Subgroups — #72303262

Order 2048.

At least 11166 conjugacy classes of subgroups; only the 2496 normal subgroups are shown.

The subgroup lattice has 1089 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72303253	C₂	1	1	yes	maximal, characteristic, complemented
2	#72303248	C₂	1	2	yes	maximal, complemented
3	#72303247	C₂	1	1	yes	maximal, characteristic, complemented
4	#72303244	C₂	1	4	yes	maximal, complemented
5	#72303243	C₂	1	2	yes	maximal, complemented
6	#72303240	C₂	1	1	yes	maximal, characteristic, complemented
7	#72303236	C₂	1	1	yes	maximal, characteristic, complemented
8	#72303229	C₂	1	4	yes	maximal, complemented
9	#72303225	C₂	1	4	yes	maximal, complemented
10	#72281798	C₂	1	1	yes	maximal, characteristic
11	#72280445	C₂	1	1	yes	maximal, characteristic, complemented
12	#72280302	C₂	1	2	yes	maximal, complemented
13	#72279525	C₂	1	2	yes	maximal, complemented
14	#72263920	C₂	1	1	yes	maximal, characteristic, complemented
15	#72214400	C₂	1	4	yes	maximal, complemented
16	#10585995	C₂²	1	1	yes	characteristic
17	C₂²×#3481	C₂²	1	1	yes	characteristic
18	#10580321	C₄	1	4	yes	complemented
19	#10580318	C₄	1	2	yes	complemented
20	#10580317	C₄	1	2	yes	complemented
21	#10580241	C₄	1	4	yes	complemented
22	#10580226	C₄	1	4	yes	complemented
23	#10577998	C₂²	1	2	yes	—
24	#10577996	C₂²	1	2	yes	—
25	#10577303	C₂²	1	2	yes	—
26	#10577301	C₂²	1	2	yes	—
27	#10575874	C₂²	1	2	yes	—
28	C₂×#60558	C₂²	1	2	yes	—
29	#10574447	C₂²	1	1	yes	characteristic
30	C₂×D₄×#117	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×#518	C₂²	1	1	yes	characteristic, complemented
32	#6372481	C₂²	1	2	yes	complemented
33	#6372481	C₂²	1	2	yes	complemented
34	#6372471	C₂²	1	2	yes	complemented
35	#6370977	C₂²	1	2	yes	complemented
36	#6370937	C₂²	1	1	yes	characteristic
37	#6343381	C₂²	1	2	yes	complemented
38	#6343354	C₂²	1	2	yes	complemented
39	#6342561	C₂²	1	1	yes	characteristic
40	#518057	C₂²	1	2	yes	complemented
41	#518050	C₂²	1	2	yes	complemented
42	#518026	C₂²	1	2	yes	complemented
43	#518019	C₂²	1	2	yes	complemented
44	#515102	C₂²	1	1	yes	characteristic, complemented
45	#514631	C₂²	1	1	yes	characteristic, complemented
46	#514212	C₂²	1	1	yes	characteristic
47	#514021	C₂²	1	1	yes	characteristic
48	#393557	C₂²	1	8	yes	complemented
49	#392685	C₂²	1	8	yes	complemented
50	#353830	C₂²	1	2	yes	complemented
51	#353774	C₂²	1	2	yes	complemented
52	#198405	C₂²	1	8	yes	complemented
53	#198404	C₂²	1	8	yes	complemented
54	#187925	C₂²	1	4	yes	—
55	#187925	C₂²	1	4	yes	complemented
56	#185652	C₂²	1	2	yes	complemented
57	#185650	C₂²	1	2	yes	complemented
58	#185647	C₂²	1	2	yes	complemented
59	#185643	C₂²	1	2	yes	complemented
60	#185258	C₂²	1	4	yes	—
61	#185258	C₂²	1	4	yes	complemented
62	#181240	C₂²	1	2	yes	complemented
63	#181085	C₂²	1	2	yes	complemented
64	#114840	C₂²	1	8	yes	complemented
65	#114839	C₂²	1	8	yes	complemented
66	#114580	C₂²	1	8	yes	complemented
67	#114579	C₂²	1	8	yes	complemented
68	#108224	C₂²	1	4	yes	complemented
69	#108224	C₂²	1	4	yes	complemented
70	#106331	C₂²	1	4	yes	complemented
71	#106331	C₂²	1	4	yes	complemented
72	#62815	C₂×C₄	1	2	yes	complemented
73	#62813	C₂×C₄	1	1	yes	characteristic, complemented
74	#62812	C₂×C₄	1	1	yes	characteristic, complemented
75	#62781	C₂×C₄	1	2	yes	complemented
76	#62781	C₂×C₄	1	2	yes	complemented
77	#62773	C₂³	1	2	yes	—
78	#62773	C₂³	1	2	yes	—
79	C₂×#3481	C₂×C₄	1	2	yes	—
80	C₂×#3481	C₂×C₄	1	2	yes	—
81	C₂×#3481	C₂×C₄	1	2	yes	—
82	C₂×#3481	C₂×C₄	1	2	yes	—
83	C₂×#3481	D₄	1	2	yes	—
84	C₂×#3481	D₄	1	2	yes	—
85	C₂×#3481	D₄	1	2	yes	—
86	C₂×#3481	D₄	1	2	yes	—
87	C₂²×#559	D₄	1	1	yes	characteristic
88	C₂²×#553	D₄	1	1	yes	characteristic
89	C₂²×#553	C₂³	1	1	yes	characteristic
90	C₂²×#554	D₄	1	1	yes	characteristic
91	C₂²×#554	C₂³	1	1	yes	characteristic
92	C₂²×#546	D₄	1	1	yes	characteristic
93	C₂²×#546	C₂³	1	1	yes	characteristic
94	C₂²×D₄²	C₂³	1	1	yes	characteristic
95	C₂×#3444	C₂³	1	2	yes	—
96	C₂²×#532	D₄	1	1	yes	characteristic
97	C₂²×#529	D₄	1	1	yes	characteristic
98	C₂²×#529	C₂³	1	1	yes	characteristic
99	C₂²×#518	C₂³	1	2	yes	—
100	C₂²×C₄×#41	D₄	1	1	yes	characteristic
101	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
102	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
103	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
104	#61709	C₂×C₄	1	8	yes	complemented
105	#61708	C₂×C₄	1	4	yes	complemented
106	#61707	C₂×C₄	1	4	yes	complemented
107	#61699	C₂×C₄	1	8	yes	complemented
108	#61698	C₂×C₄	1	4	yes	complemented
109	#61697	C₂×C₄	1	4	yes	complemented
110	#61571	C₂×C₄	1	8	yes	—
111	#61570	C₂×C₄	1	4	yes	—
112	#61569	C₂×C₄	1	4	yes	—
113	#61561	C₂×C₄	1	8	yes	—
114	#61560	C₂×C₄	1	4	yes	—
115	#61559	C₂×C₄	1	4	yes	—
116	#60960	C₂×C₄	1	4	yes	complemented
117	#60958	C₂×C₄	1	4	yes	complemented
118	#60945	C₂×C₄	1	8	yes	complemented
119	#60751	C₂³	1	4	yes	—
120	#60750	C₂³	1	4	yes	—
121	C₂×#3110	C₂×C₄	1	4	yes	—
122	C₂×#3109	C₂×C₄	1	4	yes	—
123	C₂×#3114	D₄	1	8	yes	—
124	C₂×#3105	C₂×C₄	1	8	yes	—
125	C₂×#3101	D₄	1	4	yes	—
126	C₂×#3100	D₄	1	4	yes	—
127	C₂×#3092	C₂³	1	4	yes	—
128	C₂×#3077	D₄	1	4	yes	—
129	C₂×#3036	D₄	1	4	yes	—
130	C₂×#3003	C₂³	1	4	yes	—
131	#60282	C₂×C₄	1	2	yes	complemented
132	#60282	C₂×C₄	1	2	yes	complemented
133	#60277	C₂×C₄	1	2	yes	complemented
134	#60276	C₂×C₄	1	2	yes	complemented
135	#60230	C₂³	1	2	yes	—
136	#60230	C₂³	1	2	yes	—
137	C₂×C₄×AGL(1,ℤ/8)	D₄	1	8	yes	—
138	C₂×#2920	C₂³	1	2	yes	—
139	C₂×#2920	C₂³	1	2	yes	—
140	C₂×#2344	C₂³	1	2	yes	—
141	C₂×D₄×C₂²⋊C₄	C₂³	1	2	yes	—
142	#34012	C₂³	1	2	yes	—
143	C₂×#2285	C₂³	1	1	yes	characteristic
144	C₂×#2274	C₂³	1	2	yes	—
145	C₂×C₄×#117	C₂³	1	1	yes	characteristic
146	C₂×C₄×#117	C₂³	1	1	yes	characteristic
147	C₂×C₄×#117	C₂³	1	1	yes	characteristic
148	#21420	C₂³	1	8	yes	—
149	#20983	C₂³	1	8	yes	—
150	#20979	C₂³	1	8	yes	—
151	#20722	C₂³	1	2	yes	—
152	#20722	C₂³	1	2	yes	—
153	#20700	C₂³	1	4	yes	—
154	#20598	C₂³	1	4	yes	—
155	#17592	C₂³	1	8	yes	—
156	#17578	C₂³	1	4	yes	—
