Subgroups — #86647

Order 384.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#5833	C₂	1	1	yes	maximal, characteristic, complemented
3	#5824	C₂	1	1	yes	maximal, characteristic, complemented
4	#5806	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#939	C₂	1	1	yes	maximal, characteristic, complemented
6	#5684	C₂	1	1	yes	maximal, characteristic, complemented
7	#5669	C₂	1	1	yes	maximal, characteristic, complemented
8	#5667	C₂	1	1	yes	maximal, characteristic, complemented
9	#5665	C₂	1	1	yes	maximal, characteristic, complemented
10	#5662	C₂	1	1	yes	maximal, characteristic, complemented
11	#5655	C₂	1	1	yes	maximal, characteristic, complemented
12	#5636	C₂	1	1	yes	maximal, characteristic, complemented
13	#5634	C₂	1	1	yes	maximal, characteristic, complemented
14	#5621	C₂	1	1	yes	maximal, characteristic, complemented
15	#5621	C₂	1	1	yes	maximal, characteristic, complemented
16	#5608	C₂	1	1	yes	maximal, characteristic, complemented
17	#5598	C₂	1	1	yes	maximal, characteristic, complemented
18	#5597	C₂	1	1	yes	maximal, characteristic, complemented
19	#5597	C₂	1	1	yes	maximal, characteristic, complemented
20	#5593	C₂	1	1	yes	maximal, characteristic, complemented
21	#5591	C₂	1	1	yes	maximal, characteristic, complemented
22	#5591	C₂	1	1	yes	maximal, characteristic, complemented
23	#5586	C₂	1	1	yes	maximal, characteristic, complemented
24	#5564	C₂	1	1	yes	maximal, characteristic, complemented
25	#5560	C₂	1	1	yes	maximal, characteristic, complemented
26	#5552	C₂	1	1	yes	maximal, characteristic, complemented
27	#5539	C₂	1	1	yes	maximal, characteristic, complemented
28	#5490	C₂	1	1	yes	maximal, characteristic, complemented
29	#5490	C₂	1	1	yes	maximal, characteristic, complemented
30	#5483	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#878	C₂	1	1	yes	maximal, characteristic, complemented
32	#3536	—	3	1	no	maximal, Sylow
33	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
35	C₂²×#67	C₂²	1	1	yes	characteristic
36	C₂²×#67	C₂²	1	1	yes	characteristic
37	C₂³×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×#237	C₂²	1	1	yes	characteristic, complemented
39	C₂×#237	C₂²	1	1	yes	characteristic, complemented
40	C₂×#237	C₂²	1	1	yes	characteristic, complemented
41	C₂×#237	C₂²	1	1	yes	characteristic, complemented
42	C₂×#235	C₂²	1	1	yes	characteristic, complemented
43	C₂×#235	C₂²	1	1	yes	characteristic, complemented
44	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
45	C₃×#124	C₂²	1	1	yes	characteristic, complemented
46	C₃×#123	C₂²	1	1	yes	characteristic, complemented
47	C₃×#123	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₃×#121	C₂²	1	1	yes	characteristic, complemented
50	C₃×#121	C₂²	1	1	yes	characteristic, complemented
51	C₃×#121	C₂²	1	1	yes	characteristic, complemented
52	C₃×#120	C₂²	1	1	yes	characteristic
53	C₃×#120	C₂²	1	1	yes	characteristic
54	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
55	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
58	#953	C₂²	1	1	yes	characteristic
59	#953	C₂²	1	1	yes	characteristic
60	C₂×#217	C₂²	1	1	yes	characteristic
61	C₂×#217	C₂²	1	1	yes	characteristic
62	C₂×#217	C₂²	1	1	yes	characteristic
63	#946	C₂²	1	1	yes	characteristic, complemented
64	#946	C₂²	1	1	yes	characteristic, complemented
65	#946	C₂²	1	1	yes	characteristic, complemented
66	#944	C₂²	1	1	yes	characteristic, complemented
67	#939	C₂²	1	1	yes	characteristic
68	#939	C₂²	1	1	yes	characteristic
69	#939	C₂²	1	1	yes	characteristic
70	#939	C₂²	1	1	yes	characteristic
71	#939	C₂²	1	1	yes	characteristic
72	#939	C₂²	1	1	yes	characteristic
73	#939	C₂²	1	1	yes	characteristic
74	#939	C₂²	1	1	yes	characteristic
75	#939	C₂²	1	1	yes	characteristic
76	#939	C₂²	1	1	yes	characteristic, complemented
77	#939	C₂²	1	1	yes	characteristic, complemented
78	#939	C₂²	1	1	yes	characteristic, complemented
79	#939	C₂²	1	1	yes	characteristic, complemented
80	#939	C₂²	1	1	yes	characteristic, complemented
81	#939	C₂²	1	1	yes	characteristic, complemented
82	#939	C₂²	1	1	yes	characteristic, complemented
83	#939	C₂²	1	1	yes	characteristic, complemented
84	#938	C₂²	1	1	yes	characteristic, complemented
85	#938	C₂²	1	1	yes	characteristic, complemented
86	#938	C₂²	1	1	yes	characteristic, complemented
87	#938	C₂²	1	1	yes	characteristic, complemented
88	#937	C₂²	1	1	yes	characteristic
89	#936	C₂²	1	1	yes	characteristic, complemented
90	#936	C₂²	1	1	yes	characteristic, complemented
