Subgroups — #72249704

Order 2048.

At least 9751 conjugacy classes of subgroups; only the 1508 normal subgroups are shown.

The subgroup lattice has 877 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72249700	C₂	1	1	yes	maximal, characteristic, complemented
2	#72249698	C₂	1	1	yes	maximal, characteristic, complemented
3	#72249696	C₂	1	1	yes	maximal, characteristic, complemented
4	#72249694	C₂	1	1	yes	maximal, characteristic, complemented
5	#72249693	C₂	1	1	yes	maximal, characteristic, complemented
6	#72249691	C₂	1	8	yes	maximal, complemented
7	#72249689	C₂	1	8	yes	maximal, complemented
8	#72249680	C₂	1	1	yes	maximal, characteristic, complemented
9	#72240663	C₂	1	1	yes	maximal, characteristic, complemented
10	#72239778	C₂	1	1	yes	maximal, characteristic, complemented
11	#72239697	C₂	1	1	yes	maximal, characteristic, complemented
12	#72239668	C₂	1	1	yes	maximal, characteristic, complemented
13	#72239073	C₂	1	1	yes	maximal, characteristic, complemented
14	#72239006	C₂	1	1	yes	maximal, characteristic, complemented
15	#72238966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#196123	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#6453969	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₄×#41	C₂²	1	1	yes	characteristic
19	#10575872	C₂²	1	1	yes	characteristic
20	#10575094	C₂²	1	1	yes	characteristic
21	C₂×#60558	C₂²	1	1	yes	characteristic
22	C₂²×#3109	C₂²	1	1	yes	characteristic
23	C₂×#60230	C₂²	1	1	yes	characteristic
24	C₂³×#442	C₂²	1	1	yes	characteristic
25	#7628492	C₂²	1	1	yes	characteristic, complemented
26	C₂×#34963	C₂²	1	1	yes	characteristic
27	#7625417	C₂²	1	1	yes	characteristic
28	#6454206	C₂²	1	4	yes	complemented
29	#6454205	C₂²	1	4	yes	complemented
30	#6453969	C₂²	1	8	yes	—
31	#6386073	C₂²	1	8	yes	complemented
32	#6374317	C₂²	1	1	yes	characteristic
33	#6374317	C₂²	1	1	yes	characteristic
34	#6372430	C₂²	1	1	yes	characteristic, complemented
35	C₂×#21408	C₂²	1	1	yes	characteristic
36	C₂×#21379	C₂²	1	1	yes	characteristic
37	#6372285	C₂²	1	1	yes	characteristic, complemented
38	#6370997	C₂²	1	1	yes	characteristic
39	#6370997	C₂²	1	1	yes	characteristic
40	#6370977	C₂²	1	1	yes	characteristic, complemented
41	C₂×#20739	C₂²	1	1	yes	characteristic
42	#6348995	C₂²	1	4	yes	complemented
43	#6348988	C₂²	1	4	yes	complemented
44	#6344036	C₂²	1	1	yes	characteristic
45	#6343803	C₂²	1	1	yes	characteristic, complemented
46	#6343380	C₂²	1	1	yes	characteristic, complemented
47	#6342924	C₂²	1	1	yes	characteristic
48	C₂×#17448	C₂²	1	1	yes	characteristic
49	C₂×#17448	C₂²	1	1	yes	characteristic, complemented
50	C₂×#17364	C₂²	1	1	yes	characteristic, complemented
51	#235358	C₂²	1	4	yes	complemented
52	#235354	C₂²	1	4	yes	complemented
53	#234931	C₂²	1	4	yes	complemented
54	#234930	C₂²	1	4	yes	complemented
55	#197072	C₂²	1	4	yes	complemented
56	#197071	C₂²	1	4	yes	complemented
57	#196123	C₂²	1	8	yes	complemented
58	#181794	C₂²	1	1	yes	characteristic, complemented
59	#181218	C₂²	1	1	yes	characteristic, complemented
60	#181152	C₂²	1	1	yes	characteristic, complemented
61	#181146	C₂²	1	1	yes	characteristic, complemented
62	#181126	C₂²	1	1	yes	characteristic, complemented
63	#181123	C₂²	1	1	yes	characteristic, complemented
64	C₂×#7919	C₂²	1	1	yes	characteristic, complemented
65	C₂×#7861	C₂²	1	1	yes	characteristic, complemented
66	#116384	C₂²	1	8	yes	complemented
67	#116344	C₂²	1	8	yes	complemented
68	#115390	C₂²	1	8	yes	complemented
69	#114225	C₂²	1	4	yes	complemented
70	#114223	C₂²	1	4	yes	complemented
71	#113023	C₂²	1	4	yes	complemented
72	#113022	C₂²	1	4	yes	complemented
73	#112989	C₂²	1	8	yes	complemented
74	#105654	C₂²	1	8	yes	complemented
75	C₂⁴×D₈	D₄	1	1	yes	characteristic
76	C₂×D₄×#41	D₄	1	4	yes	complemented
77	C₂×D₄×#41	C₂³	1	4	yes	—
78	C₂²×#550	D₄	1	1	yes	characteristic, complemented
79	C₂²×#547	D₄	1	1	yes	characteristic, complemented
80	C₂²×D₄×Q₈	D₄	1	1	yes	characteristic, complemented
81	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
82	C₂×#3444	C₂³	1	1	yes	characteristic
83	C₂²×#532	C₂³	1	1	yes	characteristic
84	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
85	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
86	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
87	#60864	C₂³	1	2	yes	—
88	#60803	C₂³	1	2	yes	—
89	#60562	C₂³	1	2	yes	—
90	#60561	C₂³	1	2	yes	—
91	C₂×#3110	C₂³	1	2	yes	—
92	C₂×#3109	C₂³	1	2	yes	—
93	C₂×#3109	C₂³	1	4	yes	—
94	C₂×#3101	D₄	1	2	yes	complemented
95	C₂×#3100	D₄	1	2	yes	complemented
96	C₂×#3077	D₄	1	1	yes	characteristic, complemented
97	C₂×#3077	D₄	1	1	yes	characteristic, complemented
