123	C₂×C₄	1	2	yes	—
187	#123	C₂×C₄	1	2	yes	—
188	#123	C₂×C₄	1	2	yes	—
189	#123	C₂×C₄	1	2	yes	—
190	#123	C₂×C₄	1	2	yes	—
191	#123	C₂×C₄	1	2	yes	—
192	#123	C₂×C₄	1	2	yes	—
193	#123	C₂×C₄	1	2	yes	—
194	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
195	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
196	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
197	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
198	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
199	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
200	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
201	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
202	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
203	#121	C₂×C₄	1	1	yes	characteristic
204	#121	C₂×C₄	1	1	yes	characteristic
205	#121	C₂×C₄	1	1	yes	characteristic
206	#121	C₂×C₄	1	1	yes	characteristic
207	#121	C₂×C₄	1	2	yes	—
208	#121	C₂×C₄	1	2	yes	—
209	#121	C₂×C₄	1	2	yes	—
210	#120	C₂×C₄	1	2	yes	—
211	#120	C₂×C₄	1	2	yes	—
212	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
213	C₄×Q₈	C₂×C₄	1	2	yes	—
214	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
215	C₄×Q₈	C₂³	1	2	yes	—
216	C₄×Q₈	C₂³	1	2	yes	—
217	C₄×D₄	C₂×C₄	1	1	yes	characteristic
218	C₄×D₄	C₂×C₄	1	1	yes	characteristic
219	C₄×D₄	C₂×C₄	1	1	yes	characteristic
220	C₄×D₄	C₂×C₄	1	1	yes	characteristic
221	C₄×D₄	C₂×C₄	1	2	yes	—
222	C₄×D₄	C₂×C₄	1	2	yes	—
223	C₄×D₄	C₂×C₄	1	1	yes	characteristic
224	C₄×D₄	C₂×C₄	1	2	yes	—
225	C₄×D₄	C₂×C₄	1	2	yes	—
226	C₄×D₄	C₂×C₄	1	2	yes	—
227	C₄×D₄	C₂×C₄	1	1	yes	characteristic
228	C₄×D₄	C₂³	1	1	yes	characteristic
229	C₄×D₄	C₂³	1	1	yes	characteristic
230	C₄×D₄	C₂³	1	1	yes	characteristic
231	C₄×D₄	C₂³	1	1	yes	characteristic
232	C₄×D₄	C₂³	1	2	yes	—
233	C₄×D₄	C₂³	1	2	yes	—
234	C₄×D₄	C₂³	1	2	yes	—
235	C₄×D₄	C₂³	1	2	yes	—
236	#117	C₂×C₄	1	2	yes	—
237	#117	C₂×C₄	1	2	yes	—
238	#117	C₂×C₄	1	1	yes	characteristic
239	#117	C₂×C₄	1	1	yes	characteristic
240	#117	C₂×C₄	1	1	yes	characteristic
241	#117	C₂×C₄	1	1	yes	characteristic
242	#117	C₂×C₄	1	2	yes	—
243	#117	C₂×C₄	1	2	yes	—
244	#117	C₂×C₄	1	2	yes	—
245	#117	C₂³	1	1	yes	characteristic
246	#117	C₂³	1	1	yes	characteristic
247	#117	C₂³	1	1	yes	characteristic
248	#117	C₂³	1	2	yes	—
249	#117	C₂³	1	2	yes	—
250	#117	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
258	C₂×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
260	C₂×C₄²	C₂³	1	2	yes	—
261	C₂×C₄²	C₂³	1	2	yes	—
262	C₂×C₄²	C₂³	1	1	yes	characteristic
263	C₂×C₄²	C₂³	1	2	yes	—
264	C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₄⋊C₈	C₂³	1	2	yes	—
269	C₄⋊C₈	C₂³	1	2	yes	—
270	C₄⋊C₈	C₂³	1	2	yes	—
271	C₄⋊C₈	C₂³	1	2	yes	—
272	C₄⋊C₈	C₂³	1	2	yes	—
273	C₄⋊C₈	C₂³	1	2	yes	—
274	C₄⋊C₈	C₂³	1	2	yes	—
275	C₄⋊C₈	C₂³	1	2	yes	—
276	C₄⋊C₈	C₂³	1	2	yes	—
277	C₄⋊C₈	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	C₄⋊C₈	C₂³	1	2	yes	—
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂²⋊C₈	C₂³	1	2	yes	—
295	C₂²⋊C₈	C₂³	1	2	yes	—
296	C₂²⋊C₈	C₂³	1	2	yes	—
297	C₂²⋊C₈	C₂³	1	2	yes	—
298	C₂²⋊C₈	C₂³	1	2	yes	—
299	C₂²⋊C₈	C₂³	1	2	yes	—
300	C₂²⋊C₈	C₂³	1	2	yes	—
301	C₂²⋊C₈	C₂³	1	2	yes	—
302	#97	C₂³	1	1	yes	characteristic
303	#97	C₂³	1	1	yes	characteristic
304	#97	C₂³	1	1	yes	characteristic
305	#97	C₂³	1	1	yes	characteristic
306	#97	C₂³	1	2	yes	—
307	#97	C₂³	1	2	yes	—
308	#97	C₂³	1	2	yes	—
309	#97	C₂³	1	2	yes	—
310	#97	C₂³	1	2	yes	—
