Subgroups — C₆₇×#61660 #30740911

Order 17152.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3329	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3305	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3299	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3285	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3277	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3203	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3011	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
25	C₂×#137×C₆₇	C₂²	1	2	yes	—
26	C₂×#137×C₆₇	C₂²	1	2	yes	—
27	C₂×#135×C₆₇	C₂²	1	2	yes	—
28	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
29	#562×C₆₇	—	2	2	no	—
30	#555×C₆₇	—	2	1	no	—
31	#555×C₆₇	C₂²	1	1	yes	characteristic
32	#554×C₆₇	C₂²	1	1	yes	characteristic
33	#553×C₆₇	—	2	1	no	—
34	#552×C₆₇	C₂²	1	2	yes	—
35	#550×C₆₇	—	2	1	no	—
36	#550×C₆₇	C₂²	1	1	yes	characteristic
37	#550×C₆₇	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₇	—	2	1	no	—
39	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	#548×C₆₇	—	2	2	no	—
43	#548×C₆₇	C₂²	1	2	yes	—
44	#548×C₆₇	C₂²	1	2	yes	—
45	#548×C₆₇	C₂²	1	2	yes	—
46	#547×C₆₇	C₂²	1	1	yes	characteristic
47	#544×C₆₇	—	2	1	no	—
48	#542×C₆₇	—	2	2	no	—
49	#540×C₆₇	—	2	1	no	—
50	#537×C₆₇	—	2	2	no	—
51	#537×C₆₇	C₂²	1	2	yes	—
52	#537×C₆₇	C₂²	1	2	yes	—
53	#536×C₆₇	C₂²	1	2	yes	—
54	#533×C₆₇	C₂²	1	1	yes	characteristic
55	#532×C₆₇	—	2	1	no	—
56	#532×C₆₇	—	2	1	no	—
57	#532×C₆₇	C₂²	1	1	yes	characteristic
58	#532×C₆₇	C₂²	1	1	yes	characteristic
59	#529×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
61	#495×C₆₇	C₂²	1	2	yes	—
62	#494×C₆₇	C₂²	1	1	yes	characteristic
63	#492×C₆₇	C₂²	1	1	yes	characteristic
64	#488×C₆₇	C₂²	1	2	yes	—
65	#487×C₆₇	C₂²	1	1	yes	characteristic
66	#486×C₆₇	C₂²	1	1	yes	characteristic
67	#485×C₆₇	C₂²	1	2	yes	—
68	#484×C₆₇	C₂²	1	2	yes	—
69	#484×C₆₇	C₂²	1	2	yes	—
70	#483×C₆₇	C₂²	1	1	yes	characteristic
71	#482×C₆₇	C₂²	1	2	yes	—
72	#480×C₆₇	C₂²	1	2	yes	—
73	#480×C₆₇	C₂²	1	1	yes	characteristic
74	#479×C₆₇	C₂²	1	1	yes	characteristic
75	#479×C₆₇	C₂²	1	1	yes	characteristic
76	#477×C₆₇	C₂²	1	1	yes	characteristic
77	#477×C₆₇	C₂²	1	1	yes	characteristic
78	#470×C₆₇	C₂²	1	2	yes	—
79	#468×C₆₇	C₂²	1	2	yes	—
80	#468×C₆₇	C₂²	1	2	yes	—
81	#468×C₆₇	C₂²	1	2	yes	—
82	#467×C₆₇	C₂²	1	2	yes	—
83	#467×C₆₇	C₂²	1	2	yes	—
84	#466×C₆₇	C₂²	1	2	yes	—
85	#465×C₆₇	C₂²	1	2	yes	—
86	#464×C₆₇	C₂²	1	1	yes	characteristic
87	#464×C₆₇	C₂²	1	2	yes	—
88	#464×C₆₇	C₂²	1	1	yes	characteristic
89	#464×C₆₇	C₂²	1	2	yes	—
90	#462×C₆₇	C₂²	1	1	yes	characteristic
91	#462×C₆₇	C₂²	1	1	yes	characteristic
92	#462×C₆₇	C₂²	1	1	yes	characteristic
93	#461×C₆₇	C₂²	1	1	yes	characteristic
94	#460×C₆₇	C₂²	1	1	yes	characteristic
95	#459×C₆₇	C₂²	1	1	yes	characteristic
96	#452×C₆₇	C₂²	1	2	yes	—
97	#452×C₆₇	C₂²	1	2	yes	—
98	#452×C₆₇	C₂²	1	2	yes	—
99	#452×C₆₇	C₂²	1	2	yes	—
100	#452×C₆₇	C₂²	1	2	yes	—
101	#452×C₆₇	C₂²	1	2	yes	—
102	#452×C₆₇	C₂²	1	2	yes	—
103	#451×C₆₇	C₂²	1	1	yes	characteristic
104	#451×C₆₇	C₂²	1	2	yes	—
105	#451×C₆₇	C₂²	1	2	yes	—
106	#451×C₆₇	C₂²	1	2	yes	—
107	#451×C₆₇	C₂²	1	2	yes	—
108	#451×C₆₇	C₂²	1	2	yes	—
109	#449×C₆₇	C₂²	1	2	yes	—
110	#449×C₆₇	C₂²	1	2	yes	—
111	#449×C₆₇	C₂²	1	2	yes	—
112	#448×C₆₇	C₂²	1	1	yes	characteristic
113	#448×C₆₇	C₂²	1	2	yes	—
114	#448×C₆₇	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
116	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
121	#436×C₆₇	C₂²	1	1	yes	characteristic
122	#436×C₆₇	C₂²	1	2	yes	—
123	#436×C₆₇	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₆₇	C₂²	1	2	yes	—
126	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
127	#431×C₆₇	C₂²	1	1	yes	characteristic
128	#431×C₆₇	C₂²	1	1	yes	characteristic
129	#419×C₆₇	C₂²	1	2	yes	—
130	#417×C₆₇	C₂²	1	2	yes	—
131	#416×C₆₇	C₂²	1	2	yes	—
132	C₂×#103×C₆₇	C₂²	1	2	yes	—
133	#408×C₆₇	C₂²	1	2	yes	—