157	#17577	C₂³	1	4	yes	—
158	#17362	C₂³	1	2	yes	—
159	#17362	C₂³	1	2	yes	—
160	#14258	C₂³	1	2	yes	—
161	#14257	C₂³	1	2	yes	—
162	#14138	C₂³	1	2	yes	—
163	#14136	C₂³	1	2	yes	—
164	#13957	D₄	1	2	yes	—
165	#13957	D₄	1	2	yes	—
166	#13871	C₂³	1	2	yes	—
167	#13871	C₂³	1	2	yes	—
168	#13853	D₄	1	2	yes	—
169	#13851	D₄	1	2	yes	—
170	#13839	D₄	1	1	yes	characteristic
171	#13839	D₄	1	1	yes	characteristic
172	#13839	D₄	1	1	yes	characteristic
173	#13839	D₄	1	1	yes	characteristic
174	#13839	C₂³	1	2	yes	—
175	#13839	C₂³	1	2	yes	—
176	C₄×#391	D₄	1	2	yes	—
177	C₄×#390	D₄	1	2	yes	—
178	#10738	C₂³	1	8	yes	—
179	#10716	C₂³	1	8	yes	—
180	#7983	C₂³	1	8	yes	—
181	#7929	C₂³	1	8	yes	—
182	C₂³×#41	C₂×D₄	1	1	yes	characteristic
183	C₂³×#41	C₂×D₄	1	1	yes	characteristic
184	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
186	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	—
187	#3505	C₂²×C₄	1	4	yes	—
188	#3505	C₂²×C₄	1	4	yes	—
189	#3501	C₂²×C₄	1	2	yes	—
190	#3501	C₂²×C₄	1	2	yes	—
191	#3496	C₂²×C₄	1	2	yes	—
192	#3496	C₂²×C₄	1	2	yes	—
193	C₂×#559	C₂²⋊C₄	1	2	yes	—
194	C₂×#559	C₂²⋊C₄	1	2	yes	—
195	C₂×#559	C₂²⋊C₄	1	2	yes	—
196	C₂×#559	C₂²⋊C₄	1	2	yes	—
197	C₂×#554	C₂²⋊C₄	1	2	yes	—
198	C₂×#554	C₂²⋊C₄	1	2	yes	—
199	C₂×#554	C₂²⋊C₄	1	2	yes	—
200	C₂×#554	C₂²⋊C₄	1	2	yes	—
201	C₂×#554	C₂²×C₄	1	2	yes	—
202	C₂×#554	C₂²×C₄	1	2	yes	—
203	C₂×#554	C₂×D₄	1	2	yes	—
204	C₂×#554	C₂×D₄	1	2	yes	—
205	C₂×#553	C₂²⋊C₄	1	2	yes	—
206	C₂×#553	C₂²⋊C₄	1	2	yes	—
207	C₂×#553	C₂²⋊C₄	1	2	yes	—
208	C₂×#553	C₂²⋊C₄	1	2	yes	—
209	C₂×#553	C₂²×C₄	1	2	yes	—
210	C₂×#553	C₂²×C₄	1	2	yes	—
211	C₂×#553	C₂×D₄	1	2	yes	—
212	C₂×#553	C₂×D₄	1	2	yes	—
213	C₂×#546	C₂²⋊C₄	1	2	yes	—
214	C₂×#546	C₂²⋊C₄	1	2	yes	—
215	C₂×#546	C₂²⋊C₄	1	2	yes	—
216	C₂×#546	C₂²⋊C₄	1	2	yes	—
217	C₂×#546	C₂²×C₄	1	2	yes	—
218	C₂×#546	C₂²×C₄	1	2	yes	—
219	C₂×#546	C₂×D₄	1	2	yes	—
220	C₂×#546	C₂×D₄	1	2	yes	—
221	C₂×D₄²	C₂²×C₄	1	2	yes	—
222	C₂×D₄²	C₂²×C₄	1	2	yes	—
223	C₂×D₄²	C₂×D₄	1	2	yes	—
224	C₂×D₄²	C₂×D₄	1	2	yes	—
225	C₂×#533	C₂²×C₄	1	2	yes	—
226	C₂×#533	C₂×D₄	1	2	yes	—
227	C₂×#533	C₂×D₄	1	2	yes	—
228	C₂×#532	C₂²⋊C₄	1	2	yes	—
229	C₂×#532	C₂²⋊C₄	1	2	yes	—
230	C₂×#532	C₂²⋊C₄	1	2	yes	—
231	C₂×#532	C₂²⋊C₄	1	2	yes	—
232	C₂×#532	C₂²×C₄	1	2	yes	—
233	C₂×#532	C₂×D₄	1	2	yes	—
234	C₂×#532	C₂×D₄	1	2	yes	—
235	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
236	C₂²×#127	C₂×D₄	1	1	yes	characteristic
237	C₂×#529	C₂²⋊C₄	1	2	yes	—
238	C₂×#529	C₂²⋊C₄	1	2	yes	—
239	C₂×#529	C₂²⋊C₄	1	2	yes	—
240	C₂×#529	C₂²⋊C₄	1	2	yes	—
241	C₂×#529	C₂²×C₄	1	2	yes	—
242	C₂×#529	C₂²×C₄	1	2	yes	—
243	C₂×#529	C₂²×C₄	1	4	yes	—
244	C₂×#529	C₂×D₄	1	2	yes	—
245	C₂×#529	C₂×D₄	1	2	yes	—
246	C₂×#529	C₂×D₄	1	4	yes	—
247	C₂²×#125	C₂×D₄	1	1	yes	characteristic
248	C₂²×#125	C₂×D₄	1	1	yes	characteristic
249	C₂²×#124	C₂×D₄	1	1	yes	characteristic
250	C₂²×#124	C₂×D₄	1	1	yes	characteristic
251	C₂×#525	C₂⁴	1	4	yes	—
252	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₂²⋊Q₈	C₂⁴	1	1	yes	characteristic
254	C₂²×#121	C₂×D₄	1	1	yes	characteristic
255	C₂²×#121	C₂×D₄	1	1	yes	characteristic
256	C₂²×#121	C₂×D₄	1	1	yes	characteristic
257	C₂²×#121	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×#41	C₂²⋊C₄	1	2	yes	—
259	C₂×C₄×#41	C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×#41	C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×#41	C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
263	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
264	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
265	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
266	C₂×C₄×#41	C₂×D₄	1	4	yes	—
267	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
268	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
269	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
270	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
271	C₂×C₄×#41	#41	1	1	yes	characteristic
272	C₂×C₄×#41	#41	1	1	yes	characteristic
273	C₂×C₄×#41	#41	1	1	yes	characteristic
274	C₂×C₄×#41	#41	1	1	yes	characteristic
275	C₂×C₄×#41	#41	1	1	yes	characteristic
276	C₂×C₄×#41	#41	1	1	yes	characteristic
277	C₂×C₄×#41	#41	1	1	yes	characteristic
278	C₂×C₄×#41	#41	1	1	yes	characteristic
279	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
284	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
285	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
286	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
287	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
288	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
289	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
294	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
295	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
297	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
299	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
302	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
303	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
309	C₂²×#117	C₂×D₄	1	1	yes	characteristic
310	C₂²×#117	C₂×D₄	1	1	yes	characteristic
311	C₂²×#117	C₂×D₄	1	1	yes	characteristic
312	C₂²×#117	C₂×D₄	1	1	yes	characteristic
313	C₂²×#117	C₂×D₄	1	1	yes	characteristic
314	C₂²×#117	C₂×D₄	1	1	yes	characteristic
315	C₂²×#117	C₂⁴	1	2	yes	—
316	C₂²×#117	C₂⁴	1	2	yes	—
317	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
318	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
319	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
320	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
321	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
322	#3189	C₂²×C₄	1	8	yes	—
323	#3187	C₂²×C₄	1	8	yes	—
324	#3187	C₂²×C₄	1	8	yes	—
325	#3186	C₂²×C₄	1	8	yes	—
326	C₂×#484	C₂²×C₄	1	8	yes	—
327	C₂×#481	C₂²×C₄	1	8	yes	—
328	C₂×#483	C₂×D₄	1	8	yes	—
329	C₂×#480	C₂×D₄	1	8	yes	—
330	C₂×#478	C₂²⋊C₄	1	16	yes	complemented
331	C₂×#476	C₂²⋊C₄	1	8	yes	complemented
332	C₂×#474	C₂²⋊C₄	1	8	yes	complemented
333	C₂×#463	C₂²⋊C₄	1	16	yes	complemented
334	C₂×#461	C₂²⋊C₄	1	8	yes	complemented