91	#935	C₂²	1	1	yes	characteristic, complemented
92	#935	C₂²	1	1	yes	characteristic, complemented
93	#935	C₂²	1	1	yes	characteristic, complemented
94	#935	C₂²	1	1	yes	characteristic, complemented
95	D₄×Dic₃	C₂²	1	1	yes	characteristic
96	D₄×Dic₃	C₂²	1	1	yes	characteristic
97	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
98	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
99	#930	C₂²	1	1	yes	characteristic, complemented
100	#930	C₂²	1	1	yes	characteristic, complemented
101	#930	C₂²	1	1	yes	characteristic, complemented
102	#929	C₂²	1	1	yes	characteristic, complemented
103	#929	C₂²	1	1	yes	characteristic, complemented
104	#929	C₂²	1	1	yes	characteristic, complemented
105	C₄×#67	C₂²	1	1	yes	characteristic
106	C₄×#67	C₂²	1	1	yes	characteristic, complemented
107	C₄×#67	C₂²	1	1	yes	characteristic, complemented
108	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
109	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
110	#924	C₂²	1	1	yes	characteristic
111	#924	C₂²	1	1	yes	characteristic, complemented
112	#924	C₂²	1	1	yes	characteristic, complemented
113	#924	C₂²	1	1	yes	characteristic, complemented
114	#924	C₂²	1	1	yes	characteristic, complemented
115	#924	C₂²	1	1	yes	characteristic, complemented
116	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
117	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	#898	C₂²	1	1	yes	characteristic, complemented
121	#897	C₂²	1	1	yes	characteristic, complemented
122	#897	C₂²	1	1	yes	characteristic, complemented
123	#896	C₂²	1	1	yes	characteristic, complemented
124	#896	C₂²	1	1	yes	characteristic, complemented
125	#896	C₂²	1	1	yes	characteristic, complemented
126	#896	C₂²	1	1	yes	characteristic, complemented
127	#896	C₂²	1	1	yes	characteristic, complemented
128	#896	C₂²	1	1	yes	characteristic, complemented
129	#894	C₂²	1	1	yes	characteristic, complemented
130	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
131	#890	C₂²	1	1	yes	characteristic, complemented
132	#889	C₂²	1	1	yes	characteristic, complemented
133	#889	C₂²	1	1	yes	characteristic, complemented
134	#888	C₂²	1	1	yes	characteristic, complemented
135	#887	C₂²	1	1	yes	characteristic, complemented
136	#886	C₂²	1	1	yes	characteristic, complemented
137	#886	C₂²	1	1	yes	characteristic, complemented
138	#886	C₂²	1	1	yes	characteristic, complemented
139	#885	C₂²	1	1	yes	characteristic, complemented
140	#885	C₂²	1	1	yes	characteristic, complemented
141	#885	C₂²	1	1	yes	characteristic, complemented
142	#885	C₂²	1	1	yes	characteristic, complemented
143	#885	C₂²	1	1	yes	characteristic, complemented
144	#885	C₂²	1	1	yes	characteristic, complemented
145	#884	C₂²	1	1	yes	characteristic, complemented
146	#884	C₂²	1	1	yes	characteristic, complemented
147	#884	C₂²	1	1	yes	characteristic, complemented
148	#884	C₂²	1	1	yes	characteristic, complemented
149	#884	C₂²	1	1	yes	characteristic, complemented
150	#883	C₂²	1	1	yes	characteristic, complemented
151	#883	C₂²	1	1	yes	characteristic, complemented
152	#883	C₂²	1	1	yes	characteristic, complemented
153	#883	C₂²	1	1	yes	characteristic, complemented
154	#883	C₂²	1	1	yes	characteristic, complemented
155	#882	C₂²	1	1	yes	characteristic
156	#67⋊C₄	C₂²	1	1	yes	characteristic
157	#67⋊C₄	C₂²	1	1	yes	characteristic
158	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
161	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
162	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
163	#879	C₂²	1	1	yes	characteristic, complemented
164	#879	C₂²	1	1	yes	characteristic, complemented
165	#878	C₂²	1	1	yes	characteristic
166	#878	C₂²	1	1	yes	characteristic
167	#878	C₂²	1	1	yes	characteristic
168	#878	C₂²	1	1	yes	characteristic
169	#878	C₂²	1	1	yes	characteristic
170	#878	C₂²	1	1	yes	characteristic
171	#878	C₂²	1	1	yes	characteristic
172	#878	C₂²	1	1	yes	characteristic, complemented
173	#878	C₂²	1	1	yes	characteristic, complemented
174	#878	C₂²	1	1	yes	characteristic, complemented
175	#878	C₂²	1	1	yes	characteristic, complemented
176	#878	C₂²	1	1	yes	characteristic, complemented
177	#878	C₂²	1	1	yes	characteristic, complemented
178	#878	C₂²	1	1	yes	characteristic, complemented
179	#878	C₂²	1	1	yes	characteristic, complemented
180	#878	C₂²	1	1	yes	characteristic, complemented
181	#878	C₂²	1	1	yes	characteristic, complemented
182	#878	C₂²	1	1	yes	characteristic, complemented
183	#877	C₂²	1	1	yes	characteristic, complemented
