Subgroups — C₆₇×#59806 #30739057

Order 17152.

2478 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#548×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2710	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2689	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2543	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2521	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2489	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2487	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2453	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2444	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2444	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2427	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2415	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2409	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2407	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2349	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#391×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	#553×C₆₇	—	2	8	no	—
27	#548×C₆₇	—	2	8	no	—
28	C₂×#126×C₆₇	C₂²	1	2	yes	—
29	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#124×C₆₇	C₂²	1	2	yes	—
31	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#123×C₆₇	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	2	yes	—
39	C₂×#121×C₆₇	C₂²	1	2	yes	—
40	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
54	#400×C₆₇	C₂²	1	2	yes	—
55	#400×C₆₇	C₂²	1	2	yes	—
56	#400×C₆₇	C₂²	1	2	yes	—
57	#399×C₆₇	C₂²	1	2	yes	—
58	#398×C₆₇	C₂²	1	2	yes	—
59	#397×C₆₇	C₂²	1	2	yes	—
60	#397×C₆₇	C₂²	1	2	yes	—
61	#397×C₆₇	C₂²	1	2	yes	—
62	#397×C₆₇	C₂²	1	2	yes	—
63	#397×C₆₇	C₂²	1	2	yes	—
64	#395×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#394×C₆₇	C₂²	1	2	yes	—
67	#394×C₆₇	C₂²	1	2	yes	—
68	#393×C₆₇	C₂²	1	2	yes	—
69	#392×C₆₇	C₂²	1	2	yes	—
70	#391×C₆₇	C₂²	1	2	yes	—
71	#391×C₆₇	C₂²	1	1	yes	characteristic
72	#391×C₆₇	C₂²	1	1	yes	characteristic
73	#391×C₆₇	C₂²	1	1	yes	characteristic
74	#391×C₆₇	C₂²	1	1	yes	characteristic
75	#391×C₆₇	C₂²	1	2	yes	—
76	#391×C₆₇	C₂²	1	1	yes	characteristic
77	#391×C₆₇	C₂²	1	1	yes	characteristic
78	#390×C₆₇	C₂²	1	1	yes	characteristic
79	#390×C₆₇	C₂²	1	1	yes	characteristic
80	#389×C₆₇	C₂²	1	1	yes	characteristic
81	#389×C₆₇	C₂²	1	1	yes	characteristic
82	#389×C₆₇	C₂²	1	2	yes	—
83	#389×C₆₇	C₂²	1	2	yes	—
84	#389×C₆₇	C₂²	1	1	yes	characteristic
85	#389×C₆₇	C₂²	1	1	yes	characteristic
86	#388×C₆₇	C₂²	1	1	yes	characteristic
87	#388×C₆₇	C₂²	1	2	yes	—
88	#388×C₆₇	C₂²	1	2	yes	—
89	#388×C₆₇	C₂²	1	2	yes	—
90	#388×C₆₇	C₂²	1	2	yes	—
91	#388×C₆₇	C₂²	1	1	yes	characteristic
92	#388×C₆₇	C₂²	1	2	yes	—
93	#387×C₆₇	C₂²	1	2	yes	—
94	#387×C₆₇	C₂²	1	2	yes	—
95	#386×C₆₇	C₂²	1	2	yes	—
96	#386×C₆₇	C₂²	1	2	yes	—
97	#386×C₆₇	C₂²	1	2	yes	—
98	#386×C₆₇	C₂²	1	2	yes	—
99	#386×C₆₇	C₂²	1	1	yes	characteristic
100	#386×C₆₇	C₂²	1	1	yes	characteristic
101	#386×C₆₇	C₂²	1	2	yes	—
102	#386×C₆₇	C₂²	1	2	yes	—
103	#386×C₆₇	C₂²	1	2	yes	—
104	#385×C₆₇	C₂²	1	2	yes	—
105	#385×C₆₇	C₂²	1	2	yes	—
106	#385×C₆₇	C₂²	1	2	yes	—
107	#385×C₆₇	C₂²	1	2	yes	—
108	#382×C₆₇	C₂²	1	2	yes	—
109	#381×C₆₇	C₂²	1	2	yes	—
110	#381×C₆₇	C₂²	1	2	yes	—
111	#380×C₆₇	C₂²	1	2	yes	—
112	#380×C₆₇	C₂²	1	1	yes	characteristic
113	#380×C₆₇	C₂²	1	1	yes	characteristic
114	#380×C₆₇	C₂²	1	1	yes	characteristic