335	C₂×#459	C₂²⋊C₄	1	8	yes	complemented
336	C₂×#450	C₂²×C₄	1	8	yes	—
337	C₂×#450	C₂×D₄	1	8	yes	—
338	C₂×#447	C₂²×C₄	1	8	yes	—
339	C₂×#447	C₂×D₄	1	8	yes	—
340	#2973	C₂²×C₄	1	4	yes	—
341	#2973	C₂²×C₄	1	4	yes	—
342	#2972	C₂²×C₄	1	4	yes	—
343	#2972	C₂²×C₄	1	4	yes	—
344	C₂×#442	C₂²⋊C₄	1	16	yes	complemented
345	C₂×#440	C₂²⋊C₄	1	16	yes	complemented
346	C₂×C₄×SD₁₆	C₂²⋊C₄	1	16	yes	complemented
347	C₂×C₄×D₈	C₂²⋊C₄	1	16	yes	complemented
348	C₂×#432	C₂²×C₄	1	4	yes	—
349	C₂×#432	C₂×D₄	1	4	yes	—
350	C₂×#431	C₂²×C₄	1	4	yes	—
351	C₂×#431	C₂×D₄	1	4	yes	—
352	C₂×#428	C₂×D₄	1	8	yes	—
353	C₂×#423	C₂×D₄	1	4	yes	—
354	C₂×#417	C₂×D₄	1	8	yes	—
355	C₂×#418	C₂×D₄	1	8	yes	—
356	C₂×#407	C₂⁴	1	4	yes	—
357	C₂×#407	C₂⁴	1	4	yes	—
358	C₂×C₄×M₁₆	C₂×D₄	1	4	yes	—
359	C₂×#382	C₂×D₄	1	2	yes	—
360	#2280	C₂⁴	1	4	yes	—
361	C₂×#380	C₂⁴	1	2	yes	—
362	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
363	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
366	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
367	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
368	C₂×#376	C₂×D₄	1	2	yes	—
369	C₂×C₄³	C₂×D₄	1	2	yes	—
370	#1440	C₂×D₄	1	2	yes	—
371	#1440	C₂×D₄	1	2	yes	—
372	#1440	C₂×D₄	1	2	yes	—
373	#1440	C₂×D₄	1	2	yes	—
374	#1438	C₂×D₄	1	2	yes	—
375	#1438	C₂×D₄	1	2	yes	—
376	#1438	C₂×D₄	1	2	yes	—
377	#1438	C₂×D₄	1	2	yes	—
378	#1437	C₂×D₄	1	4	yes	—
379	#1437	C₂×D₄	1	4	yes	—
380	#1436	C₂×D₄	1	4	yes	—
381	#1436	C₂×D₄	1	4	yes	—
382	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
383	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
384	C₂²×#41	C₄×D₄	1	1	yes	characteristic
385	C₂²×#41	C₄×D₄	1	1	yes	characteristic
386	C₂²×#41	C₄×D₄	1	1	yes	characteristic
387	C₂²×#41	C₄×D₄	1	1	yes	characteristic
388	C₂²×#41	#121	1	1	yes	characteristic
389	C₂²×#41	#121	1	1	yes	characteristic
390	C₂²×#41	#121	1	1	yes	characteristic
391	C₂²×#41	#121	1	1	yes	characteristic
392	C₂²×#41	C₂²×D₄	1	4	yes	—
393	C₂³×Q₈	#120	1	1	yes	characteristic
394	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
395	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
396	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
397	C₂³×D₄	#120	1	1	yes	characteristic
398	C₂³×D₄	C₂³×C₄	1	2	yes	—
399	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
400	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
401	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
402	C₂³×D₄	C₂²×D₄	1	4	yes	—
403	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
404	C₂³×D₄	C₂²×D₄	1	4	yes	—
405	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
406	C₂³×D₄	C₂²×D₄	1	2	yes	—
407	C₂⁴×C₄	#120	1	1	yes	characteristic
408	C₂⁴×C₄	#120	1	1	yes	characteristic
409	C₂⁴×C₄	#120	1	1	yes	characteristic
410	C₂⁴×C₄	#120	1	1	yes	characteristic
411	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
412	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
413	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
414	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
415	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
416	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	16	yes	—
417	C₂²×D₈	C₂×C₂²⋊C₄	1	16	yes	—
418	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
419	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
420	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
421	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	complemented
422	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	complemented
423	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	complemented
424	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
425	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
426	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	complemented
427	C₂×#125	C₂×C₂²⋊C₄	1	2	yes	—
428	C₂×#125	C₂×C₂²⋊C₄	1	2	yes	—
429	C₂×#125	C₂×C₂²⋊C₄	1	2	yes	—
430	C₂×#125	C₂×C₂²⋊C₄	1	2	yes	—
431	C₂×#125	C₂×C₂²⋊C₄	1	4	yes	complemented
432	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
433	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
434	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
435	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
436	C₂×#124	C₂×C₂²⋊C₄	1	4	yes	complemented
437	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
438	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
439	C₂×C₂²⋊Q₈	C₂³×C₄	1	4	yes	—
440	C₂×C₂²⋊Q₈	C₂³×C₄	1	2	yes	—
441	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
442	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
443	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
444	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
445	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
446	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
447	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
448	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
449	C₂×#121	C₂³×C₄	1	4	yes	—
450	C₂×#121	C₂³×C₄	1	2	yes	—
451	C₂×#121	C₂²×D₄	1	4	yes	—
452	C₂×#121	C₂²×D₄	1	2	yes	—
453	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
454	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
455	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
456	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
457	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	4	yes	complemented
462	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	4	yes	complemented
463	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
464	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
465	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
466	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
467	C₂×C₄×Q₈	#121	1	1	yes	characteristic
468	C₂×C₄×Q₈	#121	1	1	yes	characteristic
469	C₂×C₄×Q₈	#121	1	1	yes	characteristic
470	C₂×C₄×Q₈	#121	1	1	yes	characteristic
471	C₂×C₄×Q₈	#123	1	1	yes	characteristic
472	C₂×C₄×Q₈	#123	1	1	yes	characteristic
473	C₂×C₄×Q₈	#123	1	1	yes	characteristic
474	C₂×C₄×Q₈	#123	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