184	#876	C₂²	1	1	yes	characteristic, complemented
185	#875	C₂²	1	1	yes	characteristic, complemented
186	#870	C₂²	1	1	yes	characteristic, complemented
187	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
188	#562	—	3	1	no	—
189	#562	—	3	1	no	—
190	#562	—	3	1	no	—
191	#562	—	3	1	no	—
192	#554	—	3	1	no	—
193	#554	—	3	1	no	—
194	#548	—	3	1	no	—
195	#548	—	3	1	no	—
196	#547	—	3	1	no	—
197	#547	—	3	1	no	—
198	#546	—	3	1	no	—
199	#546	—	3	1	no	—
200	#546	—	3	1	no	—
201	#546	—	3	1	no	—
202	#546	—	3	1	no	—
203	#546	D₃	1	1	yes	characteristic, complemented
204	#543	—	3	1	no	—
205	#543	—	3	1	no	—
206	#542	—	3	1	no	—
207	#542	—	3	1	no	—
208	#539	—	3	1	no	—
209	#539	—	3	1	no	—
210	#538	—	3	1	no	—
211	#538	—	3	1	no	—
212	#537	—	3	1	no	—
213	#537	—	3	1	no	—
214	#537	—	3	1	no	—
215	#537	—	3	1	no	—
216	#525	—	3	1	no	—
217	C₂×C₂²⋊Q₈	—	3	1	no	—
218	C₂×#121	—	3	1	no	—
219	C₂⁴×C₃	C₂³	1	1	yes	characteristic
220	C₂⁴×C₃	C₂³	1	1	yes	characteristic
221	C₂³×D₃	C₂³	1	1	yes	characteristic
222	C₃×#41	—	4	2	no	—
223	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₃×D₄	—	4	2	no	—
225	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
232	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
233	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
240	C₂×#67	—	4	2	no	—
241	C₂×#67	—	4	2	no	—
242	C₂×#67	C₂³	1	1	yes	characteristic
243	C₂×#67	C₂³	1	1	yes	characteristic
244	C₂×#67	C₂³	1	1	yes	characteristic
245	C₂×#67	C₂³	1	1	yes	characteristic
246	C₂×#67	C₂³	1	1	yes	characteristic
247	C₂×#67	C₂³	1	1	yes	characteristic
248	C₂×#67	C₂³	1	1	yes	characteristic
249	C₂×#67	C₂³	1	1	yes	characteristic
250	C₂×#67	C₂³	1	1	yes	characteristic
251	C₂×#67	C₂³	1	1	yes	characteristic
252	C₂×#67	C₂³	1	1	yes	characteristic
253	C₂×#67	C₂³	1	1	yes	characteristic
254	C₂×#67	C₂³	1	1	yes	characteristic
255	C₂×#67	C₂³	1	1	yes	characteristic
256	C₂×#67	C₂³	1	1	yes	characteristic
257	C₂×#67	C₂³	1	1	yes	characteristic
258	C₂²×Dic₃	—	4	2	no	—
259	C₂²×Dic₃	C₂³	1	1	yes	characteristic
260	C₂²×Dic₃	C₂³	1	1	yes	characteristic
261	C₂²×Dic₃	C₂³	1	1	yes	characteristic
262	C₂²×Dic₃	C₂³	1	1	yes	characteristic
263	C₂²×Dic₃	C₂³	1	1	yes	characteristic
264	C₂²×Dic₃	C₂³	1	1	yes	characteristic
265	C₂²×Dic₃	C₂³	1	1	yes	characteristic
266	C₂²×Dic₃	C₂³	1	1	yes	characteristic
267	C₂²×Dic₃	C₂³	1	1	yes	characteristic
268	C₂²×Dic₃	C₂³	1	1	yes	characteristic
269	C₂²×Dic₃	C₂³	1	1	yes	characteristic
270	C₂²×Dic₃	C₂³	1	1	yes	characteristic
271	C₂²×Dic₃	C₂³	1	1	yes	characteristic
272	#237	—	4	2	no	—
273	#237	—	4	2	no	—
274	#237	—	4	2	no	—
275	#237	—	4	2	no	—
276	#235	—	4	2	no	—
277	#235	—	4	2	no	—
278	C₂×D₁₂	C₂³	1	1	yes	characteristic
279	C₂×D₁₂	C₂³	1	1	yes	characteristic
280	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
287	C₂×Dic₆	—	4	2	no	—
288	C₂×Dic₆	C₂³	1	1	yes	characteristic
289	C₂×Dic₆	C₂³	1	1	yes	characteristic
290	C₂×Dic₆	C₂³	1	1	yes	characteristic
291	C₂×Dic₆	C₂³	1	1	yes	characteristic
292	C₂×Dic₆	C₂³	1	1	yes	characteristic
293	C₂×Dic₆	C₂³	1	1	yes	characteristic
294	C₂×Dic₆	C₂³	1	1	yes	characteristic
295	C₂×Dic₆	C₂³	1	1	yes	characteristic
296	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
299	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
300	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
301	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
302	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
303	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
304	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
305	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
306	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₃×C₄²	C₂³	1	1	yes	characteristic
313	#217	C₂³	1	1	yes	characteristic
314	#217	C₂³	1	1	yes	characteristic
315	#217	C₂³	1	1	yes	characteristic
316	#217	C₂³	1	1	yes	characteristic
317	#217	C₂³	1	1	yes	characteristic
318	#217	C₂³	1	1	yes	characteristic
319	#217	C₂³	1	1	yes	characteristic
320	#217	C₂³	1	1	yes	characteristic
321	#217	C₂³	1	1	yes	characteristic
322	#217	C₂³	1	1	yes	characteristic
323	#217	C₂³	1	1	yes	characteristic
324	#217	C₂³	1	1	yes	characteristic
325	#217	C₂³	1	1	yes	characteristic
326	#217	C₂³	1	1	yes	characteristic
327	#217	C₂³	1	1	yes	characteristic
328	#217	C₂³	1	1	yes	characteristic
329	#217	C₂³	1	1	yes	characteristic
330	#217	C₂³	1	1	yes	characteristic
331	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
332	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