134	#408×C₆₇	C₂²	1	2	yes	—
135	2₋¹⁺⁴×C₆₇	—	4	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	4	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	2	no	—
139	C₂×#41×C₆₇	—	2	2	no	—
140	C₂×#41×C₆₇	C₂³	1	2	yes	—
141	C₂×#41×C₆₇	C₂³	1	2	yes	—
142	C₂×#41×C₆₇	C₂³	1	2	yes	—
143	C₂×#41×C₆₇	C₂³	1	2	yes	—
144	C₂×#41×C₆₇	C₂³	1	2	yes	—
145	C₂²×Q₈×C₆₇	—	2	2	no	—
146	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
150	#137×C₆₇	—	4	4	no	—
151	#137×C₆₇	—	4	4	no	—
152	#135×C₆₇	—	4	4	no	—
153	C₂×Q₁₆×C₆₇	—	4	4	no	—
154	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
167	C₂×D₈×C₆₇	C₂³	1	2	yes	—
168	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
169	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
170	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
171	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₆₇	—	2	2	no	—
173	C₄⋊Q₈×C₆₇	—	2	1	no	—
174	C₄⋊Q₈×C₆₇	—	2	1	no	—
175	C₄⋊Q₈×C₆₇	—	2	1	no	—
176	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
177	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
180	#127×C₆₇	—	2	1	no	—
181	#127×C₆₇	—	2	1	no	—
182	#127×C₆₇	D₄	1	1	yes	characteristic
183	#127×C₆₇	C₂³	1	1	yes	characteristic
184	#126×C₆₇	—	2	2	no	—
185	#126×C₆₇	—	2	1	no	—
186	#125×C₆₇	—	2	2	no	—
187	#125×C₆₇	—	2	1	no	—
188	#125×C₆₇	—	2	1	no	—
189	#125×C₆₇	C₂³	1	1	yes	characteristic
190	#124×C₆₇	—	2	2	no	—
191	#124×C₆₇	—	2	2	no	—
192	#124×C₆₇	—	2	2	no	—
193	#124×C₆₇	—	2	2	no	—
194	#124×C₆₇	—	2	2	no	—
195	#124×C₆₇	D₄	1	2	yes	—
196	#124×C₆₇	C₂³	1	2	yes	—
197	#124×C₆₇	C₂³	1	1	yes	characteristic
198	#123×C₆₇	—	2	2	no	—
199	#123×C₆₇	—	2	2	no	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	1	no	—
202	#123×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	—	2	1	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	—	2	2	no	—
212	C₂²⋊Q₈×C₆₇	—	2	2	no	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	—	2	2	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	—	2	2	no	—
226	#121×C₆₇	—	2	2	no	—
227	#121×C₆₇	—	2	2	no	—
228	#121×C₆₇	—	2	1	no	—
229	#121×C₆₇	—	2	2	no	—
230	#121×C₆₇	—	2	1	no	—
231	#121×C₆₇	—	2	1	no	—
232	#121×C₆₇	—	2	1	no	—
233	#121×C₆₇	—	2	2	no	—
234	#121×C₆₇	—	2	2	no	—
235	#121×C₆₇	D₄	1	1	yes	characteristic
236	#121×C₆₇	D₄	1	1	yes	characteristic
237	#121×C₆₇	D₄	1	2	yes	—
238	#121×C₆₇	C₂³	1	1	yes	characteristic
239	#121×C₆₇	C₂³	1	2	yes	—
240	#121×C₆₇	C₂³	1	2	yes	—
241	#121×C₆₇	C₂³	1	2	yes	—
242	C₄×Q₈×C₆₇	—	2	1	no	—
243	C₄×Q₈×C₆₇	—	2	1	no	—
244	C₄×Q₈×C₆₇	—	2	1	no	—
245	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
249	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₆₇	—	2	1	no	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	—	2	1	no	—
254	C₄×D₄×C₆₇	—	2	1	no	—
255	C₄×D₄×C₆₇	—	2	1	no	—
256	C₄×D₄×C₆₇	—	2	1	no	—
257	C₄×D₄×C₆₇	—	2	1	no	—
258	C₄×D₄×C₆₇	—	2	2	no	—
259	C₄×D₄×C₆₇	—	2	2	no	—
260	C₄×D₄×C₆₇	—	2	2	no	—
261	C₄×D₄×C₆₇	—	2	1	no	—
262	C₄×D₄×C₆₇	—	2	1	no	—
263	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₆₇	C₂³	1	2	yes	—
266	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
267	#117×C₆₇	—	2	1	no	—
268	#117×C₆₇	—	2	1	no	—
269	#117×C₆₇	—	2	2	no	—
270	#117×C₆₇	—	2	1	no	—
271	#117×C₆₇	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#107×C₆₇	C₂³	1	2	yes	—
281	#107×C₆₇	C₂³	1	1	yes	characteristic
282	#106×C₆₇	C₂³	1	1	yes	characteristic
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	1	yes	characteristic
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	1	yes	characteristic
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	2	yes	—
305	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	1	yes	characteristic
307	#102×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₆₇	C₂³	1	2	yes	—
318	#41×C₆₇	—	2	4	no	—
319	#41×C₆₇	—	2	4	no	—
320	#41×C₆₇	—	4	2	no	—
321	#41×C₆₇	—	4	2	no	—
322	#41×C₆₇	—	4	2	no	—
323	#41×C₆₇	—	4	2	no	—