98	C₂×#3036	D₄	1	1	yes	characteristic, complemented
99	C₂×#3036	D₄	1	1	yes	characteristic, complemented
100	#60230	C₂³	1	4	yes	—
101	C₂²×#442	D₄	1	4	yes	—
102	C₂²×#442	C₂³	1	4	yes	—
103	C₂×#2920	C₂³	1	1	yes	characteristic
104	C₂×#2920	C₂³	1	1	yes	characteristic
105	C₂×#2920	C₂³	1	1	yes	characteristic
106	C₂×#2920	C₂³	1	1	yes	characteristic
107	C₂×#2920	C₂³	1	1	yes	characteristic
108	C₂²×#432	C₂³	1	1	yes	characteristic
109	C₂³×#106	D₄	1	1	yes	characteristic
110	C₂³×#102	D₄	1	1	yes	characteristic
111	C₂³×#102	D₄	1	1	yes	characteristic
112	C₂³×#97	C₂³	1	1	yes	characteristic
113	#34963	C₂³	1	4	yes	—
114	#34946	C₂³	1	2	yes	complemented
115	#34936	C₂³	1	2	yes	complemented
116	#34126	C₂³	1	4	yes	—
117	D₄×#117	D₄	1	4	yes	complemented
118	#34058	D₄	1	2	yes	complemented
119	#34012	C₂³	1	1	yes	characteristic
120	#34012	C₂³	1	1	yes	characteristic
121	C₂×#2283	C₂³	1	1	yes	characteristic
122	C₄×#518	D₄	1	2	yes	complemented
123	#21816	D₄	1	4	yes	complemented
124	#21816	C₂³	1	4	yes	—
125	#21815	C₂³	1	4	yes	—
126	#21408	C₂³	1	4	yes	—
127	#21408	C₂³	1	2	yes	complemented
128	#21407	C₂³	1	2	yes	complemented
129	#21379	C₂³	1	4	yes	—
130	#21355	C₂³	1	4	yes	complemented
131	#21252	D₄	1	4	yes	complemented
132	#20748	D₄	1	4	yes	—
133	#20748	C₂³	1	4	yes	—
134	#20747	C₂³	1	4	yes	—
135	#20739	D₄	1	4	yes	complemented
136	#20739	C₂³	1	4	yes	—
137	#20739	C₂³	1	4	yes	complemented
138	#20705	D₄	1	2	yes	—
139	#20605	D₄	1	2	yes	—
140	C₂×#1762	D₄	1	2	yes	complemented
141	C₂×#1762	D₄	1	2	yes	complemented
142	#17744	C₂³	1	4	yes	—
143	#17672	C₂³	1	2	yes	complemented
144	#17671	C₂³	1	2	yes	complemented
145	#17562	C₂³	1	2	yes	complemented
146	#17561	C₂³	1	2	yes	complemented
147	#17452	C₂³	1	4	yes	—
148	#17448	D₄	1	4	yes	complemented
149	#17448	C₂³	1	4	yes	—
150	#17448	C₂³	1	4	yes	complemented
151	C₂×#1478	D₄	1	2	yes	complemented
152	C₂×#1478	D₄	1	2	yes	complemented
153	#17364	C₂³	1	4	yes	complemented
154	#8085	C₂³	1	4	yes	complemented
155	#7977	C₂³	1	4	yes	complemented
156	#7954	C₂³	1	4	yes	complemented
157	#7948	C₂³	1	4	yes	complemented
158	#7945	C₂³	1	4	yes	complemented
159	#7941	C₂³	1	4	yes	complemented
160	#7919	C₂³	1	4	yes	complemented
161	#7861	C₂³	1	4	yes	complemented
162	C₂³×#41	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
165	C₂³×D₈	C₂×D₄	1	4	yes	—
166	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×#550	C₂×D₄	1	4	yes	—
169	C₂×D₄×Q₈	C₂×D₄	1	4	yes	—
170	C₂×#547	C₂×D₄	1	4	yes	—
171	C₂×D₄²	C₂×D₄	1	4	yes	—
172	C₂×#533	C₂×D₄	1	1	yes	characteristic
173	C₂×#533	C₂×D₄	1	1	yes	characteristic
174	C₂×#533	C₂⁴	1	1	yes	characteristic
175	C₂×#532	C₂×D₄	1	2	yes	—
176	C₂×#532	C₂×D₄	1	2	yes	—
177	C₂×#532	C₂×D₄	1	1	yes	characteristic
178	C₂×#532	C₂×D₄	1	1	yes	characteristic
179	C₂×#532	C₂×D₄	1	2	yes	—
180	C₂×#532	#41	1	2	yes	—
181	C₂×#532	#41	1	2	yes	—
182	C₂×#532	C₂⁴	1	1	yes	characteristic
183	C₂×#532	C₂⁴	1	2	yes	—
184	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
185	C₂²×#127	C₂×D₄	1	1	yes	characteristic
186	C₂×C₄×#41	C₂×D₄	1	2	yes	—
187	C₂×C₄×#41	C₂×D₄	1	2	yes	—
188	C₂×C₄×#41	#41	1	2	yes	—
189	C₂×C₄×#41	C₂⁴	1	2	yes	—
190	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×Q₈	#41	1	1	yes	characteristic
192	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
193	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
194	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
199	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
204	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
208	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
209	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
210	C₂²×C₄×D₄	#41	1	1	yes	characteristic
211	C₂²×C₄×D₄	#41	1	1	yes	characteristic
212	C₂²×C₄×D₄	#41	1	1	yes	characteristic
213	C₂²×C₄×D₄	#41	1	2	yes	—
214	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
215	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
216	C₂²×#117	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
220	C₂×#476	C₂×D₄	1	2	yes	complemented
221	C₂×#476	C₂×D₄	1	2	yes	complemented
222	C₂×#474	C₂×D₄	1	2	yes	complemented
223	C₂×#474	C₂×D₄	1	2	yes	complemented
224	C₂×#461	C₂×D₄	1	2	yes	complemented
225	C₂×#461	C₂×D₄	1	2	yes	complemented
226	C₂×#459	C₂×D₄	1	2	yes	complemented
227	C₂×#459	C₂×D₄	1	2	yes	complemented
228	#2920	C₂×D₄	1	2	yes	—
229	#2920	C₂×D₄	1	2	yes	—
230	#2920	C₂×D₄	1	2	yes	—
231	#2920	C₂×D₄	1	2	yes	—
232	#2920	C₂⁴	1	2	yes	—
233	#2920	C₂⁴	1	2	yes	—
234	#2920	C₂⁴	1	2	yes	—
235	#2920	C₂⁴	1	2	yes	—
236	C₂×#432	C₂×D₄	1	2	yes	—
237	C₂×#432	C₂⁴	1	2	yes	—
238	C₂×#432	C₂⁴	1	2	yes	—
239	C₂×#431	C₂×D₄	1	2	yes	—
240	C₂×#431	C₂×D₄	1	2	yes	—