115	#380×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₂×#95×C₆₇	C₂²	1	2	yes	—
124	C₂×#95×C₆₇	C₂²	1	2	yes	—
125	C₂×#41×C₆₇	—	2	4	no	—
126	C₂×#41×C₆₇	—	2	4	no	—
127	C₂×#41×C₆₇	—	4	2	no	—
128	C₂²×Q₈×C₆₇	—	2	4	no	—
129	C₂²×Q₈×C₆₇	—	2	4	no	—
130	C₂²×Q₈×C₆₇	—	4	2	no	—
131	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
133	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
149	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
150	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
151	#126×C₆₇	—	2	8	no	—
152	#125×C₆₇	—	2	4	no	—
153	#124×C₆₇	—	2	4	no	—
154	#124×C₆₇	—	2	8	no	—
155	#123×C₆₇	—	2	8	no	—
156	C₂²⋊Q₈×C₆₇	—	2	4	no	—
157	C₂²⋊Q₈×C₆₇	—	2	4	no	—
158	C₂²⋊Q₈×C₆₇	—	2	8	no	—
159	C₂²⋊Q₈×C₆₇	—	4	2	no	—
160	#121×C₆₇	—	2	8	no	—
161	#121×C₆₇	—	2	4	no	—
162	#121×C₆₇	—	2	8	no	—
163	#121×C₆₇	—	2	4	no	—
164	#121×C₆₇	D₄	1	8	yes	complemented
165	C₄×Q₈×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	2	8	no	—
167	C₄×D₄×C₆₇	—	2	8	no	—
168	C₄×D₄×C₆₇	—	2	4	no	—
169	C₄×D₄×C₆₇	—	2	4	no	—
170	C₄×D₄×C₆₇	—	2	4	no	—
171	C₄×D₄×C₆₇	—	2	8	no	—
172	C₄×D₄×C₆₇	—	4	2	no	—
173	C₄×D₄×C₆₇	—	4	2	no	—
174	#117×C₆₇	—	2	4	no	—
175	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₆₇	—	4	2	no	—
222	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	#95×C₆₇	C₂³	1	1	yes	characteristic
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	1	yes	characteristic
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	1	yes	characteristic
245	#95×C₆₇	C₂³	1	1	yes	characteristic
246	#95×C₆₇	C₂³	1	2	yes	—
247	#95×C₆₇	C₂³	1	1	yes	characteristic
248	#95×C₆₇	C₂³	1	1	yes	characteristic
249	#95×C₆₇	C₂³	1	2	yes	—
250	#95×C₆₇	C₂³	1	2	yes	—
251	#95×C₆₇	C₂³	1	2	yes	—
252	#95×C₆₇	C₂³	1	2	yes	—
253	#95×C₆₇	C₂³	1	2	yes	—
254	#95×C₆₇	C₂³	1	2	yes	—
255	#95×C₆₇	C₂³	1	2	yes	—
256	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
259	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
260	#41×C₆₇	—	4	16	no	—
261	C₂×Q₈×C₆₇	—	2	2	no	—
262	C₂×Q₈×C₆₇	—	2	4	no	—
263	C₂×Q₈×C₆₇	—	2	2	no	—
264	C₂×Q₈×C₆₇	—	2	4	no	—
265	C₂×Q₈×C₆₇	—	2	2	no	—
266	C₂×Q₈×C₆₇	—	2	2	no	—
267	C₂×Q₈×C₆₇	—	2	2	no	—
268	C₂×Q₈×C₆₇	—	4	2	no	—
269	C₂×Q₈×C₆₇	—	4	16	no	—
270	C₂×Q₈×C₆₇	#41	1	4	yes	—
271	C₂×D₄×C₆₇	—	2	4	no	—
272	C₂×D₄×C₆₇	—	2	4	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	4	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	4	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	2	4	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	4	1	no	—
286	C₂×D₄×C₆₇	—	4	1	no	—
287	C₂×D₄×C₆₇	—	4	2	no	—
288	C₂×D₄×C₆₇	—	4	2	no	—
289	C₂×D₄×C₆₇	—	4	2	no	—
290	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
291	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
292	C₂²×C₄×C₆₇	—	2	2	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	4	no	—
295	C₂²×C₄×C₆₇	—	2	4	no	—
296	C₂²×C₄×C₆₇	—	2	2	no	—
297	C₂²×C₄×C₆₇	—	2	4	no	—
298	C₂²×C₄×C₆₇	—	2	4	no	—
299	C₂²×C₄×C₆₇	—	2	2	no	—
300	C₂²×C₄×C₆₇	—	2	2	no	—
301	C₂²×C₄×C₆₇	—	2	2	no	—
302	C₂²×C₄×C₆₇	—	2	4	no	—
303	C₂²×C₄×C₆₇	—	2	4	no	—
304	C₂²×C₄×C₆₇	—	2	2	no	—
305	C₂²×C₄×C₆₇	—	2	2	no	—
306	C₂²×C₄×C₆₇	—	2	2	no	—
307	C₂²×C₄×C₆₇	—	2	4	no	—
308	C₂²×C₄×C₆₇	—	4	1	no	—
309	C₂²×C₄×C₆₇	—	4	1	no	—
310	C₂²×C₄×C₆₇	—	4	1	no	—
311	C₂²×C₄×C₆₇	—	4	1	no	—
312	C₂²×C₄×C₆₇	—	4	2	no	—
313	C₂²×C₄×C₆₇	—	4	2	no	—
314	C₂²×C₄×C₆₇	—	4	2	no	—
315	C₂²×C₄×C₆₇	—	4	2	no	—
316	C₂²×C₄×C₆₇	—	4	2	no	—