324	#41×C₆₇	—	4	2	no	—
325	#41×C₆₇	—	4	2	no	—
326	#41×C₆₇	—	4	8	no	—
327	#41×C₆₇	—	4	8	no	—
328	#41×C₆₇	—	4	2	no	—
329	#41×C₆₇	—	4	2	no	—
330	#41×C₆₇	—	4	8	no	—
331	C₂×Q₈×C₆₇	—	2	2	no	—
332	C₂×Q₈×C₆₇	—	2	2	no	—
333	C₂×Q₈×C₆₇	—	2	1	no	—
334	C₂×Q₈×C₆₇	—	2	2	no	—
335	C₂×Q₈×C₆₇	—	2	2	no	—
336	C₂×Q₈×C₆₇	—	2	1	no	—
337	C₂×Q₈×C₆₇	—	2	2	no	—
338	C₂×Q₈×C₆₇	—	2	4	no	—
339	C₂×Q₈×C₆₇	—	2	4	no	—
340	C₂×Q₈×C₆₇	—	4	2	no	—
341	C₂×Q₈×C₆₇	—	4	2	no	—
342	C₂×Q₈×C₆₇	—	4	2	no	—
343	C₂×Q₈×C₆₇	—	4	2	no	—
344	C₂×Q₈×C₆₇	—	4	8	no	—
345	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
346	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
347	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
349	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₆₇	—	2	2	no	—
352	C₂×D₄×C₆₇	—	2	2	no	—
353	C₂×D₄×C₆₇	—	2	2	no	—
354	C₂×D₄×C₆₇	—	2	1	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	2	no	—
357	C₂×D₄×C₆₇	—	2	2	no	—
358	C₂×D₄×C₆₇	—	2	2	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
368	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	2	no	—
372	C₂²×C₄×C₆₇	—	2	1	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	—	2	1	no	—
376	C₂²×C₄×C₆₇	—	2	2	no	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	2	no	—
380	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
385	Q₁₆×C₆₇	—	2	2	no	—
386	Q₁₆×C₆₇	—	2	4	no	—
387	Q₁₆×C₆₇	—	2	2	no	—
388	Q₁₆×C₆₇	—	2	4	no	—
389	Q₁₆×C₆₇	—	4	2	no	—
390	Q₁₆×C₆₇	—	4	2	no	—
391	Q₁₆×C₆₇	—	4	2	no	—
392	SD₁₆×C₆₇	—	2	2	no	—
393	SD₁₆×C₆₇	—	2	2	no	—
394	SD₁₆×C₆₇	—	4	2	no	—
395	SD₁₆×C₆₇	—	4	2	no	—
396	SD₁₆×C₆₇	—	4	2	no	—
397	SD₁₆×C₆₇	—	4	2	no	—
398	D₈×C₆₇	—	4	2	no	—
399	M₁₆×C₆₇	—	4	2	no	—
400	M₁₆×C₆₇	—	4	2	no	—
401	C₂×C₈×C₆₇	—	4	2	no	—
402	C₂×C₈×C₆₇	—	4	2	no	—
403	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
406	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
408	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	—	2	1	no	—
410	C₄⋊C₄×C₆₇	—	2	1	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	1	no	—
413	C₄⋊C₄×C₆₇	—	2	1	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	1	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	—	2	2	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	1	no	—
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	2	no	—
425	C₄⋊C₄×C₆₇	—	2	2	no	—
426	C₄⋊C₄×C₆₇	—	2	2	no	—
427	C₄⋊C₄×C₆₇	—	2	2	no	—
428	C₄⋊C₄×C₆₇	—	2	1	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
432	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	2	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	—	2	2	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	—	2	2	no	—
445	C₂²⋊C₄×C₆₇	—	2	2	no	—
446	C₂²⋊C₄×C₆₇	—	2	1	no	—
447	C₂²⋊C₄×C₆₇	—	2	1	no	—
448	C₂²⋊C₄×C₆₇	—	2	1	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	no	—
451	C₂²⋊C₄×C₆₇	—	2	1	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	2	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
459	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
460	C₄²×C₆₇	—	2	1	no	—
461	C₄²×C₆₇	—	2	1	no	—
462	C₄²×C₆₇	—	2	1	no	—
463	C₄²×C₆₇	—	2	1	no	—
464	C₄²×C₆₇	—	2	2	no	—
465	C₄²×C₆₇	—	2	2	no	—
466	C₄²×C₆₇	—	2	1	no	—
467	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
468	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
469	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
470	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
471	C₂³×C₆₇	—	2	1	no	—
472	C₂³×C₆₇	—	2	2	no	—
473	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
474	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
475	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
476	Q₈×C₆₇	—	2	4	no	—
477	Q₈×C₆₇	—	2	1	no	—
478	Q₈×C₆₇	—	2	1	no	—
479	Q₈×C₆₇	—	2	1	no	—
480	Q₈×C₆₇	—	2	2	no	—
481	Q₈×C₆₇	—	2	2	no	—
482	Q₈×C₆₇	—	2	2	no	—
483	Q₈×C₆₇	—	2	1	no	—
484	Q₈×C₆₇	—	2	2	no	—
485	Q₈×C₆₇	—	4	2	no	—
486	Q₈×C₆₇	—	4	4	no	—