241	C₂×#431	C₂×D₄	1	2	yes	—
242	C₂²×#106	C₂×D₄	1	4	yes	—
243	C₂×#423	C₂×D₄	1	1	yes	characteristic
244	C₂×#423	C₂×D₄	1	1	yes	characteristic
245	C₂²×#102	C₂×D₄	1	4	yes	—
246	C₂²×#102	C₂×D₄	1	4	yes	—
247	C₂×#407	C₂×D₄	1	2	yes	—
248	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
249	C₂²×#97	C₂×D₄	1	2	yes	—
250	C₂²×#97	C₂×D₄	1	2	yes	—
251	C₂²×#97	C₂⁴	1	2	yes	—
252	#2293	C₂×D₄	1	8	yes	complemented
253	#2285	C₂×D₄	1	2	yes	—
254	#2285	C₂×D₄	1	2	yes	—
255	#2283	C₂×D₄	1	2	yes	—
256	#2283	C₂×D₄	1	2	yes	—
257	#2283	C₂×D₄	1	2	yes	—
258	#2283	C₂⁴	1	2	yes	—
259	#2283	C₂⁴	1	2	yes	—
260	#2280	C₂×D₄	1	2	yes	—
261	C₄²×D₄	C₂×D₄	1	8	yes	complemented
262	C₄×#117	C₂×D₄	1	2	yes	—
263	C₄×#117	C₂×D₄	1	2	yes	—
264	C₄×#117	C₂×D₄	1	2	yes	—
265	C₄×#117	C₂⁴	1	2	yes	—
266	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
267	#1980	C₂×D₄	1	16	yes	complemented
268	#1826	C₂×D₄	1	8	yes	—
269	#1789	C₂×D₄	1	8	yes	—
270	#1762	C₂×D₄	1	8	yes	—
271	#1762	C₂×D₄	1	8	yes	—
272	#1478	C₂×D₄	1	8	yes	complemented
273	#1478	C₂×D₄	1	8	yes	complemented
274	C₂²×#41	#121	1	2	yes	—
275	C₂²×#41	C₂²×D₄	1	2	yes	—
276	C₂³×Q₈	#121	1	1	yes	characteristic
277	C₂³×D₄	#120	1	1	yes	characteristic
278	C₂³×D₄	#120	1	1	yes	characteristic
279	C₂³×D₄	#120	1	1	yes	characteristic
280	C₂³×D₄	#120	1	1	yes	characteristic
281	C₂³×D₄	#120	1	2	yes	—
282	C₂³×D₄	#120	1	2	yes	—
283	C₂³×D₄	#121	1	1	yes	characteristic
284	C₂³×D₄	#121	1	1	yes	characteristic
285	C₂³×D₄	#121	1	1	yes	characteristic
286	C₂³×D₄	#121	1	2	yes	—
287	C₂³×D₄	C₂²×D₄	1	2	yes	—
288	C₂³×D₄	C₂²×D₄	1	2	yes	—
289	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
290	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
291	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂³×C₈	C₂²×D₄	1	2	yes	—
293	C₂³×C₈	C₂²×D₄	1	2	yes	—
294	#532	#121	1	4	yes	—
295	#532	#121	1	4	yes	—
296	#532	C₂²×D₄	1	4	yes	—
297	#532	C₂×#41	1	4	yes	—
298	C₂×C₄⋊Q₈	#121	1	2	yes	—
299	C₂×C₄⋊Q₈	#121	1	2	yes	—
300	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
304	C₂×#127	#121	1	2	yes	—
305	C₂×#127	#121	1	2	yes	—
306	C₂×#127	C₂²×D₄	1	1	yes	characteristic
307	C₂×#127	C₂²×D₄	1	2	yes	—
308	C₂×C₄×Q₈	#121	1	2	yes	—
309	C₂×C₄×Q₈	#121	1	2	yes	—
310	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
311	C₂×C₄×Q₈	C₂×#41	1	2	yes	—
312	C₂×C₄×D₄	#120	1	2	yes	—
313	C₂×C₄×D₄	#120	1	2	yes	—
314	C₂×C₄×D₄	#120	1	2	yes	—
315	C₂×C₄×D₄	#120	1	2	yes	—
316	C₂×C₄×D₄	#120	1	2	yes	—
317	C₂×C₄×D₄	#120	1	2	yes	—
318	C₂×C₄×D₄	#120	1	2	yes	—
319	C₂×C₄×D₄	#120	1	2	yes	—
320	C₂×C₄×D₄	#120	1	1	yes	characteristic
321	C₂×C₄×D₄	#120	1	1	yes	characteristic
322	C₂×C₄×D₄	#120	1	1	yes	characteristic
323	C₂×C₄×D₄	#120	1	1	yes	characteristic
324	C₂×C₄×D₄	#120	1	2	yes	—
325	C₂×C₄×D₄	#120	1	2	yes	—
326	C₂×C₄×D₄	#120	1	2	yes	—
327	C₂×C₄×D₄	#120	1	2	yes	—
328	C₂×C₄×D₄	#120	1	2	yes	—
329	C₂×C₄×D₄	#120	1	2	yes	—
330	C₂×C₄×D₄	#121	1	2	yes	—
331	C₂×C₄×D₄	#121	1	2	yes	—
332	C₂×C₄×D₄	#121	1	2	yes	—
333	C₂×C₄×D₄	#121	1	2	yes	—
334	C₂×C₄×D₄	#121	1	2	yes	—
335	C₂×C₄×D₄	#121	1	2	yes	—
336	C₂×C₄×D₄	#121	1	1	yes	characteristic
337	C₂×C₄×D₄	#121	1	1	yes	characteristic
338	C₂×C₄×D₄	#121	1	1	yes	characteristic
339	C₂×C₄×D₄	#121	1	1	yes	characteristic
340	C₂×C₄×D₄	#121	1	2	yes	—
341	C₂×C₄×D₄	#121	1	2	yes	—
342	C₂×C₄×D₄	#121	1	2	yes	—
343	C₂×C₄×D₄	#121	1	2	yes	—
344	C₂×C₄×D₄	#121	1	2	yes	—
345	C₂×C₄×D₄	#121	1	2	yes	—
346	C₂×C₄×D₄	#121	1	2	yes	—
347	C₂×C₄×D₄	#121	1	2	yes	—
348	C₂×C₄×D₄	#121	1	2	yes	—
349	C₂×C₄×D₄	#121	1	2	yes	—
350	C₂×C₄×D₄	#121	1	1	yes	characteristic
351	C₂×C₄×D₄	#121	1	1	yes	characteristic
352	C₂×C₄×D₄	#121	1	1	yes	characteristic
353	C₂×C₄×D₄	#121	1	1	yes	characteristic
354	C₂×C₄×D₄	#121	1	2	yes	—
355	C₂×C₄×D₄	#121	1	2	yes	—
356	C₂×C₄×D₄	#127	1	2	yes	—
357	C₂×C₄×D₄	#127	1	2	yes	—
358	C₂×C₄×D₄	#127	1	2	yes	—
359	C₂×C₄×D₄	#127	1	2	yes	—
360	C₂×C₄×D₄	#127	1	1	yes	characteristic
361	C₂×C₄×D₄	#127	1	1	yes	characteristic
362	C₂×C₄×D₄	#127	1	1	yes	characteristic
363	C₂×C₄×D₄	#127	1	1	yes	characteristic
364	C₂×C₄×D₄	#127	1	2	yes	—
365	C₂×C₄×D₄	#127	1	2	yes	—
366	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
367	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
368	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
369	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
370	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
371	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
372	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
373	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
374	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
375	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