317	C₂²×C₄×C₆₇	—	4	2	no	—
318	C₂²×C₄×C₆₇	—	4	2	no	—
319	C₂²×C₄×C₆₇	—	4	2	no	—
320	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
321	C₂²×C₄×C₆₇	#41	1	4	yes	complemented
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₄⋊C₄×C₆₇	—	2	2	no	—
342	C₄⋊C₄×C₆₇	—	2	2	no	—
343	C₄⋊C₄×C₆₇	—	2	4	no	—
344	C₄⋊C₄×C₆₇	—	2	2	no	—
345	C₄⋊C₄×C₆₇	—	2	4	no	—
346	C₄⋊C₄×C₆₇	—	2	4	no	—
347	C₄⋊C₄×C₆₇	—	2	2	no	—
348	C₄⋊C₄×C₆₇	—	2	4	no	—
349	C₄⋊C₄×C₆₇	—	2	4	no	—
350	C₄⋊C₄×C₆₇	—	2	4	no	—
351	C₄⋊C₄×C₆₇	—	2	2	no	—
352	C₄⋊C₄×C₆₇	—	2	2	no	—
353	C₄⋊C₄×C₆₇	—	2	4	no	—
354	C₄⋊C₄×C₆₇	—	2	2	no	—
355	C₄⋊C₄×C₆₇	—	4	1	no	—
356	C₄⋊C₄×C₆₇	—	4	2	no	—
357	C₄⋊C₄×C₆₇	—	4	2	no	—
358	C₄⋊C₄×C₆₇	—	4	1	no	—
359	C₄⋊C₄×C₆₇	—	4	2	no	—
360	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	2	no	—
363	C₂²⋊C₄×C₆₇	—	2	4	no	—
364	C₂²⋊C₄×C₆₇	—	2	4	no	—
365	C₂²⋊C₄×C₆₇	—	2	4	no	—
366	C₂²⋊C₄×C₆₇	—	2	4	no	—
367	C₂²⋊C₄×C₆₇	—	2	4	no	—
368	C₂²⋊C₄×C₆₇	—	2	4	no	—
369	C₂²⋊C₄×C₆₇	—	2	2	no	—
370	C₂²⋊C₄×C₆₇	—	2	2	no	—
371	C₂²⋊C₄×C₆₇	—	2	4	no	—
372	C₂²⋊C₄×C₆₇	—	2	4	no	—
373	C₂²⋊C₄×C₆₇	—	2	2	no	—
374	C₂²⋊C₄×C₆₇	—	2	2	no	—
375	C₂²⋊C₄×C₆₇	—	2	4	no	—
376	C₂²⋊C₄×C₆₇	—	4	2	no	—
377	C₂²⋊C₄×C₆₇	—	4	2	no	—
378	C₂²⋊C₄×C₆₇	—	4	1	no	—
379	C₂²⋊C₄×C₆₇	—	4	1	no	—
380	C₂²⋊C₄×C₆₇	—	4	2	no	—
381	C₂²⋊C₄×C₆₇	—	4	2	no	—
382	C₂²⋊C₄×C₆₇	—	4	1	no	—
383	C₂²⋊C₄×C₆₇	—	4	1	no	—
384	C₂²⋊C₄×C₆₇	—	4	2	no	—
385	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
386	C₄²×C₆₇	—	2	4	no	—
387	C₄²×C₆₇	—	2	2	no	—
388	C₄²×C₆₇	—	2	4	no	—
389	C₄²×C₆₇	—	2	2	no	—
390	C₄²×C₆₇	—	2	4	no	—
391	C₄²×C₆₇	—	2	2	no	—
392	C₄²×C₆₇	—	2	2	no	—
393	C₄²×C₆₇	—	4	1	no	—
394	C₄²×C₆₇	—	4	1	no	—
395	C₂³×C₆₇	—	2	1	no	—
396	C₂³×C₆₇	—	2	1	no	—
397	C₂³×C₆₇	—	2	1	no	—
398	C₂³×C₆₇	—	2	1	no	—
399	C₂³×C₆₇	—	2	2	no	—
400	C₂³×C₆₇	—	2	2	no	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	2	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	2	1	no	—
406	C₂³×C₆₇	—	2	1	no	—
407	C₂³×C₆₇	—	2	1	no	—
408	C₂³×C₆₇	—	2	1	no	—
409	C₂³×C₆₇	—	2	1	no	—
410	C₂³×C₆₇	—	2	1	no	—
411	C₂³×C₆₇	—	2	1	no	—
412	C₂³×C₆₇	—	2	1	no	—
413	C₂³×C₆₇	—	2	1	no	—
414	C₂³×C₆₇	—	2	1	no	—
415	C₂³×C₆₇	—	2	1	no	—
416	C₂³×C₆₇	—	2	1	no	—
417	C₂³×C₆₇	—	2	1	no	—
418	C₂³×C₆₇	—	2	1	no	—
419	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
420	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
421	C₂³×C₆₇	C₂×#41	1	2	yes	—
422	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
423	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
424	Q₈×C₆₇	—	2	8	no	—
425	Q₈×C₆₇	—	4	8	no	—
426	Q₈×C₆₇	—	4	4	no	—
427	D₄×C₆₇	—	2	16	no	—
428	D₄×C₆₇	—	2	8	no	—
429	D₄×C₆₇	—	4	8	no	—
430	D₄×C₆₇	—	4	4	no	—
431	D₄×C₆₇	—	4	4	no	—
432	D₄×C₆₇	—	4	4	no	—
433	D₄×C₆₇	—	8	4	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	8	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	2	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	2	1	no	—
460	C₂×C₄×C₆₇	—	2	1	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	2	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	2	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	2	no	—
484	C₂×C₄×C₆₇	—	4	4	no	—
485	C₂×C₄×C₆₇	—	4	8	no	—
486	C₂×C₄×C₆₇	—	4	8	no	—
487	C₂×C₄×C₆₇	—	4	4	no	—
488	C₂×C₄×C₆₇	—	4	4	no	—
489	C₂×C₄×C₆₇	—	4	4	no	—
490	C₂×C₄×C₆₇	—	8	4	no	—
491	C₂×C₄×C₆₇	—	8	4	no	—
492	C₂×C₄×C₆₇	—	8	4	no	—
493	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