487	Q₈×C₆₇	—	4	4	no	—
488	Q₈×C₆₇	—	8	1	no	—
489	Q₈×C₆₇	—	8	2	no	—
490	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
491	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
492	D₄×C₆₇	—	2	2	no	—
493	D₄×C₆₇	—	2	2	no	—
494	D₄×C₆₇	—	2	1	no	—
495	D₄×C₆₇	—	2	2	no	—
496	D₄×C₆₇	—	2	1	no	—
497	D₄×C₆₇	—	2	2	no	—
498	D₄×C₆₇	—	4	2	no	—
499	D₄×C₆₇	—	4	2	no	—
500	D₄×C₆₇	—	4	2	no	—
501	D₄×C₆₇	—	4	2	no	—
502	D₄×C₆₇	—	4	4	no	—
503	D₄×C₆₇	—	4	4	no	—
504	D₄×C₆₇	—	4	4	no	—
505	D₄×C₆₇	—	4	2	no	—
506	D₄×C₆₇	—	8	1	no	—
507	D₄×C₆₇	—	8	1	no	—
508	D₄×C₆₇	—	8	2	no	—
509	D₄×C₆₇	—	8	2	no	—
510	D₄×C₆₇	—	8	2	no	—
511	D₄×C₆₇	—	8	2	no	—
512	C₂×C₄×C₆₇	—	2	4	no	—
513	C₂×C₄×C₆₇	—	2	1	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	2	no	—
516	C₂×C₄×C₆₇	—	2	2	no	—
517	C₂×C₄×C₆₇	—	2	2	no	—
518	C₂×C₄×C₆₇	—	2	2	no	—
519	C₂×C₄×C₆₇	—	2	2	no	—
520	C₂×C₄×C₆₇	—	2	1	no	—
521	C₂×C₄×C₆₇	—	2	1	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	2	no	—
529	C₂×C₄×C₆₇	—	2	2	no	—
530	C₂×C₄×C₆₇	—	4	1	no	—
531	C₂×C₄×C₆₇	—	4	4	no	—
532	C₂×C₄×C₆₇	—	4	4	no	—
533	C₂×C₄×C₆₇	—	4	4	no	—
534	C₂×C₄×C₆₇	—	4	4	no	—
535	C₂×C₄×C₆₇	—	4	4	no	—
536	C₂×C₄×C₆₇	—	4	2	no	—
537	C₂×C₄×C₆₇	—	8	2	no	—
538	C₂×C₄×C₆₇	—	8	2	no	—
539	C₂×C₄×C₆₇	—	8	1	no	—
540	C₂×C₄×C₆₇	—	8	2	no	—
541	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
549	C₈×C₆₇	—	2	2	no	—
550	C₈×C₆₇	—	2	1	no	—
551	C₈×C₆₇	—	2	1	no	—
552	C₈×C₆₇	—	2	1	no	—
553	C₈×C₆₇	—	2	1	no	—
554	C₈×C₆₇	—	2	2	no	—
555	C₂²×C₆₇	—	2	1	no	—
556	C₂²×C₆₇	—	2	2	no	—
557	C₂²×C₆₇	—	2	2	no	—
558	C₂²×C₆₇	—	2	1	no	—
559	C₂²×C₆₇	—	2	2	no	—
560	C₂²×C₆₇	—	2	2	no	—
561	C₂²×C₆₇	—	2	1	no	—
562	C₂²×C₆₇	—	2	2	no	—
563	C₂²×C₆₇	—	2	2	no	—
564	C₂²×C₆₇	—	4	2	no	—
565	C₂²×C₆₇	—	4	1	no	—
566	C₂²×C₆₇	—	4	2	no	—
567	C₂²×C₆₇	—	4	1	no	—
568	C₂²×C₆₇	—	4	1	no	—
569	C₂²×C₆₇	—	4	2	no	—
570	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₆₇	—	2	1	no	—
572	C₄×C₆₇	—	2	1	no	—
573	C₄×C₆₇	—	2	2	no	—
574	C₄×C₆₇	—	2	2	no	—
575	C₄×C₆₇	—	2	1	no	—
576	C₄×C₆₇	—	2	2	no	—
577	C₄×C₆₇	—	2	2	no	—
578	C₄×C₆₇	—	2	1	no	—
579	C₄×C₆₇	—	4	1	no	—
580	C₄×C₆₇	—	4	1	no	—
581	C₄×C₆₇	—	4	1	no	—
582	C₄×C₆₇	—	4	2	no	—
583	C₄×C₆₇	—	4	2	no	—
584	C₄×C₆₇	—	4	2	no	—
585	C₄×C₆₇	—	4	1	no	—
586	C₄×C₆₇	—	4	1	no	—
587	C₄×C₆₇	#578	1	2	yes	—
588	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
589	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	#61660	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
591	C₂×C₆₇	—	4	1	no	—
592	C₂×C₆₇	—	4	2	no	—
593	C₂×C₆₇	—	4	2	no	—
594	C₂×C₆₇	—	8	2	no	—
595	C₂×C₆₇	—	8	1	no	—
596	C₂×C₆₇	#3484	1	1	yes	characteristic
597	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
598	C₂×C₆₇	#3584	1	1	yes	characteristic
599	#3547	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3333	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3329	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3327	C₂×C₆₇	1	2	yes	complemented
604	#3305	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3300	C₂×C₆₇	1	2	yes	complemented
606	#3299	C₂×C₆₇	1	1	yes	characteristic, complemented
607	D₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#3285	C₂×C₆₇	1	2	yes	complemented
609	#3284	C₂×C₆₇	1	1	yes	characteristic, complemented
610	#3278	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#3277	C₂×C₆₇	1	2	yes	complemented
612	#3276	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#3212	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3210	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3203	C₂×C₆₇	1	2	yes	complemented
616	#3201	C₂×C₆₇	1	2	yes	complemented
617	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3013	C₂×C₆₇	1	2	yes	complemented
620	#3011	C₂×C₆₇	1	2	yes	complemented
621	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
622	C₆₇	#61660	1	1	yes	characteristic, direct product factor, Sylow