476	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
477	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
478	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
479	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
480	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
481	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
482	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
483	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
484	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
485	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
486	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
487	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
488	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
489	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
490	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
491	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
492	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
493	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
494	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
495	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
497	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
498	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	complemented
500	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	complemented
501	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
502	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
503	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
504	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
505	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
506	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
507	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
508	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
509	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
510	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
511	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
512	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
513	C₂×C₄×D₄	#120	1	2	yes	—
514	C₂×C₄×D₄	#120	1	2	yes	—
515	C₂×C₄×D₄	#120	1	8	yes	—
516	C₂×C₄×D₄	#120	1	8	yes	—
517	C₂×C₄×D₄	#120	1	4	yes	—
518	C₂×C₄×D₄	#120	1	4	yes	—
519	C₂×C₄×D₄	#120	1	2	yes	—
520	C₂×C₄×D₄	#120	1	2	yes	—
521	C₂×C₄×D₄	#120	1	4	yes	—
522	C₂×C₄×D₄	#120	1	4	yes	—
523	C₂×C₄×D₄	#120	1	8	yes	—
524	C₂×C₄×D₄	#120	1	2	yes	—
525	C₂×C₄×D₄	#120	1	2	yes	—
526	C₂×C₄×D₄	#120	1	8	yes	—
527	C₂×C₄×D₄	#120	1	2	yes	—
528	C₂×C₄×D₄	#120	1	2	yes	—
529	C₂×C₄×D₄	#121	1	1	yes	characteristic
530	C₂×C₄×D₄	#121	1	1	yes	characteristic
531	C₂×C₄×D₄	#121	1	1	yes	characteristic
532	C₂×C₄×D₄	#121	1	1	yes	characteristic
533	C₂×C₄×D₄	#121	1	1	yes	characteristic
534	C₂×C₄×D₄	#121	1	1	yes	characteristic
535	C₂×C₄×D₄	#121	1	1	yes	characteristic
536	C₂×C₄×D₄	#121	1	1	yes	characteristic
537	C₂×C₄×D₄	#121	1	1	yes	characteristic
538	C₂×C₄×D₄	#121	1	1	yes	characteristic
539	C₂×C₄×D₄	#121	1	1	yes	characteristic
540	C₂×C₄×D₄	#121	1	1	yes	characteristic
541	C₂×C₄×D₄	#123	1	1	yes	characteristic
542	C₂×C₄×D₄	#123	1	1	yes	characteristic
543	C₂×C₄×D₄	#123	1	1	yes	characteristic
544	C₂×C₄×D₄	#123	1	1	yes	characteristic
545	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
546	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
547	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
548	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
549	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
554	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
555	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
556	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
557	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
558	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
559	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
560	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
561	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
562	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
563	C₂×#117	C₄×D₄	1	1	yes	characteristic
564	C₂×#117	C₄×D₄	1	1	yes	characteristic
565	C₂×#117	C₄×D₄	1	1	yes	characteristic
566	C₂×#117	C₄×D₄	1	1	yes	characteristic
567	C₂×#117	C₄×D₄	1	1	yes	characteristic
568	C₂×#117	C₄×D₄	1	1	yes	characteristic
569	C₂×#117	C₄×D₄	1	1	yes	characteristic
570	C₂×#117	C₄×D₄	1	1	yes	characteristic
571	C₂×#117	C₄×D₄	1	1	yes	characteristic
572	C₂×#117	C₄×D₄	1	1	yes	characteristic
573	C₂×#117	C₄×D₄	1	1	yes	characteristic
574	C₂×#117	C₄×D₄	1	1	yes	characteristic
575	C₂×#117	#121	1	1	yes	characteristic
576	C₂×#117	#121	1	1	yes	characteristic
577	C₂×#117	#121	1	1	yes	characteristic
578	C₂×#117	#121	1	1	yes	characteristic
579	C₂×#117	#121	1	1	yes	characteristic
580	C₂×#117	#121	1	1	yes	characteristic
581	C₂×#117	#121	1	1	yes	characteristic
582	C₂×#117	#121	1	1	yes	characteristic
583	C₂×#117	#121	1	1	yes	characteristic
584	C₂×#117	#121	1	1	yes	characteristic
585	C₂×#117	#121	1	1	yes	characteristic
586	C₂×#117	#121	1	1	yes	characteristic
587	C₂×#117	C₂²×D₄	1	4	yes	—
588	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
589	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
590	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
591	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
592	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
593	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
594	C₂²×C₄⋊C₄	C₂³×C₄	1	2	yes	—
595	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
596	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
597	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
598	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
599	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
600	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
601	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