494	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
497	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
498	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
499	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
500	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
501	C₂²×C₆₇	—	2	2	no	—
502	C₂²×C₆₇	—	2	2	no	—
503	C₂²×C₆₇	—	2	2	no	—
504	C₂²×C₆₇	—	2	2	no	—
505	C₂²×C₆₇	—	2	2	no	—
506	C₂²×C₆₇	—	2	2	no	—
507	C₂²×C₆₇	—	2	4	no	—
508	C₂²×C₆₇	—	2	4	no	—
509	C₂²×C₆₇	—	2	4	no	—
510	C₂²×C₆₇	—	4	2	no	—
511	C₂²×C₆₇	—	4	2	no	—
512	C₂²×C₆₇	—	4	2	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	1	no	—
515	C₂²×C₆₇	—	4	1	no	—
516	C₂²×C₆₇	—	4	1	no	—
517	C₂²×C₆₇	—	4	1	no	—
518	C₂²×C₆₇	—	4	1	no	—
519	C₂²×C₆₇	—	4	1	no	—
520	C₂²×C₆₇	—	4	1	no	—
521	C₂²×C₆₇	—	4	1	no	—
522	C₂²×C₆₇	—	4	1	no	—
523	C₂²×C₆₇	—	4	1	no	—
524	C₂²×C₆₇	—	4	1	no	—
525	C₂²×C₆₇	—	4	1	no	—
526	C₂²×C₆₇	—	4	1	no	—
527	C₂²×C₆₇	—	4	1	no	—
528	C₂²×C₆₇	#547	1	4	yes	—
529	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
530	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
531	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
532	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	C₂²×C₆₇	#585	1	1	yes	characteristic
535	C₂²×C₆₇	#585	1	1	yes	characteristic
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	2	4	no	—
538	C₄×C₆₇	—	2	4	no	—
539	C₄×C₆₇	—	2	2	no	—
540	C₄×C₆₇	—	2	2	no	—
541	C₄×C₆₇	—	4	1	no	—
542	C₄×C₆₇	—	4	1	no	—
543	C₄×C₆₇	—	4	2	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	2	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	2	no	—
549	C₄×C₆₇	—	4	1	no	—
550	C₄×C₆₇	—	4	2	no	—
551	C₄×C₆₇	—	4	2	no	—
552	C₄×C₆₇	—	4	1	no	—
553	C₄×C₆₇	—	4	1	no	—
554	C₄×C₆₇	#546	1	4	yes	—
555	#59806	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
556	C₂×C₆₇	—	2	4	no	—
557	C₂×C₆₇	—	4	4	no	—
558	C₂×C₆₇	—	8	1	no	—
559	C₂×C₆₇	—	8	1	no	—
560	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
561	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
562	C₂×C₆₇	#3480	1	1	yes	characteristic
563	C₂×C₆₇	#3500	1	1	yes	characteristic
564	C₂×C₆₇	#3505	1	1	yes	characteristic
565	C₂×C₆₇	#3516	1	1	yes	characteristic
566	C₂×C₆₇	#3541	1	1	yes	characteristic
567	C₂×#553	C₂×C₆₇	1	1	yes	characteristic, complemented
568	C₂×#548	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#2710	C₂×C₆₇	1	2	yes	complemented
570	#2689	C₂×C₆₇	1	2	yes	complemented
571	#2543	C₂×C₆₇	1	2	yes	complemented
572	#2521	C₂×C₆₇	1	2	yes	complemented
573	#2489	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#2488	C₂×C₆₇	1	2	yes	complemented
575	#2487	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#2453	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#2447	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#2444	C₂×C₆₇	1	2	yes	complemented
579	#2444	C₂×C₆₇	1	2	yes	complemented
580	#2427	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#2415	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#2409	C₂×C₆₇	1	1	yes	characteristic, complemented
583	#2407	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#2362	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#2349	C₂×C₆₇	1	2	yes	complemented
586	#2339	C₂×C₆₇	1	1	yes	characteristic, complemented
587	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
588	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