623	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
624	C₂×#137	C₂²×C₆₇	1	2	yes	—
625	C₂×#137	C₂²×C₆₇	1	2	yes	—
626	C₂×#135	C₂²×C₆₇	1	2	yes	—
627	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
628	#562	—	2	2	no	—
629	#555	—	2	1	no	—
630	#555	C₂²×C₆₇	1	1	yes	characteristic
631	#554	C₂²×C₆₇	1	1	yes	characteristic
632	#553	—	2	1	no	—
633	#552	C₂²×C₆₇	1	2	yes	—
634	#550	—	2	1	no	—
635	#550	C₂²×C₆₇	1	1	yes	characteristic
636	#550	C₂²×C₆₇	1	1	yes	characteristic
637	D₄×Q₈	—	2	1	no	—
638	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
639	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
640	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
641	#548	—	2	2	no	—
642	#548	C₂²×C₆₇	1	2	yes	—
643	#548	C₂²×C₆₇	1	2	yes	—
644	#548	C₂²×C₆₇	1	2	yes	—
645	#547	C₂²×C₆₇	1	1	yes	characteristic
646	#544	—	2	1	no	—
647	#542	—	2	2	no	—
648	#540	—	2	1	no	—
649	#537	—	2	2	no	—
650	#537	C₂²×C₆₇	1	2	yes	—
651	#537	C₂²×C₆₇	1	2	yes	—
652	#536	C₂²×C₆₇	1	2	yes	—
653	#533	C₂²×C₆₇	1	1	yes	characteristic
654	#532	—	2	1	no	—
655	#532	—	2	1	no	—
656	#532	C₂²×C₆₇	1	1	yes	characteristic
657	#532	C₂²×C₆₇	1	1	yes	characteristic
658	#529	C₂²×C₆₇	1	1	yes	characteristic
659	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
660	#495	C₂²×C₆₇	1	2	yes	—
661	#494	C₂²×C₆₇	1	1	yes	characteristic
662	#492	C₂²×C₆₇	1	1	yes	characteristic
663	#488	C₂²×C₆₇	1	2	yes	—
664	#487	C₂²×C₆₇	1	1	yes	characteristic
665	#486	C₂²×C₆₇	1	1	yes	characteristic
666	#485	C₂²×C₆₇	1	2	yes	—
667	#484	C₂²×C₆₇	1	2	yes	—
668	#484	C₂²×C₆₇	1	2	yes	—
669	#483	C₂²×C₆₇	1	1	yes	characteristic
670	#482	C₂²×C₆₇	1	2	yes	—
671	#480	C₂²×C₆₇	1	2	yes	—
672	#480	C₂²×C₆₇	1	1	yes	characteristic
673	#479	C₂²×C₆₇	1	1	yes	characteristic
674	#479	C₂²×C₆₇	1	1	yes	characteristic
675	#477	C₂²×C₆₇	1	1	yes	characteristic
676	#477	C₂²×C₆₇	1	1	yes	characteristic
677	#470	C₂²×C₆₇	1	2	yes	—
678	#468	C₂²×C₆₇	1	2	yes	—
679	#468	C₂²×C₆₇	1	2	yes	—
680	#468	C₂²×C₆₇	1	2	yes	—
681	#467	C₂²×C₆₇	1	2	yes	—
682	#467	C₂²×C₆₇	1	2	yes	—
683	#466	C₂²×C₆₇	1	2	yes	—
684	#465	C₂²×C₆₇	1	2	yes	—
685	#464	C₂²×C₆₇	1	1	yes	characteristic
686	#464	C₂²×C₆₇	1	1	yes	characteristic
687	#464	C₂²×C₆₇	1	2	yes	—
688	#464	C₂²×C₆₇	1	2	yes	—
689	#462	C₂²×C₆₇	1	1	yes	characteristic
690	#462	C₂²×C₆₇	1	1	yes	characteristic
691	#462	C₂²×C₆₇	1	1	yes	characteristic
692	#461	C₂²×C₆₇	1	1	yes	characteristic
693	#460	C₂²×C₆₇	1	1	yes	characteristic
694	#459	C₂²×C₆₇	1	1	yes	characteristic
695	#452	C₂²×C₆₇	1	2	yes	—
696	#452	C₂²×C₆₇	1	2	yes	—
697	#452	C₂²×C₆₇	1	2	yes	—
698	#452	C₂²×C₆₇	1	2	yes	—
699	#452	C₂²×C₆₇	1	2	yes	—
700	#452	C₂²×C₆₇	1	2	yes	—
701	#452	C₂²×C₆₇	1	2	yes	—
702	#451	C₂²×C₆₇	1	2	yes	—
703	#451	C₂²×C₆₇	1	1	yes	characteristic
704	#451	C₂²×C₆₇	1	2	yes	—
705	#451	C₂²×C₆₇	1	2	yes	—
706	#451	C₂²×C₆₇	1	2	yes	—
707	#451	C₂²×C₆₇	1	2	yes	—
708	#449	C₂²×C₆₇	1	2	yes	—
709	#449	C₂²×C₆₇	1	2	yes	—
710	#449	C₂²×C₆₇	1	2	yes	—
711	#448	C₂²×C₆₇	1	2	yes	—
712	#448	C₂²×C₆₇	1	1	yes	characteristic
713	#448	C₂²×C₆₇	1	2	yes	—
714	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
715	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
716	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
717	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
718	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
719	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
720	#436	C₂²×C₆₇	1	1	yes	characteristic
721	#436	C₂²×C₆₇	1	1	yes	characteristic
722	#436	C₂²×C₆₇	1	2	yes	—
723	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
724	C₈×D₄	C₂²×C₆₇	1	2	yes	—
725	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
726	#431	C₂²×C₆₇	1	1	yes	characteristic
727	#431	C₂²×C₆₇	1	1	yes	characteristic
728	#419	C₂²×C₆₇	1	2	yes	—
729	#417	C₂²×C₆₇	1	2	yes	—
730	#416	C₂²×C₆₇	1	2	yes	—
731	C₂×#103	C₂²×C₆₇	1	2	yes	—
732	#408	C₂²×C₆₇	1	2	yes	—
733	#408	C₂²×C₆₇	1	2	yes	—