602	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
603	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
604	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
605	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
606	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
607	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
608	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
609	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
610	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
611	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
612	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
613	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
614	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
615	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
616	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
617	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
618	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
619	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
620	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
621	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
622	C₂²×C₄²	#120	1	1	yes	characteristic
623	C₂²×C₄²	#120	1	1	yes	characteristic
624	C₂²×C₄²	#120	1	1	yes	characteristic
625	C₂²×C₄²	#120	1	1	yes	characteristic
626	C₂²×C₄²	#123	1	1	yes	characteristic
627	C₂²×C₄²	#123	1	1	yes	characteristic
628	C₂²×C₄²	#123	1	1	yes	characteristic
629	C₂²×C₄²	#123	1	1	yes	characteristic
630	C₂²×C₄²	#123	1	1	yes	characteristic
631	C₂²×C₄²	#123	1	1	yes	characteristic
632	C₂²×C₄²	#123	1	1	yes	characteristic
633	C₂²×C₄²	#123	1	1	yes	characteristic
634	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
635	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
636	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
637	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
638	C₂²×C₄²	C₂²×D₄	1	4	yes	—
639	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
640	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
641	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
642	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
643	C₂²×C₄²	C₂²×D₄	1	2	yes	—
644	C₂²×C₄²	C₂²×D₄	1	2	yes	—
645	C₂²×C₄²	C₂²×D₄	1	2	yes	—
646	C₂²×C₄²	C₂²×D₄	1	2	yes	—
647	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
648	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
649	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
650	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
651	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
652	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
653	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
654	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
655	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
656	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
657	C₂×#107	C₂×C₂²⋊C₄	1	16	yes	complemented
658	C₂×#106	C₂×C₂²⋊C₄	1	16	yes	complemented
659	C₂×C₄⋊C₈	C₂×C₂²⋊C₄	1	8	yes	complemented
660	C₂×C₄⋊C₈	C₂×C₂²⋊C₄	1	8	yes	complemented
661	C₂×#103	C₂×C₂²⋊C₄	1	16	yes	complemented
662	C₂×#102	C₂×C₂²⋊C₄	1	16	yes	—
663	C₂×#102	C₂×C₂²⋊C₄	1	16	yes	—
664	C₂×#102	C₂×C₂²⋊C₄	1	16	yes	complemented
665	C₂×C₂²⋊C₈	C₂³×C₄	1	8	yes	—
666	C₂×C₂²⋊C₈	C₂²×D₄	1	8	yes	—
667	C₂×#97	C₂×C₂²⋊C₄	1	8	yes	complemented
668	C₂×C₄×C₈	C₂×C₂²⋊C₄	1	8	yes	complemented
669	C₂×#95	C₂²×D₄	1	4	yes	—
670	C₂⁵	C₂×#120	1	1	yes	characteristic
671	C₂⁵	C₂×#120	1	1	yes	characteristic
672	C₂⁵	C₂³×D₄	1	1	yes	characteristic
673	C₂²×Q₈	#386	1	1	yes	characteristic
674	C₂²×Q₈	#386	1	1	yes	characteristic
675	C₂²×Q₈	#386	1	1	yes	characteristic
676	C₂²×Q₈	#386	1	1	yes	characteristic
677	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
678	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	—
679	C₂²×D₄	#386	1	1	yes	characteristic
680	C₂²×D₄	#386	1	1	yes	characteristic
681	C₂²×D₄	#386	1	1	yes	characteristic
682	C₂²×D₄	#386	1	1	yes	characteristic
683	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
684	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
685	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
686	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
687	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
688	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
689	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
690	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
691	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
692	C₂²×D₄	C₂×#120	1	2	yes	—
693	C₂²×D₄	C₂×#120	1	2	yes	—
694	C₂²×D₄	C₂×#120	1	8	yes	—
695	C₂²×D₄	C₂×#120	1	2	yes	—
696	C₂²×D₄	C₂×#120	1	2	yes	—
697	C₂²×D₄	C₂×#121	1	1	yes	characteristic
698	C₂²×D₄	C₂×#121	1	1	yes	characteristic
699	C₂²×D₄	C₂×#121	1	1	yes	characteristic
700	C₂²×D₄	C₂×#121	1	1	yes	characteristic
701	C₂³×C₄	#386	1	1	yes	characteristic
702	C₂³×C₄	#386	1	1	yes	characteristic
703	C₂³×C₄	#386	1	1	yes	characteristic
704	C₂³×C₄	#386	1	1	yes	characteristic
705	C₂³×C₄	#386	1	1	yes	characteristic
706	C₂³×C₄	#386	1	1	yes	characteristic
707	C₂³×C₄	#386	1	1	yes	characteristic
708	C₂³×C₄	#386	1	1	yes	characteristic
709	C₂³×C₄	#386	1	1	yes	characteristic
710	C₂³×C₄	#386	1	1	yes	characteristic
711	C₂³×C₄	#386	1	1	yes	characteristic
712	C₂³×C₄	#386	1	1	yes	characteristic
713	C₂³×C₄	#386	1	1	yes	characteristic
714	C₂³×C₄	#386	1	1	yes	characteristic
715	C₂³×C₄	#386	1	1	yes	characteristic
716	C₂³×C₄	#386	1	1	yes	characteristic
717	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
718	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
719	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
720	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
721	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
722	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
723	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
724	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
725	C₂³×C₄	C₂×#120	1	1	yes	characteristic