333	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
334	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
335	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
336	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
337	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
338	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
339	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
340	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
341	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
342	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
343	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
344	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
345	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
346	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
347	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
348	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
349	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
350	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
351	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
352	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
353	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
354	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
355	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
356	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
357	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
358	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
359	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
360	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
361	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
368	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
369	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
370	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
371	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
372	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
373	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
374	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
375	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
376	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
377	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
378	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
379	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
380	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
381	C₄×Dic₃	C₂³	1	1	yes	characteristic
382	C₄×Dic₃	C₂³	1	1	yes	characteristic
383	C₄×Dic₃	C₂³	1	1	yes	characteristic
384	C₄×Dic₃	C₂³	1	1	yes	characteristic
385	C₄×Dic₃	C₂³	1	1	yes	characteristic
386	C₂×#41	—	3	1	no	—
387	C₂×#41	—	3	1	no	—
388	C₂×#41	—	3	1	no	—
389	C₂×#41	—	3	1	no	—
390	C₂×#41	—	3	1	no	—
391	C₂×#41	—	3	1	no	—
392	C₂×#41	C₂×D₃	1	1	yes	characteristic, complemented
393	C₂²×Q₈	—	3	1	no	—
394	C₂²×D₄	—	3	1	no	—
395	C₂²×D₄	—	3	1	no	—
396	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
397	C₂³×C₄	—	3	1	no	—
398	C₄⋊Q₈	—	3	1	no	—
399	C₄⋊Q₈	—	3	1	no	—
400	#126	—	3	1	no	—
401	#126	—	3	1	no	—
402	#126	—	3	1	no	—
403	#126	—	3	1	no	—
404	#125	—	3	1	no	—
405	#125	—	3	1	no	—
406	#125	—	3	1	no	—
407	#125	—	3	1	no	—
408	#124	—	3	1	no	—
409	#124	—	3	1	no	—
410	#124	—	3	1	no	—
411	#124	—	3	1	no	—
412	#124	—	3	1	no	—
413	#124	—	3	1	no	—
414	#124	—	3	1	no	—
415	#124	—	3	1	no	—
416	#124	—	3	1	no	—
417	#124	C₂×D₃	1	1	yes	characteristic, complemented
418	#123	—	3	1	no	—
419	#123	—	3	1	no	—
420	#123	—	3	1	no	—
421	#123	—	3	1	no	—
422	#123	—	3	1	no	—
423	#123	—	3	1	no	—
424	#123	—	3	1	no	—
425	#123	—	3	1	no	—
426	#123	—	3	1	no	—
427	#123	—	3	1	no	—
428	#123	—	3	1	no	—
429	#123	—	3	1	no	—
430	#123	—	3	1	no	—
431	#123	—	3	1	no	—
432	#123	—	3	1	no	—
433	#123	—	3	1	no	—
434	#123	C₂×D₃	1	1	yes	characteristic, complemented
435	#123	C₂×D₃	1	1	yes	characteristic, complemented
436	C₂²⋊Q₈	—	3	1	no	—
437	C₂²⋊Q₈	—	3	1	no	—
438	C₂²⋊Q₈	—	3	1	no	—
439	C₂²⋊Q₈	—	3	1	no	—
440	C₂²⋊Q₈	—	3	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
442	C₂²⋊Q₈	—	3	1	no	—
443	C₂²⋊Q₈	—	3	1	no	—
444	C₂²⋊Q₈	—	3	1	no	—
445	C₂²⋊Q₈	—	3	1	no	—
446	C₂²⋊Q₈	—	3	1	no	—
447	C₂²⋊Q₈	—	3	1	no	—
448	C₂²⋊Q₈	—	3	1	no	—
449	C₂²⋊Q₈	—	3	1	no	—
450	C₂²⋊Q₈	—	3	1	no	—
451	C₂²⋊Q₈	—	3	1	no	—
452	C₂²⋊Q₈	—	3	1	no	—
453	C₂²⋊Q₈	—	3	1	no	—
454	C₂²⋊Q₈	—	3	1	no	—
455	C₂²⋊Q₈	—	3	1	no	—
456	C₂²⋊Q₈	—	3	1	no	—
457	C₂²⋊Q₈	—	3	1	no	—
458	C₂²⋊Q₈	—	3	1	no	—