734	2₋¹⁺⁴	—	4	4	no	—
735	2₋¹⁺⁴	—	4	4	no	—
736	C₂×#41	—	2	2	no	—
737	C₂×#41	—	2	2	no	—
738	C₂×#41	—	2	2	no	—
739	C₂×#41	C₂³×C₆₇	1	2	yes	—
740	C₂×#41	C₂³×C₆₇	1	2	yes	—
741	C₂×#41	C₂³×C₆₇	1	2	yes	—
742	C₂×#41	C₂³×C₆₇	1	2	yes	—
743	C₂×#41	C₂³×C₆₇	1	2	yes	—
744	C₂²×Q₈	—	2	2	no	—
745	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
746	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
747	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
748	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
749	#137	—	4	4	no	—
750	#137	—	4	4	no	—
751	#135	—	4	4	no	—
752	C₂×Q₁₆	—	4	4	no	—
753	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
755	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
757	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
758	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
759	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
765	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
766	C₂×D₈	C₂³×C₆₇	1	2	yes	—
767	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
768	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
769	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
770	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
771	C₄⋊Q₈	—	2	2	no	—
772	C₄⋊Q₈	—	2	1	no	—
773	C₄⋊Q₈	—	2	1	no	—
774	C₄⋊Q₈	—	2	1	no	—
775	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
776	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
779	#127	—	2	1	no	—
780	#127	—	2	1	no	—
781	#127	D₄×C₆₇	1	1	yes	characteristic
782	#127	C₂³×C₆₇	1	1	yes	characteristic
783	#126	—	2	2	no	—
784	#126	—	2	1	no	—
785	#125	—	2	2	no	—
786	#125	—	2	1	no	—
787	#125	—	2	1	no	—
788	#125	C₂³×C₆₇	1	1	yes	characteristic
789	#124	—	2	2	no	—
790	#124	—	2	2	no	—
791	#124	—	2	2	no	—
792	#124	—	2	2	no	—
793	#124	—	2	2	no	—
794	#124	D₄×C₆₇	1	2	yes	—
795	#124	C₂³×C₆₇	1	1	yes	characteristic
796	#124	C₂³×C₆₇	1	2	yes	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	1	no	—
801	#123	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	—	2	2	no	—
812	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
813	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
814	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
815	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
816	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
817	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
818	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	1	no	—
828	#121	—	2	2	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	D₄×C₆₇	1	1	yes	characteristic
835	#121	D₄×C₆₇	1	1	yes	characteristic
836	#121	D₄×C₆₇	1	2	yes	—
837	#121	C₂³×C₆₇	1	1	yes	characteristic
838	#121	C₂³×C₆₇	1	2	yes	—
839	#121	C₂³×C₆₇	1	2	yes	—
840	#121	C₂³×C₆₇	1	2	yes	—
841	C₄×Q₈	—	2	1	no	—
842	C₄×Q₈	—	2	1	no	—
843	C₄×Q₈	—	2	1	no	—
844	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
845	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
846	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
847	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
848	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
849	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
863	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
864	C₄×D₄	C₂³×C₆₇	1	2	yes	—
865	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
866	#117	—	2	1	no	—
867	#117	—	2	1	no	—
868	#117	—	2	2	no	—
869	#117	—	2	1	no	—
870	#117	C₂³×C₆₇	1	2	yes	—
871	C₂×C₄⋊C₄	—	2	1	no	—
872	C₂×C₄⋊C₄	—	2	1	no	—
873	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
875	C₂×C₄²	—	2	1	no	—
876	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
877	#107	C₂³×C₆₇	1	2	yes	—
878	#107	C₂³×C₆₇	1	1	yes	characteristic
879	#107	C₂³×C₆₇	1	2	yes	—
880	#107	C₂³×C₆₇	1	1	yes	characteristic
881	#106	C₂³×C₆₇	1	1	yes	characteristic
882	#106	C₂³×C₆₇	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