311	C₄×C₈	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	C₂⁴	C₂²×C₄	1	1	yes	characteristic
317	C₂⁴	C₂²×C₄	1	1	yes	characteristic
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	4	4	no	—
321	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
322	C₂×Q₈	C₂²×C₄	1	2	yes	—
323	C₂×Q₈	C₂²×C₄	1	2	yes	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄	C₂²×C₄	1	2	yes	—
327	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄	C₂²×C₄	1	2	yes	—
329	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄	C₂²×C₄	1	2	yes	—
331	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
332	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
333	C₂×D₄	C₂²×C₄	1	2	yes	—
334	C₂×D₄	C₂²×C₄	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂²×C₄	1	2	yes	—
340	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄	1	2	yes	—
348	C₂²×C₄	C₂²×C₄	1	2	yes	—
349	C₂²×C₄	C₂²×C₄	1	2	yes	—
350	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄	1	2	yes	—
352	C₂²×C₄	C₂²×C₄	1	2	yes	—
353	C₂²×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴	1	2	yes	—
356	C₂²×C₄	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴	1	1	yes	characteristic
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	4	1	no	—
364	M₁₆	—	4	1	no	—
365	M₁₆	—	4	1	no	—
366	M₁₆	—	4	1	no	—
367	M₁₆	—	4	2	no	—
368	M₁₆	—	4	2	no	—
369	M₁₆	—	4	2	no	—
370	M₁₆	—	4	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	1	no	—
377	C₂×C₈	—	4	1	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	—	4	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	C₂⁴	1	2	yes	—
384	C₂×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₈	C₂⁴	1	2	yes	—
389	C₂×C₈	C₂⁴	1	2	yes	—
390	C₂×C₈	C₂⁴	1	2	yes	—
391	C₂×C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₈	C₂⁴	1	1	yes	characteristic
394	C₂×C₈	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
409	C₄⋊C₄	C₂²×C₄	1	2	yes	—
410	C₄⋊C₄	C₂²×C₄	1	2	yes	—
411	C₄⋊C₄	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄	C₂²×C₄	1	2	yes	—
413	C₄⋊C₄	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄	C₂²×C₄	1	2	yes	—
418	C₄⋊C₄	C₂²×C₄	1	2	yes	—
419	C₄⋊C₄	C₂²×C₄	1	2	yes	—
420	C₄⋊C₄	C₂²×C₄	1	2	yes	—
421	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
423	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
428	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
431	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
432	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
433	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
435	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
436	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
443	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
446	C₄²	C₂²×C₄	1	2	yes	—
447	C₄²	C₂²×C₄	1	2	yes	—
448	C₄²	C₂²×C₄	1	2	yes	—
449	C₄²	C₂²×C₄	1	2	yes	—
450	C₄²	C₂²×C₄	1	2	yes	—
451	C₄²	C₂²×C₄	1	1	yes	characteristic
452	C₄²	C₂²×C₄	1	1	yes	characteristic
453	C₄²	C₂²×C₄	1	2	yes	—
454	C₄²	C₂⁴	1	1	yes	characteristic
455	C₄²	C₂⁴	1	2	yes	—
456	C₄²	C₂⁴	1	2	yes	—
457	C₄²	C₂⁴	1	1	yes	characteristic
458	C₄²	C₂⁴	1	2	yes	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	C₂³×C₄	1	1	yes	characteristic
466	C₂³	C₂³×C₄	1	1	yes	characteristic
467	C₂³	C₂³×C₄	1	2	yes	—
468	C₂³	C₂³×C₄	1	1	yes	characteristic
469	C₂³	C₂³×C₄	1	1	yes	characteristic
470	C₂³	C₂³×C₄	1	1	yes	characteristic
471	Q₈	—	2	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	D₄	—	2	4	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	2	no	—