459	C₂²⋊Q₈	—	3	1	no	—
460	C₂²⋊Q₈	—	3	1	no	—
461	C₂²⋊Q₈	—	3	1	no	—
462	C₂²⋊Q₈	—	3	1	no	—
463	C₂²⋊Q₈	—	3	1	no	—
464	C₂²⋊Q₈	—	3	1	no	—
465	C₂²⋊Q₈	—	3	1	no	—
466	C₂²⋊Q₈	—	3	1	no	—
467	C₂²⋊Q₈	—	3	1	no	—
468	C₂²⋊Q₈	—	3	1	no	—
469	C₂²⋊Q₈	—	3	1	no	—
470	C₂²⋊Q₈	—	3	1	no	—
471	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
472	#121	—	3	1	no	—
473	#121	—	3	1	no	—
474	#121	—	3	1	no	—
475	#121	—	3	1	no	—
476	#121	—	3	1	no	—
477	#121	—	3	1	no	—
478	#121	—	3	1	no	—
479	#121	—	3	1	no	—
480	#121	—	3	1	no	—
481	#121	—	3	1	no	—
482	#121	—	3	1	no	—
483	#121	—	3	1	no	—
484	#121	—	3	1	no	—
485	#121	—	3	1	no	—
486	#121	—	3	1	no	—
487	#121	—	3	1	no	—
488	#121	—	3	1	no	—
489	#121	—	3	1	no	—
490	#121	—	3	1	no	—
491	#121	—	3	1	no	—
492	#121	—	3	1	no	—
493	#121	—	3	1	no	—
494	#121	—	3	1	no	—
495	#121	—	3	1	no	—
496	#121	—	3	1	no	—
497	#121	—	3	1	no	—
498	#121	—	3	1	no	—
499	#121	—	3	1	no	—
500	#121	—	3	1	no	—
501	#121	C₂×D₃	1	1	yes	characteristic, complemented
502	#121	C₂×D₃	1	1	yes	characteristic, complemented
503	#121	C₂×D₃	1	1	yes	characteristic, complemented
504	#120	—	3	1	no	—
505	#120	—	3	1	no	—
506	#120	—	3	1	no	—
507	#120	—	3	1	no	—
508	#120	C₂×D₃	1	1	yes	characteristic
509	#120	C₂×D₃	1	1	yes	characteristic
510	C₄×Q₈	—	3	1	no	—
511	C₄×Q₈	—	3	1	no	—
512	C₄×D₄	—	3	1	no	—
513	C₄×D₄	—	3	1	no	—
514	C₄×D₄	—	3	1	no	—
515	C₄×D₄	—	3	1	no	—
516	C₄×D₄	—	3	1	no	—
517	C₄×D₄	—	3	1	no	—
518	C₄×D₄	—	3	1	no	—
519	C₄×D₄	—	3	1	no	—
520	C₄×D₄	—	3	1	no	—
521	C₄×D₄	—	3	1	no	—
522	C₄×D₄	—	3	1	no	—
523	C₄×D₄	—	3	1	no	—
524	C₄×D₄	C₂×D₃	1	1	yes	characteristic
525	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
526	#117	—	3	1	no	—
527	C₂×C₄⋊C₄	—	3	1	no	—
528	C₂×C₄⋊C₄	—	3	1	no	—
529	C₂×C₄⋊C₄	—	3	1	no	—
530	C₂×C₄⋊C₄	—	3	1	no	—
531	C₂×C₄⋊C₄	—	3	1	no	—
532	C₂×C₄⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	—	3	1	no	—
534	C₂×C₂²⋊C₄	—	3	1	no	—
535	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₂²⋊C₄	—	3	1	no	—
539	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
541	C₂³×C₃	—	2	2	no	—
542	C₂³×C₃	—	2	2	no	—
543	C₂³×C₃	—	2	2	no	—
544	C₂³×C₃	—	4	1	no	—
545	C₂³×C₃	—	4	1	no	—
546	C₂³×C₃	—	4	1	no	—
547	C₂³×C₃	C₂⁴	1	1	yes	characteristic
548	C₂³×C₃	C₂⁴	1	1	yes	characteristic
549	C₂³×C₃	C₂⁴	1	1	yes	characteristic
550	C₂³×C₃	C₂⁴	1	1	yes	characteristic
551	C₂³×C₃	C₂⁴	1	1	yes	characteristic
552	C₂³×C₃	C₂⁴	1	1	yes	characteristic
553	C₂²×D₃	—	2	2	no	—
554	C₂²×D₃	—	4	1	no	—
555	C₂²×D₃	—	4	1	no	—
556	C₂²×D₃	C₂⁴	1	1	yes	characteristic
557	C₂²×D₃	C₂⁴	1	1	yes	characteristic
558	C₂²×D₃	C₂⁴	1	1	yes	characteristic
559	C₃×Q₈	—	4	1	no	—
560	C₃×D₄	—	2	2	no	—
561	C₃×D₄	—	2	2	no	—
562	C₃×D₄	—	2	2	no	—
563	C₃×D₄	—	2	2	no	—
564	C₃×D₄	—	4	1	no	—
565	C₃×D₄	—	4	1	no	—
566	C₃×D₄	—	4	1	no	—
567	C₃×D₄	—	4	1	no	—
568	C₃×D₄	—	4	1	no	—
569	C₂×C₃×C₄	—	2	2	no	—
570	C₂×C₃×C₄	—	4	1	no	—
571	C₂×C₃×C₄	—	4	1	no	—
572	C₂×C₃×C₄	—	4	1	no	—
573	C₂×C₃×C₄	—	4	1	no	—
574	C₂×C₃×C₄	—	4	1	no	—
575	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
582	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
584	#67	—	2	2	no	—
585	#67	—	2	2	no	—
586	#67	—	2	2	no	—
587	#67	—	2	2	no	—
588	#67	—	2	2	no	—
589	#67	—	2	2	no	—
590	#67	—	4	1	no	—
591	#67	—	4	1	no	—
592	#67	—	4	1	no	—
593	#67	—	4	1	no	—
594	#67	—	4	1	no	—
595	#67	—	4	1	no	—
596	#67	—	4	1	no	—
597	#67	—	4	1	no	—
598	#67	—	4	1	no	—
599	#67	—	4	1	no	—
600	C₂×Dic₃	—	2	2	no	—
601	C₂×Dic₃	—	2	2	no	—
602	C₂×Dic₃	—	2	2	no	—
603	C₂×Dic₃	—	2	2	no	—
604	C₂×Dic₃	—	2	2	no	—
605	C₂×Dic₃	—	4	1	no	—
606	C₂×Dic₃	—	4	1	no	—
607	C₂×Dic₃	—	4	1	no	—
608	C₂×Dic₃	—	4	1	no	—
609	C₂×Dic₃	—	4	1	no	—
610	C₂×Dic₃	—	4	1	no	—
611	C₂×Dic₃	—	4	1	no	—
612	C₂×Dic₃	—	4	1	no	—
613	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
614	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
615	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
616	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
617	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
618	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
619	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
620	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
621	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
622	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
623	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
624	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
625	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