589	C₂×#391	C₂×C₆₇	1	1	yes	characteristic, complemented
590	C₆₇	#59806	1	1	yes	characteristic, direct product factor, Sylow
591	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
592	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
593	#553	—	2	8	no	—
594	#548	—	2	8	no	—
595	C₂×#126	C₂²×C₆₇	1	2	yes	—
596	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
597	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
598	C₂×#124	C₂²×C₆₇	1	2	yes	—
599	C₂×#123	C₂²×C₆₇	1	2	yes	—
600	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
601	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
603	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
604	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
605	C₂×#121	C₂²×C₆₇	1	2	yes	—
606	C₂×#121	C₂²×C₆₇	1	2	yes	—
607	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
608	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
609	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
610	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
611	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
612	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
613	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
614	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
615	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
617	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
618	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
619	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
620	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
621	#400	C₂²×C₆₇	1	2	yes	—
622	#400	C₂²×C₆₇	1	2	yes	—
623	#400	C₂²×C₆₇	1	2	yes	—
624	#399	C₂²×C₆₇	1	2	yes	—
625	#398	C₂²×C₆₇	1	2	yes	—
626	#397	C₂²×C₆₇	1	2	yes	—
627	#397	C₂²×C₆₇	1	2	yes	—
628	#397	C₂²×C₆₇	1	2	yes	—
629	#397	C₂²×C₆₇	1	2	yes	—
630	#397	C₂²×C₆₇	1	2	yes	—
631	#395	C₂²×C₆₇	1	2	yes	—
632	#394	C₂²×C₆₇	1	2	yes	—
633	#394	C₂²×C₆₇	1	2	yes	—
634	#394	C₂²×C₆₇	1	2	yes	—
635	#393	C₂²×C₆₇	1	2	yes	—
636	#392	C₂²×C₆₇	1	2	yes	—
637	#391	C₂²×C₆₇	1	1	yes	characteristic
638	#391	C₂²×C₆₇	1	1	yes	characteristic
639	#391	C₂²×C₆₇	1	1	yes	characteristic
640	#391	C₂²×C₆₇	1	1	yes	characteristic
641	#391	C₂²×C₆₇	1	1	yes	characteristic
642	#391	C₂²×C₆₇	1	1	yes	characteristic
643	#391	C₂²×C₆₇	1	2	yes	—
644	#391	C₂²×C₆₇	1	2	yes	—
645	#390	C₂²×C₆₇	1	1	yes	characteristic
646	#390	C₂²×C₆₇	1	1	yes	characteristic
647	#389	C₂²×C₆₇	1	2	yes	—
648	#389	C₂²×C₆₇	1	2	yes	—
649	#389	C₂²×C₆₇	1	1	yes	characteristic
650	#389	C₂²×C₆₇	1	1	yes	characteristic
651	#389	C₂²×C₆₇	1	1	yes	characteristic
652	#389	C₂²×C₆₇	1	1	yes	characteristic
653	#388	C₂²×C₆₇	1	2	yes	—
654	#388	C₂²×C₆₇	1	2	yes	—
655	#388	C₂²×C₆₇	1	2	yes	—
656	#388	C₂²×C₆₇	1	2	yes	—
657	#388	C₂²×C₆₇	1	1	yes	characteristic
658	#388	C₂²×C₆₇	1	2	yes	—
659	#388	C₂²×C₆₇	1	1	yes	characteristic
660	#387	C₂²×C₆₇	1	2	yes	—
661	#387	C₂²×C₆₇	1	2	yes	—
662	#386	C₂²×C₆₇	1	2	yes	—
663	#386	C₂²×C₆₇	1	2	yes	—
664	#386	C₂²×C₆₇	1	2	yes	—
665	#386	C₂²×C₆₇	1	2	yes	—
666	#386	C₂²×C₆₇	1	2	yes	—
667	#386	C₂²×C₆₇	1	1	yes	characteristic
668	#386	C₂²×C₆₇	1	1	yes	characteristic
669	#386	C₂²×C₆₇	1	2	yes	—
670	#386	C₂²×C₆₇	1	2	yes	—
671	#385	C₂²×C₆₇	1	2	yes	—
672	#385	C₂²×C₆₇	1	2	yes	—
673	#385	C₂²×C₆₇	1	2	yes	—
674	#385	C₂²×C₆₇	1	2	yes	—
675	#382	C₂²×C₆₇	1	2	yes	—
676	#381	C₂²×C₆₇	1	2	yes	—
677	#381	C₂²×C₆₇	1	2	yes	—