726	C₂³×C₄	C₂×#120	1	1	yes	characteristic
727	C₂³×C₄	C₂×#120	1	1	yes	characteristic
728	C₂³×C₄	C₂×#120	1	1	yes	characteristic
729	C₂³×C₄	C₂×#120	1	1	yes	characteristic
730	C₂³×C₄	C₂×#120	1	1	yes	characteristic
731	C₂³×C₄	C₂×#120	1	1	yes	characteristic
732	C₂³×C₄	C₂×#120	1	1	yes	characteristic
733	C₂³×C₄	C₂×#120	1	1	yes	characteristic
734	C₂³×C₄	C₂×#120	1	1	yes	characteristic
735	C₂³×C₄	C₂×#121	1	1	yes	characteristic
736	C₂³×C₄	C₂×#121	1	1	yes	characteristic
737	C₂³×C₄	C₂×#121	1	1	yes	characteristic
738	C₂³×C₄	C₂×#121	1	1	yes	characteristic
739	C₂³×C₄	C₂×#123	1	1	yes	characteristic
740	C₂³×C₄	C₂×#123	1	1	yes	characteristic
741	C₂³×C₄	C₂×#123	1	1	yes	characteristic
742	C₂³×C₄	C₂×#123	1	1	yes	characteristic
743	C₂³×C₄	D₄²	1	2	yes	—
744	C₂³×C₄	D₄²	1	2	yes	—
745	C₂³×C₄	D₄²	1	2	yes	—
746	C₂³×C₄	D₄²	1	2	yes	—
747	C₂³×C₄	D₄²	1	2	yes	—
748	C₂³×C₄	D₄²	1	2	yes	—
749	C₂³×C₄	D₄²	1	2	yes	—
750	C₂³×C₄	D₄²	1	2	yes	—
751	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
752	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
753	C₂³×C₄	C₂³×D₄	1	2	yes	—
754	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
755	C₂³×C₄	C₂³×D₄	1	2	yes	—
756	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
757	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
758	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
759	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
760	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
761	C₂²×C₈	C₂²×C₂²⋊C₄	1	16	yes	—
762	C₄×D₄	#379	1	4	yes	—
763	C₄×D₄	#379	1	4	yes	—
764	C₄×D₄	#379	1	4	yes	—
765	C₄×D₄	#379	1	4	yes	—
766	C₄×D₄	#379	1	4	yes	—
767	C₄×D₄	#379	1	4	yes	—
768	C₄×D₄	#379	1	4	yes	—
769	C₄×D₄	#379	1	4	yes	—
770	C₄×D₄	#379	1	8	yes	—
771	C₄×D₄	#379	1	8	yes	—
772	C₄×D₄	#379	1	8	yes	—
773	C₄×D₄	#379	1	8	yes	—
774	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
775	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
776	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
777	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
778	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
779	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
780	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
781	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
782	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
783	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
784	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
785	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
786	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
787	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
788	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
789	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
791	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
792	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
793	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
794	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
795	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
796	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	—
797	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
802	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
803	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
804	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
805	C₂×C₄⋊C₄	C₂×#120	1	8	yes	—
806	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
807	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
808	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
809	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
810	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
811	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
812	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
813	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
814	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
819	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
820	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
821	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
822	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
823	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
824	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
825	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
826	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
827	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
828	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
829	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
832	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
833	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
834	C₂×C₄²	#386	1	1	yes	characteristic
835	C₂×C₄²	#386	1	1	yes	characteristic
836	C₂×C₄²	#386	1	1	yes	characteristic
837	C₂×C₄²	#386	1	1	yes	characteristic
838	C₂×C₄²	#386	1	1	yes	characteristic
839	C₂×C₄²	#386	1	1	yes	characteristic
840	C₂×C₄²	#386	1	1	yes	characteristic
841	C₂×C₄²	#386	1	1	yes	characteristic
842	C₂×C₄²	#386	1	1	yes	characteristic
843	C₂×C₄²	#386	1	1	yes	characteristic
844	C₂×C₄²	#386	1	1	yes	characteristic
845	C₂×C₄²	#386	1	1	yes	characteristic
846	C₂×C₄²	#386	1	1	yes	characteristic
847	C₂×C₄²	#386	1	1	yes	characteristic
848	C₂×C₄²	#386	1	1	yes	characteristic
849	C₂×C₄²	#386	1	1	yes	characteristic
850	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
851	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
852	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
853	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
854	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
855	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
856	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
857	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
858	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
859	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
860	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