887	#103	C₂³×C₆₇	1	1	yes	characteristic
888	#103	C₂³×C₆₇	1	2	yes	—
889	#103	C₂³×C₆₇	1	2	yes	—
890	#103	C₂³×C₆₇	1	2	yes	—
891	#103	C₂³×C₆₇	1	1	yes	characteristic
892	#103	C₂³×C₆₇	1	1	yes	characteristic
893	#103	C₂³×C₆₇	1	2	yes	—
894	#103	C₂³×C₆₇	1	1	yes	characteristic
895	#103	C₂³×C₆₇	1	2	yes	—
896	#103	C₂³×C₆₇	1	2	yes	—
897	#103	C₂³×C₆₇	1	1	yes	characteristic
898	#103	C₂³×C₆₇	1	2	yes	—
899	#103	C₂³×C₆₇	1	2	yes	—
900	#103	C₂³×C₆₇	1	1	yes	characteristic
901	#102	C₂³×C₆₇	1	2	yes	—
902	#102	C₂³×C₆₇	1	2	yes	—
903	#102	C₂³×C₆₇	1	2	yes	—
904	#102	C₂³×C₆₇	1	2	yes	—
905	#102	C₂³×C₆₇	1	1	yes	characteristic
906	#102	C₂³×C₆₇	1	1	yes	characteristic
907	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
908	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
909	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
914	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
916	C₄×C₈	C₂³×C₆₇	1	2	yes	—
917	#41	—	2	4	no	—
918	#41	—	2	4	no	—
919	#41	—	4	2	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	2	no	—
925	#41	—	4	8	no	—
926	#41	—	4	8	no	—
927	#41	—	4	2	no	—
928	#41	—	4	2	no	—
929	#41	—	4	8	no	—
930	C₂×Q₈	—	2	2	no	—
931	C₂×Q₈	—	2	2	no	—
932	C₂×Q₈	—	2	1	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	2	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	—	2	2	no	—
937	C₂×Q₈	—	2	4	no	—
938	C₂×Q₈	—	2	4	no	—
939	C₂×Q₈	—	4	2	no	—
940	C₂×Q₈	—	4	2	no	—
941	C₂×Q₈	—	4	2	no	—
942	C₂×Q₈	—	4	2	no	—
943	C₂×Q₈	—	4	8	no	—
944	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
945	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
946	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
947	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
948	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
949	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
961	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
962	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
963	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
964	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
965	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
966	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
967	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
980	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
982	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
983	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
984	Q₁₆	—	2	2	no	—
985	Q₁₆	—	2	4	no	—
986	Q₁₆	—	2	2	no	—
987	Q₁₆	—	2	4	no	—
988	Q₁₆	—	4	2	no	—
989	Q₁₆	—	4	2	no	—
990	Q₁₆	—	4	2	no	—
991	SD₁₆	—	2	2	no	—
992	SD₁₆	—	2	2	no	—
993	SD₁₆	—	4	2	no	—
994	SD₁₆	—	4	2	no	—
995	SD₁₆	—	4	2	no	—
996	SD₁₆	—	4	2	no	—
997	D₈	—	4	2	no	—
998	M₁₆	—	4	2	no	—
999	M₁₆	—	4	2	no	—
1000	C₂×C₈	—	4	2	no	—
1001	C₂×C₈	—	4	2	no	—
1002	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1005	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1006	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1007	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1031	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1033	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1034	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1035	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1036	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1056	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	1	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	2	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1067	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1068	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1069	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	2	no	—