626	D₁₂	—	4	1	no	—
627	D₁₂	—	4	1	no	—
628	C₄×D₃	—	2	2	no	—
629	C₄×D₃	—	4	1	no	—
630	C₄×D₃	—	4	1	no	—
631	C₄×D₃	—	4	1	no	—
632	C₄×D₃	—	4	1	no	—
633	C₄×D₃	—	4	1	no	—
634	C₄×D₃	—	4	1	no	—
635	Dic₆	—	2	2	no	—
636	Dic₆	—	2	2	no	—
637	Dic₆	—	4	1	no	—
638	Dic₆	—	4	1	no	—
639	Dic₆	—	4	1	no	—
640	Dic₆	—	4	1	no	—
641	Dic₆	—	4	1	no	—
642	Dic₆	—	4	1	no	—
643	C₂⁴	—	3	1	no	—
644	C₂⁴	C₂²×D₃	1	1	yes	characteristic
645	C₂⁴	C₂²×D₃	1	1	yes	characteristic
646	#41	—	4	2	no	—
647	#41	—	12	2	no	—
648	#41	—	12	2	no	—
649	#41	—	12	2	no	—
650	#41	—	12	2	no	—
651	#41	—	12	2	no	—
652	#41	—	12	2	no	—
653	C₂×Q₈	—	3	1	no	—
654	C₂×Q₈	—	3	1	no	—
655	C₂×Q₈	—	3	1	no	—
656	C₂×Q₈	—	3	1	no	—
657	C₂×Q₈	—	3	1	no	—
658	C₂×Q₈	—	3	1	no	—
659	C₂×Q₈	—	3	1	no	—
660	C₂×Q₈	—	3	1	no	—
661	C₂×Q₈	—	12	2	no	—
662	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
663	C₂×D₄	—	3	1	no	—
664	C₂×D₄	—	3	1	no	—
665	C₂×D₄	—	3	1	no	—
666	C₂×D₄	—	3	1	no	—
667	C₂×D₄	—	3	1	no	—
668	C₂×D₄	—	3	1	no	—
669	C₂×D₄	—	3	1	no	—
670	C₂×D₄	—	3	1	no	—
671	C₂×D₄	—	3	1	no	—
672	C₂×D₄	—	3	1	no	—
673	C₂×D₄	—	3	1	no	—
674	C₂×D₄	—	3	1	no	—
675	C₂×D₄	—	3	1	no	—
676	C₂×D₄	—	3	1	no	—
677	C₂×D₄	—	3	1	no	—
678	C₂×D₄	—	3	1	no	—
679	C₂×D₄	—	3	1	no	—
680	C₂×D₄	—	3	1	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	12	2	no	—
683	C₂×D₄	—	12	2	no	—
684	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
685	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
686	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
687	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
688	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
689	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
690	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
691	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
692	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
693	C₂²×C₄	—	3	1	no	—
694	C₂²×C₄	—	3	1	no	—
695	C₂²×C₄	—	3	1	no	—
696	C₂²×C₄	—	3	1	no	—
697	C₂²×C₄	—	3	1	no	—
698	C₂²×C₄	—	3	1	no	—
699	C₂²×C₄	—	3	1	no	—
700	C₂²×C₄	—	3	1	no	—
701	C₂²×C₄	—	3	1	no	—
702	C₂²×C₄	—	3	1	no	—
703	C₂²×C₄	—	3	1	no	—
704	C₂²×C₄	—	3	1	no	—
705	C₂²×C₄	—	3	1	no	—
706	C₂²×C₄	—	3	1	no	—
707	C₂²×C₄	—	3	1	no	—
708	C₂²×C₄	—	3	1	no	—
709	C₂²×C₄	—	3	1	no	—
710	C₂²×C₄	—	3	1	no	—
711	C₂²×C₄	—	3	1	no	—
712	C₂²×C₄	—	3	1	no	—
713	C₂²×C₄	—	12	2	no	—
714	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
715	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
716	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
719	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
720	C₄⋊C₄	—	3	1	no	—
721	C₄⋊C₄	—	3	1	no	—
722	C₄⋊C₄	—	3	1	no	—
723	C₄⋊C₄	—	3	1	no	—
724	C₄⋊C₄	—	3	1	no	—
725	C₄⋊C₄	—	3	1	no	—
726	C₄⋊C₄	—	3	1	no	—
727	C₄⋊C₄	—	3	1	no	—
728	C₄⋊C₄	—	3	1	no	—
729	C₄⋊C₄	—	3	1	no	—
730	C₄⋊C₄	—	3	1	no	—
731	C₄⋊C₄	—	3	1	no	—
732	C₄⋊C₄	—	3	1	no	—
733	C₄⋊C₄	—	3	1	no	—
734	C₄⋊C₄	—	3	1	no	—
735	C₄⋊C₄	—	3	1	no	—
736	C₄⋊C₄	—	3	1	no	—
737	C₄⋊C₄	—	3	1	no	—
738	C₄⋊C₄	—	3	1	no	—
739	C₄⋊C₄	—	3	1	no	—
740	C₄⋊C₄	—	3	1	no	—
741	C₄⋊C₄	—	3	1	no	—
742	C₄⋊C₄	—	3	1	no	—
743	C₄⋊C₄	—	3	1	no	—
744	C₄⋊C₄	—	3	1	no	—
745	C₄⋊C₄	—	3	1	no	—
746	C₄⋊C₄	—	3	1	no	—
747	C₄⋊C₄	—	3	1	no	—
748	C₄⋊C₄	—	3	1	no	—
749	C₄⋊C₄	—	3	1	no	—
750	C₄⋊C₄	—	3	1	no	—
751	C₄⋊C₄	—	3	1	no	—
752	C₄⋊C₄	—	3	1	no	—
753	C₄⋊C₄	—	3	1	no	—
754	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
758	C₂²⋊C₄	—	3	1	no	—
759	C₂²⋊C₄	—	3	1	no	—
760	C₂²⋊C₄	—	3	1	no	—
761	C₂²⋊C₄	—	3	1	no	—
762	C₂²⋊C₄	—	3	1	no	—
763	C₂²⋊C₄	—	3	1	no	—
764	C₂²⋊C₄	—	3	1	no	—
765	C₂²⋊C₄	—	3	1	no	—
766	C₂²⋊C₄	—	3	1	no	—
767	C₂²⋊C₄	—	3	1	no	—
768	C₂²⋊C₄	—	3	1	no	—
769	C₂²⋊C₄	—	3	1	no	—
770	C₂²⋊C₄	—	3	1	no	—
771	C₂²⋊C₄	—	3	1	no	—
772	C₂²⋊C₄	—	3	1	no	—
773	C₂²⋊C₄	—	3	1	no	—
774	C₂²⋊C₄	—	3	1	no	—
775	C₂²⋊C₄	—	3	1	no	—
776	C₂²⋊C₄	—	3	1	no	—
777	C₂²⋊C₄	—	3	1	no	—
778	C₂²⋊C₄	—	3	1	no	—
779	C₂²⋊C₄	—	3	1	no	—
780	C₂²⋊C₄	—	3	1	no	—
781	C₂²⋊C₄	—	3	1	no	—
782	C₂²⋊C₄	—	3	1	no	—
783	C₂²⋊C₄	—	3	1	no	—
784	C₂²⋊C₄	—	3	1	no	—
785	C₂²⋊C₄	—	3	1	no	—
786	C₂²⋊C₄	—	3	1	no	—
787	C₂²⋊C₄	—	3	1	no	—
788	C₂²⋊C₄	—	3	1	no	—
789	C₂²⋊C₄	—	3	1	no	—
790	C₂²⋊C₄	—	3	1	no	—
791	C₂²⋊C₄	—	3	1	no	—
792	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
804	C₄²	—	3	1	no	—
805	C₄²	—	3	1	no	—
806	C₄²	—	3	1	no	—
807	C₄²	—	3	1	no	—
808	C₄²	—	3	1	no	—
809	C₄²	C₂²×D₃	1	1	yes	characteristic
810	C₂²×C₃	—	2	1	no	—
811	C₂²×C₃	—	2	1	no	—
812	C₂²×C₃	—	2	1	no	—
813	C₂²×C₃	—	2	1	no	—
814	C₂²×C₃	—	2	1	no	—
815	C₂²×C₃	—	2	1	no	—