861	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
862	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
863	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
864	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
865	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
866	C₂×C₄²	#518	1	2	yes	—
867	C₂×C₄²	#518	1	2	yes	—
868	C₂×C₄²	#518	1	2	yes	—
869	C₂×C₄²	#518	1	2	yes	—
870	C₂×C₄²	C₂×#120	1	1	yes	characteristic
871	C₂×C₄²	C₂×#120	1	2	yes	—
872	C₂×C₄²	C₂×#120	1	2	yes	—
873	C₂×C₄²	C₂×#120	1	1	yes	characteristic
874	C₂×C₄²	C₂×#120	1	1	yes	characteristic
875	C₂×C₄²	C₂×#120	1	1	yes	characteristic
876	C₂×C₄²	C₂×#120	1	2	yes	—
877	C₂×C₄²	C₂×#120	1	2	yes	—
878	C₂×C₄²	C₂×#120	1	2	yes	—
879	C₂×C₄²	C₂×#120	1	2	yes	—
880	C₂×C₄²	C₂×#121	1	1	yes	characteristic
881	C₂×C₄²	C₂×#121	1	1	yes	characteristic
882	C₂×C₄²	C₂×#121	1	1	yes	characteristic
883	C₂×C₄²	C₂×#121	1	1	yes	characteristic
884	C₂×C₄²	C₂×#123	1	1	yes	characteristic
885	C₂×C₄²	C₂×#123	1	1	yes	characteristic
886	C₂×C₄²	C₂×#123	1	1	yes	characteristic
887	C₂×C₄²	C₂×#123	1	1	yes	characteristic
888	C₂×C₄²	C₂×#123	1	1	yes	characteristic
889	C₂×C₄²	C₂×#123	1	1	yes	characteristic
890	C₂×C₄²	C₂×#123	1	1	yes	characteristic
891	C₂×C₄²	C₂×#123	1	1	yes	characteristic
892	C₂×C₄²	#534	1	1	yes	characteristic
893	C₂×C₄²	#534	1	2	yes	—
894	C₂×C₄²	#534	1	2	yes	—
895	C₂×C₄²	#534	1	1	yes	characteristic
896	C₂×C₄²	#534	1	1	yes	characteristic
897	C₂×C₄²	#534	1	1	yes	characteristic
898	C₂×C₄²	#534	1	2	yes	—
899	C₂×C₄²	#534	1	2	yes	—
900	C₂×C₄²	#534	1	2	yes	—
901	C₂×C₄²	#534	1	2	yes	—
902	C₂×C₄²	D₄²	1	2	yes	—
903	C₂×C₄²	D₄²	1	2	yes	—
904	C₂×C₄²	D₄²	1	2	yes	—
905	C₂×C₄²	D₄²	1	2	yes	—
906	C₂×C₄²	D₄²	1	2	yes	—
907	C₂×C₄²	D₄²	1	2	yes	—
908	C₂×C₄²	D₄²	1	2	yes	—
909	C₂×C₄²	D₄²	1	2	yes	—
910	C₂×C₄²	#546	1	2	yes	—
911	C₂×C₄²	#546	1	2	yes	—
912	C₂×C₄²	#546	1	2	yes	—
913	C₂×C₄²	#546	1	2	yes	—
914	C₂×C₄²	#546	1	2	yes	—
915	C₂×C₄²	#546	1	2	yes	—
916	C₂×C₄²	#546	1	2	yes	—
917	C₂×C₄²	#546	1	2	yes	—
918	C₂×C₄²	#546	1	2	yes	—
919	C₂×C₄²	#546	1	2	yes	—
920	C₂×C₄²	#546	1	2	yes	—
921	C₂×C₄²	#546	1	2	yes	—
922	C₂×C₄²	#546	1	2	yes	—
923	C₂×C₄²	#546	1	2	yes	—
924	C₂×C₄²	#546	1	2	yes	—
925	C₂×C₄²	#546	1	2	yes	—
926	C₂⁴	C₂×#386	1	1	yes	characteristic
927	C₂⁴	C₂×#386	1	1	yes	characteristic
928	C₂⁴	C₂×#386	1	1	yes	characteristic
929	C₂⁴	C₂×#386	1	1	yes	characteristic
930	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
931	C₂⁴	C₂²×#120	1	1	yes	characteristic
932	C₂⁴	C₂²×#121	1	1	yes	characteristic
933	C₂⁴	C₂×D₄²	1	2	yes	—
934	C₂⁴	C₂×D₄²	1	2	yes	—
935	C₂×D₄	C₂×#379	1	4	yes	—
936	C₂×D₄	C₂×#379	1	4	yes	—
937	C₂×D₄	#3025	1	8	yes	—
938	C₂²×C₄	C₂×#386	1	1	yes	characteristic
939	C₂²×C₄	C₂×#386	1	1	yes	characteristic
940	C₂²×C₄	C₂×#386	1	1	yes	characteristic
941	C₂²×C₄	C₂×#386	1	1	yes	characteristic
942	C₂²×C₄	C₂×#386	1	1	yes	characteristic
943	C₂²×C₄	C₂×#386	1	1	yes	characteristic
944	C₂²×C₄	C₂×#386	1	1	yes	characteristic
945	C₂²×C₄	C₂×#386	1	1	yes	characteristic
946	C₂²×C₄	C₂×#386	1	1	yes	characteristic
947	C₂²×C₄	C₂×#386	1	1	yes	characteristic
948	C₂²×C₄	C₂×#386	1	1	yes	characteristic
949	C₂²×C₄	C₂×#386	1	1	yes	characteristic
950	C₂²×C₄	C₂×#386	1	1	yes	characteristic
951	C₂²×C₄	C₂×#386	1	1	yes	characteristic
952	C₂²×C₄	C₂×#386	1	1	yes	characteristic
953	C₂²×C₄	C₂×#386	1	1	yes	characteristic
954	C₂²×C₄	C₂×#386	1	1	yes	characteristic
955	C₂²×C₄	C₂×#386	1	1	yes	characteristic
956	C₂²×C₄	C₂×#386	1	1	yes	characteristic
957	C₂²×C₄	C₂×#386	1	1	yes	characteristic
958	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
959	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
960	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
961	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
962	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
963	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
964	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
965	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
966	C₂²×C₄	#2403	1	1	yes	characteristic
967	C₂²×C₄	#2403	1	1	yes	characteristic
968	C₂²×C₄	#2403	1	2	yes	—
969	C₂²×C₄	#2403	1	1	yes	characteristic
970	C₂²×C₄	#2403	1	2	yes	—
971	C₂²×C₄	#2403	1	1	yes	characteristic
972	C₂²×C₄	#2403	1	1	yes	characteristic
973	C₂²×C₄	#2403	1	1	yes	characteristic
974	C₂²×C₄	#2403	1	1	yes	characteristic
975	C₂²×C₄	#2403	1	2	yes	—
976	C₂²×C₄	#2403	1	2	yes	—
977	C₂²×C₄	#2403	1	1	yes	characteristic
978	C₂²×C₄	#2410	1	2	yes	—
979	C₂²×C₄	#2410	1	2	yes	—
980	C₂²×C₄	#2410	1	2	yes	—
981	C₂²×C₄	#2410	1	2	yes	—
982	C₂²×C₄	#2410	1	2	yes	—
983	C₂²×C₄	#2410	1	2	yes	—
984	C₂²×C₄	#2410	1	2	yes	—
985	C₂²×C₄	#2410	1	2	yes	—
986	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
987	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
988	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
989	C₂²×C₄	C₂×#518	1	2	yes	—
990	C₂²×C₄	C₂²×#120	1	2	yes	—
991	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
992	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
993	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
994	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
995	C₂²×C₄	C₂×#534	1	1	yes	characteristic
996	C₂²×C₄	C₂×#534	1	1	yes	characteristic
997	C₂²×C₄	C₂×#534	1	2	yes	—
998	C₂²×C₄	C₂×D₄²	1	2	yes	—
999	C₂²×C₄	C₂×D₄²	1	2	yes	—
1000	C₂²×C₄	C₂×#546	1	2	yes	—
1001	C₂²×C₄	C₂×#546	1	2	yes	—
1002	C₂²×C₄	C₂×#546	1	2	yes	—
1003	C₂²×C₄	C₂×#546	1	2	yes	—
1004	C₄⋊C₄	C₂×#379	1	4	yes	—
1005	C₄⋊C₄	C₂×#379	1	4	yes	—
1006	C₄²	C₂×#379	1	2	yes	—
1007	C₄²	C₂×#379	1	1	yes	characteristic
1008	C₄²	C₂×#379	1	2	yes	—
1009	C₄²	C₂×#379	1	1	yes	characteristic
1010	C₄²	C₂×#379	1	1	yes	characteristic
1011	C₄²	C₂×#379	1	1	yes	characteristic
1012	C₄²	#2308	1	1	yes	characteristic
1013	C₄²	#2308	1	1	yes	characteristic
1014	C₄²	#2308	1	1	yes	characteristic
1015	C₄²	#2308	1	2	yes	—
1016	C₄²	#2308	1	2	yes	—
1017	C₄²	#2308	1	1	yes	characteristic
1018	C₄²	D₄×C₂²⋊C₄	1	2	yes	—