376	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
377	C₂×C₄×D₄	C₂×#41	1	2	yes	—
378	C₂×C₄×D₄	C₂×#41	1	2	yes	—
379	C₂×C₄×D₄	C₂×#41	1	2	yes	—
380	C₂×#117	#120	1	4	yes	—
381	C₂×#117	#121	1	2	yes	—
382	C₂×#117	C₂²×D₄	1	2	yes	—
383	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	#120	1	2	yes	—
385	C₂²×C₄⋊C₄	#120	1	2	yes	—
386	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
390	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
391	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	#121	1	2	yes	—
394	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
395	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
396	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
398	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
399	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
400	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
401	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
402	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
403	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
404	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
405	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
406	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
407	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
408	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
409	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
411	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
412	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
413	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
414	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
415	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
416	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
417	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
419	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
421	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
422	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
423	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
424	#431	C₂²×D₄	1	4	yes	—
425	#431	C₂²×D₄	1	4	yes	—
426	C₂×C₄⋊C₈	C₂²×D₄	1	2	yes	—
427	C₂×C₄⋊C₈	C₂²×D₄	1	2	yes	—
428	#407	C₂²×D₄	1	4	yes	—
429	C₄×M₁₆	C₂²×D₄	1	4	yes	—
430	C₂×#97	C₂²×D₄	1	4	yes	—
431	C₄×C₄⋊C₄	#120	1	4	yes	—
432	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
433	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
434	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
435	C₄×C₂²⋊C₄	#120	1	4	yes	—
436	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
437	#376	#120	1	4	yes	—
438	C₄³	C₂²×D₄	1	4	yes	—
439	C₂⁵	D₄²	1	1	yes	characteristic
440	C₂²×Q₈	C₂×#121	1	2	yes	—
441	C₂²×D₄	#392	1	1	yes	characteristic
442	C₂²×D₄	#392	1	1	yes	characteristic
443	C₂²×D₄	#392	1	1	yes	characteristic
444	C₂²×D₄	#392	1	2	yes	—
445	C₂²×D₄	#392	1	2	yes	—
446	C₂²×D₄	#392	1	2	yes	—
447	C₂²×D₄	#392	1	1	yes	characteristic
448	C₂²×D₄	#392	1	2	yes	—
449	C₂²×D₄	#392	1	2	yes	—
450	C₂²×D₄	#392	1	2	yes	—
451	C₂²×D₄	C₂×#120	1	2	yes	—
452	C₂²×D₄	C₂×#120	1	2	yes	—
453	C₂²×D₄	C₂×#120	1	2	yes	—
454	C₂²×D₄	C₂×#120	1	2	yes	—
455	C₂²×D₄	C₂×#121	1	2	yes	—
456	C₂²×D₄	C₂×#121	1	2	yes	—
457	C₂²×D₄	C₂×#121	1	2	yes	—
458	C₂³×C₄	C₂×#120	1	1	yes	characteristic
459	C₂³×C₄	C₂×#120	1	1	yes	characteristic
460	C₂³×C₄	C₂×#120	1	1	yes	characteristic
461	C₂³×C₄	C₂×#120	1	1	yes	characteristic
462	C₂³×C₄	C₂×#120	1	1	yes	characteristic
463	C₂³×C₄	C₂×#120	1	1	yes	characteristic
464	C₂³×C₄	C₂×#121	1	1	yes	characteristic
465	C₂³×C₄	C₂×#121	1	1	yes	characteristic
466	C₂³×C₄	C₂×#121	1	1	yes	characteristic
467	C₂³×C₄	C₂×#121	1	1	yes	characteristic
468	C₂³×C₄	#525	1	1	yes	characteristic
469	C₂³×C₄	#525	1	1	yes	characteristic
470	C₂³×C₄	#534	1	1	yes	characteristic
471	C₂³×C₄	#534	1	1	yes	characteristic
472	C₂³×C₄	#534	1	1	yes	characteristic
473	C₂³×C₄	#534	1	1	yes	characteristic
474	C₂³×C₄	#538	1	1	yes	characteristic
475	C₂³×C₄	#538	1	1	yes	characteristic
476	C₂³×C₄	D₄²	1	1	yes	characteristic
477	C₂³×C₄	D₄²	1	1	yes	characteristic
478	C₂³×C₄	D₄²	1	1	yes	characteristic
479	C₂³×C₄	D₄²	1	1	yes	characteristic
480	C₂³×C₄	D₄²	1	1	yes	characteristic
481	C₂³×C₄	D₄²	1	1	yes	characteristic
482	C₂³×C₄	D₄²	1	1	yes	characteristic
483	C₂³×C₄	D₄²	1	1	yes	characteristic
484	C₂³×C₄	D₄²	1	1	yes	characteristic
485	C₂³×C₄	D₄²	1	1	yes	characteristic
486	C₂³×C₄	D₄²	1	1	yes	characteristic
487	C₂³×C₄	D₄²	1	1	yes	characteristic
488	C₂³×C₄	D₄²	1	1	yes	characteristic
489	C₂³×C₄	#546	1	1	yes	characteristic
490	C₂³×C₄	#546	1	1	yes	characteristic
491	C₂³×C₄	#546	1	1	yes	characteristic
492	C₂³×C₄	#546	1	1	yes	characteristic