479	D₄	—	4	1	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
509	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
510	C₂×C₄	C₂³×C₄	1	2	yes	—
511	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
512	C₂×C₄	C₂³×C₄	1	2	yes	—
513	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄	C₂³×C₄	1	2	yes	—
515	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄	C₂³×C₄	1	2	yes	—
517	C₂×C₄	C₂³×C₄	1	2	yes	—
518	C₂×C₄	C₂³×C₄	1	2	yes	—
519	C₂×C₄	C₂³×C₄	1	2	yes	—
520	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
522	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
523	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
526	C₂×C₄	C₂⁵	1	1	yes	characteristic
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₈	—	2	2	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	2	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	8	2	no	—
557	C₂²	#520	1	2	yes	—
558	C₂²	#568	1	2	yes	—
559	C₂²	C₂⁴×C₄	1	1	yes	characteristic
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	1	no	—
575	C₄	#520	1	2	yes	—
576	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
578	C₂	—	2	2	no	—
579	C₂	—	2	2	no	—
580	C₂	—	4	2	no	—
581	C₂	—	4	1	no	—
582	C₂	—	4	1	no	—
583	C₂	—	4	1	no	—
584	C₂	C₂×#520	1	1	yes	characteristic
585	C₂	C₂×#568	1	1	yes	characteristic
586	C₂	#3573	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	#3475	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2995	C₂	semidirect
3. #2995	C₂	semidirect
4. #2994	C₂	semidirect
5. #2993	C₂	semidirect
6. #2992	C₂	semidirect
7. #2992	C₂	semidirect
8. #2990	C₂	semidirect
9. #2989	C₂	semidirect
10. #2962	C₂	semidirect
11. #2961	C₂	semidirect
12. D₄×M₁₆	C₂	semidirect
13. #2933	C₂	semidirect
14. #2933	C₂	semidirect
15. #2930	C₂	semidirect
16. #2929	C₂	semidirect
17. C₂×#435	C₂	semidirect
18. #2924	C₂	semidirect
19. #2924	C₂	semidirect
20. #2923	C₂	semidirect
21. #2906	C₂	semidirect
22. #2905	C₂	semidirect
23. C₂×#424	C₂	semidirect
53. #446	C₂²	semidirect
54. #446	C₂²	semidirect
55. #446	C₂²	semidirect
56. #446	C₂²	semidirect
57. #446	C₂²	semidirect
58. #446	C₂²	semidirect
59. #446	C₂²	semidirect
60. C₈×Q₈	C₂²	semidirect
62. #436	C₂²	semidirect
63. #436	C₂²	semidirect
64. #436	C₂²	semidirect
65. #436	C₂²	semidirect
76. #435	C₂²	semidirect
77. #435	C₂²	semidirect
78. #435	C₂²	semidirect
79. #435	C₂²	semidirect
80. #435	C₂²	semidirect
81. #435	C₂²	semidirect
82. #435	C₂²	semidirect
83. #435	C₂²	semidirect
85. C₈×D₄	C₂²	semidirect
86. C₈×D₄	C₂²	semidirect
87. C₈×D₄	C₂²	semidirect
88. C₈×D₄	C₂²	semidirect
89. #433	C₂²	semidirect
90. #433	C₂²	semidirect
91. #433	C₂²	semidirect
92. #433	C₂²	semidirect
93. #433	C₂²	semidirect
94. #433	C₂²	semidirect
95. #432	C₂²	semidirect
96. #432	C₂²	semidirect
97. #432	C₂²	semidirect
98. #432	C₂²	semidirect
99. #431	C₂²	semidirect
100. #431	C₂²	semidirect
109. #424	C₂²	semidirect
110. #424	C₂²	semidirect
111. #424	C₂²	semidirect
112. #424	C₂²	semidirect
113. #424	C₂²	semidirect
114. #424	C₂²	semidirect
116. #423	C₂²	semidirect
117. #423	C₂²	semidirect
118. #423	C₂²	semidirect
120. C₂×C₄⋊C₈	C₂²	semidirect
121. C₂×C₄⋊C₈	C₂²	semidirect
122. 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
#3475	2
#2995	2
#2994	2
#2993	2
#2992	2
#2990	2
#2989	2
#2962	2
#2961	2
D₄×M₁₆	2
#2933	2
#2930	2
#2929	2
C₂×#435	2
#2924	2
#2923	2
#2906	2
#2905	2
C₂×#424	2