816	C₂²×C₃	—	2	1	no	—
817	C₂²×C₃	—	2	1	no	—
818	C₂²×C₃	—	2	1	no	—
819	C₂²×C₃	—	2	1	no	—
820	C₂²×C₃	—	2	1	no	—
821	C₂²×C₃	—	2	1	no	—
822	C₂²×C₃	—	2	1	no	—
823	C₂²×C₃	—	2	1	no	—
824	C₂²×C₃	—	2	1	no	—
825	C₂²×C₃	—	2	1	no	—
826	C₂²×C₃	—	4	4	no	—
827	C₂²×C₃	—	8	2	no	—
828	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
829	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
830	C₂²×C₃	C₂⁵	1	1	yes	characteristic
831	C₂×D₃	—	2	1	no	—
832	C₂×D₃	—	2	1	no	—
833	C₂×D₃	—	2	1	no	—
834	C₂×D₃	—	2	1	no	—
835	C₂×D₃	—	2	1	no	—
836	C₂×D₃	—	2	1	no	—
837	C₂×D₃	—	2	1	no	—
838	C₂×D₃	—	2	1	no	—
839	C₂×D₃	—	2	1	no	—
840	C₂×D₃	—	8	2	no	—
841	C₃×C₄	—	2	1	no	—
842	C₃×C₄	—	2	1	no	—
843	C₃×C₄	—	2	1	no	—
844	C₃×C₄	—	2	1	no	—
845	C₃×C₄	—	2	1	no	—
846	C₃×C₄	—	2	1	no	—
847	C₃×C₄	—	2	1	no	—
848	C₃×C₄	—	2	1	no	—
849	C₃×C₄	—	2	1	no	—
850	Dic₃	—	2	1	no	—
851	Dic₃	—	2	1	no	—
852	Dic₃	—	2	1	no	—
853	Dic₃	—	2	1	no	—
854	Dic₃	—	2	1	no	—
855	Dic₃	—	2	1	no	—
856	Dic₃	—	2	1	no	—
857	Dic₃	—	2	1	no	—
858	Dic₃	—	2	1	no	—
859	Dic₃	—	2	1	no	—
860	Dic₃	—	2	1	no	—
861	Dic₃	—	2	1	no	—
862	Dic₃	H(5,𝔽₂)	1	2	yes	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	3	1	no	—
867	C₂³	—	3	1	no	—
868	C₂³	—	3	1	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	4	1	no	—
871	C₂³	—	4	1	no	—
872	C₂³	—	6	2	no	—
873	C₂³	—	12	1	no	—
874	C₂³	—	12	1	no	—
875	C₂³	C₂³×D₃	1	1	yes	characteristic
876	C₂³	C₂³×D₃	1	1	yes	characteristic
877	C₂³	C₂³×D₃	1	1	yes	characteristic
878	C₂³	C₂³×D₃	1	1	yes	characteristic
879	C₂³	C₂³×D₃	1	1	yes	characteristic
880	C₂³	C₂³×D₃	1	1	yes	characteristic
881	Q₈	—	4	1	no	—
882	Q₈	—	6	2	no	—
883	Q₈	—	6	2	no	—
884	Q₈	—	12	1	no	—
885	Q₈	—	12	1	no	—
886	Q₈	—	12	1	no	—
887	Q₈	—	12	1	no	—
888	Q₈	—	12	1	no	—
889	Q₈	—	12	1	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	1	no	—
895	D₄	—	4	1	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	1	no	—
898	D₄	—	4	1	no	—
899	D₄	—	6	2	no	—
900	D₄	—	6	2	no	—
901	D₄	—	6	2	no	—
902	D₄	—	6	2	no	—
903	D₄	—	6	2	no	—
904	D₄	—	6	2	no	—
905	D₄	—	12	1	no	—
906	D₄	—	12	1	no	—
907	D₄	—	12	1	no	—
908	D₄	—	12	1	no	—
909	D₄	—	12	1	no	—
910	D₄	—	12	1	no	—
911	D₄	—	12	1	no	—
912	D₄	—	12	1	no	—
913	D₄	—	12	1	no	—
914	D₄	—	12	1	no	—
915	D₄	—	12	1	no	—
916	D₄	—	12	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	3	1	no	—
919	C₂×C₄	—	3	1	no	—
920	C₂×C₄	—	3	1	no	—
921	C₂×C₄	—	3	1	no	—
922	C₂×C₄	—	3	1	no	—
923	C₂×C₄	—	3	1	no	—
924	C₂×C₄	—	3	1	no	—
925	C₂×C₄	—	3	1	no	—
926	C₂×C₄	—	3	1	no	—
927	C₂×C₄	—	3	1	no	—
928	C₂×C₄	—	3	1	no	—
929	C₂×C₄	—	3	1	no	—
930	C₂×C₄	—	3	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	6	2	no	—
937	C₂×C₄	—	6	2	no	—
938	C₂×C₄	—	6	2	no	—
939	C₂×C₄	—	6	2	no	—
940	C₂×C₄	—	6	2	no	—
941	C₂×C₄	—	6	2	no	—
942	C₂×C₄	—	12	1	no	—
943	C₂×C₄	—	12	1	no	—
944	C₂×C₄	—	12	1	no	—
945	C₂×C₄	—	12	1	no	—
946	C₂×C₄	—	12	1	no	—
947	C₂×C₄	—	12	1	no	—
948	C₂×C₄	—	12	1	no	—
949	C₂×C₄	—	12	1	no	—
950	C₂×C₄	—	12	1	no	—
951	C₂×C₄	—	12	1	no	—
952	C₂×C₄	—	12	1	no	—
953	C₂×C₄	—	12	1	no	—
954	C₂×C₄	—	12	1	no	—
955	C₂×C₄	—	12	1	no	—
956	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
965	C₂×C₃	—	2	2	no	—
966	C₂×C₃	—	2	2	no	—
967	C₂×C₃	—	4	1	no	—
968	C₂×C₃	—	4	1	no	—
969	C₂×C₃	—	4	1	no	—
970	C₂×C₃	—	4	1	no	—
971	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
972	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
973	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
974	D₃	—	4	1	no	—
975	D₃	—	4	1	no	—
976	D₃	—	4	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	4	4	no	—
994	C₂²	—	6	1	no	—
995	C₂²	—	6	1	no	—
996	C₂²	—	6	1	no	—
997	C₂²	—	6	1	no	—
998	C₂²	—	6	1	no	—
999	C₂²	—	6	1	no	—
1000	C₂²	—	6	1	no	—
1001	C₂²	—	6	1	no	—
1002	C₂²	—	6	1	no	—
1003	C₂²	—	8	2	no	—
1004	C₂²	—	24	2	no	—
1005	C₂²	#1004	1	2	yes	—
1006	C₂²	#1010	1	2	yes	—
1007	C₂²	C₂⁴×D₃	1	1	yes	characteristic
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	3	2	no	—
1018	C₄	—	6	1	no	—
1019	C₄	—	6	1	no	—
1020	C₄	—	6	1	no	—
1021	C₄	—	6	1	no	—
1022	C₄	—	6	1	no	—
1023	C₄	—	6	1	no	—
1024	C₄	—	6	1	no	—
1025	C₄	—	6	1	no	—
1026	C₄	—	6	1	no	—
1027	C₄	—	6	1	no	—
1028	C₄	—	6	1	no	—
1029	C₄	—	6	1	no	—
1030	C₃	#3536	1	1	yes	characteristic, complemented, Sylow
1031	C₂	—	2	2	no	—
1032	C₂	—	2	2	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	4	1	no	—
1036	C₂	—	4	1	no	—
1037	C₂	—	12	1	no	—
1038	C₂	—	12	1	no	—
1039	C₂	—	12	1	no	—
1040	C₂	C₂×#1004	1	1	yes	characteristic
1041	C₂	C₂×#1010	1	1	yes	characteristic