678	#380	C₂²×C₆₇	1	1	yes	characteristic
679	#380	C₂²×C₆₇	1	1	yes	characteristic
680	#380	C₂²×C₆₇	1	2	yes	—
681	#380	C₂²×C₆₇	1	1	yes	characteristic
682	#380	C₂²×C₆₇	1	1	yes	characteristic
683	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
684	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
685	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
686	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
687	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
688	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
689	C₂×#95	C₂²×C₆₇	1	2	yes	—
690	C₂×#95	C₂²×C₆₇	1	2	yes	—
691	C₂×#95	C₂²×C₆₇	1	2	yes	—
692	C₂×#41	—	2	4	no	—
693	C₂×#41	—	2	4	no	—
694	C₂×#41	—	4	2	no	—
695	C₂²×Q₈	—	2	4	no	—
696	C₂²×Q₈	—	2	4	no	—
697	C₂²×Q₈	—	4	2	no	—
698	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
699	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
700	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
701	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
702	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
703	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
704	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
705	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
706	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
708	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
709	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
711	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
712	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
713	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
714	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
715	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
716	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
717	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
718	#126	—	2	8	no	—
719	#125	—	2	4	no	—
720	#124	—	2	4	no	—
721	#124	—	2	8	no	—
722	#123	—	2	8	no	—
723	C₂²⋊Q₈	—	2	4	no	—
724	C₂²⋊Q₈	—	2	4	no	—
725	C₂²⋊Q₈	—	2	8	no	—
726	C₂²⋊Q₈	—	4	2	no	—
727	#121	—	2	8	no	—
728	#121	—	2	4	no	—
729	#121	—	2	8	no	—
730	#121	—	2	4	no	—
731	#121	D₄×C₆₇	1	8	yes	complemented
732	C₄×Q₈	—	2	4	no	—
733	C₄×D₄	—	2	8	no	—
734	C₄×D₄	—	2	8	no	—
735	C₄×D₄	—	2	4	no	—
736	C₄×D₄	—	2	4	no	—
737	C₄×D₄	—	2	4	no	—
738	C₄×D₄	—	2	8	no	—
739	C₄×D₄	—	4	2	no	—
740	C₄×D₄	—	4	2	no	—
741	#117	—	2	4	no	—
742	C₂×C₄⋊C₄	—	2	4	no	—
743	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
771	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
788	C₂×C₄²	—	4	2	no	—
789	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
790	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
791	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
792	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
793	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
795	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
798	#95	C₂³×C₆₇	1	1	yes	characteristic
799	#95	C₂³×C₆₇	1	2	yes	—
800	#95	C₂³×C₆₇	1	2	yes	—
801	#95	C₂³×C₆₇	1	2	yes	—
802	#95	C₂³×C₆₇	1	2	yes	—
803	#95	C₂³×C₆₇	1	2	yes	—
804	#95	C₂³×C₆₇	1	2	yes	—
805	#95	C₂³×C₆₇	1	2	yes	—
806	#95	C₂³×C₆₇	1	2	yes	—
807	#95	C₂³×C₆₇	1	2	yes	—
808	#95	C₂³×C₆₇	1	2	yes	—
809	#95	C₂³×C₆₇	1	1	yes	characteristic
810	#95	C₂³×C₆₇	1	2	yes	—
811	#95	C₂³×C₆₇	1	1	yes	characteristic
812	#95	C₂³×C₆₇	1	1	yes	characteristic
813	#95	C₂³×C₆₇	1	2	yes	—