493	C₂³×C₄	#546	1	1	yes	characteristic
494	C₂³×C₄	#546	1	1	yes	characteristic
495	C₂³×C₄	#546	1	1	yes	characteristic
496	C₂³×C₄	#546	1	1	yes	characteristic
497	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
498	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
499	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₄⋊Q₈	C₂×#121	1	4	yes	—
501	#127	C₂×#121	1	4	yes	—
502	C₄×D₄	#392	1	2	yes	—
503	C₄×D₄	#392	1	2	yes	—
504	C₄×D₄	#392	1	2	yes	—
505	C₄×D₄	#392	1	2	yes	—
506	C₄×D₄	#392	1	2	yes	—
507	C₄×D₄	#392	1	2	yes	—
508	C₄×D₄	#392	1	2	yes	—
509	C₄×D₄	#392	1	2	yes	—
510	C₄×D₄	#392	1	2	yes	—
511	C₄×D₄	#392	1	2	yes	—
512	C₄×D₄	#392	1	2	yes	—
513	C₄×D₄	#392	1	2	yes	—
514	C₄×D₄	#392	1	2	yes	—
515	C₄×D₄	#392	1	2	yes	—
516	C₄×D₄	#392	1	2	yes	—
517	C₄×D₄	#392	1	2	yes	—
518	C₄×D₄	C₂×#120	1	2	yes	—
519	C₄×D₄	C₂×#120	1	2	yes	—
520	C₄×D₄	C₂×#120	1	2	yes	—
521	C₄×D₄	C₂×#120	1	2	yes	—
522	C₄×D₄	C₂×#121	1	2	yes	—
523	C₄×D₄	C₂×#121	1	2	yes	—
524	C₄×D₄	C₂×#121	1	2	yes	—
525	C₄×D₄	C₂×#121	1	2	yes	—
526	C₄×D₄	C₂×#121	1	2	yes	—
527	C₄×D₄	C₂×#121	1	2	yes	—
528	C₄×D₄	C₂×#121	1	2	yes	—
529	C₄×D₄	C₂×#121	1	2	yes	—
530	C₄×D₄	C₂×#127	1	2	yes	—
531	C₄×D₄	C₂×#127	1	2	yes	—
532	C₄×D₄	C₂×#127	1	2	yes	—
533	C₄×D₄	C₂×#127	1	2	yes	—
534	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
535	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
536	C₂×C₄⋊C₄	#392	1	2	yes	—
537	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
538	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
539	C₂×C₄⋊C₄	#392	1	2	yes	—
540	C₂×C₄⋊C₄	#392	1	2	yes	—
541	C₂×C₄⋊C₄	#392	1	2	yes	—
542	C₂×C₄⋊C₄	#392	1	2	yes	—
543	C₂×C₄⋊C₄	#392	1	2	yes	—
544	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
545	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
546	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
547	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
548	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
549	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
550	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
551	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
552	C₂×C₄²	C₂×#120	1	8	yes	—
553	C₂×C₄²	C₂×#120	1	1	yes	characteristic
554	C₂×C₄²	C₂×#120	1	1	yes	characteristic
555	C₂×C₄²	C₂×#120	1	1	yes	characteristic
556	C₂×C₄²	C₂×#120	1	1	yes	characteristic
557	C₂×C₄²	C₂×#120	1	1	yes	characteristic
558	C₂×C₄²	C₂×#120	1	1	yes	characteristic
559	C₂×C₄²	C₂×#120	1	1	yes	characteristic
560	C₂×C₄²	C₂×#120	1	1	yes	characteristic
561	C₂×C₄²	C₂×#120	1	1	yes	characteristic
562	C₂×C₄²	C₂×#120	1	1	yes	characteristic
563	C₂×C₄²	C₂×#121	1	1	yes	characteristic
564	C₂×C₄²	C₂×#121	1	1	yes	characteristic
565	C₂×C₄²	C₂×#121	1	1	yes	characteristic
566	C₂×C₄²	C₂×#121	1	1	yes	characteristic
567	C₂×C₄²	C₂×#121	1	1	yes	characteristic
568	C₂×C₄²	C₂×#121	1	1	yes	characteristic
569	C₂×C₄²	C₂×#121	1	1	yes	characteristic
570	C₂×C₄²	C₂×#121	1	1	yes	characteristic
571	C₂×C₄²	C₂×#121	1	1	yes	characteristic
572	C₂×C₄²	C₂×#121	1	1	yes	characteristic
573	C₂×C₄²	C₂×#121	1	1	yes	characteristic
574	C₂×C₄²	C₂×#121	1	1	yes	characteristic
575	C₂×C₄²	C₂×#121	1	1	yes	characteristic
576	C₂×C₄²	C₂×#121	1	1	yes	characteristic
577	C₂×C₄²	C₂×#121	1	1	yes	characteristic
578	C₂×C₄²	C₂×#121	1	1	yes	characteristic
579	C₂×C₄²	#525	1	1	yes	characteristic
580	C₂×C₄²	#525	1	1	yes	characteristic
581	C₂×C₄²	#525	1	1	yes	characteristic
582	C₂×C₄²	#525	1	1	yes	characteristic
583	C₂×C₄²	#525	1	1	yes	characteristic
584	C₂×C₄²	#525	1	1	yes	characteristic
585	C₂×C₄²	#525	1	1	yes	characteristic
586	C₂×C₄²	#525	1	1	yes	characteristic
587	C₂×C₄²	#525	1	1	yes	characteristic
588	C₂×C₄²	#525	1	1	yes	characteristic
589	C₂×C₄²	C₂×#127	1	1	yes	characteristic
590	C₂×C₄²	C₂×#127	1	1	yes	characteristic
591	C₂×C₄²	C₂×#127	1	1	yes	characteristic
592	C₂×C₄²	C₂×#127	1	1	yes	characteristic
593	C₂×C₄²	#534	1	1	yes	characteristic
594	C₂×C₄²	#534	1	1	yes	characteristic
595	C₂×C₄²	#534	1	1	yes	characteristic
596	C₂×C₄²	#534	1	1	yes	characteristic
597	C₂×C₄²	#534	1	1	yes	characteristic
598	C₂×C₄²	#534	1	1	yes	characteristic
599	C₂×C₄²	#534	1	1	yes	characteristic
600	C₂×C₄²	#534	1	1	yes	characteristic
601	C₂×C₄²	#535	1	1	yes	characteristic
602	C₂×C₄²	#535	1	1	yes	characteristic
603	C₂×C₄²	#535	1	1	yes	characteristic
604	C₂×C₄²	#535	1	1	yes	characteristic
605	C₂×C₄²	#538	1	1	yes	characteristic
606	C₂×C₄²	#538	1	1	yes	characteristic
607	C₂×C₄²	#538	1	1	yes	characteristic
608	C₂×C₄²	#538	1	1	yes	characteristic
609	C₂×C₄²	#538	1	1	yes	characteristic
610	C₂×C₄²	#538	1	1	yes	characteristic
611	C₂×C₄²	D₄²	1	1	yes	characteristic