1042	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#546	C₂
hypercenter	#546	D₃
hypocenter	C₃	#3536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₃×#546	C₂	semidirect
2. #5833	C₂	semidirect
3. #5824	C₂	semidirect
4. #5806	C₂	semidirect
5. C₂×#939	C₂	semidirect
6. #5684	C₂	semidirect
7. #5669	C₂	semidirect
8. #5667	C₂	semidirect
9. #5665	C₂	semidirect
10. #5662	C₂	semidirect
11. #5655	C₂	semidirect
12. #5636	C₂	semidirect
13. #5634	C₂	semidirect
14. #5621	C₂	semidirect
15. #5621	C₂	semidirect
16. #5608	C₂	semidirect
17. #5598	C₂	semidirect
18. #5597	C₂	semidirect
19. #5597	C₂	semidirect
20. #5593	C₂	semidirect
21. #5591	C₂	semidirect
22. #5591	C₂	semidirect
23. #5586	C₂	semidirect
24. #5564	C₂	semidirect
25. #5560	C₂	semidirect
26. #5552	C₂	semidirect
27. #5539	C₂	semidirect
28. #5490	C₂	semidirect
29. #5490	C₂	semidirect
30. #5483	C₂	semidirect
31. C₂×#878	C₂	semidirect
33. C₂×C₃×#41	C₂²	semidirect
38. C₂×#237	C₂²	semidirect
39. C₂×#237	C₂²	semidirect
40. C₂×#237	C₂²	semidirect
41. C₂×#237	C₂²	semidirect
42. C₂×#235	C₂²	semidirect
43. C₂×#235	C₂²	semidirect
44. C₂²×Dic₆	C₂²	semidirect
45. C₃×#124	C₂²	semidirect
46. C₃×#123	C₂²	semidirect
47. C₃×#123	C₂²	semidirect
49. C₃×#121	C₂²	semidirect
50. C₃×#121	C₂²	semidirect
51. C₃×#121	C₂²	semidirect
55. C₃×C₄×D₄	C₂²	semidirect
63. #946	C₂²	semidirect
64. #946	C₂²	semidirect
65. #946	C₂²	semidirect
66. #944	C₂²	semidirect
76. #939	C₂²	semidirect
77. #939	C₂²	semidirect
78. #939	C₂²	semidirect
79. #939	C₂²	semidirect
80. #939	C₂²	semidirect
81. #939	C₂²	semidirect
82. #939	C₂²	semidirect
83. #939	C₂²	semidirect
84. #938	C₂²	semidirect
85. #938	C₂²	semidirect
86. #938	C₂²	semidirect
87. #938	C₂²	semidirect
89. #936	C₂²	semidirect
90. #936	C₂²	semidirect
91. #935	C₂²	semidirect
92. #935	C₂²	semidirect
93. #935	C₂²	semidirect
94. #935	C₂²	semidirect
97. D₄×Dic₃	C₂²	semidirect
98. D₄×Dic₃	C₂²	semidirect
99. #930	C₂²	semidirect
100. #930	C₂²	semidirect
101. #930	C₂²	semidirect
102. #929	C₂²	semidirect
103. #929	C₂²	semidirect
104. #929	C₂²	semidirect
106. C₄×#67	C₂²	semidirect
107. C₄×#67	C₂²	semidirect
109. C₂×C₄⋊Dic₃	C₂²	semidirect
111. #924	C₂²	semidirect
112. #924	C₂²	semidirect
113. #924	C₂²	semidirect
114. #924	C₂²	semidirect
115. #924	C₂²	semidirect
117. C₂×Dic₃⋊C₄	C₂²	semidirect
118. C₂×Dic₃⋊C₄	C₂²	semidirect
119. C₂×Dic₃⋊C₄	C₂²	semidirect
120. #898	C₂²	semidirect
121. #897	C₂²	semidirect
122. #897	C₂²	semidirect
123. #896	C₂²	semidirect
124. #896	C₂²	semidirect
125. #896	C₂²	semidirect
126. #896	C₂²	semidirect
127. #896	C₂²	semidirect
128. #896	C₂²	semidirect
129. #894	C₂²	semidirect
130. D₃×C₄⋊C₄	C₂²	semidirect
131. #890	C₂²	semidirect
132. #889	C₂²	semidirect
133. #889	C₂²	semidirect
134. #888	C₂²	semidirect
135. #887	C₂²	semidirect
136. #886	C₂²	semidirect
137. #886	C₂²	semidirect
138. #886	C₂²	semidirect
139. #885	C₂²	semidirect
140. #885	C₂²	semidirect
141. #885	C₂²	semidirect
142. #885	C₂²	semidirect
143. #885	C₂²	semidirect
144. #885	C₂²	semidirect
145. #884	C₂²	semidirect
146. #884	C₂²	semidirect
147. #884	C₂²	semidirect
148. #884	C₂²	semidirect
149. #884	C₂²	semidirect
150. #883	C₂²	semidirect
151. #883	C₂²	semidirect
152. #883	C₂²	semidirect
153. #883	C₂²	semidirect
154. #883	C₂²	semidirect
158. #67⋊C₄	C₂²	semidirect
159. #67⋊C₄	C₂²	semidirect
160. #67⋊C₄	C₂²	semidirect
163. #879	C₂²	semidirect
164. #879	C₂²	semidirect
172. #878	C₂²	semidirect
173. #878	C₂²	semidirect
174. #878	C₂²	semidirect
175. #878	C₂²	semidirect
176. #878	C₂²	semidirect
177. #878	C₂²	semidirect
178. #878	C₂²	semidirect
179. #878	C₂²	semidirect
180. #878	C₂²	semidirect
181. #878	C₂²	semidirect
182. #878	C₂²	semidirect
183. #877	C₂²	semidirect
184. #876	C₂²	semidirect
185. #875	C₂²	semidirect
186. #870	C₂²	semidirect
187. C₄×Dic₆	C₂²	semidirect
203. #546	D₃	semidirect
392. C₂×#41	C₂×D₃	semidirect
417. #124	C₂×D₃	semidirect
434. #123	C₂×D₃	semidirect
435. #123	C₂×D₃	semidirect
501. #121	C₂×D₃	semidirect
502. #121	C₂×D₃	semidirect
503. #121	C₂×D₃	semidirect
525. C₄×D₄	C₂×D₃	semidirect
1030. C₃	#3536	semidirect

Maximal subgroups

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

subgroup	index
C₃×#546	2
#5833	2
#5824	2
#5806	2
C₂×#939	2
#5684	2
#5669	2
#5667	2
#5665	2
#5662	2
#5655	2
#5636	2
#5634	2
#5621	2
#5608	2
#5598	2
#5597	2
#5593	2
#5591	2
#5586	2
#5564	2
#5560	2
#5552	2
#5539	2
#5490	2
#5483	2
C₂×#878	2
#3536	3