814	#95	C₂³×C₆₇	1	1	yes	characteristic
815	#95	C₂³×C₆₇	1	1	yes	characteristic
816	#95	C₂³×C₆₇	1	2	yes	—
817	#95	C₂³×C₆₇	1	2	yes	—
818	#95	C₂³×C₆₇	1	2	yes	—
819	#95	C₂³×C₆₇	1	2	yes	—
820	#95	C₂³×C₆₇	1	2	yes	—
821	#95	C₂³×C₆₇	1	2	yes	—
822	#95	C₂³×C₆₇	1	2	yes	—
823	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
825	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
826	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
827	#41	—	4	16	no	—
828	C₂×Q₈	—	2	2	no	—
829	C₂×Q₈	—	2	4	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	4	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	4	16	no	—
837	C₂×Q₈	#41×C₆₇	1	4	yes	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	4	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	4	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	4	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	4	1	no	—
853	C₂×D₄	—	4	2	no	—
854	C₂×D₄	—	4	1	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
858	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	4	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	2	4	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	4	no	—
870	C₂²×C₄	—	2	4	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	4	no	—
875	C₂²×C₄	—	4	1	no	—
876	C₂²×C₄	—	4	1	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	1	no	—
880	C₂²×C₄	—	4	1	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
888	C₂²×C₄	#41×C₆₇	1	4	yes	complemented
889	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
897	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
907	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	4	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	4	no	—
913	C₄⋊C₄	—	2	4	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	4	no	—
916	C₄⋊C₄	—	2	4	no	—
917	C₄⋊C₄	—	2	4	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	4	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	4	1	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	4	1	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	2	4	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	1	no	—
945	C₂²⋊C₄	—	4	1	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	1	no	—
950	C₂²⋊C₄	—	4	1	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
953	C₄²	—	2	4	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	4	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	4	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	4	1	no	—
961	C₄²	—	4	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
987	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
988	C₂³	C₂×#41×C₆₇	1	2	yes	—
989	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
990	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
991	Q₈	—	2	8	no	—
992	Q₈	—	4	8	no	—
993	Q₈	—	4	4	no	—
994	D₄	—	2	16	no	—
995	D₄	—	2	8	no	—
996	D₄	—	4	8	no	—
997	D₄	—	4	4	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	4	no	—
1000	D₄	—	8	4	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	8	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	8	no	—
1053	C₂×C₄	—	4	8	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	4	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	8	4	no	—
1058	C₂×C₄	—	8	4	no	—
1059	C₂×C₄	—	8	4	no	—