1019	C₄²	D₄×C₂²⋊C₄	1	2	yes	—
1020	C₄²	D₄×C₂²⋊C₄	1	2	yes	—
1021	C₄²	D₄×C₂²⋊C₄	1	2	yes	—
1022	C₄²	D₄×C₂²⋊C₄	1	2	yes	—
1023	C₄²	D₄×C₂²⋊C₄	1	2	yes	—
1024	C₄²	D₄×C₂²⋊C₄	1	2	yes	—
1025	C₄²	D₄×C₂²⋊C₄	1	2	yes	—
1026	C₄²	#2405	1	1	yes	characteristic
1027	C₄²	#2405	1	1	yes	characteristic
1028	C₄²	#2405	1	1	yes	characteristic
1029	C₄²	#2405	1	1	yes	characteristic
1030	C₄²	#2405	1	1	yes	characteristic
1031	C₄²	#2405	1	1	yes	characteristic
1032	C₄²	#2405	1	2	yes	—
1033	C₄²	#2405	1	2	yes	—
1034	C₄²	#2405	1	2	yes	—
1035	C₄²	#2405	1	2	yes	—
1036	C₄²	#2405	1	1	yes	characteristic
1037	C₄²	#2405	1	1	yes	characteristic
1038	C₄²	#2410	1	2	yes	—
1039	C₄²	#2410	1	2	yes	—
1040	C₄²	#2410	1	2	yes	—
1041	C₄²	#2410	1	2	yes	—
1042	C₄²	#2410	1	2	yes	—
1043	C₄²	#2410	1	2	yes	—
1044	C₄²	#2410	1	2	yes	—
1045	C₄²	#2410	1	2	yes	—
1046	C₂³	#20998	1	2	yes	—
1047	C₂³	C₂²×#386	1	1	yes	characteristic
1048	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
1049	C₂³	C₂×#2403	1	1	yes	characteristic
1050	C₂³	C₂×#2403	1	1	yes	characteristic
1051	C₂³	C₂×#2410	1	2	yes	—
1052	D₄	#20608	1	8	yes	—
1053	C₂×C₄	#13867	1	1	yes	characteristic
1054	C₂×C₄	#13867	1	1	yes	characteristic
1055	C₂×C₄	#13867	1	1	yes	characteristic
1056	C₂×C₄	#13867	1	1	yes	characteristic
1057	C₂×C₄	#13867	1	1	yes	characteristic
1058	C₂×C₄	#13867	1	1	yes	characteristic
1059	C₂×C₄	#13867	1	2	yes	—
1060	C₂×C₄	#13867	1	2	yes	—
1061	C₂×C₄	#13867	1	2	yes	—
1062	C₂×C₄	#13867	1	2	yes	—
1063	C₂×C₄	#13867	1	1	yes	characteristic
1064	C₂×C₄	#13867	1	1	yes	characteristic
1065	C₂×C₄	#20998	1	2	yes	—
1066	C₂×C₄	#23882	1	2	yes	—
1067	C₂×C₄	#23883	1	2	yes	—
1068	C₂×C₄	C₂²×#379	1	1	yes	characteristic
1069	C₂×C₄	C₂×#2308	1	1	yes	characteristic
1070	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
1071	C₂×C₄	C₂×#2410	1	2	yes	—
1072	C₂×C₄	C₂×#2405	1	1	yes	characteristic
1073	C₂×C₄	C₂×#2405	1	1	yes	characteristic
1074	C₂×C₄	C₂×#3025	1	4	yes	—
1075	C₂²	C₂×#13867	1	1	yes	characteristic
1076	C₂²	C₂×#20998	1	1	yes	characteristic
1077	C₂²	C₂×#20998	1	1	yes	characteristic
1078	C₂²	C₂×#23882	1	1	yes	characteristic
1079	C₂²	C₂×#23883	1	1	yes	characteristic
1080	C₂²	#6437616	1	2	yes	—
1081	C₄	#359576	1	2	yes	—
1082	C₄	#359576	1	2	yes	—
1083	C₄	C₂×#20608	1	2	yes	—
1084	C₄	#6440456	1	2	yes	—
1085	C₂	C₂×#359576	1	1	yes	characteristic
1086	C₂	#72302250	1	1	yes	characteristic
1087	C₂	#72302353	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13867
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
socle	C₂²	C₂×#13867
prime radical	#72281798	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72303253	C₂	semidirect
2. #72303248	C₂	semidirect
3. #72303247	C₂	semidirect
4. #72303244	C₂	semidirect
5. #72303243	C₂	semidirect
6. #72303240	C₂	semidirect
7. #72303236	C₂	semidirect
8. #72303229	C₂	semidirect
9. #72303225	C₂	semidirect
11. #72280445	C₂	semidirect
12. #72280302	C₂	semidirect
13. #72279525	C₂	semidirect
14. #72263920	C₂	semidirect
15. #72214400	C₂	semidirect
18. #10580321	C₄	semidirect
19. #10580318	C₄	semidirect
20. #10580317	C₄	semidirect
21. #10580241	C₄	semidirect
22. #10580226	C₄	semidirect
30. C₂×D₄×#117	C₂²	semidirect
31. C₂×C₄×#518	C₂²	semidirect
32. #6372481	C₂²	semidirect
33. #6372481	C₂²	semidirect
34. #6372471	C₂²	semidirect
35. #6370977	C₂²	semidirect
37. #6343381	C₂²	semidirect
38. #6343354	C₂²	semidirect
40. #518057	C₂²	semidirect
41. #518050	C₂²	semidirect
42. #518026	C₂²	semidirect
43. #518019	C₂²	semidirect
44. #515102	C₂²	semidirect
45. #514631	C₂²	semidirect
48. #393557	C₂²	semidirect
49. #392685	C₂²	semidirect
50. #353830	C₂²	semidirect
51. #353774	C₂²	semidirect
52. #198405	C₂²	semidirect
53. #198404	C₂²	semidirect
55. #187925	C₂²	semidirect
56. #185652	C₂²	semidirect
57. #185650	C₂²	semidirect
58. #185647	C₂²	semidirect
59. #185643	C₂²	semidirect
61. #185258	C₂²	semidirect
62. #181240	C₂²	semidirect
63. #181085	C₂²	semidirect
64. #114840	C₂²	semidirect
65. #114839	C₂²	semidirect
66. #114580	C₂²	semidirect
67. #114579	C₂²	semidirect
68. #108224	C₂²	semidirect
69. #108224	C₂²	semidirect
70. #106331	C₂²	semidirect
71. #106331	C₂²	semidirect
72. #62815	C₂×C₄	semidirect
73. #62813	C₂×C₄	semidirect
74. #62812	C₂×C₄	semidirect
75. #62781	C₂×C₄	semidirect
76. #62781	C₂×C₄	semidirect
104. #61709	C₂×C₄	semidirect
105. #61708	C₂×C₄	semidirect
106. #61707	C₂×C₄	semidirect
107. #61699	C₂×C₄	semidirect
108. #61698	C₂×C₄	semidirect
109. #61697	C₂×C₄	semidirect
116. #60960	C₂×C₄	semidirect
117. #60958	C₂×C₄	semidirect
118. #60945	C₂×C₄	semidirect
131. #60282	C₂×C₄	semidirect
132. #60282	C₂×C₄	semidirect
133. #60277	C₂×C₄	semidirect
134. #60276	C₂×C₄	semidirect
330. C₂×#478	C₂²⋊C₄	semidirect
331. C₂×#476	C₂²⋊C₄	semidirect
332. C₂×#474	C₂²⋊C₄	semidirect
333. C₂×#463	C₂²⋊C₄	semidirect
334. C₂×#461	C₂²⋊C₄	semidirect
335. C₂×#459	C₂²⋊C₄	semidirect
344. C₂×#442	C₂²⋊C₄	semidirect
345. C₂×#440	C₂²⋊C₄	semidirect
346. C₂×C₄×SD₁₆	C₂²⋊C₄	semidirect
347. C₂×C₄×D₈	C₂²⋊C₄	semidirect
421. C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	semidirect
422. C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	semidirect
423. C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	semidirect
426. C₂×#127	C₂×C₂²⋊C₄	semidirect
431. C₂×#125	C₂×C₂²⋊C₄	semidirect
436. C₂×#124	C₂×C₂²⋊C₄	semidirect
461. C₂×C₄×Q₈	C₂×C₂²⋊C₄	semidirect
462. C₂×C₄×Q₈	C₂×C₂²⋊C₄	semidirect
499. C₂×C₄×D₄	C₂×C₂²⋊C₄	semidirect
500. C₂×C₄×D₄	C₂×C₂²⋊C₄	semidirect
657. C₂×#107	C₂×C₂²⋊C₄	semidirect
658. C₂×#106	C₂×C₂²⋊C₄	semidirect
659. C₂×C₄⋊C₈	C₂×C₂²⋊C₄	semidirect
660. C₂×C₄⋊C₈	C₂×C₂²⋊C₄	semidirect
661. C₂×#103	C₂×C₂²⋊C₄	semidirect
664. C₂×#102	C₂×C₂²⋊C₄	semidirect
667. C₂×#97	C₂×C₂²⋊C₄	semidirect
668. C₂×C₄×C₈	C₂×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72303253	2
#72303248	2
#72303247	2
#72303244	2
#72303243	2
#72303240	2
#72303236	2
#72303229	2
#72303225	2
#72281798	2
#72280445	2
#72280302	2
#72279525	2
#72263920	2
#72214400	2