612	C₂×C₄²	D₄²	1	1	yes	characteristic
613	C₂×C₄²	D₄²	1	1	yes	characteristic
614	C₂×C₄²	D₄²	1	1	yes	characteristic
615	C₂×C₄²	D₄²	1	1	yes	characteristic
616	C₂×C₄²	D₄²	1	1	yes	characteristic
617	C₂×C₄²	D₄²	1	1	yes	characteristic
618	C₂×C₄²	D₄²	1	1	yes	characteristic
619	C₂×C₄²	D₄²	1	1	yes	characteristic
620	C₂×C₄²	D₄²	1	1	yes	characteristic
621	C₂×C₄²	D₄²	1	1	yes	characteristic
622	C₂×C₄²	D₄²	1	1	yes	characteristic
623	C₂×C₄²	D₄²	1	1	yes	characteristic
624	C₂×C₄²	D₄²	1	1	yes	characteristic
625	C₂×C₄²	D₄²	1	1	yes	characteristic
626	C₂×C₄²	D₄²	1	1	yes	characteristic
627	C₂×C₄²	D₄²	1	1	yes	characteristic
628	C₂×C₄²	D₄²	1	1	yes	characteristic
629	C₂×C₄²	#546	1	1	yes	characteristic
630	C₂×C₄²	#546	1	1	yes	characteristic
631	C₂×C₄²	#546	1	1	yes	characteristic
632	C₂×C₄²	#546	1	1	yes	characteristic
633	C₂×C₄²	#546	1	1	yes	characteristic
634	C₂×C₄²	#546	1	1	yes	characteristic
635	C₂×C₄²	#546	1	1	yes	characteristic
636	C₂×C₄²	#546	1	1	yes	characteristic
637	C₂×C₄²	#546	1	1	yes	characteristic
638	C₂×C₄²	#546	1	1	yes	characteristic
639	C₂×C₄²	#546	1	1	yes	characteristic
640	C₂×C₄²	#546	1	1	yes	characteristic
641	C₂×C₄²	#546	1	1	yes	characteristic
642	C₂×C₄²	#546	1	1	yes	characteristic
643	C₂×C₄²	#546	1	1	yes	characteristic
644	C₂×C₄²	#546	1	1	yes	characteristic
645	C₂×C₄²	#546	1	1	yes	characteristic
646	C₂×C₄²	#546	1	1	yes	characteristic
647	C₂×C₄²	#546	1	1	yes	characteristic
648	C₂×C₄²	#546	1	1	yes	characteristic
649	C₂×C₄²	#546	1	1	yes	characteristic
650	C₂×C₄²	#546	1	1	yes	characteristic
651	C₂×C₄²	#546	1	1	yes	characteristic
652	C₂×C₄²	#546	1	1	yes	characteristic
653	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
654	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
655	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
656	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
657	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
659	C₂×C₄²	C₂²×#41	1	1	yes	characteristic
660	C₂×C₄²	C₂²×#41	1	1	yes	characteristic
661	C₂×C₄²	C₂²×#41	1	1	yes	characteristic
662	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂⁴	#2403	1	1	yes	characteristic
666	C₂⁴	#2403	1	1	yes	characteristic
667	C₂⁴	#2410	1	1	yes	characteristic
668	C₂⁴	#2410	1	1	yes	characteristic
669	C₂⁴	#2424	1	1	yes	characteristic
670	C₂⁴	#2424	1	1	yes	characteristic
671	C₂⁴	C₂×D₄²	1	1	yes	characteristic
672	C₂×D₄	#2010	1	4	yes	—
673	C₂×D₄	C₂×#392	1	2	yes	—
674	C₂×D₄	C₂×#392	1	2	yes	—
675	C₂×D₄	C₂×#392	1	2	yes	—
676	C₂×D₄	C₂×#392	1	2	yes	—
677	C₂²×C₄	C₂×#392	1	1	yes	characteristic
678	C₂²×C₄	C₂×#392	1	1	yes	characteristic
679	C₂²×C₄	C₂×#392	1	1	yes	characteristic
680	C₂²×C₄	C₂×#392	1	1	yes	characteristic
681	C₂²×C₄	#2403	1	1	yes	characteristic
682	C₂²×C₄	#2403	1	1	yes	characteristic
683	C₂²×C₄	#2403	1	1	yes	characteristic
684	C₂²×C₄	#2403	1	1	yes	characteristic
685	C₂²×C₄	#2403	1	1	yes	characteristic
686	C₂²×C₄	#2403	1	1	yes	characteristic
687	C₂²×C₄	#2404	1	1	yes	characteristic
688	C₂²×C₄	#2404	1	1	yes	characteristic
689	C₂²×C₄	#2404	1	1	yes	characteristic
690	C₂²×C₄	#2404	1	1	yes	characteristic
691	C₂²×C₄	#2410	1	1	yes	characteristic
692	C₂²×C₄	#2410	1	1	yes	characteristic
693	C₂²×C₄	#2410	1	1	yes	characteristic
694	C₂²×C₄	#2410	1	1	yes	characteristic
695	C₂²×C₄	#2410	1	1	yes	characteristic
696	C₂²×C₄	#2410	1	1	yes	characteristic
697	C₂²×C₄	#2410	1	1	yes	characteristic
698	C₂²×C₄	#2410	1	1	yes	characteristic
699	C₂²×C₄	#2410	1	1	yes	characteristic
700	C₂²×C₄	#2410	1	1	yes	characteristic
701	C₂²×C₄	#2410	1	1	yes	characteristic
702	C₂²×C₄	#2410	1	1	yes	characteristic
703	C₂²×C₄	#2410	1	1	yes	characteristic
704	C₂²×C₄	#2410	1	1	yes	characteristic
705	C₂²×C₄	#2410	1	1	yes	characteristic
706	C₂²×C₄	#2410	1	1	yes	characteristic
707	C₂²×C₄	#2410	1	1	yes	characteristic
708	C₂²×C₄	#2410	1	1	yes	characteristic
709	C₂²×C₄	#2424	1	1	yes	characteristic
710	C₂²×C₄	#2424	1	1	yes	characteristic
711	C₂²×C₄	#2424	1	1	yes	characteristic
712	C₂²×C₄	#2424	1	1	yes	characteristic
713	C₂²×C₄	#2424	1	1	yes	characteristic
714	C₂²×C₄	#2424	1	1	yes	characteristic
715	C₂²×C₄	#2424	1	1	yes	characteristic
716	C₂²×C₄	#2424	1	1	yes	characteristic
717	C₂²×C₄	#2424	1	1	yes	characteristic
718	C₂²×C₄	#2424	1	1	yes	characteristic
719	C₂²×C₄	#2424	1	1	yes	characteristic
720	C₂²×C₄	#2424	1	1	yes	characteristic
721	C₂²×C₄	#2424	1	1	yes	characteristic
722	C₂²×C₄	#2424	1	1	yes	characteristic
723	C₂²×C₄	#2424	1	1	yes	characteristic
724	C₂²×C₄	#2424	1	1	yes	characteristic
725	C₂²×C₄	#2424	1	1	yes	characteristic
726	C₂²×C₄	#2424	1	1	yes	characteristic
727	C₂²×C₄	#2433	1	1	yes	characteristic