1060	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1061	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1062	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1063	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1064	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1065	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1066	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1067	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	4	no	—
1075	C₂²	—	2	4	no	—
1076	C₂²	—	2	4	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	#547×C₆₇	1	4	yes	—
1096	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1097	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1098	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1099	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1100	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1101	C₂²	#585×C₆₇	1	1	yes	characteristic
1102	C₂²	#585×C₆₇	1	1	yes	characteristic
1103	C₄	—	2	2	no	—
1104	C₄	—	2	4	no	—
1105	C₄	—	2	4	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	#546×C₆₇	1	4	yes	—
1122	C₂	—	2	4	no	—
1123	C₂	—	4	4	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	1	no	—
1126	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1127	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
1128	C₂	C₆₇×#3480	1	1	yes	characteristic
1129	C₂	C₆₇×#3500	1	1	yes	characteristic
1130	C₂	C₆₇×#3505	1	1	yes	characteristic
1131	C₂	C₆₇×#3516	1	1	yes	characteristic
1132	C₂	C₆₇×#3541	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#553×C₆₇	C₂	semidirect
2. C₂×#548×C₆₇	C₂	semidirect
3. C₆₇×#2710	C₂	semidirect
4. C₆₇×#2689	C₂	semidirect
5. C₆₇×#2543	C₂	semidirect
6. C₆₇×#2521	C₂	semidirect
7. C₆₇×#2489	C₂	semidirect
8. C₆₇×#2488	C₂	semidirect
9. C₆₇×#2487	C₂	semidirect
10. C₆₇×#2453	C₂	semidirect
11. C₆₇×#2447	C₂	semidirect
12. C₆₇×#2444	C₂	semidirect
13. C₆₇×#2444	C₂	semidirect
14. C₆₇×#2427	C₂	semidirect
15. C₆₇×#2415	C₂	semidirect
16. C₆₇×#2409	C₂	semidirect
17. C₆₇×#2407	C₂	semidirect
18. C₆₇×#2362	C₂	semidirect
19. C₆₇×#2349	C₂	semidirect
20. C₆₇×#2339	C₂	semidirect
21. C₄×#121×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₂×#391×C₆₇	C₂	semidirect
164. #121×C₆₇	D₄	semidirect
321. C₂²×C₄×C₆₇	#41	semidirect
555. #59806	C₆₇	direct (N × H)
567. C₂×#553	C₂×C₆₇	semidirect
568. C₂×#548	C₂×C₆₇	semidirect
569. #2710	C₂×C₆₇	semidirect
570. #2689	C₂×C₆₇	semidirect
571. #2543	C₂×C₆₇	semidirect
572. #2521	C₂×C₆₇	semidirect
573. #2489	C₂×C₆₇	semidirect
574. #2488	C₂×C₆₇	semidirect
575. #2487	C₂×C₆₇	semidirect
576. #2453	C₂×C₆₇	semidirect
577. #2447	C₂×C₆₇	semidirect
578. #2444	C₂×C₆₇	semidirect
579. #2444	C₂×C₆₇	semidirect
580. #2427	C₂×C₆₇	semidirect
581. #2415	C₂×C₆₇	semidirect
582. #2409	C₂×C₆₇	semidirect
583. #2407	C₂×C₆₇	semidirect
584. #2362	C₂×C₆₇	semidirect
585. #2349	C₂×C₆₇	semidirect
586. #2339	C₂×C₆₇	semidirect
587. C₄×#121	C₂×C₆₇	semidirect
588. C₄×#121	C₂×C₆₇	semidirect
589. C₂×#391	C₂×C₆₇	semidirect
590. C₆₇	#59806	direct (N × H)
731. #121	D₄×C₆₇	semidirect
888. C₂²×C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₆₇	2
C₂×#548×C₆₇	2
C₆₇×#2710	2
C₆₇×#2689	2
C₆₇×#2543	2
C₆₇×#2521	2
C₆₇×#2489	2
C₆₇×#2488	2
C₆₇×#2487	2
C₆₇×#2453	2
C₆₇×#2447	2
C₆₇×#2444	2
C₆₇×#2427	2
C₆₇×#2415	2
C₆₇×#2409	2
C₆₇×#2407	2
C₆₇×#2362	2
C₆₇×#2349	2
C₆₇×#2339	2
C₄×#121×C₆₇	2
C₂×#391×C₆₇	2
#59806	67

Subgroups — C67×#59806 #30739057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59806 #30739057