1072	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1073	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1074	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1075	Q₈	—	2	4	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	2	2	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	2	no	—
1084	Q₈	—	4	2	no	—
1085	Q₈	—	4	4	no	—
1086	Q₈	—	4	4	no	—
1087	Q₈	—	8	2	no	—
1088	Q₈	—	8	1	no	—
1089	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1090	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1091	D₄	—	2	2	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	2	no	—
1095	D₄	—	2	1	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	4	2	no	—
1101	D₄	—	4	4	no	—
1102	D₄	—	4	4	no	—
1103	D₄	—	4	4	no	—
1104	D₄	—	4	2	no	—
1105	D₄	—	8	1	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	1	no	—
1108	D₄	—	8	2	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	2	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	—	8	2	no	—
1139	C₂×C₄	—	8	1	no	—
1140	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1142	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1143	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1144	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1145	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1146	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1147	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1148	C₈	—	2	2	no	—
1149	C₈	—	2	1	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	2	2	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	2	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1170	C₄	—	2	1	no	—
1171	C₄	—	2	1	no	—
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	2	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	#578×C₆₇	1	2	yes	—
1187	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1188	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1189	C₂	—	4	1	no	—
1190	C₂	—	4	2	no	—
1191	C₂	—	4	2	no	—
1192	C₂	—	8	1	no	—
1193	C₂	—	8	2	no	—
1194	C₂	C₆₇×#3484	1	1	yes	characteristic
1195	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1196	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3547	C₂	semidirect
2. C₆₇×#3497	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3329	C₂	semidirect
5. C₆₇×#3327	C₂	semidirect
6. C₆₇×#3305	C₂	semidirect
7. C₆₇×#3300	C₂	semidirect
8. C₆₇×#3299	C₂	semidirect
9. D₄×Q₁₆×C₆₇	C₂	semidirect
10. C₆₇×#3285	C₂	semidirect
11. C₆₇×#3284	C₂	semidirect
12. C₆₇×#3278	C₂	semidirect
13. C₆₇×#3277	C₂	semidirect
14. C₆₇×#3276	C₂	semidirect
15. C₆₇×#3212	C₂	semidirect
16. C₆₇×#3210	C₂	semidirect
17. C₆₇×#3203	C₂	semidirect
18. C₆₇×#3201	C₂	semidirect
19. C₆₇×#3108	C₂	semidirect
20. C₆₇×#3104	C₂	semidirect
21. C₆₇×#3013	C₂	semidirect
22. C₆₇×#3011	C₂	semidirect
23. C₆₇×#2979	C₂	semidirect
590. #61660	C₆₇	direct (N × H)
599. #3547	C₂×C₆₇	semidirect
600. #3497	C₂×C₆₇	semidirect
601. #3333	C₂×C₆₇	semidirect
602. #3329	C₂×C₆₇	semidirect
603. #3327	C₂×C₆₇	semidirect
604. #3305	C₂×C₆₇	semidirect
605. #3300	C₂×C₆₇	semidirect
606. #3299	C₂×C₆₇	semidirect
607. D₄×Q₁₆	C₂×C₆₇	semidirect
608. #3285	C₂×C₆₇	semidirect
609. #3284	C₂×C₆₇	semidirect
610. #3278	C₂×C₆₇	semidirect
611. #3277	C₂×C₆₇	semidirect
612. #3276	C₂×C₆₇	semidirect
613. #3212	C₂×C₆₇	semidirect
614. #3210	C₂×C₆₇	semidirect
615. #3203	C₂×C₆₇	semidirect
616. #3201	C₂×C₆₇	semidirect
617. #3108	C₂×C₆₇	semidirect
618. #3104	C₂×C₆₇	semidirect
619. #3013	C₂×C₆₇	semidirect
620. #3011	C₂×C₆₇	semidirect
621. #2979	C₂×C₆₇	semidirect
622. C₆₇	#61660	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3547	2
C₆₇×#3497	2
C₆₇×#3333	2
C₆₇×#3329	2
C₆₇×#3327	2
C₆₇×#3305	2
C₆₇×#3300	2
C₆₇×#3299	2
D₄×Q₁₆×C₆₇	2
C₆₇×#3285	2
C₆₇×#3284	2
C₆₇×#3278	2
C₆₇×#3277	2
C₆₇×#3276	2
C₆₇×#3212	2
C₆₇×#3210	2
C₆₇×#3203	2
C₆₇×#3201	2
C₆₇×#3108	2
C₆₇×#3104	2
C₆₇×#3013	2
C₆₇×#3011	2
C₆₇×#2979	2
#61660	67

Subgroups — C67×#61660 #30740911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61660 #30740911