728	C₂²×C₄	#2433	1	1	yes	characteristic
729	C₂²×C₄	#2433	1	1	yes	characteristic
730	C₂²×C₄	#2433	1	1	yes	characteristic
731	C₂²×C₄	#2539	1	1	yes	characteristic
732	C₂²×C₄	#2539	1	1	yes	characteristic
733	C₂²×C₄	#2539	1	1	yes	characteristic
734	C₂²×C₄	#2539	1	1	yes	characteristic
735	C₂²×C₄	#2617	1	1	yes	characteristic
736	C₂²×C₄	#2617	1	1	yes	characteristic
737	C₂²×C₄	#2617	1	1	yes	characteristic
738	C₂²×C₄	#2617	1	1	yes	characteristic
739	C₂²×C₄	#2847	1	1	yes	characteristic
740	C₂²×C₄	#2847	1	1	yes	characteristic
741	C₂²×C₄	#2847	1	1	yes	characteristic
742	C₂²×C₄	#2847	1	1	yes	characteristic
743	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
744	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
745	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
746	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
747	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
748	C₂²×C₄	C₂×#525	1	1	yes	characteristic
749	C₂²×C₄	C₂×#534	1	1	yes	characteristic
750	C₂²×C₄	C₂×#534	1	1	yes	characteristic
751	C₂²×C₄	C₂×#538	1	1	yes	characteristic
752	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
753	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
755	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
757	C₂²×C₄	C₂×#546	1	1	yes	characteristic
758	C₂²×C₄	C₂×#546	1	1	yes	characteristic
759	C₂²×C₄	C₂×#546	1	1	yes	characteristic
760	C₂²×C₄	C₂×#546	1	1	yes	characteristic
761	C₄⋊C₄	C₂×#392	1	2	yes	—
762	C₄⋊C₄	C₂×#392	1	2	yes	—
763	C₄⋊C₄	C₂×#392	1	2	yes	—
764	C₄⋊C₄	C₂×#392	1	2	yes	—
765	C₄²	C₂×#392	1	1	yes	characteristic
766	C₄²	C₂×#392	1	1	yes	characteristic
767	C₄²	C₂×#392	1	1	yes	characteristic
768	C₄²	C₂×#392	1	1	yes	characteristic
769	C₄²	#2404	1	1	yes	characteristic
770	C₄²	#2404	1	1	yes	characteristic
771	C₄²	#2404	1	1	yes	characteristic
772	C₄²	#2404	1	1	yes	characteristic
773	C₄²	#2410	1	1	yes	characteristic
774	C₄²	#2410	1	1	yes	characteristic
775	C₄²	#2410	1	1	yes	characteristic
776	C₄²	#2410	1	1	yes	characteristic
777	C₄²	#2410	1	1	yes	characteristic
778	C₄²	#2410	1	1	yes	characteristic
779	C₄²	#2410	1	1	yes	characteristic
780	C₄²	#2410	1	1	yes	characteristic
781	C₄²	#2410	1	1	yes	characteristic
782	C₄²	#2410	1	1	yes	characteristic
783	C₄²	#2410	1	1	yes	characteristic
784	C₄²	#2410	1	1	yes	characteristic
785	C₄²	#2424	1	1	yes	characteristic
786	C₄²	#2424	1	1	yes	characteristic
787	C₄²	#2424	1	1	yes	characteristic
788	C₄²	#2424	1	1	yes	characteristic
789	C₄²	#2424	1	1	yes	characteristic
790	C₄²	#2424	1	1	yes	characteristic
791	C₄²	#2424	1	1	yes	characteristic
792	C₄²	#2424	1	1	yes	characteristic
793	C₄²	#2424	1	1	yes	characteristic
794	C₄²	#2424	1	1	yes	characteristic
795	C₄²	#2424	1	1	yes	characteristic
796	C₄²	#2424	1	1	yes	characteristic
797	C₄²	#2433	1	1	yes	characteristic
798	C₄²	#2433	1	1	yes	characteristic
799	C₄²	#2433	1	1	yes	characteristic
800	C₄²	#2433	1	1	yes	characteristic
801	C₄²	#2539	1	1	yes	characteristic
802	C₄²	#2539	1	1	yes	characteristic
803	C₄²	#2539	1	1	yes	characteristic
804	C₄²	#2539	1	1	yes	characteristic
805	C₄²	#2617	1	1	yes	characteristic
806	C₄²	#2617	1	1	yes	characteristic
807	C₄²	#2617	1	1	yes	characteristic
808	C₄²	#2617	1	1	yes	characteristic
809	C₄²	#2847	1	1	yes	characteristic
810	C₄²	#2847	1	1	yes	characteristic
811	C₄²	#2847	1	1	yes	characteristic
812	C₄²	#2847	1	1	yes	characteristic
813	C₄²	C₂²×#120	1	1	yes	characteristic
814	C₄²	C₂²×#121	1	1	yes	characteristic
815	C₄²	C₂²×#121	1	1	yes	characteristic
816	C₄²	C₂²×#121	1	1	yes	characteristic
817	C₄²	C₂×#525	1	1	yes	characteristic
818	C₄²	C₂×#525	1	1	yes	characteristic
819	C₄²	C₂²×#127	1	1	yes	characteristic
820	C₄²	C₂×#534	1	1	yes	characteristic
821	C₄²	C₂×#535	1	1	yes	characteristic
822	C₄²	C₂×#538	1	1	yes	characteristic
823	C₄²	C₂×D₄²	1	1	yes	characteristic
824	C₄²	C₂×D₄²	1	1	yes	characteristic
825	C₄²	C₂×#546	1	1	yes	characteristic
826	C₄²	C₂×#546	1	1	yes	characteristic
827	C₄²	C₂×#546	1	1	yes	characteristic
828	C₄²	C₂×#546	1	1	yes	characteristic
829	C₂³	#14716	1	1	yes	characteristic
830	C₂³	#14716	1	1	yes	characteristic
831	C₂³	#14716	1	1	yes	characteristic
832	C₂³	#14716	1	1	yes	characteristic
833	C₂³	#23882	1	4	yes	—
834	C₂³	C₂×#2403	1	1	yes	characteristic
835	C₂³	C₂×#2410	1	1	yes	characteristic
836	C₂³	C₂×#2424	1	1	yes	characteristic
837	D₄	C₂×#2010	1	4	yes	—
838	C₂×C₄	#14716	1	1	yes	characteristic
839	C₂×C₄	#14716	1	1	yes	characteristic
840	C₂×C₄	#14716	1	1	yes	characteristic
841	C₂×C₄	#14716	1	1	yes	characteristic
842	C₂×C₄	#14716	1	1	yes	characteristic
843	C₂×C₄	#14716	1	1	yes	characteristic
844	C₂×C₄	#14716	1	1	yes	characteristic
845	C₂×C₄	#14716	1	1	yes	characteristic
846	C₂×C₄	#14716	1	1	yes	characteristic
847	C₂×C₄	#14716	1	1	yes	characteristic
848	C₂×C₄	#14716	1	1	yes	characteristic
849	C₂×C₄	#14716	1	1	yes	characteristic
850	C₂×C₄	C₂×#2010	1	2	yes	—
851	C₂×C₄	#23414	1	2	yes	—
852	C₂×C₄	C₂²×#392	1	1	yes	characteristic
853	C₂×C₄	C₂×#2617	1	1	yes	characteristic
854	C₂×C₄	C₂×#2410	1	1	yes	characteristic
855	C₂×C₄	C₂×#2410	1	1	yes	characteristic
856	C₂×C₄	C₂×#2410	1	1	yes	characteristic
857	C₂×C₄	C₂×#2424	1	1	yes	characteristic
858	C₂×C₄	C₂×#2424	1	1	yes	characteristic
859	C₂×C₄	C₂×#2424	1	1	yes	characteristic
860	C₂×C₄	C₂×#2433	1	1	yes	characteristic
861	C₂×C₄	C₂×#2404	1	1	yes	characteristic
862	C₂×C₄	C₂×#2539	1	1	yes	characteristic
863	C₂×C₄	C₂×#2847	1	1	yes	characteristic
864	C₂²	#394249	1	2	yes	—
865	C₂²	#394249	1	2	yes	—
866	C₂²	#394261	1	2	yes	—
867	C₂²	C₂×#14716	1	1	yes	characteristic
868	C₂²	C₂×#23882	1	2	yes	—
869	C₂²	#6437950	1	2	yes	—
870	C₄	#394261	1	2	yes	—
871	C₄	C₂²×#2010	1	1	yes	characteristic
872	C₄	C₂×#23414	1	1	yes	characteristic
873	C₂	C₂×#394249	1	1	yes	characteristic
874	C₂	C₂×#394261	1	1	yes	characteristic
875	C₂	#72239618	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#14716
commutator, Frattini, cosocle	C₂²×C₄²	C₂⁵
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72249700	C₂	semidirect
2. #72249698	C₂	semidirect
3. #72249696	C₂	semidirect
4. #72249694	C₂	semidirect
5. #72249693	C₂	semidirect
6. #72249691	C₂	semidirect
7. #72249689	C₂	semidirect
8. #72249680	C₂	semidirect
9. #72240663	C₂	semidirect
10. #72239778	C₂	semidirect
11. #72239697	C₂	semidirect
12. #72239668	C₂	semidirect
13. #72239073	C₂	semidirect
14. #72239006	C₂	semidirect
15. #72238966	C₂	semidirect
16. C₂×#196123	C₂	semidirect
17. C₂×#6453969	C₂	semidirect
25. #7628492	C₂²	semidirect
28. #6454206	C₂²	semidirect
29. #6454205	C₂²	semidirect
31. #6386073	C₂²	semidirect
34. #6372430	C₂²	semidirect
37. #6372285	C₂²	semidirect
40. #6370977	C₂²	semidirect
42. #6348995	C₂²	semidirect
43. #6348988	C₂²	semidirect
45. #6343803	C₂²	semidirect
46. #6343380	C₂²	semidirect
49. C₂×#17448	C₂²	semidirect
50. C₂×#17364	C₂²	semidirect
51. #235358	C₂²	semidirect
52. #235354	C₂²	semidirect
53. #234931	C₂²	semidirect
54. #234930	C₂²	semidirect
55. #197072	C₂²	semidirect
56. #197071	C₂²	semidirect
57. #196123	C₂²	semidirect
58. #181794	C₂²	semidirect
59. #181218	C₂²	semidirect
60. #181152	C₂²	semidirect
61. #181146	C₂²	semidirect
62. #181126	C₂²	semidirect
63. #181123	C₂²	semidirect
64. C₂×#7919	C₂²	semidirect
65. C₂×#7861	C₂²	semidirect
66. #116384	C₂²	semidirect
67. #116344	C₂²	semidirect
68. #115390	C₂²	semidirect
69. #114225	C₂²	semidirect
70. #114223	C₂²	semidirect
71. #113023	C₂²	semidirect
72. #113022	C₂²	semidirect
73. #112989	C₂²	semidirect
74. #105654	C₂²	semidirect
76. C₂×D₄×#41	D₄	semidirect
78. C₂²×#550	D₄	semidirect
79. C₂²×#547	D₄	semidirect
80. C₂²×D₄×Q₈	D₄	semidirect
81. C₂²×D₄²	D₄	semidirect
94. C₂×#3101	D₄	semidirect
95. C₂×#3100	D₄	semidirect
96. C₂×#3077	D₄	semidirect
97. C₂×#3077	D₄	semidirect
98. C₂×#3036	D₄	semidirect
99. C₂×#3036	D₄	semidirect
114. #34946	C₂³	semidirect
115. #34936	C₂³	semidirect
117. D₄×#117	D₄	semidirect
118. #34058	D₄	semidirect
122. C₄×#518	D₄	semidirect
123. #21816	D₄	semidirect
127. #21408	C₂³	semidirect
128. #21407	C₂³	semidirect
130. #21355	C₂³	semidirect
131. #21252	D₄	semidirect
135. #20739	D₄	semidirect
137. #20739	C₂³	semidirect
140. C₂×#1762	D₄	semidirect
141. C₂×#1762	D₄	semidirect
143. #17672	C₂³	semidirect
144. #17671	C₂³	semidirect
145. #17562	C₂³	semidirect
146. #17561	C₂³	semidirect
148. #17448	D₄	semidirect
150. #17448	C₂³	semidirect
151. C₂×#1478	D₄	semidirect
152. C₂×#1478	D₄	semidirect
153. #17364	C₂³	semidirect
154. #8085	C₂³	semidirect
155. #7977	C₂³	semidirect
156. #7954	C₂³	semidirect
157. #7948	C₂³	semidirect
158. #7945	C₂³	semidirect
159. #7941	C₂³	semidirect
160. #7919	C₂³	semidirect
161. #7861	C₂³	semidirect
220. C₂×#476	C₂×D₄	semidirect
221. C₂×#476	C₂×D₄	semidirect
222. C₂×#474	C₂×D₄	semidirect
223. C₂×#474	C₂×D₄	semidirect
224. C₂×#461	C₂×D₄	semidirect
225. C₂×#461	C₂×D₄	semidirect
226. C₂×#459	C₂×D₄	semidirect
227. C₂×#459	C₂×D₄	semidirect
252. #2293	C₂×D₄	semidirect
261. C₄²×D₄	C₂×D₄	semidirect
267. #1980	C₂×D₄	semidirect
272. #1478	C₂×D₄	semidirect
273. #1478	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72249700	2
#72249698	2
#72249696	2
#72249694	2
#72249693	2
#72249691	2
#72249689	2
#72249680	2
#72240663	2
#72239778	2
#72239697	2
#72239668	2
#72239073	2
#72239006	2
#72238966	2
C₂×#196123	2
C₂×#6453969	2